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I

Definition: I

I

Adjective

1. Used of a single unit or thing; not two or more; "`ane' is Scottish".

Noun

1. A nonmetallic element belonging to the halogens; used especially in medicine and photography and in dyes; occurs naturally only in combination in small quantities (as in sea water or rocks).

2. The smallest whole number or a numeral representing this number; "he has the one but will need a two and three to go with it"; "they had lunch at one".

3. The 9th letter of the Roman alphabet.

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

Date "i" was first used in popular English literature: sometime before 1010. (references)

"I" is a common misspelling or typo for: bomb, bombs.

 

Specialty Definition: I

DomainDefinition

Literature

I This letter represents a finger, and is called in Hebrew yod or jod (a hand).
I per se [I by itself], i.e. without compeer, pre-eminently so.
"If then your I [yes] agreement want,
I to your I [yes] must answer, `No.'
Therefore leave off your spelling plea,
And let your I [yes] be I per se."
I.s. let your yes be yes decidedly.
Wits Interpreter, p. 116.
Many other letters are similarly used; as, A per se. (See A-Per-Se.) Thus in Restituta Eliza is called "The E per ce of all that ere hath been." So again, "C," signifies a crier, from "O yes! O yes!" We have "Villanies discovered by ... the help of a new crier, called O per se [i.e. superior to his predecessors]." 1666.
Shakespeare, in Troilus and Cressida, 1, 2, even uses the phrase "a very man per se" = A 1. Source: Brewer's Dictionary.

Multilingual Slang

Vietnamese (qua). (references)

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

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Specialty Definition: Aozora Bunko: I

(From Wikipedia, the free Encyclopedia)

See Aozora Bunko

1899)

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

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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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Complex number

(From Wikipedia, the free Encyclopedia)

The complex numbers are an extension of the real numbers, in which all polynomials have roots. The complex numbers contain a number i, the imaginary unit, with i2= -1. Every complex number can be represented in the form x+iy, where x and y are real numbers called the real part and the imaginary part of the complex number respectively.

The sum and product of two complex numbers are:

(a+ib) + (c+id) = (a+c) + i(b+d)
(a+ib) · (c+id) = ac-bd + i (bc+ad)

Complex numbers were first introduced in connection with explicit formulas for the roots of cubic polynomials. In mathematics, the term "complex" when used as an adjective means that the field of complex numbers is the underlying number field considered. For example complex matrix, complex polynomial and complex Lie algebra.

History

The earliest fleeting reference to square roots of negative numbers occurred in the work of the Greek mathematician and inventor Heron of Alexandria in the 1st century AD, when he considered the volume of an impossible frustum of a pyramid. They became more prominent when in the 16th century closed formulas for the roots of third and fourth degree polynomials were discovered by Italian mathematicians (see Tartaglia, Cardano). It was soon realized that these formulas, even if one was only interested in real solutions, sometimes required the manipulation of square roots of negative numbers. This was doubly unsettling since not even negative numbers were considered to be on firm ground at the time. The term "imaginary" for these quantities was coined by René Descartes in the 17th century and was meant to be derogatory. The existence of complex numbers was not completely accepted until the geometrical interpretation (see below) had been described by Caspar Wessel in 1799; it was rediscovered several years later and popularized by Carl Friedrich Gauss. The formally correct definition using pairs of real numbers was given in the 19th century.

Definition

Formally we may define complex numbers as ordered pairs of real numbers (a, b) together with the operations:

So defined, the complex numbers form a field, the complex number field, denoted by C (or in blackboard bold).

We identify the real number a with the complex number (a, 0), and in this way the field of real numbers R becomes a subfield of C. The imaginary unit i is the complex number (0,1).

C could also be defined as the topological closure of algebraic numbers and the algebraic closure of R.

Geometry

A complex number can also be viewed as a point or a position vector on the two dimensional Cartesian coordinate system. This representation is sometimes called an Argand diagram. In the figure, we have

z = x + iy = r (cos φ + i sin φ).
The latter expression is sometimes shorthanded as r cis φ, where r is called the absolute value of z and φ is called the complex argument of z. By simple trigonometric identities, we see that
r1 cis φ1 · r2 cis φ2 = r1r2 cis (φ1+φ2);
r1 cis φ1 / r2 cis φ2 = r1 / r2 cis (φ1-φ2);
Now the addition of two complex numbers is just the vector addition of two vectors, and the multiplication with a fixed complex number can be seen as a simultaneous rotation and stretching.

Multiplication with i corresponds to a counter clockwise rotation by 90 degrees. The geometric content of the equation i2 = -1 is that a sequence of two 90 degree rotation results in a 180 degree rotation. Even the fact (-1) · (-1) = +1 from arithmetic can be understood geometrically as the combination of two 180 degree turns.

