Generators info

Arakor Nicodemus is a fictional wizard from the Fighting Fantasy gamebook series by Steve Jackson and Ian Livingstone. He was one of the three pupils (including Gereth Yaztromo and Pen Ty Kora) of Vermithrax Moonchaser, the Grand Wizard of Yore. He lives in the world of Titan, in the city of Port Blacksand (otherwise known as the “City of Thieves”), under a bridge known as the Singing Bridge that crossed the Catfish River. He was saved from a curse, that was laid upon him by necromancers, by his friend and fellow pupil Pen Ty Kora some years ago. Though he is an irritable recluse to the locals, he is known to help those who seek his wisdom at times.

In probability theory, two random variables being uncorrelated does not imply their independence. In some contexts, uncorrelatedness implies at least pairwise independence (as when the random variables involved have Bernoulli distributions).

It is sometimes mistakenly thought that one context in which uncorrelatedness implies independence is when the random variables involved are normally distributed. Here are the facts:

• Suppose two random variables X and Y are jointly normally distributed. That is the same as saying that the random vector (X, Y) has a multivariate normal distribution. It means that the joint probability distribution of X and Y is such that for any two constant (i.e., non-random) scalars a and b, the random variable aX + bY is normally distributed. In that case if X and Y are uncorrelated, i.e., their covariance cov(X, Y) is zero, then they are independent.

• But it is possible for two random variables X and Y to be so distributed jointly that each one alone is normally distributed, and they are uncorrelated, but they are not independent. Examples appear below.

Examples

• Suppose X has a normal distribution with expected value 0 and variance 1. Let W = 1 or −1, each with probability 1/2, and assume W is independent of X. Let Y = WX. Then
  • X and Y are uncorrelated;
  • Both have the same normal distribution; and
  • X and Y are not independent.

Again, the distribution of X + Y concentrates positive probability at 0, since Pr(X + Y = 0) = 1/2.

To see that X and Y are uncorrelated, consider

<math> \begin{align}

\operatorname{cov}(X,Y) &{} = E(XY) - E(X)E(Y) = E(XY) = E(E(XY\mid W)) \\
& {} = E(X^2)\Pr(W=1) + E(-X^2)\Pr(W=-1) \\
& {} = 1\cdot\frac12 + (-1)\cdot\frac12 = 0.
\end{align}
</math>

To see that Y has the same normal distribution as X, consider

<math>\begin{align}

\Pr(Y \le x) & {} = E(\Pr(Y \le x\mid W)) \\
& {} = \Pr(X \le x)\Pr(W = 1) + \Pr(-X\le x)\Pr(W = -1) \\
& {} = \Phi(x) \cdot\frac12 + \Phi(x)\cdot\frac12
\end{align}</math>

(since X and −X both have the same normal distribution).

To see that X and Y are not independent, observe that Pr(Y > 1|X = 1/2) = 0.

• Suppose X has a normal distribution with expected value 0 and variance 1. Let

<math>Y=\left\{\begin{matrix} -X & \mbox{if}\ \left|X\right|<c \\

X & \mbox{if}\ \left|X\right|>c \end{matrix}\right.</math>

where c is a positive number to be specified below. If c is very small, then the correlation corr(X, Y) is near 1; if c is very large, then corr(X, Y) is near −1. Since the correlation is a continuous function of c, the intermediate value theorem implies there is some particular value of c that makes the correlation 0. That value is approximately 1.54. In that case, X and Y are uncorrelated, but they are clearly not independent, since X completely determines Y.

To see that Y is normally distributed—indeed, that its distribution is the same as that of X—let us find its cumulative distribution function:

<math>\Pr(Y \leq x) = \Pr(\{|X|<c\mbox{ and }-X<x\}\mbox{ or }\{|X|>c\mbox{ and }X<x\})\,</math>

<math>= \Pr(|X|<c\mbox{ and }-X<x) + \Pr(|X|>c\mbox{ and }X<x)\,</math>

<math>= \Pr(|X|<c\mbox{ and }X<x) + \Pr(|X|>c\mbox{ and }X<x)\,</math>

(This follows from the symmetry of the distribution of X and the symmetry of the condition that |X| < c.)

