R

  

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R

Definition: R

R

Noun

1. A unit of radiation exposure; the dose of ionizing radiation that will produce 1 electrostatic unit of electricity in 1 cc of dry air.

2. (physics) the universal constant in the gas equation: pressure times volume = R times temperature; equal to 8.3143 joules per kelvin per mole.

3. The 18th letter of the Roman alphabet.

4. The length of a line segment between the center and circumference of a circle or sphere.

Source: WordNet 1.7.1 Copyright © 2001 by Princeton University. All rights reserved.
 

Date "R" was first used in popular English literature: sometime before 1350. (references)

 

Specialty Definition: R

DomainDefinition

Literature

R in prescriptions. The ornamental part of this letter is the symbol of Jupiter , under whose special protection all medicines were placed. The letter itself (Recipe, take) and its flourish may be thus paraphrased: "Under the good auspices of Jove, the patron of medicines, take the following drugs in the proportions set down." It has been suggested that the symbol is for Responsum Raphaelis, from the assertion of Dr. Napier and other physicians of the seventeenth century, that the angel Raphael imparted them.
R is called the dog-letter, because a dog in snarling utters the letter r-r-r-r, r-r, r-r-r-r-r, etc.- sometimes preceded by a g.
"Irritata canis quod RR quam plurima dicat."
Lucillus.
"[R] that's the dog's name. R is for the dog."
- Shakespeare: Romeo and Juliet, ii. 4.
The three R's. Sir William Curtis being asked to give a toast, said, "I will give you the three R's- writing, reading, and arithmetic."
"The House is aware that no payment is made except on the `three R's.' "- Mr. Cory. M.P.: Address to the House of Commons, February 28th, 1867. Source: Brewer's Dictionary.

Source: compiled by the editor from various references; see credits.

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Specialty Definition: Aozora Bunko: R

(From Wikipedia, the free Encyclopedia)

See Aozora Bunko

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Cantor's first uncountability proof

(From Wikipedia, the free Encyclopedia)

The misconception

Contrary to what most mathematicians believe, Georg Cantor's first proof that the set of all real numbers is uncountable was not his famous diagonal argument, and did not mention decimal expansions or any other numeral system. The theorem and proof below were found by Cantor in December 1873, and published in 1874 in Crelle's Journal, more formally known as Journal für die Reine und Angewandte Mathematik (German for Journal for Pure and Applied Mathematics). Cantor discovered the diagonal argument in 1877.

The theorem

Suppose a set R is

Then R is not countable.

The proof

The proof begins by assuming some sequence x1, x2, x3, ... has all of R as its range. Define two other sequences as follows:

a1 = x1.

b1 = xi, where i is the smallest index such that xi is not equal to a1.

an+1 = xi, where i is the smallest index greater than the one considered in the previous step such that xi is between an and bn.

bn+1 = xi, where i is the smallest index greater than the one considered in the previous step such that xi is between an+1 and bn.

The two monotone sequences a and b move toward each other. By the "gaplessness" of R, some point c must lie between them. The claim is that c cannot be in the range of the sequence x, and that is the contradiction. If c were in the range, then we would have c = xi for some index i. But then, when that index was reached in the process of defining a and b, then c would have been added as the next member of one or the other of those two sequences, contrary to the assumption that it lies between their ranges.

Real algebraic numbers and real transcendental numbers

In the same paper, published in 1874, Cantor showed that the set of all real algebraic numbers is countable, and inferred the existence of transcendental numbers as a corollary. That corollary had earlier been proved by quite different methods by Joseph Liouville.

Source: adapted by the editor from Wikipedia, the free encyclopedia under a copyleft GNU Free Documentation License (GFDL) from the article "Cantor's first uncountability proof."

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Casualties of the September 11, 2001 Terrorist Attacks

(From Wikipedia, the free Encyclopedia)

Any tributes to the individuals lost in this tragedy are welcome and encouraged at our memorial site. Some articles originally posted to wikipedia have been moved there - if you are looking for such an article, please check there.

See also Missing Persons, Foreign casualties, and Survivors.

Casualties

Planes - World Trade Center - Pentagon
A - B - C - D - E - F - G - H - I - J - K - L - M - N - O - P - Q - R - S - T - U - V - W - X - Y - Z

As of October 29, 2003, 2,995 people were presumed dead as a result of all four September 11 attacks. This includes the casualties at the World Trade Center, the Pentagon, on the airplanes and the hijackers.

Planes

265 people killed on four planes; 232 passengers, 25 flight attendants, 8 pilots. (Note that this total includes the 19 hijackers, who reportedly boarded the planes as passengers.)

See also: Memorial wiki tributes to the occupants of each plane

World Trade Center

By October 29, 2003, 2605 people were listed as confirmed dead and 1058 bodies had been identified. (Note: this total does not include the 127 passengers and 20 crew on the two aircraft or the 10 hijackers).

The listing and memorial.

See also:

Missing Persons

The number of missing people grew to estimates as high as over 6000 in the months following the attack, but steadily declined as stories were checked and duplicate entries removed. (See Timeline of WTC missing).

As of August 2002, there were approximately 90 people who were officially missing; that is, their remains had not been identified and no family members had requested a death certificate.

Detailed listing.

Survivors

The great majority of the over 40,000 people working at the World Trade Center at the time of the attack evacuated safely, including 18 who escaped from above the impact zone in the second tower hit. By 9/20/2001 6291 people, including rescue and recovery workers, had been treated for injuries.

Detailed listing.

Pentagon

The Pentagon reports 125 staffers killed or missing, with 121 remains recovered and identified, as of Sept. 11, 2002. At least one person died later as a result of wounds incurred.

The listing and memorial.

Missing Persons

The Pentagon reports 4 staffers missing. One passenger on the airliner which hit the Pentagon was also never identified.

Detailed listing.

Survivors

88 treated at hospital.

Detailed entry.

Victim legends

Due to the very large number of World Trade Center casualties and missing persons, victim legends were a common form of September 11, Terrorist Attack urban legends. These were tales of victims who did not exist, spread by word-of-mouth and the Internet. Official sites, such as http://www.september11victims.com, contain accurate entries and are trusted content. Because Wikipedia, and many other websites allowed freely adding victims, there were no doubt many obvious fake entries. Fake victims added to these lists were often simply missing at the time of the attacks, or actually survivors of the attacks.

See also

September 11, 2001 Terrorist Attack - Donations - Assistance - Memorials and Services

Source: adapted by the editor from Wikipedia, the free encyclopedia under a copyleft GNU Free Documentation License (GFDL) from the article "Casualties of the September 11, 2001 Terrorist Attacks."

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Colombeau algebra

(From Wikipedia, the free Encyclopedia)

The algebra of moderate functions over Rn,

The ideal (subalgebra) of negligible functions:

The Colombeau algebra is the quotient algebra .

Source: adapted by the editor from Wikipedia, the free encyclopedia under a copyleft GNU Free Documentation License (GFDL) from the article "Colombeau algebra."

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Coordinates

(From Wikipedia, the free Encyclopedia)

coordinates in mathematics

A point P in the Euclidean space Rn is given by an n-tuple P=(r1,...,rn) of real numbers r1,...,rn.

These numbers r1,...,rn are called the coordinates of the point P.

If a subset S of an Euclidean space is mapped continuously onto another topological space, this defines coordinates in the image of S.

See also

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Covariant

(From Wikipedia, the free Encyclopedia)

In category theory, see covariant functor.

In tensor analysis, a covariant coordinate system is reciprocal to a corresponding contravariant coordinate system.

Roughly speaking, a covariant tensor is a vector field that defines the topology of a space; it is the base which one measures against.

A contravariant vector is thus a measurement or a displacement on this space.

Thus, their relationship can be represented simply as:

Another way of defining covariant vectors is to say that "covariant vectors" are actually one-forms, that is to say, real-valued linear functions on "contravariant" vectors. These one-forms can then be said to form a dual space to the vector space they take their arguments from.

If e1, e2, e3 are contravariant basis vectors of R3 (not necessarily orthogonal nor of unit norm) then the covariant basis vectors of their reciprocal system are:

Then the contravariant coordinates of any vector v can be obtained by the dot product of v with the contravariant basis vectors:

Likewise, the covariant components of v can be obtained from the dot product of v with covariant basis vectors, viz.

Then v can be expressed in two (reciprocal) ways, viz.

.

The indices of covariant coordinates, vectors, and tensors are subscripts. If the contravariant basis vectors are orthonormal then they are equivalent to the covariant basis vectors, so there is no need to distinguish between the covariant and contravariant coordinates, and all indices are subscripts.

Source: adapted by the editor from Wikipedia, the free encyclopedia under a copyleft GNU Free Documentation License (GFDL) from the article "Covariant."

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Earth radius

(From Wikipedia, the free Encyclopedia)

Earth radii are sometimes used to measure distance. The radius of Earth is approximately 6,378 km. This distance is usually denoted by RE.

See also: Effective Earth radius

Source: adapted by the editor from Wikipedia, the free encyclopedia under a copyleft GNU Free Documentation License (GFDL) from the article "Earth radius."

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Elementary group theory

(From Wikipedia, the free Encyclopedia)

First Theorems about Groups

A group (G,*) is usually defined as:

G is a set and * is an associative binary operation on G, obeying the following rules (or axioms):

A1. (G,*) has closure. That is, if a and b are in G, then a*b is in G
A2. The operation * is associative, that is, if a, b, and c are in G, then (a*b)*c=a*(b*c).
A3. G contains an identity element, often denoted e, such that for all a in G, e*a=a*e=a.
A4. Every element in (G,*) has an inverse; if a is in G, then there exists an element b in G such that a*b=b*a=e.

Axioms A1 and A2 follow from the definition of "associative binary operation", and are sometimes omitted, particularly A1.

Where no danger of confusion is possible, the group (G,*) will simply be referred to as "the group G"; but it is important to remember that the operation "*" is fundamental to the description of the group. For example, in the real numbers, we can speak of both the group (R,+), which is the additive group of reals with identity 0; and the group (R#, *), which is the multiplicative group of the reals (excluding 0), which has identity 1.

We can state simpler versions of A3 and A4:

A3'. G contains an identity element, often denoted e, such that for all a in G, a*e=a.
A4'. Every element in (G,*) has an inverse; for all a in G, there exists an element in G, denoted a -1, such that a*a -1 = e.

In the sequel, we will assume the axioms A1, A2, A3' and A4'. We first show in Theorem 1.1 and 1.2 that these assumptions actually imply A3 and A4. We will then go on to prove several other theorems, the most important of which are that every group has a unique identity, and every element in a group has a unique inverse.

Theorem 1.1: For all a in G, a -1*a = e.

Thus every right inverse in a group is necessarily a left inverse.

Theorem 1.2: For all a in G, e*a = a.

Thus, the identity in a group is both a left and right identity. (We will justify the use of the term "the identity" momentarily).

The following theorem demonstrates a fundamental property enjoyed by groups, which other more general structures (such as semigroups) lack:

Theorem 1.3: For all a,b in G, there exists a unique x in G such that a*x = b.

Theorem 1.4: The identity element of a group (G,*) is unique. As a result, we can speak of the identity element of (G,*) rather than an identity element. Where different groups are being discussed and compared, often eG will be used to identify the identity in (G,*). By analogy to the group of reals, the identity is also sometimes denoted as 1 (or 1G ) in groups that are written multiplicatively, and as 0 (or 0G ) in groups that are written additively.

Theorem 1.4: The inverse of each element in (G,*) is unique; equivalently, for all a in G, a*x = e if and only if x=a -1.

As a result, we can speak of the inverse of an element x, rather than an inverse. When the group operation is written multiplicatively (as it is here), we denote the inverse of x as x -1. When the group is written additively (i.e., in (G,+)), the inverse of x is written as -x.

Theorem 1.5: For all a belonging to a group (G,*), (a -1) -1=a.

Theorem 1.6: For all a,b belonging to a group (G,*), (a*b) -1=b -1*a -1. The results of the following theorem are often called the cancellation rules for a group:

Theorem 1.7: For all a,x,y, belonging to a group (G,*), if a*x=a*y, then x=y; and if x*a=y*a, then x=y.

Given a group (G, *), if the total number of elements in G is finite, then the group is called a finite group. The order of a group (G,*) is the number of elements in G (for a finite group), or the cardinality of the group if G is not finite. The order of a group G is written as |G| or (less frequently) o(G).

A subset H of G is called a subgroup of a group (G,*) if H satisfies the axioms of a group, using the same operator "*", and restricted to the subset H. Thus if H is a subgroup of (G,*), then (H,*) is also a group, and obeys the above theorems, restricted to H. The order of subgroup H is the number of elements in H.