Euler's formula states that ei φ = cisφ. The exponential form gives us a better insight then the shorthand rcisφ, which is almost never used in serious mathematical articles.

Absolute value, conjugation and distance

Recall that the absolute value (or modulus or magnitude) of a complex number z = r eiφ is defined as |z| = r. Algebraically, if z = a + ib, then |z| = &radic(a2 + b2 ).

One can check readily that the absolute value has three important properties:

|z + w| ≤ |z| + |w|
|z w| = |z| |w|
|z / w| = |z| / |w|
for all complex numbers z and w. By defining the distance function d(z, w) = |z - w| we turn the complex numbers into a metric space and we can therefore talk about limits and continuity. The addition, subtraction, multiplication and division of complex numbers are then continuous operations. Unless anything else is said, this is always the metric being used on the complex numbers.

The complex conjugate of the complex number z = a + ib is defined to be a - ib, written as or z*. As seen in the figure, is the "reflection" of z about the real axis. The following can be checked:

if and only if z is real
if z is non-zero
The latter formula is the method of choice to compute the inverse of a complex number if it is given in rectangular coordinates.

The complex argument of z=reiφ is φ. Note that the complex argument is unique up to modulo 2π.

Matrix representation of complex numbers

While usually not useful, alternative representations of complex field can give some insight into their nature. One particularly elegant representation interprets every complex number as 2x2 matrix with real entries which stretches and rotates the points of the plane. Every such matrix has the form

with real numbers a and b. The sum and product of two such matrices is again of this form. Every non-zero such matrix is invertible, and its inverse is again of this form. Therefore, the matrices of this form are a field. In fact, this is exactly the field of complex numbers. Every such matrix can be written as
which suggests that we should identify the real number 1 with the matrix
and the imaginary unit i with

a counter-clockwise rotation by 90 degrees. Note that the square of this latter matrix is indeed equal to -1.

The absolute value of a complex number expressed as a matrix is equal to the square root of the determinant of that matrix. If the matrix is viewed as a transformation of a plane, then the transformation rotates points through an angle equal to the argument of the complex number and scales by a factor equal to the complex number's absolute value. The conjugate of the complex number z corresponds to the transformation which rotates through the same angle as z but in the opposite direction, and scales in the same manner as z; this can be described by the transpose of the matrix corresponding to z.

Some properties

Real vector space

C is a two-dimensional real vector space. Unlike the reals, complex numbers cannot be ordered in any way that is compatible with its arithmetic operations: C cannot be turned into an ordered field.

Solutions of polynomial equations

A root of the polynomial p is a complex number z such that p(z) = 0. A most striking result is that all polynomials of degree n with real or complex coefficients have exactly n complex roots (counting multiple roots according to their multiplicity). This is known as the Fundamental Theorem of Algebra, and shows that the complex numbers are an algebraically closed field.

Indeed, the complex number field is the algebraic closure of the real number field. It can be identified as the quotient ring of the polynomial ring R[X] by the ideal generated by the polynomial X2 + 1:

C = R[X] / (X2 + 1).
This is indeed a field because X2 + 1 is irreducible. The image of X in this quotient ring becomes the imaginary unit i.

Complex analysis

The study of functions of a complex variable is known as complex analysis and has enormous practical use in applied mathematics as well as in other branches of mathematics. Often, the most natural proofs for statements in real analysis or even number theory employ techniques from complex analysis (see prime number theorem for an example). Unlike real functions which are commonly represented as two dimensional graphs, complex functions have four dimensional graphs and may usefully be illustrated by color coding a three dimensional graph to suggest four dimensions, or by animating the complex function's dynamic transformation of the complex plane.

Applications

Complex numbers are used in signal analysis and other fields as a convenient description for periodically varying signals. The absolute value |z| is interpreted as the amplitude and the argument arg(z) as the phase of a sine wave of given frequency.

If Fourier analysis is employed to write a given real-valued signal as a sum of periodic functions, these periodic functions are often written as the real part of complex valued functions of the form

f(t) = z eiωt
where ω represents the angular frequency and the complex number z encodes the phase and amplitude as explained above.

In electrical engineering, this is done for varying voltages and currentss. The treatment of resistors, capacitors and inductors can then be unified by introducing imaginary frequency-dependent resistances for the latter two and combining all three in a single complex number called the impedance. (Electrical engineers and some physicists use the letter j for the imaginary unit since i is typically reserved for varying currents.)

The residue theorem of complex analysis is often used in applied fields to compute certain improper integrals.

The complex number field is also of utmost importance in quantum mechanics since the underlying theory is built on (infinite dimensional) Hilbert spaces over C.

In Special and general relativity, some formulas for the metric on spacetime become simpler if one takes the time variable to be imaginary.

In differential equations, it is common to first find all complex roots r of the characteristic equation of a linear differential equation and then attempt to solve the system in terms of base functions of the form f(t) = ert.