<math>= \Pr(X<x).\,</math>

Observe that the sum X + Y is nowhere near being normally distributed, since it has a substantial probability (about 0.88) of it being equal to 0, whereas the normal distribution, being a continuous distribution, has no discrete part, i.e., does not concentrate more than zero probability at any single point. Consequently X and Y are not jointly normally distributed, even though they are separately normally distributed.

Maxim Integrated Products , commonly known as “Maxim,” is a semiconductor company that designs and manufactures analog and mixed-signal integrated circuits. It was founded in 1983 and has headquarters in Sunnyvale, California, United States. In 2001, Maxim acquired Dallas Semiconductor, which it operated under the Dallas Semiconductor brand until 2007, when the brand was retired and the company applied the Maxim brand name to all products.

As of October 1, 2007 Maxim’s common stock was delisted from the Nasdaq Stock Exchange and is now traded Over-the-Counter and quoted on the Pink Sheets.

Product range

Maxim specializes in integrated circuits (ICs, “chips”) that go between analog signals such as audio, video, and sensor signals and digital signals such as those used by microprocessor-based systems. The company has 75 product lines which include amplifiers, data converters (digital-to-analog and analog-to-digital), interface circuits, power supply chips, wireless, fiber and telecommunications, clock parts, automotive electronic components, audio, video, analog switches, sensor circuits, filters, thermal management, and battery management. Maxim also manufactures its own lines of microcontrollers.

Maxim has over 5400 products. It has about 8000 employees. Net revenues for the year ended June 30, 2007 were $2.007 billion.

External links

• Official company website
• Dallas Semiconductor history and products

Fantasy name generators are programs that use a computer algorithm to create a fantasy name at random probability, usually for use in a role-playing game. They have been around since at least 1994. Early fantasy name generators often generated nonsense, creating names such as “Rsi’sskoo” or “Gbbtti”. Modern fantasy name generators are typically better at creating usable names.

In mathematics and signal processing, a metaplectomorphism is a transformation by way of an operator from a metaplectic group of operators.

Examples of metaplectomorphisms, in time-frequency, include:

• translation

in time;

Boży bojownicy (Warriors of God) is a historical novel with fantasy elements, written by Andrzej Sapkowski. It is the sequel to Narrenturm. Its events take place in Bohemia and Silesia, during the time of Hussite Wars.

The Trilogy includes:

• Narrenturm
• Boży bojownicy
• Lux perpetua

External links

• Andrzej Sapkowski’s official page

Two-phase electrical power was an early 20th century polyphase alternating current electric power distribution system. Two circuits, or “phases”, were used, with voltages 90 electrical degrees apart in time. Usually circuits used four wires, two for each phase. Less frequently, three wires were used, with a common wire with a larger-diameter conductor. The generators at Niagara Falls installed in 1895 were the largest generators in the world at the time and were two-phase machines. Some early two-phase generators had two complete rotor and field assemblies, mechanically shifted by 90 mechanical degrees to provide two-phase power.

The advantage of two-phase electrical power was that it allowed for simple, self-starting electric motors. In the early days of electrical engineering, it was easier to analyze and design two-phase systems where the phases were completely separated, since this avoided the need for the effect of unbalanced loads. It was not until the invention of symmetrical components that three-phase power systems had a convenient mathematical tool for describing unbalanced load cases. The revolving magnetic field produced with a two-phase system allowed electric motors to provide torque from zero motor speed, which was not possible with a single-phase induction motor (without extra starting means). Induction motors designed for two-phase operation use the same winding configuration as capacitor start single-phase motors.

Three-phase electric power requires less conductor mass for the same voltage and overall amount of power. It has all but replaced two-phase power for commercial distribution of electrical energy, but two-phase circuits are still found in certain control systems.