A proper subgroup of a group G is a subgroup which is not identical to G. A non-trivial subgroup of G is (usually) any subgroup of G which contains an element other than e.

Theorem 2.1: If H is a subgroup of (G,*), then the identity eH in H is identical to the identity e in (G,*).

Theorem 2.2: If H is a subgroup of G, and h is an element of H, then the inverse of h in H is identical to the inverse of h in G. Given a subset S of G, we often want to determine whether or not S is also a subgroup of G. One handy theorem that covers the case for both both finite and infinite groups is:

Theorem 2.3: If S is a non-empty subset of G, then S is a subgroup of G if and only if for all a,b in S, a*b -1 is in S.

The intersection of two or more subgroups is again a subgroup.

Theorem 2.4: The intersection of any non-empty set of subgroups of a group G is a subgroup.

In a group (G,*), define x0 = e. We write x*x as x² ; and in general, x*x*x*...*x (n times) as xn. Similarly, we write x -n for (x -1)n.

Theorem: Let a be an element of a group (G,*). Then the set {an: n is an integer} is a subgroup of G.

A subgroup of this type is called a cyclic subgroup; the subgroup of the powers of a is often written as <a>, and we say that a generates <a>.

If there is a positive integer n such that an=e, then we say the element a has order n in G. Sometimes this is written as "o(a)=n.

If S and T are subsets of G, and a is an element of G, we write "a*S" to refer to the subset of G made up of all elements of the form a*s, where s is an element of S; similarly, we write "S*a" to indicate the set of elements of the form s*a. We write S*T for the subset of G made up of elements of the form s*t, where s is an element of S and t is an element of T.

If H is a subgroup of G, then a left coset of H is a set of the form a*H, for some a in G. A right coset is a subset of the form H*a.

Some useful theorems about cosets, stated without proof:

Theorem: If H is a subgroup of G, and x and y are elements of G, then either x*H = y*H, or x*H and y*H have empty intersection.

Theorem: If H is a subgroup of G, every left (right) coset of H in G contains the same number of elements.

\'Theorem': If H is a subgroup of G, then G is the disjoint union of the left (right) cosets of H.

Theorem: If H is a subgroup of G, then the number of distinct left cosets of H is the same as the number of distinct right cosets of H.

Define the index of a subgroup H of a group G (written "[G:H]" ) to be the number of distinct left cosets of H in G.

From these theorems, we can deduce the important Lagrange's Theorem relating the order of a subgroup to the order of a group:

Lagrange's Theorem: If H is a subgroup of G, then |G| = |H|*[G:H].

For finite groups, this also allows us to state:

Lagrange's Theorem: If H is a subgroup of a finite group G, then the order of H divides the order of G.

References

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List of airports: R

(From Wikipedia, the free Encyclopedia)

List of airports: A - B - C - D - E - F - G - H - I - J - K - L - M - N - O - P - Q - R - S - T - U - V - W - X - Y - Z

R

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List of Biblical names starting with R

(From Wikipedia, the free Encyclopedia)

List of Biblical names
A - B - C - D - E - F - G - H - I - J - K - L - M - N - O - P - Q - R - S - T - U - V - Y - Z

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List of books by title: R

(From Wikipedia, the free Encyclopedia)

List of books in alphabetical order by title:

A - B - C - D - E - F - G - H - I - J - K - L - M - N - O - P - Q - R - S - T - U - V - W - X - Y - Z

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List of cities in Germany starting with R

(From Wikipedia, the free Encyclopedia)

List of cities in Germany: A - B - C - D - E - F - G - H - I - J - K - L - M - N - O - P - Q - R - S - T - U - V - W - X - Y - Z

TownPopulationDistrictBundesland
Rainau3,203OstalbkreisBaden-Württemberg
Rathenow29,000HavellandBrandenburg
Ratzeburg12,300LauenburgSchleswig-Holstein
Regensburg 125,100--Bavaria
Remscheid120,600--North Rhine-Westphalia
Remshalden13,510Rems-MurrBaden-Württemberg
Rendsburg29,400Rendsburg-EckernfördeSchleswig-Holstein
Rheine76,000SteinfurtNorth Rhine-Westphalia
Riesbürg2,384OstalbkreisBaden-Württemberg
Ribnitz-Damgarten17,600NordvorpommernMecklenburg-Western Pomerania
Rinteln28,500SchaumburgLower Saxony
Rosenberg2,639OstalbkreisBaden-Württemberg
Rosenheim58,800--Bavaria
Rostock212,700--Mecklenburg-Western Pomerania
Rotenburg21,500RotenburgLower Saxony

A "--" in the district column means, that the town is a district-free town, i.e. it is by itself a district.

Source: adapted by the editor from Wikipedia, the free encyclopedia under a copyleft GNU Free Documentation License (GFDL) from the article "List of cities in Germany starting with R."

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List of colleges and universities starting with R

(From Wikipedia, the free Encyclopedia)

A -- B -- C -- D -- E -- F -- G -- H -- I -- J -- K -- L -- M -- N -- O -- P -- Q -- R -- S -- T -- U -- V -- W -- X -- Y -- Z
  1. Radford University
  2. Rajamangala Institute of Technology
  3. Ramrao Adik Institute of Engineering
  4. Rand Afrikaans University
  5. Randolph-Macon College
  6. Randolph-Macon Woman's College
  7. Rapperswil School of Engineering
  8. Rashtreeya Vidyalaya College of Engineering
  9. Rayapati Venkata Rangarao and Jagarlamudi Chandramouli College of Engineering
  10. Reading University
  11. Red River Community College
  12. Red de Interconexion Universitaria (RIU)
  13. Reed College (Portland, Oregon)
  14. Regent College
  15. Regent University
  16. Regent University College of Communication
  17. Regional Engineering College, Calicut
  18. Regional Engineering College, Durgapur
  19. Regional Engineering College, Rourkela
  20. Regional Engineering College, Suratkal
  21. Regional Engineering College, Tiruchirappalli, India
  22. Regional Engineering College, Trichy
  23. Regional Engineering College, Warangal
  24. Regional Institute of Technology, Jamshedpur
  25. Regional Technical College Cork
  26. Regional Technical College Galway
  27. Regional Technical College Letterkenny
  28. Regional Technical College Limerick
  29. Regional Technical College Sligo
  30. Regional Technical College Tallaght
  31. Regional Technical College, Carlow
  32. Regional Technical College, Dundalk
  33. Regis College
  34. Reitaku University
  35. Rensselaer Polytechnic Institute
  36. Rheinisch-Westfälische Technische Hochschule Aachen (RWTH)
  37. Rhode Island College
  38. Rhode Island School of Design
  39. Rhodes College
  40. Rhodes University
  41. Rice University (Houston, Texas)
  42. Richard Huish College
  43. Richard Stockton University
  44. Richland College
  45. Richland Community College
  46. Ricks College
  47. Rider University
  48. Riga Technical University
  49. Rio Salado Community College
  50. Ripon College
  51. Ritsumeikan University
  52. Riverside Community College
  53. Roanoke Bible College
  54. Roanoke College
  55. Robert Gordon University
  56. Rochester Institute of Technology
  57. Rockefeller University
  58. Rockford College
  59. Rockhurst College
  60. Rocky Mountain College
  61. Rollins College
  62. Rollins School of Public Health
  63. Roosevelt University
  64. Rose-Hulman Institute of Technology (Terre Haute, Indiana)
  65. Roskilde University
  66. Ross University School of Veterinary Medicine
  67. Ross University Schoole of Medicine
  68. Rostov State University
  69. Rowan College of New Jersey
  70. Royal College of Surgeons
  71. Royal Danish School of Educational Studies
  72. Royal Danish School of Pharmacy
  73. Royal Holloway, University of London
  74. Royal Institute of Technology (Stockholm, Sweden)
  75. Royal Melbourne Institute of Technology
  76. Royal Military Academy of Belgium
  77. Royal Military College of Canada
  78. Royal Postgraduate Medical School
  79. Royal Roads University
  80. Royal Veterinary College, London
  81. Royal Veterinary and Agricultural University
  82. Rudolf Steiner College
  83. Ruhr-Universitat Bochum
  84. Russell Sage College
  85. Russian Academy of Sciences
  86. Rutgers University
  87. Rutgers University - Campus at Newark
  88. Rutgers University, Camden
  89. Ryerson Polytechnic University

See also : Colleges and universities

Source: adapted by the editor from Wikipedia, the free encyclopedia under a copyleft GNU Free Documentation License (GFDL) from the article "List of colleges and universities starting with R."

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List of people by name: R

(From Wikipedia, the free Encyclopedia)

List of people by name: A - B - C - D - E - F - G - H - I - J - K - L - M - N - O - P - Q - R - S - T - U - V - W - X - Y - Z Ra - Rb - Rc - Rd - Re - Rf - Rg - Rh - Ri - Rj - Rk - Rl - Rm - Rn - Ro - Rp - Rq - Rr - Rs - Rt - Ru - Rv - Rw - Rx - Ry - Rz

Source: adapted by the editor from Wikipedia, the free encyclopedia under a copyleft GNU Free Documentation License (GFDL) from the article "List of people by name: R."

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List of people by name: Re

(From Wikipedia, the free Encyclopedia)

List of people by name: A - B - C - D - E - F - G - H - I - J - K - L - M - N - O - P - Q - R - S - T - U - V - W - X - Y - Z Ra - Rb - Rc - Rd - Re - Rf - Rg - Rh - Ri - Rj - Rk - Rl - Rm - Rn - Ro - Rp - Rq - Rr - Rs - Rt - Ru - Rv - Rw - Rx - Ry - Rz

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List of people by name: Rh

(From Wikipedia, the free Encyclopedia)

List of people by name: A - B - C - D - E - F - G - H - I - J - K - L - M - N - O - P - Q - R - S - T - U - V - W - X - Y - Z Ra - Rb - Rc - Rd - Re - Rf - Rg - Rh - Ri - Rj - Rk - Rl - Rm - Rn - Ro - Rp - Rq - Rr - Rs - Rt - Ru - Rv - Rw - Rx - Ry - Rz

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List of people by name: Ri

(From Wikipedia, the free Encyclopedia)

List of people by name: A - B - C - D - E - F - G - H - I - J - K - L - M - N - O - P - Q - R - S - T - U - V - W - X - Y - Z Ra - Rb - Rc - Rd - Re - Rf - Rg - Rh - Ri - Rj - Rk - Rl - Rm - Rn - Ro - Rp - Rq - Rr - Rs - Rt - Ru - Rv - Rw - Rx - Ry - Rz

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List of people by name: Ro

(From Wikipedia, the free Encyclopedia)

List of people by name: A - B - C - D - E - F - G - H - I - J - K - L - M - N - O - P - Q - R - S - T - U - V - W - X - Y - Z

Ra - Rb - Rc - Rd - Re - Rf - Rg - Rh - Ri - Rj - Rk - Rl - Rm - Rn - Ro - Rp - Rq - Rr - Rs - Rt - Ru - Rv - Rw - Rx - Ry - Rz

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List of people by name: Ru

(From Wikipedia, the free Encyclopedia)

List of people by name: A - B - C - D - E - F - G - H - I - J - K - L - M - N - O - P - Q - R - S - T - U - V - W - X - Y - Z Ra - Rb - Rc - Rd - Re - Rf - Rg - Rh - Ri - Rj - Rk - Rl - Rm - Rn - Ro - Rp - Rq - Rr - Rs - Rt - Ru - Rv - Rw - Rx - Ry - Rz

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List of people by name: Ry

(From Wikipedia, the free Encyclopedia)

List of people by name: A - B - C - D - E - F - G - H - I - J - K - L - M - N - O - P - Q - R - S - T - U - V - W - X - Y - Z Ra - Rb - Rc - Rd - Re - Rf - Rg - Rh - Ri - Rj - Rk - Rl - Rm - Rn - Ro - Rp - Rq - Rr - Rs - Rt - Ru - Rv - Rw - Rx - Ry - Rz

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List of rare diseases starting with R

(From Wikipedia, the free Encyclopedia)

This list of rare diseases was originally taken from the NIH public domain resource at http://ord.aspensys.com/asp/diseases/diseases.asp .

A B C D E F G H I J K L M N O P Q R S T U V W X Y Z

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List of songs by name: R

(From Wikipedia, the free Encyclopedia)

List of songs by name: 0 - A - B - C - D - E - F - G - H - I - J - K - L - M - N - O - P - Q - R - S - T - U - V - W - X - Y - Z

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Normed vector space

(From Wikipedia, the free Encyclopedia)

In mathematics, with 2- or 3-dimensional vectors with real-valued entries, the idea of the "length" of a vector is intuitive. This can be extended to any Euclidean space Rn. For more abstract vector spaces, a norm is a generalization of this idea. A vector space on which a norm is defined is then called a normed vector space.