See also

quaternions, complex geometry, local fields, phasors, Leonhard Euler, the most remarkable formula in the world, Hypercomplex number, Complex numbers at Wikibooks

Further Reading

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First Epistle to the Corinthians

(From Wikipedia, the free Encyclopedia)

The First Epistle to the Corinthians is a book of the Bible in the New Testament. It is a letter from Paul to the people of Corinth, Greece.

It was written from Ephesus (16:8) about the time of the Passover in the third year of the apostle's sojourn there (Acts 19:10; 20:31), and when he had formed the purpose to visit Macedonia, and then return to Corinth (probably AD 57).

The news which had reached him, however, from Corinth frustrated his plan. He had heard of the abuses and contentions that had arisen among them, first from Apollos (Acts 19:1), and then from a letter they had written him on the subject, and also from some of the "household of Chloe," and from Stephanas and his two friends who had visited him (1:11; 16:17). Paul thereupon wrote this letter, for the purpose of checking the factious spirit and correcting the erroneous opinions that had sprung up among them, and remedying the many abuses and disorderly practices that prevailed. Titus and a brother whose name is not given were probably the bearers of the letter (2 Corinthians 2:13; 8:6, 16-18).

The epistle may be divided into four parts:

1. The apostle deals with the subject of the lamentable divisions and party strifes that had arisen among them (chapters 1-4).

2. He next treats of certain cases of immorality that had become notorious among them. They had apparently set at nought the very first principles of morality (5, 6).

3. In the third part he discusses various questions of doctrine and of Christian ethics in reply to certain communications they had made to him. He especially rectifies certain flagrant abuses regarding the celebration of the Lord's supper (7-14).

4. The concluding part (15, 16) contains an elaborate defense of the doctrine of the resurrection of the dead, which had been called in question by some among them, followed by some general instructions, intimations, and greetings.

This epistle "shows the powerful self-control of the apostle in spite of his physical weakness, his distressed circumstances, his incessant troubles, and his emotional nature. It was written, he tells us, in bitter anguish, 'out of much affliction and pressure of heart...and with streaming eyes' (2 Corinthians 2:4); yet he restrained the expression of his feelings, and wrote with a dignity and holy calm which he thought most calculated to win back his erring children. It gives a vivid picture of the early church... It entirely dissipates the dream that the apostolic church was in an exceptional condition of holiness of life or purity of doctrine." The apostle in this epistle unfolds and applies great principles fitted to guide the church of all ages in dealing with the same and kindred evils in whatever form they may appear.

The subscription to this epistle states erroneously in the Authorized Version that it was written at Philippi. This error arose from a mistranslation of verse 16:5, "For I do pass through Macedonia," which was interpreted as meaning, "I am passing through Macedonia." In 16:8 he declares his intention of remaining some time longer in Ephesus. After that, his purpose is to "pass through Macedonia."

Initial text from Easton's Bible Dictionary, 1897 -- Please update as needed

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

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I

(From Wikipedia, the free Encyclopedia)

I is the ninth letter in the Latin alphabet, derived from the Greek iota (Ι, ι). It stood for the vowel /i/, the same as in the Etruscan alphabet. In Latin (as in Modern Greek) /j/ (as English Y in YOKE) was added. In Semitic, /j/ was the usual sound value of Jôd (probably originally a pictogram for an arm with hand), /i/ only in foreign words. In English, I represents different sounds, among them a diphthong that developed from /i:/ as well as short, open /I/ as in BILL. The dot over the lowercase 'i' is called a tittle.

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

India represents the letter I in the NATO phonetic alphabet.

In context, I is also:

See also: Ì, Í, Î, Ï, Ĭ

Two-letter combinations starting with I:

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

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I PAT

(From Wikipedia, the free Encyclopedia)

I=PAT

Influence (I) on the environment equals the product of population (P), affluence (A) (or per capita income) and technology (T).

This describes how our growing population, affluence, and technological resources contribute toward our environment, both positively and negatively.

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

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I²C

(From Wikipedia, the free Encyclopedia)

I2C (for Inter-Integrated Circuit, pronounced I-squared-C) is a serial computer bus by Philips. It is used to connect low-speed peripherals in an embedded system or motherboard.

The original system was created in the early 1980s as a battery control interface, but it was later used as a simple internal bus system for building control electronics with various Philips chips.

I2C uses only two bi-directional pins, clock and data, both running at +5V and pulled high with resistors. The bus operates at 100 kbit/s in standard mode but also includes a 10 kbit/s low-speed mode.

Buses of this type became popular when engineers realized that much of the expense of an integrated circuit results from the size of the package and the number of pins. A large package has more pins, thus more assembly steps when manufactured, more area on a printed circuit board, more weight, and more connections to fail. All of those cost money to make, assemble and test, and can increase operational expenses (fuel), or decrease convenience (weight is critical in cell-phones, for example).