Two-phase power can be derived from a three-phase source using two transformers in a Scott connection. One transformer primary is connected across two phases of the supply. The second transformer is connected to a center-tap of the first transformer, and is wound for 86.6% of the phase-to-phase voltage on the 3-phase system. The secondaries of the transformers will have two phases 90 degrees apart in time, and a balanced two-phase load will be evenly balanced over the three supply phases.

Three-wire, 120/240 volt single phase power used in the USA and Canada is sometimes incorrectly called “two-phase”. The proper term is split phase or 3-wire single-phase.

See also

• Polyphase system

References

• Terrell Croft and Wilford Summers (ed), American Electricans’ Handbook, Eleventh Edition, McGraw Hill, New York (1987) ISBN 0-07-013932-6
• Donald G. Fink and H. Wayne Beaty, Standard Handbook for Electrical Engineers, Eleventh Edition,McGraw-Hill, New York, 1978, ISBN 0-07-020974-X
• Edwin J. Houston and Arthur Kennelly, Recent Types of Dynamo-Electric Machinery, copyright American Technical Book Company 1897, published by P.F. Collier and Sons New York, 1902

In a low-IF receiver, the RF signal is mixed down to a non-zero low or moderate intermediate frequency, typically a few megahertz. Low-IF receiver topologies have many of the desirable properties of zero-IF architectures, but avoid the DC offset and 1/f noise problems.

The use of a non-zero IF re-introduces the image issue. However, when there are relatively relaxed image and neighbouring channel rejection requirements they can be satisfied by carefully designed low-IF receivers. Image signal and unwanted blockers can be rejected by quadrature downconversion (complex mixing) and subsequent filtering.

This technique is now widely used in the tiny FM receivers incorporated into MP3 players and mobile phones, and is becoming commonplace in both analog and digital TV receiver designs. Using advanced analog and digital signal processing techniques, cheap, high quality receivers using no resonant circuits at all are now possible.

The Tax Reform Act of 1986 redesignated the Internal Revenue Code of 1954 as the Internal Revenue Code of 1986 and made numerous other amendments. The ‘86 Act, however, did not change the overall structure of the Code. See Internal Revenue Code.

Internal Revenue Code of 1954

The 1954 Code was enacted by the United States Congress as Chapter 736, , and became law on August 16, 1954, succeeding the Internal Revenue Code of 1939. As enacted, the 1954 Code was published as Volume 68A of the United States Statutes at Large. The 1954 Code temporarily extended the Revenue Act of 1951’s 5 percentage point increase in corporate tax rates through March 31, 1955, increased depreciation deductions by providing additional depreciation schedules, and created a 4 percent dividend tax credit for individuals.

References to the Internal Revenue Code in the United States Code and other statutes of Congress subsequent to 1954 generally mean Title 26 of the Code as amended. The basic structure of the Title 26 remained the same until the enactment of the comprehensive revision contained in Tax Reform Act of 1986, although of course individual provisions of the law were changed on a regular basis.

The 1954 Code and progressivity

With respect to the Federal income tax on individuals, the 1954 Code imposed a progressive tax with 24 income brackets applying to tax rates ranging from 20% to 91%. For example, the following is a schedule showing the Federal income tax rate imposed on each level of taxable income of a single (unmarried) individual under the 1954 Code:

Source

• Internal Revenue Code of 1954, (modified from text of the statute).

In telecommunication, a ternary signal is a signal that can assume, at any given instant, one of three significant conditions, such as power level, phase position, pulse duration, or frequency.

Note: Examples of ternary signals are (a) a pulse that can have a positive, zero, or negative voltage value at any given instant, (b) a sine wave that can assume phases of 0°, 120°, or 240° relative to a clock pulse, and (c) a carrier wave that can assume any one of three different frequencies depending on three different modulation signal significant conditions.

Source: From Federal Standard 1037C

See also

• 4B3T
• bipolar encoding

PSR J0737-3039 is a binary pulsar system discovered in 2003, the first known double pulsar.