If V is a vector space over a field K (which must be either the real numbers or the complex numbers), a norm on V is a function from V to R, the real numbers — that is, it associates to each vector v in V a real number, which is usually denoted ||v||. The norm must satisfy the following conditions:

For all a in K and all u and v in V,
  1. ||v|| ≥ 0 with equality if and only if v = 0.
  2. ||av|| = |a| ||v||.
  3. ||u + v|| ≤ ||u|| + ||v||.

These conditions essentially demand that the norm behave in the same way that we intuitively expect for it to be a notion of length:

  1. a vector always has a strictly positive length. The only exception is the zero vector which has length zero.
  2. multiplying a vector by a number has the same effect on the length.
  3. the triangle inequality, which amounts roughly to saying that the distance from A to B to C is never shorter than going directly from A to C.

Most of property 1 follows from the other axioms; it is enough to require that ||v|| be non-zero whenever v is non-zero.

A useful consequence of the norm axioms is the inequality

||u ± v|| ≥ | ||u|| - ||v|| |
for all vectors u and v.

Examples of Norms

Euclidean norm. On Rn, the intuitive notion of length of the vector x = (x1, x2, ..., xn) is captured by the formula

This gives the ordinary distance from the origin to the point x, a consequence of the Pythagorean theorem. The Euclidean norm is by far the most commonly used norm on Rn, but there are other norms on this vector space as will be shown below.

Taxicab norm.

The name comes from the fact that the norm gives the distance a taxi has to drive in a rectangular street grid to get from the origin to the point x.

Illustrations of unit circles in different norms.
p-norm. Let p≥1 be a real number.

Note that for p=1 we get the taxicab norm and for p=2 we get the Euclidean norm. See also Lp space.

Infinity norm or maximum norm.

The concept of unit circle (the set of all vectors of norm 1) is different in different norms: for the 1-norm the unit circle in R2 is a rhomboid, for the 2-norm (Euclidean norm) it is the well-known unit circle, while for the infinity norm it is a square. See the accompanying illustration.

Other norms on Rn can be constructed by combining the above; for example

is a norm on R4.

All the above formulas also yield norms on Cn without modification.

Examples of infinite dimensional normed vector spaces can be found in the Banach space article. In addition, inner product space becomes a normed vector space if we define the norm as

Distances in Normed Vector Spaces

For any normed vector space we can define the distance between two vectors u and v as ||u-v||. (Note that the Euclidean norm gives rise to the Euclidean distance in this fashion.) This turns the normed space into a metric space and allows the definition of notions such as continuity and convergence. The norm is then a continuous map. If this metric space is complete then the normed space is called a Banach space. Every normed vector space V sits as a dense subspace inside a Banach space; this Banach space is essentially uniquely defined by V and is called the completion of V.

Two norms ||.||1 and ||.||2 on a vector space V are called equivalent if there exist positive real numbers C and D such that

for all x in V. In this case, the two norms define the same notions of continuity and convergence and do not need to be distinguished for most purposes.

Finite-dimensional normed vector spaces

All norms on a finite-dimensional vector space V are equivalent. Since Euclidean space is complete, we can thus conclude that all finite-dimensional normed vector spaces are Banach spaces.

A normed vector space V is finite-dimensional if and only if the unit ball B = {x : ||x|| ≤ 1} is compact, which is the case if and only if V is locally compact.

Linear maps and dual spaces

The most important maps between two normed vector spaces are the continuous linear maps. Together with these maps, normed vector spaces form a category. An isometry between two normed vector spaces is a linear map f which preserves the norm (meaning ||f(v)|| = ||v|| for all vectors v). Isometries are always continuous and injective. A surjective isometry between the normed vector spaces V and W is called a isometric isomorphism, and V and W are called isometrically isomorphic. Isometrically isomorphic normed vector spaces are identical for all practical purposes.

When speaking of normed vector spaces, we augment the notion of dual space to take the norm into account. The dual V ' of a normed vector space V is the space of all continuous linear maps from V to the base field (the complexes or the reals) — such linear maps are called "functionals". The norm of a functional φ is defined as the supremum of |φ(v)| where v ranges over all unit vectors (i.e. vectors of norm 1) in V. This turns V ' into a normed vector space. An important theorem about continuous linear functionals on normed vector spaces is the Hahn-Banach theorem.

See also Finsler manifold.

Source: adapted by the editor from Wikipedia, the free encyclopedia under a copyleft GNU Free Documentation License (GFDL) from the article "Normed vector space."

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Poker jargon starting with R

(From Wikipedia, the free Encyclopedia)

Poker jargon:

A - B - C - D - E - F - G - H - I - J - K - L - M - N - O - P - Q - R - S - T - U - V - W - X - Y - Z

No jargon listed at this time

Source: adapted by the editor from Wikipedia, the free encyclopedia under a copyleft GNU Free Documentation License (GFDL) from the article "Poker jargon starting with R."

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R

(From Wikipedia, the free Encyclopedia)

R is the eighteenth letter of the Latin alphabet.

Semitic Rêš (the head) developed into Greek Ρω (Rô). The sound value /r/ however was maintained in Greek as well as Etruscan and Latin.

A, B, C, D, E, F, G, H, I, J, K, L, M, N, O, P, Q, R, S, T, U, V, W, X, Y, Z

Romeo represents the letter R in the NATO phonetic alphabet.

R is also:

Two-letter combinations starting with R:

Source: adapted by the editor from Wikipedia, the free encyclopedia under a copyleft GNU Free Documentation License (GFDL) from the article "R."

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R (album)

(From Wikipedia, the free Encyclopedia)

Tracks

  1. "Feel Good Hit Of The Summer"
  2. "The Lost Art Of Keeping A Secret"
  3. "Leg Of Lamb"
  4. "Auto Pilot"
  5. "Better Living Through Chemistry"
  6. "Monsters In The Parasol"
  7. "A Quick And To The Pointless"
  8. "In The Fade"
  9. "Tension Fade"
  10. "Lightning Song"
  11. "I Think I Lost My Headache"

Charts of the album

Song Charts of the album

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R programming language

(From Wikipedia, the free Encyclopedia)

The R programming language, sometimes described as "GNU S", is a mathematical language and environment used for statistical analysis and display.

It is based upon S which was developed by John Chambers of Bell Laboratories and described in the paper "Evolution of the S Language" [1]. R is considered by its developers to be an implementation of S, with semantics derived from Scheme.

R is freely available under the GNU GPL and is available for Windows, Macintosh, and many Unix operating systems.

External links

Source: adapted by the editor from Wikipedia, the free encyclopedia under a copyleft GNU Free Documentation License (GFDL) from the article "R programming language."

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Radio

(From Wikipedia, the free Encyclopedia)

This article is about radio, the medium of communication. For other article subjects named radio see radio (disambiguation).

Radio is a technology that allows for the transmission of signals by modulation of electromagnetic waves. These waves travel (propagate) through the air and the vacuum of space equally well, not requiring a medium of transport.

A radio wave is created whenever a charged object accelerates with a frequency that lies in the radio frequency (RF) portion of the electromagnetic spectrum. By contrast, other types of emissions which fall outside the RF range are gamma rays, X-rays, cosmic rays, infrared & ultraviolet light, and light visible to humans.

When a radio wave passes a wire, it induces a moving electric charge (voltage) that can be transformed into audio or other signals that carry information. Although the word 'radio' is used to describe this phenomenon, the transmissions which we know as television, radio, radar, and cell phone are all in the class of radio frequency emissions.

Discovery

The theoretical basis of the propagation of electromagnetic waves was first described by James Clerk Maxwell in his paper to the Royal Society A dynamical theory of the electromagnetic field, which followed his work between 1861 and 1865.

It was Heinrich Rudolf Hertz who, between 1886 and 1888, first validated Maxwell's theory through experiment, demonstrating that radio radiation had all the properties of waves, and discovering that the electromagnetic equations could be reformulated into a partial differential equation called the wave equation.

Invention and history

The identity of the original inventor of radio, at the time called wireless telegraphy, is contentious.

In St. Louis, Missouri, Nikola Tesla made the first public demonstration of radio communication in 1893. Addressing the Franklin Institute in Philadelphia and the National Electric Light Association, he described and demonstrated in detail the principles of radio communication. The apparatus that he used contained all the elements that were incorporated into radio systems before the development of the vacuum tube.

Guglielmo Marconi was awarded what is sometimes recognised as the world's first patent for radio with British Patent 12039, Improvements in transmitting electrical impulses and signals and in apparatus there-for.

In the USA, some key developments in radio's early history were created and patented in 1897 by Nikola Tesla. However the US Patent Office reversed its decision in 1904, awarding Guglielmo Marconi a patent for the invention of radio, possibly influenced by Marconi's financial backers in the States, who included Thomas Edison and Andrew Carnegie. In 1909 Marconi, with Karl Ferdinand Braun, was also awarded the Nobel Prize in Physics for "contributions to the development of wireless telegraphy".

However, Tesla's patent (number 645576) was reinstated in 1943 by the US Supreme Court, shortly after his death. This decision was based on the fact that there was prior work existing before the establishment of Marconi's patent. Some believe it was apparently made for financal reasons, to allow the US Government to avoid having to the pay damages that were being claimed by the Marconi Company for use of its patents during World War I.

Claims have also been made that Nathan Stubblefield invented radio before either Tesla or Marconi, but his device seems to have worked by induction transmission rather than radio transmission. Marconi opened the world's first "wireless" factory in Hall Street, Chelmsford, England in 1898, employing around 50 people. The next great invention was the vacuum tube detector, invented by a team of Westinghouse engineers.

On Christmas Eve, 1906, using his heterodyne principle, Reginald Fessenden transmitted the first radio audio broadcast in history from Brant Rock Station, Massachusetts. Ships at sea heard a broadcast that included Fessenden playing the song O Holy Night on the violin and reading a passage from the Bible. The world's first regular wireless broadcasts for entertainment commenced in 1922 from the Marconi Research Centre at Writtle near Chelmsford, England, which was also the location of the world's first "wireless" factory.

Early radios ran the entire power of the transmitter through a carbon microphone. In the 1920s, amplifying vacuum tubes revolutionized both radio receivers and radio transmitters.

Developments in the 20th century:

Uses of radio

Many of its early uses were naval, for sending Morse code messages between ships and land. Today, radio takes many forms, including wireless networks, mobile communications of all types, as well as radio broadcasting. Read more about radio's history.

Before the advent of television, commercial radio broadcasts included not only news and music, but dramas, comedies, variety shows, and many other forms of entertainment. Radio was unique among dramatic presentation that it used only sound. For more, see radio programming.

There are a number of uses of radio:

See also: Radio propagation and ionosphere, Radio programming, old-time radio, international broadcasting, transistor radio, crystal radio receiver, software radio, Radio hardware, Internet radio, types of radio emissions

Source: adapted by the editor from Wikipedia, the free encyclopedia under a copyleft GNU Free Documentation License (GFDL) from the article "Radio."

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Real number

(From Wikipedia, the free Encyclopedia)

The real numbers are intuitively defined as numbers that are in one-to-one correspondence with the points on an infinite line—the number line. The term "real number" is a retronym coined in response to "imaginary number".

Real numbers may be rational or irrational; algebraic or transcendental; and positive, negative, or zero.

Real numbers measure continuous quantities. They may in theory be expressed by decimal fractions that have an infinite sequence of digits to the right of the decimal point; these are often (mis-)represented in the same form as 324.823211247... (where the three dots express that there would still be more digits to come, no matter how many more might be added at the end).

Measurements in the physical sciences are almost always conceived as approximations to real numbers. Writing them as decimal fractions (which are rational numbers that could be written as ratios, with an explicit denominator) is not only more compact, but to some extent expresses the sense of an underlying real number. It is as if one says "I'm writing down only the part of the number that I know; it's infinitely long, and my stopping after a finite number of digits echoes the fact that I'm stopping short of doing more and more refined experiments forever, and getting further along in the infinite series of digits, which would be the only way to avoid an approximate final result."

The real numbers are the central object of study in real analysis.

A real number is said to be computable if there exists an algorithm that yields its digits. Because there are only countably many algorithms, but an uncountable number of reals, most real numbers are not computable. Some constructivists accept the existence of only those reals that are computable. The set of definable numbers is broader, but still only countable.