A particular strength of I2C is that a microcontroller can control a network of several chips with just two general-purpose I/O pins and software.

Although much slower than most bus systems, the low expense is excellent for peripherals that have to exist, but need not be fast. The bus is often used for built-in-tests, volume, tone and color balance controls, low-speed analog-to-digital and digital-to-analog controllers, real-time-clocks, small non-volatile memories (used to preserve user-settable options), control of clock-generators (for computers that can vary their clock speeds) and integrated circuits that combine a shift-register and power transistors. Chips can also be added to or removed from the bus while the system is running, which makes I2C useful for hot swappable components.

The basic bus has a seven-bit address space, allowing up to 112 nodes on one bus (16 of the 128 addresses are reserved). In 1992 the first standardized version was released, v1.0. This added a new fast mode at 400 kbit/s and a ten-bit addressing mode to support up to 1024 nodes. v2.0 from 1998 added high-speed mode at 3.4 Mbit/s, while reducing the voltage and current requirements when run in that mode (thus saving power as well as being faster). The latest v.2.1 from 2001 is a minor cleanup of 2.0.

I2C was also used as the basis for ACCESS.bus and VESA's monitor data interface (Display Data Channel or DDC) - both for low-speed control and built-in-test.

External links

I2C Bus / Access Bus

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

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Ilocos Region

(From Wikipedia, the free Encyclopedia)

The Ilocos Region of the Philippines, designated as Region I is located in the northwestern part of Luzon. It is bounded by Cordillera Administrative Region and Cagayan Valley to the east, Central Luzon to the south and by the South China Sea to the west.

The region is composed of four provinces, namely: Ilocos Norte, Ilocos Sur, La Union and Pangasinan. Its administrative center is San Fernando City, La Union. The region is occupied mostly by Ilocanos.

REPUBLIC OF THE PHILIPPINES
Ilocos Region (Region I)

Administrative Center: San Fernando City, La Union
Population:
2000 census—4,200,478 (Xth largest).
Density—327 per km² (Xth highest).
Area: 12,840 km² (Xth largest)
Divisions:
Provinces—4.
Component Cities—8.
Municipalities—117.
Barangays—3,265.
Congressional districts—12.
Languages: Iloko, Tagalog, English

People and Culture

[Demographic detail (population, languages, religion, education, etc.), festivals, etc.]

Economy

[...]

Geography

Political

Ilocos Region is composed of 4 provinces and a total of 8 cities.

Provinces

Cities

Physical

Ilocos Region occupies the narrow plain between the Cordillera Central mountain range and the South China Sea. The region also occupies the northern portion of the Central Luzon plain, to the northeast of the Zambales Mountains. Lingayen Gulf is the most notable body of water in the region and it contains a number of islands, including the Hundred Islands National Park. To the north of the region is Luzon Strait.

The Agno river runs through Pangasinan and empties into Lingayen Gulf. The river flow into a broad delta in the vicinity of Lingayen and Dagupan City.

Tourist Attractions

Hundred Islands National Park. Located in the Lingayen Gulf in Pangasinan.

Vigan colonial houses. Vigan City is famous for its cobblestone streets and Spanish-style houses. Many films depicting the Spanish era have been shot here.

History

[...]

External Links

Regions of the Philippines, Luzon: I | II | III | IV-A | IV-B | V | CAR | NCR

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

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IMAP

(From Wikipedia, the free Encyclopedia)

Short for Internet Message Access Protocol (Previously called Interactive Mail Access Protocol). It is used for accessing emails on a remote server while leaving them there instead of deleting them. In this way, users can access email from several different machines, once configured to use the IMAP protocol to access a certain account. (POP clients are typically configured to delete email messages from the server once they are accessed, making it possible to read one's email only on the machine first used to access it).

Unlike POP, IMAP includes functionality for remotely managing messages as well as mailboxes. IMAP has commands that allow clients to create, rename and delete folders on the mail server, as well as commands for moving messages to and from such folders. With IMAP, messages can also have meta-data associated with them. For example, IMAP servers keep track of which messages have or have not been read (such states are called "flags" in IMAP).

Other mail protocols include SMTP and POP.