The object is similar to PSR B1913+16, which was discovered in 1974 by Taylor and Hulse, and for which the two won the 1993 Nobel Prize in Physics. Objects of this kind enable precise testing of Einstein’s theory of general relativity, because relativistic effects can be seen in the timing of the pulsar pulses. However most such binary systems are merely known to consist of one pulsar and one neutron star; J0737-3039 is the first case where both components are known to be not just neutron stars but pulsars.

The orbital period of J0737-3039 (2.4 hours) is the smallest yet known for such an object (one-third that of the Taylor-Hulse object), which enables the most precise tests yet. In 2005, it was announced that measurements had shown an excellent agreement between general relativity theory and observation. In particular, the predictions for energy loss due to gravitational waves appear to match the theory.

As a result of energy loss due to gravitational waves, the common orbit shrinks by 7 mm per day. The two components will coalesce in about 85 million years.

The pulsars

The pulses from Pulsar B are only detectable for about 20 minutes in each orbit.

External links

• http://skyandtelescope.com/news/article_1124_1.asp (discovery)
• http://skyandtelescope.com/news/article_1473_1.asp (verification of general relativity)
• http://www.physicsweb.org/articles/world/18/3/6/1
• http://www.jb.man.ac.uk/news/doublepulsar/

The iQuest is a device used for answering trivia questions developed by Leapfrog Enterprises. The device uses solid state cartridges to save data.

Software for this device covers topics in mathematics, science, and social studies.

See also

• Leapster
• Cybiko

External links

• Product homepage
• iQuest emulator - allows a trial of the product online.

The A2W reactor is a naval reactor used by the United States Navy to provide electricity generation and propulsion on warships. The A2W designation stands for:

• A = Aircraft carrier platform
• 2 = Second generation core designed by the contractor
• W = Westinghouse was the contracted designer

This nuclear reactor was used in the world’s first nuclear-powered aircraft carrier, the USS Enterprise (CVN-65). The four propulsion plants on Enterprise each contain two reactors, numbered 1A-1B, 4A - 4B, 2A - 2B, and 3A - 3B (numbered as they are located from fore to aft). Each propulsion plant is capable of operating on one reactor plant through most of the power range required to propel the ship at speeds in excess of 33 knots (61 km/h) (with a possible maximum speed up to approximately 35 knots; higher speeds such as the 40-50 knots sometimes rumored would rapidly become impossible due to hydrodynamic drag even if the reactors were capable of delivering enough power). Both reactors would be on-line to simultaneously provide maximum ship speed and plane launching capability.

Design and operation

The reactors are pressurized water reactors fueled by highly-enriched (upwards of 93%) U-235. Light water is used as both neutron-moderator and reactor coolant. Hafnium Control rods are used to control the operation of the reactor. Extracting the rods to a calculated height allows the reactor to reach “criticality” - the point at which the nuclear fission reactions reach a self-sustaining level. Thereafter, steam flow (from the steam generators) regulates reactor power as explained below. The control rods are “shimmed” in or out to regulate average coolant temperature or lowered to the bottom of the reactor vessel to shut the reactor down (either done in a slow controlled manner or dropped rapidly during what is referred to as a SCRAM to immediately shut the reactor down.

Much of the reactor power control during steady state operation comes as a result of the coolant water’s negative temperature coefficient. The “power” of the reactor is determined by the number of fission events that takes place in the fuel at any given moment. As the water heats up, it expands and becomes less dense which provides fewer molecules per volume to moderate the neutrons, hence fewer neutrons are slowed to the required thermal energies to sustain thermal fission. Conversely, when the coolant water temperature decreases, its density increases and a greater number of neutrons reach the required thermal energy, increasing the number of fissions per unit of time, creating more heat. This has the effect of allowing “steam demand” to control reactor power, requiring little intervention by the Reactor Operator for changes in the power demanded by the ship’s operations.