Computers can only approximate most real numbers with rational numbers; these approximations are known as floating point numbers or fixed point numbers; see Real data type. Computer algebra systems are able to treat some real numbers exactly by storing an algebraic description (such as "sqrt(2)") rather than their decimal approximation.

Mathematicians use the symbol R (or alternatively, , the letter "R" in blackboard bold) to represent the set of all real numbers.

In mathematics, the term "real XXX" means that the underlying number field is the field of real numbers. For example real matrix, real polynomial and real Lie algebra.

History

Fractions had been used by the Egyptians around 1000 BC; around 500 BC, the Greek mathematicians lead by Pythagoras realized the need for irrational numbers. Negative numbers began to be generally accepted in the 1600s and were invented by Muslim mathematicians. The development of the calculus in the 1700s used the entire set of real numbers without having defined them cleanly. The first rigorous definition was given by Georg Cantor in 1871.

Definition

Construction from the rational numbers

Real numbers could be constructed as the topological completion of rational numbers. For details and other construction of real numbers, see Construction of real numbers

Axiomatic approach

Let R denote the set of all real numbers. Then:

The latter property is what differentiates the reals from the rationals. For example, the set of rationals with square less than 2 has a rational upper bound (e.g., 1.5) but no rational least upper bound, because the square root of 2 is not rational.

The real numbers are uniquely specified by the above properties. More precisely, given any two Dedekind complete ordered fields R1 and R2, there exists a unique field isomorphism from R1 to R2, allowing us to think of them as essentially the same mathematical object.

Properties

Completeness

The main reason for introducing the reals is that the reals contain all limits. More technically, the reals are complete (in the sense of metric spaces or uniform spaces, which is a different sense than the Dedekind completeness of the order in the previous section). This means the following:

A sequence (xn) of real numbers is called a Cauchy sequence if for any ε > 0 there exists an integer N (possibly depending on ε) such that the distance |xn - xm| is less than ε provided that n and m are both greater than N. In other words, a sequence is a Cauchy sequence if its elements xn eventually come and remain arbitrarily close to each other.

A sequence (xn) converges to the limit x if for any ε > 0 there exists an integer N (possibly depending on ε) such that the distance |xn - x| is less than ε provided that n is greater than N. In other words, a sequence has limit x if its elements eventually come and remain arbitrarily close to x.

It is easy to see that every convergent sequence is a Cauchy sequence. Now the important fact about the real numbers is that the converse is true:

Every Cauchy sequence of real numbers is convergent.
That is, the reals are complete.

Note that the rationals are not complete. For example, the sequence (1,1.4,1.41,1.414,1.4142,1.41421,...) is Cauchy but it does not converge to a rational number. (In the real numbers, in contrast, it converges to the square root of 2.)

The existence of limits of Cauchy sequences is what makes calculus work and is of great practical use. The standard numerical test to determine if a sequence has a limit is to test if it is a Cauchy sequence, as the limit is typically not known in advance.

For example the standard series of the exponential function

converges to a real number because for every x the sums

can be made arbitrarily small by choosing N sufficiently large. This proves that the sequence is Cauchy, so we know that the sequence converges even if we don't know ahead of time what the limit is.

"The complete ordered field"

The real numbers are often described as "the complete ordered field", a phrase that can be interpreted in several ways.

First, an order can be lattice complete. It's easy to see that no ordered field can be lattice complete, because it can have no largest element (given any element z, z + 1 is larger). So this is not the sense that is meant.

Additionally, an order can be Dedekind-complete, as defined in the section Axioms. The uniqueness result at the end of that section justifies using the word "the" in the phrase "complete ordered field" when this is the sense of "complete" that is meant. This sense of completeness is most closely related to the construction of the reals from Dedekind cuts, since that construction starts from an ordered field (the rationals) and then forms the Dedekind-completion of it in a standard way.

These two notions of completeness ignore the field structure. However, an ordered group (and a field is a group under the operations of addition and subtraction) defines a uniform structure, and uniform structures have a notion of completeness (topology); the description in the section Completeness above is a special case. (We refer to the notion of completeness in uniform spaces rather than the related and better known notion for metric spaces, since the definition of metric space relies on already having a characterisation of the real numbers.) It is not true that R is the only uniformly complete ordered field, but it is the only uniformly complete Archimedean field, and indeed one often hears the phrase "complete Archimedean field" instead of "complete ordered field". Since it can be proved that any uniformly complete Archimedean field must also be Dedekind complete (and vice versa, of course), this justifies using "the" in the phrase "the complete Archimedean field". This sense of completeness is most closely related to the construction of the reals from Cauchy sequences (the construction carried out in full in this article), since it starts with an Archimedean field (the rationals) and forms the uniform completion of it in a standard way.

But the original use of the phrase "complete Archimedean field" was by David Hilbert, who meant still something else by it. He meant that the real numbers form the largest Archimedean field in the sense that every other Archimedean field is a subfield of R. Thus R is "complete" in the sense that nothing further can be added to it without making it no longer an Archimedean field. This sense of completeness is most closely related to the construction of the reals from surreal numbers, since that construction starts with a proper class that contains every ordered field (the surreals) and then selects from it the largest Archimedean subfield.

Advanced properties

The reals are uncountable, that is, there are strictly more real numbers than natural numbers (even though both sets are infinite). This is proved with Cantor's diagonal argument. In fact, the cardinality of the reals is 2ω (see cardinal numbers), i.e., the cardinality of the set of subsets of the natural numbers. Since only a countable set of real numbers can be algebraic, almost all real numbers are transcendental. The nonexistence of a subset of the reals with cardinality strictly in between that of the integers and the reals is known as the continuum hypothesis. This can neither be proved nor be disproved, but is independent from the axioms of set theory.

The real numbers form a metric space: the distance between x and y is defined to be the absolute value |x - y|. By virtue of being a totally ordered set, they also carry an order topology; the topology arising from the metric and the one arising from the order are identical. The reals are a contractible (hence connected and simply connected), locally compact separable metric space, of dimension 1, and are everywhere dense. The real numbers are not compact. There are various properties that uniquely specify them; for instance, all unbounded, continuous, and separable order topologies are necessarily homeomorphic to the reals.

Every nonnegative real number has a square root in R, and no negative number does. This shows that the order on R is determined by its algebraic structure. Also, every polynomial of odd degree admits at least one root: these two properties make R the premier example of a real closed field. Proving this is the first half of one proof of the fundamental theorem of algebra.

The reals carry a canonical measure, the Lebesgue measure, which is the Haar measure on their structure as a topological group normalised such that the unit interval [0,1] has measure 1.

The supremum axiom of the reals refers to subsets of the reals and is therefore a second-order logical statement. It is not possible to characterize the reals with first-order logic alone: the Löwenheim-Skolem theorem implies that there exists a countable dense subset of the real numbers satisfying exactly the same sentences in first order logic as the real numbers themselves. The set of hyperreal numbers is much bigger than R but also satisfies the same first order sentences as R. Ordered fields that satisfy the same first-order sentences as R are called nonstandard models of R. This is what makes nonstandard analysis work; by proving a first-order statement in some nonstandard model (which may be easier than proving it in R), we know that the same statement must also be true of R.

Generalizations and Extensions

The real numbers can be generalized and extended in several different directions. Perhaps the most natural extension are the complex numbers which contain solutions to all polynomial equations. However, the complex numbers are not an ordered field. Ordered fields extending the reals are the hyperreal numbers and the surreal numbers; both of them contain infinitesimal and infinitely large numbers and thus are not Archimedean. Occasionally, formal elements +∞ and -∞ are added to the reals to form the extended real number line, a compact space which is not a field anymore but retains many of the properties of the real numbers. Self-adjoint operatorss on a Hilbert space (for example, self-adjoint square complex matrices) generalize the reals in many respects: they can be ordered (though not totally ordered), they are complete, all their eigenvalues are real and they form a real associative algebra. Positive-definite operators correspond to the positive reals and normal operators correspond to the complex numbers.

Source: adapted by the editor from Wikipedia, the free encyclopedia under a copyleft GNU Free Documentation License (GFDL) from the article "Real number."

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Reign

(From Wikipedia, the free Encyclopedia)

A Reign is a period of time a person serves as a monarch or pope. No time limit exists on reigns, nor is there a term of office. Thus a reign usually lasts for the lifetime of the monarch, unless the monarchy itself is abolished or the monarch abdicates.

Reigns

A reign can be ended in three ways:

Abdications

Abolitions of Monarchies

King Constantine II of Greece reigned from 1963 until the abolition of the Greek monarchy in 1973.

King Humbert II of Italy reigned for only a few weeks in 1946 before the abolition of the Italian Monarchy.

Source: adapted by the editor from Wikipedia, the free encyclopedia under a copyleft GNU Free Documentation License (GFDL) from the article "Reign."

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Renormalization group

(From Wikipedia, the free Encyclopedia)

Let's say we have a family of models over a certain space which admits rescalings which are automorphisms but not isometries. Let me explain what I mean by that. For example, in Euclidean space, the isometries preserve the distance between any two points. Even though a rescaling of a Euclidean space is an automorphism in the sense that a rescaled n-dimensional Euclidean space is simply another n-dimensional Euclidean space, which are isomorphic, it's not an isometry because it changes distances by a constant factor. The same thing goes for Minkowski space. However, this isn't true for conformal geometries because rescalings are isometries there. The set of all models of the family is called the parameter space, which is sometimes a manifold. At any rate, it usually admits a differentiable structure. Because of the rescaling automorphisms of the underlying space, given any particular model in the family, by rescaling the space, we get another model which may or may not be the same as the original model. Here, we make the further assumption that by rescaling the underlying space, any rescaled model of the family also belongs to the family. The group of rescalings is isomorphic to R+, the group of positive real numbers under multiplication. What I've said previously amounts to saying that there's a group action of the rescaling group on the parameter space. In addition, we will assume this group action is differentiable (or maybe continuous/smooth, depending on the needs the renormalization group is put to). The rescaling group is called the renormalization group and the group action is called the renormalization group flow. The idea of the renormalization group was developed by Kenneth Wilson.

Relevant, Marginal and Irrelevant

Under the action of enlarging rescalings, a parameter could have a positive, zero or negative Lyapunov exponent. That parameter is then called relevant, marginal or irrelavant respectively. In the limit as the rescaling parameter approaches infinity, the RG flows converge to infrared attractors. The points on this attractor are called universality classes because many different models in parameter space start to look like this model at large enough scales, which basically means small scale effects only affect large scale effects insignificantly (a scale independence of sorts). Oftentimes, the parameter space is infinite-dimensional (very huge), but the infrared attractors are only finite dimensional, so that the space of universality classes are much much smaller than the original parameter space. This means, provided we work at large enough scales and don't mind using approximations, we can reduce the entire parameter space to the space of universality classes. The group action of the RG restricted to this attractor is still a group action. So, for models within a sufficiently small neighborhood of the attractor in parameter space, we can project this neighborhood to the attractor, so that running the renormalization group action forward leads to even better approximations but running it backwards eventually leads to divergence out of the neighborhood for almost every point in the neighborhood. This means the RG should really be treated as a monoid in this restriction. Similarly, RG flows can have ultraviolet attractors.

See also Critical exponents, Lyapunov exponent.

In statistical mechanics, a second order phase transition corresponds to an infrared repellor (i.e. an "unstable" infrared fixed point).

Source: adapted by the editor from Wikipedia, the free encyclopedia under a copyleft GNU Free Documentation License (GFDL) from the article "Renormalization group."

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Republican

(From Wikipedia, the free Encyclopedia)

In political science, a republican is a person who advocates the establishment of a republic as a form of government, in contrast to a monarchist.

In politics a Republican is a member, delegate or supporter of a Republican Political party; for example the United States Republican Party, Fianna Fáil the Republic Party in the Republic of Ireland, etc. The politics of these parties varies widely with the context, although there is a common thread of support for an "independent" state.

See also: republicanism

In the Spanish Civil War Republican was the name given for the side which fought unsuccessfully in defence of the Second Spanish Republic, and which were defeated by the forces of General Francisco Franco.

A republican in the context of Northern Ireland is someone who supports a range of Northern Irish parties, most notably Sinn Féin, from the nationalist community who possess an armed wing and engaged in what are seen as terrorist activity. Republican can also mean a supporter of the military organisation, such as the Irish Republican Army or the Irish National liberation Army. Many of these organisations claim descent from earlier Irish republican movements such as the Irish Republican Brotherhood or the Easter Rising mounted in 1916.

Source: adapted by the editor from Wikipedia, the free encyclopedia under a copyleft GNU Free Documentation License (GFDL) from the article "Republican."