RFC2060 - describes the IMAP version 4 revision 1

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

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Iodine

(From Wikipedia, the free Encyclopedia)

General
Name, Symbol, NumberIodine, I, 53
Series Halogens
Group, Period, Block17 (VIIA), 5 , p
Density, Hardness 4940 kg/m3, no data
Appearance violet-dark grey,
lustrous
Atomic Properties
Atomic weight 126.90447 amu
Atomic radius (calc.) 140 (115) pm
Covalent radius 133 pm
van der Waals radius 198 pm
Electron configuration [Kr]44d10 5s2 5p5
e- 's per energy level2, 8, 18, 18, 7
Oxidation states (Oxide) ±1,5,7 (strong acid)
Crystal structure Orthorhombic
Physical Properties
State of matter solid (nonmagnetic)
Melting point 386.85 K (236.66 °F)
Boiling point 457.4 K (363.7 °F)
Molar volume 25.72 ×1010-3 m3/mol
Heat of vaporization 20.752 kJ/mol
Heat of fusion 7.824 kJ/mol
Vapor pressure __ Pa at __ K
Speed of sound __ m/s at __ K
Miscellaneous
Electronegativity 2.66 (Pauling scale)
Specific heat capacity 145 J/(kg*K)
Electrical conductivity 8.0 10-8/m ohm
Thermal conductivity 0.449 W/(m*K)
1st ionization potential 1008.4 kJ/mol
2nd ionization potential 1845.9 kJ/mol
3rd ionization potential 3180 kJ/mol
Most Stable Isotopes
isoNAhalf-life DMDE MeVDP
127I100%I is stable with 74 neutrons
129I{syn.}1.57E7yBeta-0.194129Xe
131I{syn.}8.02070 dBeta-0.971131Xe
SI units & STP are used except where noted.

Iodine is a chemical element in the periodic table that has the symbol I and atomic number 53. This is an insoluble element that is required as a trace element for living organisms. Chemically, iodine is the least reactive of the halogens, and the most electropositive metallic halogen. Iodine is primarily used in medicine, photography and in dyes.

Notable Characteristics

Iodine is a bluish-black, lustrous solid that sublimes at standard temperatures into a blue-violet gas that has an irritating odor. This halogen also forms compounds with many elements, but is less active than the other member of its series and has some metallic-like properties. Iodine dissolves easily in chloroform, carbon tetrachloride, or carbon disulfide to form purple solutions (It is only slightly soluble in water). The deep blue color with starch solution is characteristic of the free element.

Applications

In areas where there is little iodine in the diet - typically remote inland areas where no marine foods are eaten - iodine deficiency gives rise to goitre, so called endemic goitre. In many (but not all) such areas, this is now prevented by the addition of small amounts of sodium iodide to table salt - this product is known as iodised salt Other uses:

History

Iodine (Gr iodes meaning violet) was discovered by Barnard Courtois in 1811.

Occurrence

Iodine can be prepared in an ultrapure form through the reaction of potassium iodide with copper sulfate. There are also several other methods of isolating this element.

Isotopes

There are thirty isotopes of iodine and only one, I-127, is stable. The artificial radioisotope I-131 (a beta emitter) which has a half-life of 8 days, has been used in treating cancer and other pathologies of the thyroid glands. The most common compounds of iodine are the iodides of sodium and potassium (KI) and the iodates (KIO3).

Iodine has only one stable isotope, I-127. However, radioactive isotopes of iodine have been used extensively. I-129 (half-life 17 million years) is a product of Xe-129 spallation in the atmosphere, but is also the result of U-238 decay. As U-238 is produced during a number of nuclear power- related activities, its presence (as an I-129/I ratio) can indicate the type of activity going on at any one site. For this reason, I-129 was used in rainwater studies following the Chernobyl accident. It also has been used as a ground-water tracer and as an indicator of waste dispersion into the natural environment. Other applications may be hampered by the production of I-129 in the lithosphere through a number of decay mechanisms.

In many ways, I-129 is similar to Cl-36. It is a soluble halogen, fairly non-reactive, exists mainly as a non-sorbing anion, and is produced by cosmogenic, thermonuclear, and in-situ reactions. In hydrologic studies, I-129 concentrations are usually reported as the ratio of I-129 to total I (which is virtually all I-127). As is the case with Cl-36/Cl, I-129/I ratios in nature are quite small, 10-14 to 10-10 (peak thermonuclear I-129/I during the 1960s and 1970s reached about 10-7). I-129 differs from Cl-36 in that its half-life is longer (1.6 vs 0.3 million years), it is highly biophilic, and occurs in multiple ionic forms (commonly, I- and iodate) which have different chemical behaviors.

Precautions

Direct contact with skin can cause lesions so care needs to be taken in handling iodine. Iodine vapor is very irritating to eyes and mucous membranes. The maximum allowable concentration of iodine in air should not exceed 1 mg/m³ (8-hour time-weighted average - 40-hour).

External Links

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IOP

(From Wikipedia, the free Encyclopedia)

IOP is an abbriviation for several computer (microprocessor) terms:

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Irrational number

(From Wikipedia, the free Encyclopedia)

In mathematics, an irrational number is any real number that is not a rational number, i.e., one that cannot be written as a fraction a / b with a and b integers and b not zero. The irrational numbers are precisely those numbers whose decimal expansion never ends and never enters a periodic pattern. "Almost all" real numbers are irrational, in a sense which is defined more precisely below.