The hot water from the reactors is sent, via large pipes, into heat exchangers called steam generators. There the heat from the reactor coolant water is transferred, through tube walls, to water being fed into the steam generators from a separate feed system. In the A1W and A2W systems, the pressurized water reactor coolant is kept between 525 and 545 °F (274 and 285 °C). In the steam generators, the water from the feed system is converted to steam at 535 °F (279 °C) and a pressure of about 600 lb/in² (4 MPa). Once the reactor coolant water has given off its heat in the steam generators, it is returned, via large electric pumps (four per reactor), to the reactors to repeat the cycle.

Saturated steam at 600 lb/in² (4 MPa) is channeled from each steam generator to a common header, where the steam is then sent to the main engine, electrical generators, aircraft catapult system, and various auxiliaries. The main propulsion turbines are double-ended, in which the steam enters at the center and divides into two streams as it enters the actual turbine wheels, expanding and giving up its energy as it does so, causing the turbine to spin at high speed. The main shaft enters a reduction gear in which the high rotational velocity of the turbine shaft is stepped down to a usable turn rate for propelling the ship. The expended steam from the main engine and other auxiliaries enters condensers to be cooled into water and recycled to the feed system.

Differential pulse voltammetry is a kind of electrochemical measurement. It can be considered as a series of regular voltage pulses superimposed on a linearly changing voltage, in which the resulting current is measured between the ramped baseline voltage and the pulse voltage. A digital staircase voltage is commonly used as the ramped baseline.

By contrast, in normal pulse voltammetry the current resulting from a series of ever larger potential pulses is compared with the current at a constant ‘baseline’ voltage. Another type of pulse voltammetry is square wave or square pulse voltammetry, which can be considered a special type of differential pulse voltammetry in which equal time is spent at the potential of the ramped baseline and potential of the superimposed pulse.

These measurements can be used to study the redox properties of extremely small amounts of chemicals because of the following two features:

(1) In these measurements, the effect of the charging current can be minimized, so high sensitivity is achieved.

(2) Faradaic current is extracted, so electrode reactions can be analyzed more precisely.

Differential pulse voltammetry has these characteristics:

(1) Reversible reactions show symmetrical peaks, and irreversible reactions show asymmetrical peaks.

(2) The peak potential is equal to E_1/2^r-ΔE in reversible reactions, and the peak current is proportional to the concentration.

(3) The detection limit is about 10^-8 M.

The system of this measurement is usually the same as that of cyclic voltammetry. The potential between the working electrode and the reference electrode is changed as a pulse from an initial potential to an interlevel potential and remains at the interlevel potential for about 5 to 100 milliseconds; then it changes to the final potential, which is different from the initial potential. The pulse is repeated, changing the final potential, and a constant difference is kept between the initial and the interlevel potential. The value of the current before and after the pulse are sampled and their differences are plotted versus potential

See Also

Electroanalytical Methods

is a seiyū born on August 1, 1941 in Tokyo. He is a member of 81 Produce.

Notable voice roles

• Cornelius Lutz in Legend of the Galactic Heroes
• Narrator in Les Mondes Engloutis (Onigiri Arkadia Monogatari)
• Johji Futagami in RahXephon
• Richard James in Stellvia of the Universe
• Michael Seebach / Schwarzwald in The Big O
• Georg von Trapp in The Trapp Family Story
• Dr. Torataro Shima in Paprika

External links

• Katsunosuke Hori at the Anime News Network

A Device Register is the view any device presents to a programmer.
Each programmable bit in the device is presented with a logical address and it appears as a part of a byte in the device registers. Then programming of these bits can be achieved by reading from or writing to these device registers.
Most devices have at least these two device registers:

1. Data Register: to which the data to be input/output is read from/written to the device.
2. Control/Status: Which selects/shows the mode of operation of the device.
   

We are the Pigs is the first single off the album Dog Man Star by Suede, released on September 12, 1994 on Nude Records. The single announced the darker tone that the band had taken for Dog Man Star, that contrasted heavily with their debut. The challenging sound on the single was not characteristic of the popular Britpop bands of the time. That along with the departure of guitarist Bernard Butler during its release, contributed to its relatively poor charting.