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Run (baseball statistics)

(From Wikipedia, the free Encyclopedia)

In baseball, the object of the game is for a team to score more runs than its opponent. Runs are scored when a player advances safely around all three bases and returns safely to home plate. A player who does so is credited with a run, or sometimes referred to as a "run scored."

Source: adapted by the editor from Wikipedia, the free encyclopedia under a copyleft GNU Free Documentation License (GFDL) from the article "Run (baseball statistics)."

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Simple Lie group

(From Wikipedia, the free Encyclopedia)

The classification of Lie groups that are also simple groups depends on the prior classification of the complex simple Lie algebras: for which see the page on root systems. It is shown that a simple Lie group has a simple Lie algebra that will occur on the list given there, once it is complexified (that is, made into a complex vector space rather than a real one. This reduces the classification to two further matters

Firstly, for example, the SO(p,q,R) and SO(p+q,R) give rise to different Lie algebras with the same Dynkin diagram. In general there may be different real forms of the same complex Lie algebra.

Secondly the Lie algebra only determines uniquely the simply connected (universal) cover G* of the component containing the identity of a Lie group G. It may well happen that G* isn't actually a simple group, for example having a non-trivial center. We have therefore to worry about the global topology), by computing the fundamental group of G. This was done by Cartan.

For an example, the special orthogonal groups in even dimension: with -I a scalar matrix in the center these aren't actually simple groups, and having a two-fold spin cover. They aren't simply-connected either: they lie 'between' G* and G, in the notation above.

Classification by Lie algebra and Dynkin diagram

(duplicates root system)

According to his classification, we have

Infinite series

A series

A1, A2, ...

Ar corresponds to the special unitary group, SU(r+1).

B series

B1, B2, ...

Br corresponds to the special orthogonal group, SO(2r+1).

C series

C1, C2, ...

Cr corresponds to the symplectic group, Sp(2r).

D series

D1, D2, ...

Dr corresponds to the special orthogonal group, SO(2r).

Exceptional algebras

G2

See G2.

F4

See F4.

E6

See E6.

E7

See E7.

E8

See E8.

See also Cartan matrix, Coxeter matrix, Dynkin diagram, Weyl group, Coxeter group, Kac-Moody algebras.

Source: adapted by the editor from Wikipedia, the free encyclopedia under a copyleft GNU Free Documentation License (GFDL) from the article "Simple Lie group."

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T1 space

(From Wikipedia, the free Encyclopedia)

In topology and related branches of mathematics, T1 spaces and R0 spaces are particularly nice kinds of topological spaces. The T1 and R0 properties are examples of separation axioms.

A T1 space is also called an accessible space or a Fréchet space and a R0 space is also called an symmetric space.

Definitions

A topological space X is T1 if and only if either of the following equivalent conditions is satisfied:

X is R0 if and only if either of the following conditions is satisfied: As before, the above conditions are equivalent.

A space is T1 if and only if it's both R0 and T0 (which says that topologically indistinguishable points must be equal). Conversely, a space is R0 if and only if its Kolmogorov quotient (which identifies topologially indistinguishable points) is T1.

Do not confuse the term "Fréchet topology", which is equivalent to "T1 topology", with the term "Fréchet space" which refers to an entirely different notion from functional analysis.

Examples

The Zariski topology on an algebraic variety is T1. To see this, note that a point with local coordinates (c1,...,cn) is the zero set of the polynomials x1-c1, ..., xn-cn. Thus, the point is closed. However, this example is well known as a space that is not Hausdorff (T2).

For a more concrete example, let's look at the cofinite topology on an infinite set. Specifically, let X be the set of integers, and define the open sets OA to be those subsets of X which contain all but a finite subset A of X. Then given distinct integers x and y:

so the resulting space is T1 by each of the definitions above. This space is not T2, because the intersection of any two open sets OA and OB is OA∪B, which is never empty. Alternatively, the set of even integers is compact but not closed, which would be impossible in a Hausdorff space.

We can modify this example slightly to get an R0 space that is neither T1 nor R1. Let X be the set of integers again, and using the definition of OA from the previous example, define a basis of open sets Gx for any integer x to be Gx = O{x, x+1} if x is an even number, and Gx = O{x-1, x} if x is odd. Then the open sets of X are, unionss of the basis sets

UA := ∪x in A Gx.
The resulting space is not T0 (and hence not T1), because the points x and x + 1 (for x even) are topologically indistinguishable; but otherwise it is essentially equivalent to the previous example.

Generalisations to other kinds of spaces

The terms "T1", "R0", and their synonyms can also be applied to such variations of topological spaces as uniform spaces, Cauchy spaces, and convergence spaces. The characteristic that unites the concept in all of these examples is that limits of fixed ultrafilters (or constant netss) are unique (for T1 spaces) or unique up to topological indistinguishability (for R0 spaces).

As it turns out, uniform spaces, and more generally Cauchy spaces, are always R0, so the T1 condition in these cases reduces to the T0 condition. But R0 alone can be an interesting condition on other sorts of convergence spaces, such as pretopological spaces.

Source: adapted by the editor from Wikipedia, the free encyclopedia under a copyleft GNU Free Documentation License (GFDL) from the article "T1 space."

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United States Republican Party

(From Wikipedia, the free Encyclopedia)

The Republican Party (often GOP for Grand Old Party) is a United States political party that was organized in Ripon, Wisconsin on February 28, 1854, as a party against the expansion of slavery. It is not to be confused with the Democratic-Republican party of Thomas Jefferson. The first convention of the U.S. Republican Party was held on July 6, 1854, in Jackson, Michigan. Many of its initial policies were inspired by the defunct Whig Party. Since its inception, its chief opponent has been the United States Democratic Party.

The official symbol of the Republican Party is the elephant. Although the elephant had occasionally been associated with the party earlier, a cartoon by Thomas Nast, published in Harper's Weekly on November 7, 1874, is considered the first important use of the symbol [1].

History

John C. Frémont ran as the first Republican for President in 1856, using the political slogan: "Free soil, free labor, free speech, free men, Fremont."

The party of Lincoln was originally characterized by its opposition to the expansion of slavery. During the Reconstruction era, the Republicans benefitted from the Democrats' association with the Confederacy and dominated national politics virtually without opposition for several years. With the two-term presidency of Ulysses S. Grant, the party became known for its strong advocacy of commerce, industry, and veterans' rights, which continued through the end of the 19th century.

The assassination of William McKinley and subsequent ascendance of Theodore Roosevelt led to a brief dominance of Progressivism for the party. However, that gave way to the laissez faire economic policies of the 1920s with Warren G. Harding, Calvin Coolidge, and Herbert Hoover. Following Hoover's sound defeat by Franklin Delano Roosevelt in 1932, the Republican Party was driven into the opposition for two decades. The Republicans finally regained the presidency in 1952 with the election of the former Supreme Allied Commander Dwight Eisenhower.

The party was still split between a conservative wing (dominant in the western U.S.) and a liberal wing (dominant in the northeastern U.S.). The seeds of conservative dominance in the Republican party were planted in the nomination of Barry Goldwater over Nelson Rockefeller as the Republican candidate for the 1964 presidential election. Goldwater represented the conservative wing of the party, while Rockefeller represented the liberal wing.

The party's current position as firmly to the right of the Democrats was cemented by the "Southern strategy" employed by Richard Nixon in the 1968 presidential election, followed by the Goldwater-inspired candidacy and election of Ronald Reagan in the 1980 election. Today, "conservative" and "Republican" are practically synonymous.

In 1994, Georgia Representative Newt Gingrich led the Republican Party in taking control of both the House of Representatives and the Senate in midterm congressional elections on November 8. That was the first time in 40 years that the Republicans secured control of both houses of Congress.

After the 1994 sweep of Congress by the Republicans, the GOP began to engage in supporting major reforms of government with measures such as a balanced budget amendment and welfare reform. These measures and others formed the famous, "Contract with America" which was passed by Congress, but with a Democrat, Bill Clinton, as President, only certain provisions such as welfare reform were enacted after bitter fighting.

With the election of George W. Bush in 2000, the Republican party controlled both the presidency and both houses of Congress for the first time since 1952. The party solidified its Congressional margins in the 2002 midterm elections, bucking the historic trend. It marked just the third time since the Civil War that the party in control of the White House gained seats in both houses of Congress in a midterm election (others were 1902 and 1934).

Republican Party Presidents

  1. Abraham Lincoln (1861-1865)
  2. Ulysses S. Grant (1869-1877)
  3. Rutherford B. Hayes (1877-1881)
  4. James Garfield (1881)
  5. Chester A. Arthur (1881-1885)
  6. Benjamin Harrison (1889-1893)
  7. William McKinley (1897-1901)
  8. Theodore Roosevelt (1901-1909)
  9. William Howard Taft (1909-1913)
  10. Warren G. Harding (1921-1923)
  11. Calvin Coolidge (1923-1929)
  12. Herbert Hoover (1929-1933)
  13. Dwight Eisenhower (1953-1961)
  14. Richard Nixon (1969-1974)
  15. Gerald R. Ford (1974-1977)
  16. Ronald Reagan (1981-1989)
  17. George H. W. Bush (1989-1993)
  18. George W. Bush (2001-present)

Presidential candidates

Other noted Republicans

Joseph Gurney Cannon
Newt Gingrich
Thomas Brackett Reed
Nelson Aldrich Rockefeller
Robert Alphonso Taft

External links

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Abbreviations & Acronyms: R

The following table is compiled from various sources, across various languages. When English abbreviations or acronyms come from a non-English source, this is noted.
EntrySourceExpressionField

R

DanishGrad RankineMechanical Engineering, Meteorology & Standards

R

EnglishRayleighN/A

R

FinnishRöntgenPublic Administration

R

FrenchRoyalSocial Sciences

R

GermanResultierende FeinheitFood & Agriculture

R

Greekτελική γραμμική πυκνότηταFood & Agriculture

R

ItalianMassa risultante per unità di lunghezzaFood & Agriculture

R

SpanishMasa lineal resultanteFood & Agriculture
R 10DanishBrandfarligeEuropean Union, Chemistry
K + RDutchZoen- en ZoefplekSocial Sciences, Transportation
AAPTS REnglishAustralian Association for Predetermined Time Standards and ResearchMeteorology & Standards
R 10GermanEntzündlichEuropean Union, Chemistry
R 10GreekεύφλεκτοEuropean Union, Chemistry
R 10ItalianInfiammabileEuropean Union, Chemistry
R 10PortugueseInflamávelEuropean Union, Chemistry
R 10SpanishInflamableEuropean Union, Chemistry

Source: compiled by the editor, based on several corpora (additional references).

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Synonyms: R

Synonyms: gas constant (n), radius (n), roentgen (n), universal gas constant (n). (additional references)

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Synonyms within Context: R

ContextSynonyms within Context (source: adapted from Roget's Thesaurus).

Dueness

Square, unexceptionable, right; equitable; due, en r

Fitting; correct, proper, meet, befitting, becoming, seemly; decorous; creditable, up to the mark, right as a trivet; just the thing, quite the thing; selon les r

Source: adapted from Roget's Thesaurus.

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Crosswords: R

English words defined with "R": acyl, acyl group ♦ Canine letter, Cartesion oval ♦ diazonium ♦ Filical ♦ gas constant ♦ Lima/on ♦ To roll one's r's ♦ universal gas constant ♦ Whur, Word square. (references)
Specialty definitions using "R": alloy 11, Amino Acids, Neutral, antisymmetric, autoconvective lapse rate, Axiom of Choice ♦ Bemporad formula, Biot number, Borel-Tanner distribution ♦ Cartesian product, Cochran's criterion, context clash, Continuation Passing Style, cutting theorem, cylindrical coordinates ♦ dual-chamber rate modulated asynchronous ♦ equivalence relation ♦ fixed-point, floating-point, Froude's curve, functional dependency, functionally dependent ♦ Gene Products, vpr, Genes, vpr, Grad-Shafranov Equation, g-test ♦ homogeneous atmosphere ♦ inclusion-exclusion principle, inductive relation, irreflexive ♦ JK flip-flop ♦ k-statistics ♦ Larmor radius ♦ Milliroentgen ♦ Newton law of gravitation, Number of the Beast ♦ Pólya's distribution, parallel random access machine, partial equivalence relation, partial ordering, path system problem, pH value, photosensitizer, platinum 13% rhodium, polar coordinates, POP-1, potential density, pre-order, pyramid of numbers ♦ QRS complex, Quotient ♦ radio horizon, range attenuation, reflux ratio, Reynolds number, roentgen equivalent man, Rosin-Rammler equation, rotating Reynolds number, Russell's Paradox ♦ Schwarzschild radius, set associative cache, Shift-Or, Smith chart, Smith diagram, Snarling Letter, SR flip-flop, SUNSPOT NUMBER, surround channel, symmetric set difference, System R ♦ temperature coefficient, transitive closure, transmission coefficient ♦ Viologens, vu. (references)
Non-English Usage: "R" is also a word in the following languages with English translations in parentheses.