Some irrational numbers are algebraic numbers such as 21/2 (the square root of two) and 31/3 (the cube root of 3); others are transcendental numbers such as &pi and e.

Irrationality of certain logarithms

Perhaps the numbers most easily proved to be irrational are logarithms like log23. The argument by reductio ad absurdum is as follows:

Irrationality of the square root of 2

The discovery of irrational number is usually attributed attributed to Pythagoras or one of his followers, who produced a (most likely geometrical) proof of the irrationality of the square root of 2.

One proof of this irrationality is the following reductio ad absurdum. The proposition is proved by assuming the opposite and showing that that is false, which in mathematics means that the proposition must be true.

  1. Assume tha √2 is a rational number. Meaning that there exists an integer a and b so that a / b = √2.
  2. Then √2 can be written as an irreducible fraction (the fraction is shortened as much as possible) a / b such that a and b are coprime integers and (a / b)2 = 2.
  3. It follows that a2 / b2 = 2 and a2 = 2 b2.
  4. Therefore a2 is even because it is equal to 2 b2 which is obviously even.
  5. It follows that a must be even. (Odd numbers have odd squares and even numbers have even squares.)
  6. Because a is even, there exists a k that fullfills: a = 2k.
  7. We insert the last equation of (3) in (6): 2b2 = (2k)2 is equivalent to 2b2 = 4k2 is equivalent to b2 = 2k2.
  8. Because 2k2 is even it follows that b2 is also even which means that b is even because only even numbers have even squares.
  9. By (5) and (8) a and b are both even, which contradicts that a / b is irreducible as stated in (2).

Since we have found a contradiction the assumption (1) that √2 is a rational number must be false. The opposite is proven. √2 is irrational.

This proof can be generalized to show that any root of any natural number is either a natural number or irrational.

A different proof

Another reductio ad absurdum showing that √2 is irrational is less well-known and has sufficient charm that it is worth including here. It proceeds by observing that if √2=m/n then √2=(2n−m)/(m−n), so that a fraction in lowest terms is reduced to yet lower terms. That is a contradiction if n and m are positive integers, so the assumption that √2 is rational must be false. It is possible to construct from an isosceles right triangle whose leg and hypotenuse have respective lengths n and m, by a classic straightedge-and-compass construction, a smaller isosceles right triangle whose leg and hypotenuse have respective lengths m−n and 2n−m. That construction proves the irrationality of √2 by the kind of method that was employed by ancient Greek geometers.

Other irrational numbers

All transcendental numbers are irrational, and the article on transcendental numbers lists several examples. er is irrational if r ≠ 0 is rational; πn is irrational for positive integers n.

Another way to construct irrational numbers is as zeros of polynomials: start with a polynomial equation

p(x) = an xn + an-1 xn−1 + ... + a1 x + a0 = 0
where the coefficients ai are integers. Suppose you know that there exists some real number x with p(x) = 0 (for instance because of the intermediate value theorem). The only possible rational roots of this polynomial equation are of the form r/s where r is a divisor of a0 and s is a divisor of an; there are only finitely many such candidates which you can all check by hand. If neither of them is a root of p, then x must be irrational. For example, this technique can be used to show that x = (21/2 + 1)1/3 is irrational: we have (x3 − 1)2 = 2 and hence x6 − 2x3 − 1 = 0, and this latter polynomial doesn't have any rational roots (the only candidates to check are ±1).

Because the algebraic numbers form a field, many irrational numbers can be constructed by combining transcendental and algebraic numbers. For example 3π+2, π + √2 and e√3 are irrational (and even transcendental).

Irrational numbers and decimal expansions

It is often erroneously assumed that mathematicians define "irrational number" in terms of decimal expansions, calling a number irrational if its decimal expansion neither repeats nor terminates. No mathematician takes that to be the definition, since the choice of base 10 would be arbitrary and since the standard definition is simpler and more well-motivated. Nonetheless it is true that a number is of the form n/m where n and m are integers, if and only if its decimal expansion repeats or terminates. When the long division algorithm that everyone learns in grammar school is applied to the division of n by m, only m remainders are possible. If 0 appears as a remainder, the decimal expansion terminates. If 0 never occurs, then the algorithm can run at most m − 1 steps without using any remainder more than once. After that, a remainder must recur, and then the decimal expansion repeats! Conversely, suppose we are faced with a repeating decimal, for example:

Since the length of the repitend is 3, multiply by 103:

and then subtract A from both sides:

Then

(The "135" above can be found quickly via the Euclid's algorithm.)

Numbers not known to be irrational

It is not known whether π + e or π − e are irrational or not. In fact, there is no pair of non-zero integers m and n for which it is known whether mπ + ne is irrational or not. It is not known whether 2e, πe, π√2 or the Euler-Mascheroni gamma constant γ are irrational.