The video, directed by David and Raphael Vital-Durand, features a grim, 1984-like setting. It was initially banned by some TV stations including MTV for being too violent. The video features car burnings, cross burnings, and various violence to humans. Also notable, the video features the video debut of new guitarist Richard Oakes.

The b-side Killing of a Flashboy also became a staple of Suede’s live set list and became one of their most popular songs. It is also available on the B-sides album Sci-Fi Lullabies.

Single track listings

CD

All Songs by Anderson/Butler

1. “We are the Pigs [edit]”
2. “Killing of a Flashboy”
3. “Whipsnade”

12″

1. “We are the Pigs [edit]”
2. “Killing of a Flashboy”
3. “Whipsnade”

Ltd. 7″

1. “We are the Pigs [edit]”
2. “Killing of a Flashboy”

Ispan Shefar is an Aes Sedai of the Black Ajah in the The Wheel of Time fantasy book series by Robert Jordan.

Before she was exposed as one of the Black Ajah, Ispan had belonged to the Blue Ajah.

She was from Tarabon.

Ispan was captured by Elayne, Nynaeve al’Maera and several others in Ebou Dar. As Elayne and the others made their way towards Caemlyn she was murdered by unknown darkfriends .

Ispan has very gentle sensibilities. Note in Lord of Chaos: “she wiped her hands on her skirts, as if she had done it herself” (killing a cockroach) despite her evil allegiances.

Torbjørn Andersen (born January 5, 1957 in Grimstad, Aust-Agder) is a Norwegian politician and member of Stortinget for the Progress Party, his third term. He is a former member of Froland municipality-council (1991-1999). He is a member of the Energy and Environment Committee in the Storting.

In economics, the inflation rate is the rate of increase of the average price level (a measure of inflation), usually some form of consumer price index. Alternatively, the inflation rate is the rate of decrease in the purchasing power of money. This is sometimes expressed as an “annualized” number, even if the period measured is less than a year.

The rate of inflation is a variable used to calculate the real interest rate, as well as real increases in wages. In general inflation rates are calculated so that they can be directly subtracted from some other rate. In general an inflation rate will be stated in seasonally adjusted terms.

If <math>P_0</math> is the current average price level and <math>P_{-1}</math> is the price level a year ago, the rate of inflation during the year might be measured as follows:

<math>\text{inflation rate} = \frac{P_0 - P_{-1}}{P_{-1}} \times 100</math>

There are other ways of calculating the inflation rate, such as <math>\log P_0 - \log P_{-1}</math> (using the natural log), again stated as a percentage.

There are two general methods for calculating inflation rates - one is to use a base period, the other is to use “chained” measurements. Chained measurements adjust not only the prices, but the contents of the market basket involved, with each price period. More common, however, is the base period reference. This can be seen from inflation reports from the “relative weight” assigned to each component, and by looking at the technical notes to see what each item in an inflation basket represents and how it is calculated.

See also econometrics, interest rate

External links

• Consumer Price Index Home Page Bureau of Labor Statistics, United States Department of Labor.

Jahsh is a Arabic male given name.

list

• Ubayd-Allah ibn Jahsh
• Abd-Allah Jahsh
• Zaynab bint Jahsh
• Abdu ibn Jahsh

See also

• Arabic Name
• List of Arabic names

Sartosa is a fictional island in the tabletop wargame Warhammer.

Sartosa is an island located off the Tilean and Estalian coasts of the Old World in the backstory of the game. Games Workshop released a Pirate fleet for the discontinued Warhammer Fantasy setting naval game Man O’ War.

Various plastic Pirate sprues are available through the Games Workshop catalogue, which allows enthusiasts to collect and use a Pirate warband in the skirmish game of Mordheim.

The Estalians, Tileans and Sartosans are featured in the Dan Abnett Warhammer novel Fell Cargo published by Black Library.