German (letter), Italian (r), Latin (rad., radius), Portuguese (River), Spanish (letter).

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Modern Usage: R

DomainUsage

Screenplays

18 is R. M-R-E (Batman Forever; writing credit: Bob Kane; Lee Batchler)

What are you, R Kelly (25th Hour; writing credit: David Benioff)

The Gap, Starbucks, Toys R Us, who will remember all those landmarks unless we tell the world about them (Buffy the Vampire Slayer; writing credit: Doreen Spicer)

I think it's T double E double R double I double F double I double C C C C C. (Charlotte's Web; writing credit: E.B. White; Earl Hamner Jr.)

Varjak, V A R J A K. I'm a writer, W R I T E R (Breakfast at Tiffany's; writing credit: George Axelrod)

Lyrics

Double R so of course it's better (Put Ya Hands Up; performing artist: KISS)

It's not a front, F to the R to the O to the N to the T (O.P.P.; performing artist: Naughty By Nature)

Honey, I know, I know, I know times r changing ("Purple Rain"; performing artist: Prince)

Movie/TV Titles

Elizabeth R (1971)

R de REPSOL (1970)

Simpaticul domn R (1969)

Sheep R Us (2001)

L + R (2000)

Source: compiled by the editor from various references; see credits.

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Commercial Usage: R

DomainTitle

References

  • H & R Johnson Berhad: International Competitive Benchmarks and Financial Gap Analysis (reference)

  • H & R REAL ESTATE INVT TR: International Competitive Benchmarks and Financial Gap Analysis (reference)

  • R + V Lebensversicherung AG: International Competitive Benchmarks and Financial Gap Analysis (reference)

    (more reference examples)

  

Books

  • Management for Research Libraries Cooperation: (Papers from the Association of American Universities and Arl(Association of Research Libraries) Program for Electronic Publishing and Shared Global r (reference)

  • The Best of James Herriot: Favourite Memories of a Country Vet: James Herriot's Own Selection from His Original Books, With Additional Material by r (reference)

  • Invasion of the Body Squeezers; I Am Your Evil Twin; Revenge R Us; Fright Camp: Book 2 (Goosebumps Series 2000, Nos. 5-8) (reference)

  • Ashrae Transactions 1999 (American Society of Heating, Refrigerating and Airconditioning Engineers.//a S H R A E Transactions, Vol 105, Pt 1) (reference)

  • Schnellmethoden zur Analyse von Plutonium und anderen Aktiniden in Umweltproben : Bericht einer Ad-hoc-Arbeitsgruppe des Arbeitskreises Umweltèuberwachung (AKU) = Rapid methods for the analysis of plutonium and other actinides in environmental samples : r (reference)

    (more book examples)

  

Periodicals

  

Theater & Movies

  • Dinosaur Valley/Carnivore in R (reference)

  • Heritage of Rome/Garlands of R (reference)

  • Barney Google:Hillbillies R Us (reference)

  • Sailor Moon R The Movie - The Promise of the Rose (reference)

  • Legends-The Statesmen of the R (reference)

    (more DVD examples; more video examples)

  

Music

  

High Tech

  • Olympus Outback 10x25 RC II R All-Weather Compact Roof Prism Binocular (reference)

  • Adtran Router Module Provides Ip/Ipx Routing For Frame R (reference)

  • LIL SLIK R DESKTOP/NOTEBOOK ED (reference)

  • Cisco Systems Service Adapter; Compression (6 R Vcs Stac) (reference)

  • Monster Cable JM VCPC R RP-10 VCR/Camcorder to Computer Audio/Video Using RCA Connections (10 ft.) (reference)

    (more camera examples; more video game examples; more computer examples; more electronic examples; more software examples)

Source: compiled by the editor from various references; see credits.

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Image Slideshow: R

Photos:
R

More pictures...

Illustrations:
R

More pictures...

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Photo Album: R

ThumbnailDescription & CreditThumbnailDescription & Credit

Illustration of structure of hyphal tip. er - endoplasmic reticulum, s - septum, m - mitochondrion, n - nucleus, vgs - Golgi, r - ribosome, p - plasma membrane, v - vesicles. Credit: CDC.

Launch wiredrag operations L to r - guide launch, tender, end launch Launches off of PATHFINDER. Credit: Coast & Geodetic Survey Historical Image Collection.

Indulging in a little "Mountain Dew" L to R - Hodges, Toadvine, Bryant, Ramsey. Credit: Coast & Geodetic Survey Historical Image Collection.

Foreground - l to r - Marv Paulsen, Junius Jarman, Paul Mears. Credit: Paths Less Taken - NOAA at the Ends of the Earth.

Cruising through an ice field - l to r - Ted Shanahan, Stan Jeffers, Jerry Gray, and Simon Tagarook. Credit: Paths Less Taken - NOAA at the Ends of the Earth.

Figure 39. Massey sounder, a propeller driven sounding device first developed in 1802 by Edward Massey. Many improvements were made to this device through the Nineteenth Century. The instrument in the image was created by Thomas Walke r in 1874. It consists of a propeller driven registering device which is fixed to a sounding line and weighted by ballast. Credit: Sailing for Science - the NOAA Fleet Then and Now.

Raptor 4004, the first Lockheed Martin-Boeing F-22 to fly with advanced avionics hardware and integrated software, lifts off Nov. 15 on its maiden flight from Marietta, Ga. The application of advanced avionics software in the F-22 is key to the Raptor's r.

Staff Sgt. Charles Sauvage, 85th Security Forces Squadron, Sembach Air Base, Germany, instructs a class of Navy And Air Force members assigned to Naval Air Station Keflavik, Iceland on anti-terrorism and detection awareness. (P.; photo by Master. Sgt. Keith R..

District Conservationist Rhonda Foster and Grasslands Specialist Ralph Harris evaluating an intensive grazing system that is utilizing a 3 week rotation of cattle grazing. The area on the right has been grazed for 3 weeks while the area on the left has r. Credit: Jeff Vanuga.

L to R Daniel Kent, construction forman, Robert Kent, housing director and USDA Community development Manager Sylvester Pomerlee inspect plans for self help homes in Indianola, MS. Credit: USDA.

Source: pictures compiled by the editor from various references; see picture credits.

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Digital Photo Gallery: R
 

"C O N V E R G E" by Kevin C
Commentary: "I had my friend brian bang some sticks with embers together at night, some of what you see is the resulting sparks, some is the swinging embers. ah yet another memory from senior survival! visit my manip site: blindgorgon.deviantart ..."		"R.park 2" by A D C
Commentary: "View of a parking in town...."

Source: photographs selected by the editor, with permission from the photographers.

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Non-Fiction Usage: R

SubjectTopicQuote

Health

Joynt, R (ed). Clinical Neurology. (references)

Berkow, R (ed) The Merck Manual of Diagnosis and Therapy. (references)

Turnbull PCB, Bohm R et al., 1993, Guidelines for the Surveillance and Control of Anthrax in Humans and Animals, Geneva. (references)

Business

The GOST R certificate is issued by accredited testing centers. (references)

Certificates of conformity (or GOST R certificates) are issued by testing centers accredited by Gosstandart. (references)

Obtaining a hygiene conclusion from the Center of Hygienic Standards and Certification has become a prerequisite for issuing a GOST R certificate. (references)

Economic History

Malaysia

U.S. firms in the retail sector include Avon, Toys R Us, Hallmark and Levi's, among others. (references)

Japan

American retail giants Kinko's, Office Max, Toys' R Us, and The Sports Authority have also opened outlets in the area. (references)

Mauritius

Several U.S. franchises, notably Kentucky Fried Chicken, Pizza Hut, Toys R Us, and McDonald's have opened in recent years. (references)

Trade

Dominican Rep

The exception applies for r shipments from countries where there is not a Dominican Consulate. (references)

Kenya

The Kenyan Embassy in Washington, DC (address: 2249 R Street, N.W. Washington, DC 20008; Tel: 202-387-6101) and other Kenyan embassies may issue the import license. (references)

Ireland

These incentives include an attractive 10 percent corporate tax rate for qualifying industries guaranteed until December 31 2002, capital investment, R & D, and training grants; rent subsidy for industries in certain regions; and assistance in site location. (references)

Travel

Chad

U.S. travelers can obtain tourist, business and diplomatic visas from the Embassy of the Republic of Chad, 2002 R Street, NW, Washington, D.C. 20009, Tel: (202) 462-4009. Fax: (202) 265-1937. (references)

Chad

The Embassy of the Republic of Chad in the U.S. is located on 2002 R Street N.W., Washington, D.C. 20009, Tel: (202) 462-4009, Fax: (202) 265-1937. There is no Chad-U.S. Chamber of Commerce in Washington. (references)

Kenya

Travelers may obtain the latest information on visas as well as any additional details regarding entry requirements from the Embassy of Kenya, 2249 R street, N.W., Washington, DC 20008, telephone (202) 387-6101, or the Kenyan Consulates General in Los Angeles and New York City. (references)

Lexicography

Devil's Dictionary

QUOTIENT, n. A number showing how many times a sum of money belonging to one person is contained in the pocket of another -- usually about as many times as it can be got there. R

Source: compiled by the editor from ICON Group International, Inc.; see credits.

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Speeches: R

SpeakerTermPhrase(s)

George Bush

1989-1993It's there for research and development, R and D, a record high.

Source: compiled by the editor from various references.

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Usage Frequency: R

"R" is generally used as an alphabetical symbol -- approximately 69.31% of the time. "R" is used about 6,765 times out of a sample of 100 million words spoken or written in English. Its rank is based on over 700,000 words used in the English language. Some parts-of-speech are not covered due to the samples used by the British National Corpus. (note: percents less than one-hundredth of one percent have been omitted)
Parts of SpeechPercentUsage per
100 Million Words		Rank in English
Alphabetical Symbol69.31%4,6892,089
Noun (proper)27.29%1,8464,611
Unclassified Items3.4%23019,815
                    Total100.00%6,765N/A

Source: compiled by the editor from several corpora; see credits.

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Usage in Company Names: R

CountryNameCountryName
Canada

H & R REAL ESTATE INVT TR

Germany

R + V Lebensversicherung AG

Malaysia

H & R Johnson Berhad

 (more examples...)  

Source: compiled by the editor from Icon Group International, Inc.

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Expressions: R

Expressions using "R": coenzyme R ♦ Columbia Cross R ♦ Humulin R ♦ Novolin R ♦ Pearson's r ♦ r & d ♦ R aconitifolius ♦ R aculeatus ♦ R Americana ♦ R and B ♦ R and D ♦ R Asiaticus ♦ R aureum ♦ R bulbosus ♦ R caesius ♦ R calendula ♦ R canadensis ♦ R caribou ♦ R Catesbiana ♦ R catharticus ♦ R chrysops ♦ R clavata ♦ R communis ♦ R cristatus ♦ R elegans ♦ R equina ♦ R erinacea ♦ R factor ♦ R Factors ♦ R floridum ♦ R Gallica ♦ R Groenlandicus ♦ R hispidus ♦ R Hydrolapathum ♦ R interface ♦ R interruptus ♦ R laevis ♦ R lead ♦ R longirostris ♦ R Mangle ♦ R mucronata ♦ R nigra ♦ R Pseudacacia ♦ R quadriloba ♦ R reference point ♦ R regulus ♦ R roulroul ♦ R rubiginosa ♦ R Sondaicus ♦ R Stelleri ♦ R succedanea ♦ R tarandus ♦ R tinctorum ♦ R venenata ♦ R vernicifera ♦ R villosus ♦ R Virginianus ♦ R wire ♦ system R. Additional references.

Hyphenated Usage

Beginning with "R": R-a-f, R-and-d, r-axis, r-banded, r-complex, r-detector, r-DNA, R-DS(on), r-ful, r-ii, r-interval, r-intervals, r-less, r-lessness, R-M, r-o-l-l, r-plate, r-pronouncing, r-related, R-rmax, R-rmax-r-rmin, R-rmin, r-RNS, R-robert, r-roomf, r-r-rien, r-r-ruup, r-selected, r-series, R-series-based, R-series-to-alpha, r-shaped, R-s-p-c-a, r-squared, r-to, R-Type, r-type, R-u-a-r-a-i-d-h, R-uw, R-uwaf, r-value, r-values, R-york, r-zacopride.