The set of all irrational numbers

The set of all irrational numbers is uncountable (since the rationals are countable and the reals are uncountable). Using the absolute value to measure distances, the irrational numbers become a metric space which is not complete. However, this metric space is homeomorphic to the complete metric space of all sequences of positive integers; the homeomorphism is given by the infinite continued fraction expansion. This shows that the Baire category theorem applies to the space of irrational numbers.

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

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List of airports: I

(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

I

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List of Biblical names starting with I

(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: I

(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 IJ

(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
Idar-Oberstein42,100BirkenfeldRhineland-Palatinate
Ingolstadt113,500--Bavaria
Iserlohn99,474Märkischer KreisNorth Rhine-Westphalia
Itzehoe34,100SteinburgSchleswig-Holstein
Jagstzell2,443OstalbkreisBaden-Württemberg
Jena101,100--Thuringia
Jever13,600FrieslandLower 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 IJ."

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List of colleges and universities starting with I

(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. ICI University
  2. IJselland Polytechnic
  3. Idaho State University
  4. Illinois Benedictine College
  5. Illinois College
  6. Illinois Institute of Technology
  7. Illinois State University
  8. Illinois Wesleyan University
  9. Imperial College of Science, Technology and Medicine (London, UK)
  10. Imperial Valley College
  11. Incarnate Word College
  12. Indian Institute of Management, Calcutta
  13. Indian Institute of Science, Bangalore
  14. Indian Institute of Technology, Bombay
  15. Indian Institute of Technology, Delhi
  16. Indian Institute of Technology, Kanpur
  17. Indian Institute of Technology, Kharagpu
  18. Indian Institute of Technology, Kharagpur
  19. Indian Institute of Technology, Madras
  20. Indiana Institute of Technology
  21. Indiana State University
  22. Indiana University
  23. Indiana University Kokomo
  24. Indiana University Purdue University, Indianapolis
  25. Indiana University South Bend
  26. Indiana University Southeast
  27. Indiana University of Pennsylvania
  28. Indiana University, Bloomington
  29. Indiana Wesleyan University
  30. Ingenieurschule HTL Chu
  31. Inha University
  32. Institut d'Informatique d'Entreprise
  33. Institut des Sciences de l'Ingenieur de Montpellier
  34. Institut f. Semantische Informationsverarbeitung
  35. Institut fur Lasertechnik
  36. Institut Francais de Recherche pour l'Exploitation de la Mer
  37. Institut Jozef Stefan
  38. Institut National de la Recherche Scientifique
  39. Institut National de Physique Nucleaire et de Physique des Particules
  40. Institut National des Sciences Appliquees de Lyon
  41. Institut National des Sciences Appliquees de Toulouse
  42. Institut National des Télécommunications
  43. Institut National Polytechnique de Grenoble
  44. Institut National Polytechnique de Toulouse
  45. Institut Superieur d'Informatique et d'Automatique
  46. Institut Superieur de Technologie
  47. Institut Superieur de Gestion
  48. Institut Superieure D'Electronique du Nord
  49. Institut Teknologi Bandung
  50. Institut Universitaire de Technologie de Sceaux
  51. Institut Universitari de l'Audiovisual
  52. Institute for Mathematical Sciences
  53. Institute of Clinical Pharmacology and Toxicology
  54. Institute of Historical Research
  55. Institute of Industrial Science
  56. Institute of Paper Science and Technology
  57. Institute of Technology, Benaras Hindu University
  58. Institute of Telecommunications and Information Technology
  59. Instituto Centroamericano de Adminstracion de Empresas
  60. Instituto Militar de Engenharia
  61. Instituto Peruano de Administracion de Empresas
  62. Instituto Politecnico Nacional
  63. Instituto Politecnico do Porto
  64. Instituto Superior de Ciencias do Trabalho e da Empresa
  65. Instituto Superior de Transportes
  66. Instituto Tecnologico de Merida
  67. Instituto Tecnologico y de Estudios Superiores de Monterrey Campus Ciudad de Mexico
  68. Instituto Tecnologico de Costa Rica
  69. Instituto Tecnologico y de Estudios Superiores de Monterrey
  70. Instituto Tecnologico y de Estudios Superiores de Monterrey, Campus Chihuahua
  71. Instituto Tecnologico y de Estudios Superiores de Monterrey, Campus Chihuahua
  72. Instituto Tecnologico y de Estudios Superiores de Monterrey, Campus Guaymas
  73. Instituto Tecnologico y de Estudios Superiores de Monterrey, Campus Sonora Norte
  74. Instituto Tecnologico y de Estudios Superiores de Occidente
  75. Instituto de Ciencias de la Educacion
  76. Inter American University
  77. Intercultural Open University
  78. International American University
  79. International College Penang
  80. International Islamic University Malaysia
  81. International Islamic University, Malaysia
  82. International Reform University
  83. International School for Advanced Studies
  84. International University Bremen
  85. International University College
  86. International University of Japan
  87. Interstaatliche Ingenieurschule Neu-Technikum Buchs (NTB)
  88. Interstate Institute of Technology St. Gallen
  89. Iona College
  90. Iowa State University (Ames, Iowa, USA)
  91. Istanbul Technical University
  92. Istituto Universitario di Architettura (Venezia)
  93. Istituto di Teologia Ecumenico-Patristica Greco-Bizantina «San Nicola»
  94. Itasca Community College
  95. Ithaca College
  96. Ivanovo State Power University
  97. Ivy Tech State College