Ending with "R": e-r, Gti-r, Tri-r.

Containing "R": anonymity-r-us, chr-r-eek, c-r-a-p, c-r-e-a-m-s, D'-a-r-c-y, G-r-r-r-r-owf, G-r-r-ruff, har-r-room-mff, Har-r-r-ooo-m-m-f, har-r-r-r-r-o-o-o-o-m-m-m-f-f-f, h-u-r-r-y, I-r-a, k-r-y-t-r-o-n, L-o-r-i, N-e-r-v-o-u-s, o-b-i-t-r-y, over-r-r-rl, p-a-r-e-n-t-s, P-o-p-c-o-r-n, p-r-o-g-r-a-m-m-e-d, Ser-r-geant, s-t-r-e-t-c-h, toys-r-us, trees-r-us, V-e-r-n, v-e-r-y, weir-r-rd.

Source: compiled by the editor from various references; see credits.

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Frequency of Internet Keywords: R

The following statistics estimate the number of searches per day across the major English-language search engines as identified by various trade publications. Hyperlinks lead to commercial use of the expression at Amazon.com.
 
ExpressionFrequency
per Day		ExpressionFrequency
per Day

toy r us

32,856

r b music

544

baby r us

28,384

y r

538

r kelly

26,228

r kelly sex tape

513

r

6,599

j r music world

513

dvd r

2,852

r l carrier

496

h r block

2,727

j r music

449

r ygold

1,916

baby r us.com

425

r kelly lyrics

1,566

r c

380

toy r us.com

1,395

baby r us and registry

379

babys r us

1,373

integra type r

363

r b lyrics

1,351

toy r us canada

346

r b

1,291

type r

334

percent r

1,226

picture of r kelly

323

control control r c radio rc remote

1,201

ignition kelly lyrics r remix

310

kid r us

1,189

kelly.com r

308

j and r

1,104

ignition kelly lyrics r

304

dvd r media

881

baby r us coupon

302

r c car

742

r c airplane

296

leg r us

628

r h

286

ignition kelly r

566

r kelly video

283
Source: compiled by the editor from various references; see credits.

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Modern Translation: R

Language Translations for "R"; alternative meanings/domain in parentheses.

Danish

  

Ruiter's sygdom (profound nodular arteritis R), vasculitis allergica (profound nodular arteritis R), Program for De Europæiske Fællesskaber på området for informationsteknologi og telekommunikation i forbindelse med vejtransport (Community programme in the field of road transport informatics and telecommunications(D edicated R oad I nfrastructure for V ehicle Safety in E urope)), ponceau 6 R (ponceau 6 R), Pearsons korrelations-koefficient (Pearson coefficient of correlation, Pearson's correlation coefficient, Pearson's r), Fællesskabsprogram til udvikling af visse ugunstigt stillede regioner i Fællesskabet gennem bedre adgang til avancerede telekommunikationstjenester (Community programme for the development of certain less-favoured regions of the Community by improving access to advanced telecommunications services-S pecial T elecommunications A ction for R egional Development), Fællesskabsinitiativ,der skal forberede virksomheder til det indre marked (Community initiative concerning the preparation of businesses for the Single Market(P reparation of R egional I ndustry for the S ingle Ma rket), PRISMA), E126 (ponceau 6 R), afrikansk bomuldsugle (Cluster caterpillar, cotton worm, Egyptian cotton leafworm, Heliothis cluster caterpillar, Heliothis cluster pillar, Mediterranean climbing cutworm, Tobacco caterpillar, Tobacco cutworm, tobacco leaf caterpilla r, Tobacco leaf caterpillar). (various references)

   

Dutch

  

eiernestrups (Cluster caterpillar, cotton worm, Egyptian cotton leafworm, Heliothis cluster caterpillar, Heliothis cluster pillar, Mediterranean climbing cutworm, Tobacco caterpillar, Tobacco cutworm, tobacco leaf caterpilla r, Tobacco leaf caterpillar), allergische vasculitis (profound nodular arteritis R), brouwen (brew, make a uvular R), Communautair initiatief om het bedrijfsleven voor te bereiden op de eenwording van de Europese markt (Community initiative concerning the preparation of businesses for the Single Market(P reparation of R egional I ndustry for the S ingle Ma rket), PRISMA), Communautair programma op het gebied van informatica en telecommunicatie voor het wegvervoer (Community programme in the field of road transport informatics and telecommunications(D edicated R oad I nfrastructure for V ehicle Safety in E urope)), Communautair programma voor de ontwikkeling van bepaalde minder ontwikkelde regio's van de Gemeenschap door een betere toegang tot geavanceerde telecommunicatiediensten (Community programme for the development of certain less-favoured regions of the Community by improving access to advanced telecommunications services-S pecial T elecommunications A ction for R egional Development), <met keel-r spreken> (make a uvular R), E126 (ponceau 6 R), tabaksrups (cluster caterpillar, cotton worm, Egyptian cotton leafworm, Heliothis cluster pillar, Mediterranean climbing cutworm, tobacco caterpillar, tobacco cutworm, tobacco leaf caterpilla r), klaprozenrood (ponceau 6 R), ponceau 6 R (ponceau 6 R), correlatiecoëfficiënt van Pearson (Pearson coefficient of correlation, Pearson's correlation coefficient, Pearson's r). (various references)

   

Esperanto

  

kartavi (make a uvular R). (various references)

   

Finnish

  

R-liitäntä (existing interface, non-ISDN interface, R interface, R reference point), R-geeni (R gene, VPR gene), R-faktori (R factor, resistance factor, resistance-transfer factor), resistenssitekijä (R factor, resistance factor, resistance-transfer factor), R-entsyymi (R-enzyme), vpr-geeni (R gene, VPR gene), soittojohto (R lead, R wire, ring, ring conductor, ring lead, ring wire), Pearsonin korrelaatiokerroin (Pearson coefficient of correlation, Pearson's correlation coefficient, Pearson's r), krysanteemiyökkönen (Cluster caterpillar, cotton worm, Egyptian cotton leafworm, Heliothis cluster caterpillar, Heliothis cluster pillar, Mediterranean climbing cutworm, Tobacco caterpillar, Tobacco cutworm, tobacco leaf caterpilla r, Tobacco leaf caterpillar), jättää erohakemus (hand in one's r). (various references)

   

French

  

R 53 (R 52, R 53, R 59), R 42 (R 42, R 43), R 52 (R 52, R 53, R 59), R 59 (R 52, R 53, R 59), R42 (R 42, R 43), R43 (R 42, R 43), R52 (R 52, R 53, R 59), R53 (R 52, R 53, R 59), R59 (R 52, R 53, R 59), révolution (r or rev. 2), Recherche fondamentale sur l'intelligence adaptative et le neurocalcul (B asic r esearch in a daptive i ntelligence and n eurocomputing), R-enzyme (R-enzyme), R-s (R-s), R 43 (R 42, R 43), Réseau de centres d'information sur les initiatives en matière de développement rural et sur les marchés agricoles (M odel scheme for i nformation on r ural development i nitiatives and a gricultural m arkets), Initiative communautaire concernant la préparation des entreprises dans la perspective du Marché Unique (Community initiative concerning the preparation of businesses for the Single Market(P reparation of R egional I ndustry for the S ingle Ma rket)), facteur de transfert de résistance (R factor), facteur R (R factor), fil de nuque (R lead, R wire), facteur de résistance (R factor), gène vpr (R gene), Applications des Technologies de l'Information et de la Communication dans les zones rurales (O pportunities for Applications of Information and Communication Technologies in R ural A reas), interface non RNIS (R interface, R reference point), gène R (R gene), E126 (ponceau 6 R), dangereux pour l'environnement (R 52, R 53, R 59), chenille défoliante (tobacco leaf caterpilla r), Actions communautaires en faveur du tourisme rural (C ommunity A ction for R ural T ourism), interface R (R interface, R reference point), Programme communautaire relatif au développement de certaines régions défavorisées de la Communauté par un meilleur accès aux services avancés de télécommunications (Community programme for the development of certain less-favoured regions of the Community by improving access to advanced telecommunications services-S pecial T elecommunications A ction for R egional Development), antigène R (R-antigen), coefficient de corrélation de Pearson (Pearson's r), vascularite nodulaire profonde de R (profound nodular arteritis R), tr (r or rev. 2), tour (r or rev. 2), sensibilisant (R 42, R 43), Programme spécifique de recherche et de développement technologique dans le domaine de la biotechnologie 1990-1994-Recherches biotechnologiques pour l'innovation,le développement et la croissance en Europe (Specific research and technological development programme in the field of biotechnology(1990 to 1994)-B iotechnology r esearch for i nnovation), Programme communautaire dans le domaine de l'informatique du transport routier et des télécommunications (Community programme in the field of road transport informatics and telecommunications(D edicated R oad I nfrastructure for V ehicle Safety in E urope)), Large Scale Reprocessing (L arge S cale R eprocessing), 1 roentgen par seconde (R-s), ponceau 6 R (ponceau 6 R), phrase R (R phrase), organisme à ADN recombiné (r-DNA organism), noctuelle rayee (tobacco leaf caterpilla r), N (R 52, R 53, R 59). (various references)

   

German

  

R 52 (dangerous for the environment, R 52, R 53, R 59), R 43 (R 42, R 43, sensitizing), R 53 (dangerous for the environment, R 52, R 53, R 59), R 59 (dangerous for the environment, R 52, R 53, R 59), R Gen (R gene, VPR gene), R42 (R 42, R 43, sensitizing), R43 (R 42, R 43, sensitizing), R52 (dangerous for the environment, harmful to aquatic organisms, R 52, R 53, R 59, R52), R53 (dangerous for the environment, R 52, R 53, R 59), R59 (dangerous for the environment, R 52, R 53, R 59), R-Antigen (R-antigen), Rauh-Antigen (R-antigen), R-Bezugspunkt (existing interface, non-ISDN interface, R interface, R reference point), R-Enzym (R-enzyme), Rest R (radical R), R-Faktor (R factor, resistance factor, resistance-transfer factor), R-Referenzpunkt (existing interface, non-ISDN interface, R interface, R reference point), R-s (R-s), R-Satz (R phrase), R 42 (R 42, R 43, sensitizing), Resistenz-Faktor (R factor, resistance factor, resistance-transfer factor), Arteriitis Vasculitis nodularis profunda Ruiter (profound nodular arteritis R), Gemeinschaftsprogramm zur Entwicklung bestimmter benachteiligter Regionen der Gemeinschaft durch einen besseren Zugang zu den fortgeschrittenen Telekommunikationsdiensten (Community programme for the development of certain less-favoured regions of the Community by improving access to advanced telecommunications services-S pecial T elecommunications A ction for R egional Development), Gemeinschaftsprogramm auf dem Gebiet der Strassenverkehrsinformatik und-telekommunikation (Community programme in the field of road transport informatics and telecommunications(D edicated R oad I nfrastructure for V ehicle Safety in E urope)), Gemeinschaftsmassnahmen zur Förderung des ländlichen Fremdenverkehrs (C ommunity A ction for R ural T ourism, CART), Gemeinschaftsinitiative zur Vorbereitung der Unternehmen auf den Binnenmarkt (Community initiative concerning the preparation of businesses for the Single Market(P reparation of R egional I ndustry for the S ingle Ma rket), PRISMA), E126 (E126, ponceau 6 R), bestehende Endgeräteschnittstelle (existing interface, non-ISDN interface, R interface, R reference point), Informationszentrennetz für Massnahmen zur Entwicklung des ländlichen Raumes und der Agrarmärkte (M odel scheme for i nformation on r ural development i nitiatives and a gricultural m arkets, MIRIAM), asiatischer Baumwollwurm (cluster caterpillar, cotton worm, Egyptian cotton leafworm, Heliothis cluster pillar, Mediterranean climbing cutworm, tobacco caterpillar, tobacco cutworm, tobacco leaf caterpilla r), N (n, untrans), Anwendungen von Informations-und Kommunikationstechnologien (O pportunities for Applications of Information and Communication Technologies in R ural A reas), afrikanischer Baumwollwurm (cluster caterpillar, cotton worm, Egyptian cotton leafworm, Heliothis cluster pillar, Mediterranean climbing cutworm, tobacco caterpillar, tobacco cutworm, tobacco leaf caterpilla r), aegyptischer Baumwollwurm (cluster caterpillar, cotton worm, Egyptian cotton leafworm, Heliothis cluster pillar, Mediterranean climbing cutworm, tobacco caterpillar, tobacco cutworm, tobacco leaf caterpilla r), aegyptische Baumwollraupe (cluster caterpillar, cotton worm, Egyptian cotton leafworm, Heliothis cluster pillar, Mediterranean climbing cutworm, tobacco caterpillar, tobacco cutworm, tobacco leaf caterpilla r), Basic research in adaptive intelligence and neurocomputing (B asic r esearch in a daptive i ntelligence and n eurocomputing, BRAIN), 1 Röntgen pro Sekunde (R-s), schnarren (buzz, clatter, creak, croak, make a uvular R, rasp), sensibilisierend (R 42, R 43, sensitizing), U (non-recoverable), Umdrehung (Rev, reversal, revolution, rotation, turn), umweltgefährlich (dangerous for the environment, R 52, R 53, R 59), Programm zur Unterstützung der Bewertung von Forschungsarbeiten auf Gemeinschaftsebene (S upport P rogramme for the E valuation of A ctivities in the field of R esearch, SPEAR), Ponceau 6 R (E126, ponceau 6 R), Periarteriitis cutanea benigna (profound nodular arteritis R), Pearson'scher Korrelationskoeffizient (Pearson coefficient of correlation, Pearson's correlation coefficient, Pearson's r), Large Scale Reprocessing (L arge S cale R eprocessing, LASCAR), VPR Gen (R gene, VPR gene). (various references)

   

Greek 

  

R 53 (dangerous for the environment, R 52, R 53, R 59), roentgen ανά δευτερόλεπτο (R-s), R 42 (R 42, R 43, sensitizing), R 52 (dangerous for the environment, R 52, R 53, R 59), R 59 (dangerous for the environment, R 52, R 53, R 59), R/sec (R-s), R42 (R 42, R 43, sensitizing), R43 (R 42, R 43, sensitizing), R52 (dangerous for the environment, R 52, R 53, R 59), R53 (dangerous for the environment, R 52, R 53, R 59), R59 (dangerous for the environment, R 52, R 53, R 59), R 43 (R 42, R 43, sensitizing), ευαισθητοποιός ουσία (R 42, R 43, sensitizing), Ευκαιρίες για εφαρμογές των τεχνολογιών πληροφόρησης και επικοινωνίας σε αγροτικές περιοχές (O pportunities for Applications of Information and Communication Technologies in R ural A reas), φράση R (R phrase), φυλλοφάγος κάμπια του βαμβακιού (cluster caterpillar, cotton worm, Egyptian cotton leafworm, Heliothis cluster pillar, Mediterranean climbing cutworm, tobacco caterpillar, tobacco cutworm, tobacco leaf caterpilla r), επικίνδυνο για το περιβάλλον (dangerous for the environment, R 52, R 53, R 59), αντιγόνο R (R-antigen), Δίκτυο κέντρων πληροφόρησης για τις πρωτοβουλίες σε θέματα αγροτικής ανάπτυξης και για τις γεωργικές αγορές (M odel scheme for i nformation on r ural development i nitiatives and a gricultural m arkets, MIRIAM), δακτύλιος (annulus), Πρόγραμμα ενίσχυσης για την ευρωπαϊκή αξιολόγηση της έρευνας (S upport P rogramme for the E valuation of A ctivities in the field of R esearch, SPEAR), συντελεστής συσχέτισης Pearson (Pearson coefficient of correlation, Pearson's correlation coefficient, Pearson's r), Πολυετές πρόγραμμα έρευνας και ανάπτυξης της Ευρωπαϊκής Οικονομικής Κοινότητας στους τομείς της βασικής τεχνολογικής έρευνας και της εφα (BRITE, Multiannual research and development programme of the European Economic Community in the fields of basic technological research and the applications of new technologies.(B asic R esearch in I ndustrial T echnologies for E urope)(1985-88)), δακτυλιοειδής αγωγός (R lead, R wire, ring, ring conductor, ring lead, ring wire), ρίζα R (radical R), N (dangerous for the environment, R 52, R 53, R 59), Large Scale Reprocessing (L arge S cale R eprocessing, LASCAR), Κοινοτικό πρόγραμμα σχετικά με την ανάπτυξη ορισμένων μειονεκτικών περιοχών της Κοινότητας μέσω καλύτερης πρόσβασης στις προηγμένες υπη (Community programme for the development of certain less-favoured regions of the Community by improving access to advanced telecommunications services-S pecial T elecommunications A ction for R egional Development), Κοινοτικό πρόγραμμα στον τομέα της εφαρμογής της πληροφορικής και των τηλεπικοινωνιών στις οδικές μεταφορές (Community programme in the field of road transport informatics and telecommunications(D edicated R oad I nfrastructure for V ehicle Safety in E urope)), Κοινοτικές δράσεις προς όφελος του αγροτικού τουρισμού (C ommunity A ction for R ural T ourism, CART), Κοινοτική πρωτοβουλία σχετικά με την προετοιμασία των επιχειρήσεων στην προοπτική της Ενιαίας Αγοράς (Community initiative concerning the preparation of businesses for the Single Market(P reparation of R egional I ndustry for the S ingle Ma rket), PRISMA), γονίδιο vpr (R gene, VPR gene), ρ-ένζυμο (R-enzyme), στροφή (bend, curve, stanza, stave, turn, turning, turnover, twiddle, twist, verticil, wind, winding, wrest), Basic research in adaptive intelligence and neurocomputing (B asic r esearch in a daptive i ntelligence and n eurocomputing, BRAIN), γονίδιο R (R gene, VPR gene), βαθιά οζώδης αρτηρίτις του Ruiter (profound nodular arteritis R), παράγοντας μεταφοράς αντίστασης (R factor, resistance factor, resistance-transfer factor), παράγοντας αντίστασης (R factor, resistance factor, resistance-transfer factor), καλοήθης υποδόρια περιαρτηρίτις (profound nodular arteritis R). (various references)

   

Hungarian

  

kultúrprogram-szervezõ tiszt (recreation and welfare officer), jobboldali (Dexter, right, right hand, righthand, rightist). (various references)

   

Italian

  

r (degree Rankine, r or rev. 2, radicals, resultant linear density, revolution). (various references)

   

Japanese Kanji 

  

研究開発 (R and D, research and development), ルーン文字 (look, looks, Louis Vuitton, Louisiana, lure, lutetium, lux, Luxembourg, R and B, Renaissance, Renault, ressentiment, rhythm, rhythm and blues, rhythm box, rhythm machine, ruby, ruby glass, rune, ruthenium). (various references)

   

Japanese Katakana 

  

ルズムアンドブルース (R and B, rhythm and blues), けんきゅうかいはつ (R and D, research and development). (various references)

   

Pig Latin

  

ray.(various references)

   

Portuguese

  

R 53 (dangerous for the environment, R 52, R 53, R 59), R 42 (R 42, R 43, sensitizing), R 52 (dangerous for the environment, R 52, R 53, R 59), R 59 (dangerous for the environment, R 52, R 53, R 59), r/s (R-s), R42 (R 42, R 43, sensitizing), R43 (R 42, R 43, sensitizing), R52 (dangerous for the environment, harmful to aquatic organisms, R 52, R 53, R 59, R52), R59 (dangerous for the environment, R 52, R 53, R 59), Rede de Informação sobre as Iniciativas em matéria de Desenvolvimento Rural e sobre os Mercados Agrícolas (M odel scheme for i nformation on r ural development i nitiatives and a gricultural m arkets, MIRIAM), R-enzima (R-enzyme), RTF (R factor, resistance factor, resistance-transfer factor), R53 (dangerous for the environment, R 52, R 53, R 59), R 43 (R 42, R 43, sensitizing), gene VPR (R gene, VPR gene), gene R (R gene, VPR gene), frase R (R phrase), factor R (R factor, resistance factor, resistance-transfer factor), factor de resistência (R factor, resistance factor, resistance-transfer factor), E126 (E126, ponceau 6 R), coeficiente de correlação de Pearson (Pearson coefficient of correlation, Pearson's correlation coefficient, Pearson's product moment correlation, Pearson's r), Basic research in adaptive intelligence and neurocomputing (B asic r esearch in a daptive i ntelligence and n eurocomputing, BRAIN), antígeno R (R-antigen), Iniciativa Comunitária relativa à Preparação das Empresas com vista ao Mercado Único (Community initiative concerning the preparation of businesses for the Single Market(P reparation of R egional I ndustry for the S ingle Ma rket), PRISMA), Acções Comunitárias a favor do Turismo Rural (C ommunity A ction for R ural T ourism, CART), Programa de Apoio a uma Avaliação da Investigação a Nível Europeu (S upport P rogramme for the E valuation of A ctivities in the field of R esearch, SPEAR), arterite nodular profunda de R (profound nodular arteritis R), vasculite nodular profunda de R (profound nodular arteritis R), sensibilizante (R 42, R 43, sensitizing), Programa Comunitário relativo ao Desenvolvimento de Certas Regiões Desfavorecidas da Comunidade por meio de um Melhor Acesso aos Serviços Avançados de Telecomunicações (Community programme for the development of certain less-favoured regions of the Community by improving access to advanced telecommunications services-S pecial T elecommunications A ction for R egional Development), volta,revolução (r or rev. 2, revolution), Large Scale Reprocessing (L arge S cale R eprocessing, LASCAR), 1 roentgen por segundo (R-s), Programa Comunitário no domínio da Informática e das Telecomunicações aplicadas aos Transportes Rodoviários (Community programme in the field of road transport informatics and telecommunications(D edicated R oad I nfrastructure for V ehicle Safety in E urope)), ponto de referência R (existing interface, non-ISDN interface, R interface, R reference point), ponceau 6R (E126, ponceau 6 R), perigoso para o ambiente (dangerous for the environment, R 52, R 53, R 59), N (dangerous for the environment, R 52, R 53, R 59). (various references)

   

Scottish

  

seann (d, l, n, s). (various references)

   

Spanish

  

net. (various references)

   

Swedish

  

R-referenspunkt (existing interface, non-ISDN interface, R interface, R reference point), R-gränssnitt (existing interface, non-ISDN interface, R interface, R reference point), R-gen (R gene, VPR gene), R-faktor (R factor, resistance factor, resistance-transfer factor), resistensfaktor (R factor, resistance factor, resistance-transfer factor), R-enzym (R-enzyme), VPR-gen (R gene, VPR gene), Pearsons korrelationskoefficient (Pearson coefficient of correlation, Pearson's correlation coefficient, Pearson's r), egyptiskt lövfly (Cluster caterpillar, cotton worm, Egyptian cotton leafworm, Heliothis cluster caterpillar, Heliothis cluster pillar, Mediterranean climbing cutworm, Tobacco caterpillar, Tobacco cutworm, tobacco leaf caterpilla r, Tobacco leaf caterpillar). (various references)

   

Turkish

  

r harfi. (various references)

Source: compiled by the editor from various translation references.

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Anagrams: R

Scrabble® Enable2K-Verified Anagrams

 Words containing the letters "r"
 

+1 letter: ar, er, or, re.

 

+2 letters: air, arb, arc, are, arf, ark, arm, ars, art, bar, bra, bro, brr, bur, car, cor, cry, cur, dor, dry, ear, era, ere, erg, ern, err, ers, far, fer, fir, for, fro, fry, fur, gar, gor, her, ire, irk, jar, kir, kor, lar, mar, mir, mor, nor, oar, ora, orb, orc, ore, ors, ort, our, par, per, pro, pry, pur, rad, rag, rah, raj, ram, ran, rap, ras, rat, raw, rax, ray, reb, rec, red, ree, ref, reg, rei, rem, rep, res, ret, rev, rex, rho, ria, rib, rid, rif, rig, rim, rin, rip, rob, roc, rod, roe, rom, rot, row, rub, rue, rug, rum, run, rut, rya, rye, ser, sir, sri, tar, tor, try, urb, urd, urn, var, war, wry, yar.

Source: compiled by the editor from various references; see credits.

SCRABBLE® is a registered trademark. All intellectual property rights in and to the game are owned in the U.S.A and Canada by Hasbro Inc., and throughout the rest of the world by J.W. Spear & Sons Limited of Maidenhead, Berkshire, England, a subsidiary of Mattel Inc. Mattel and Spear are not affiliated with Hasbro.

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INDEX

1. Definition
2. Synonyms
3. Crosswords
4. Usage: Modern 		5. Usage: Commercial
6. Images: Slideshow
7. Images: Photo Album
8. Images: Digital Art 		9. Quotations: Non-fiction
10. Quotations: Speeches
11. Usage Frequency
12. Names: Company Usage 		13. Expressions
14. Expressions: Internet
15. Translations: Modern
16. Abbreviations 		17. Acronyms
18. Anagrams
19. Bibliography


  

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