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 I."

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List of Japanese authors:I

(From Wikipedia, the free Encyclopedia)

List of Japanese authors

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List of people by name: I

(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 Ia - Ib - Ic - Id - Ie-If - Ig - Ih - Ii-Ik - Il - Im - In - Io - Ip-Iq - Ir - Is - It - Iu-Iv - Iw - Ix-Iz

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: I."

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List of people by name: Ia

(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 Ia - Ib - Ic - Id - Ie-If - Ig - Ih - Ii-Ik - Il - Im - In - Io - Ip-Iq - Ir - Is - It - Iu-Iv - Iw - Ix-Iz

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List of people by name: Ib

(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 Ia - Ib - Ic - Id - Ie-If - Ig - Ih - Ii-Ik - Il - Im - In - Io - Ip-Iq - Ir - Is - It - Iu-Iv - Iw - Ix-Iz

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List of people by name: Ic

(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 Ia - Ib - Ic - Id - Ie-If - Ig - Ih - Ii-Ik - Il - Im - In - Io - Ip-Iq - Ir - Is - It - Iu-Iv - Iw - Ix-Iz

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List of people by name: Id

(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 Ia - Ib - Ic - Id - Ie-If - Ig - Ih - Ii-Ik - Il - Im - In - Io - Ip-Iq - Ir - Is - It - Iu-Iv - Iw - Ix-Iz

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List of people by name: Ie-If

(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 Ia - Ib - Ic - Id - Ie-If - Ig - Ih - Ii-Ik - Il - Im - In - Io - Ip-Iq - Ir - Is - It - Iu-Iv - Iw - Ix-Iz

Ie

If

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: Ie-If."

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List of people by name: Ig

(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 Ia - Ib - Ic - Id - Ie-If - Ig - Ih - Ii-Ik - Il - Im - In - Io - Ip-Iq - Ir - Is - It - Iu-Iv - Iw - Ix-Iz

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List of people by name: Ih

(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 Ia - Ib - Ic - Id - Ie-If - Ig - Ih - Ii-Ik - Il - Im - In - Io - Ip-Iq - Ir - Is - It - Iu-Iv - Iw - Ix-Iz

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List of people by name: Ii-Ik

(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 Ia - Ib - Ic - Id - Ie-If - Ig - Ih - Ii-Ik - Il - Im - In - Io - Ip-Iq - Ir - Is - It - Iu-Iv - Iw - Ix-Iz

Ii

Ij

Ik

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List of people by name: Il

(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 Ia - Ib - Ic - Id - Ie-If - Ig - Ih - Ii-Ik - Il - Im - In - Io - Ip-Iq - Ir - Is - It - Iu-Iv - Iw - Ix-Iz

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List of people by name: Im

(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 Ia - Ib - Ic - Id - Ie-If - Ig - Ih - Ii-Ik - Il - Im - In - Io - Ip-Iq - Ir - Is - It - Iu-Iv - Iw - Ix-Iz

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List of people by name: In

(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 Ia - Ib - Ic - Id - Ie-If - Ig - Ih - Ii-Ik - Il - Im - In - Io - Ip-Iq - Ir - Is - It - Iu-Iv - Iw - Ix-Iz

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List of people by name: Io

(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 Ia - Ib - Ic - Id - Ie-If - Ig - Ih - Ii-Ik - Il - Im - In - Io - Ip-Iq - Ir - Is - It - Iu-Iv - Iw - Ix-Iz

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List of people by name: Ip-Iq

(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 Ia - Ib - Ic - Id - Ie-If - Ig - Ih - Ii-Ik - Il - Im - In - Io - Ip-Iq - Ir - Is - It - Iu-Iv - Iw - Ix-Iz

Ip

Iq

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: Ip-Iq."

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List of people by name: Ir

(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 Ia - Ib - Ic - Id - Ie-If - Ig - Ih - Ii-Ik - Il - Im - In - Io - Ip-Iq - Ir - Is - It - Iu-Iv - Iw - Ix-Iz