EECS (sometimes pronounced “eeks”) is an abbreviation for Electrical Engineering and Computer Sciences. It is a designation used at some universities for the major or department of the same name. One reason behind linking the two areas of study is to provide students with a broad overview of both software and hardware.

Not every university uses the EECS designation. Several universities, for example, have separate EE/ECE and CS departments/majors. Other schools use the similar ECE (Electrical and Computer Engineering) designation. Additionally, some schools which offer an EECS degree also offer degrees in Electrical Engineering or Computer Science separately.

See also

• Academic major

A return receipt is a postal service document confirming the arrival of a message or parcel at its intended destination. Internationally, the service is known as avis de réception (AR), but in some English-speaking countries, acknowledgement of receipt is used.

E-mail

Return receipts for E-mail are called Message Disposition Notifications (MDN). Their format and usage is outlined in RFC 3798.

A description of how multiple Mail User Agents (MUAs) should handle the generation of MDNs in an Internet Message Access Protocol (IMAP4) environment is provided in RFC 3503.

Another type of receipt is the Delivery Status Notification (DSN) receipt. The only purpose of DSN receipts is to let a sender know when the recipient’s server received the message. Sender cannot be sure the message will be read but DSN is less intrusive of the recipient’s privacy than MDN and nearly all servers support it.

All MUAs can receive MDNs and DSNs but not all can request them (notably: many Webmail services). Third-party tools exist to activate MDNs and DSNs in any MUA.

Cellular

MDN also stands for Mobile Directory Number

Library

Upon request, a library patron may ask for a receipt for returns.
</br>

In abstract algebra, a generating set of a group <math>G</math> is a subset S such that every element of G can be expressed as the product of finitely many elements of S and their inverses.

More generally, if S is a subset of a group G, then <S>, the subgroup generated by <math>S</math>, is the smallest subgroup of G containing every element of S, meaning the intersection over all subgroups containing the elements of S; equivalently, <S> is the subgroup of all elements of G that can be expressed as the finite product of elements in S and their inverses.

If G = <S>, then we say S generates G; and the elements in S are called generators or group generators. If S is the empty set, then <S> is the trivial group {e}, since we consider the empty product to be the identity.

When there is only a single element x in S, <S> is usually written as <x>. In this case, <x> is the cyclic subgroup of the powers of x, a cyclic group, and we say this group is generated by x. Equivalent to saying an element x generates a group is saying that it has order |G|, or that <x> equals the entire group G.

Finitely generated group

If S is finite, then a group G = <S> is called finitely generated. The structure of finitely generated abelian groups in particular is easily described. Many theorems that are true for finitely generated groups fail for groups in general.

Every finite group is finitely generated since <G> = G. The integers under addition are an example of an infinite group which is finitely generated by both <1> and <-1>, but the group of rationals under addition cannot be finitely generated. No uncountable group can be finitely generated.

Different subsets of the same group can be generating subsets; for example, if p and q are integers with gcd(p, q) = 1, then <{p, q}> also generates the group of integers under addition (by Bézout’s identity).

While it is true that every quotient of a finitely generated group is finitely generated (simply take the images of the generators in the quotient), a subgroup of a finitely generated group need not be finitely generated. For example, let G be the free group in two generators, x and y (which is clearly finitely generated, since G = <{x,y}>), and let S be the subset consisting of all elements of G of the form yⁿxy⁻ⁿ, for n a natural number. Since <S> is clearly isomorphic to the free group in countable generators, it cannot be finitely generated. However, every subgroup of a finitely generated abelian group is in itself finitely generated. Rather more can be said about this though: the class of all finitely generated groups is closed under extensions. To see this, take a generating set for the (finitely generated) normal subgroup and quotient: then the generators for the normal subgroup, together with preimages of the generators for the quotient, generate the group.

Free group

The most general group generated by a set S is the group freely generated by S. Every group generated by S is isomorphic to a factor group of this group, a feature which is utilized in the expression of a group’s presentation.

Frattini subgroup

An interesting companion topic is that of non-generators. An element x of the group G is a non-generator if every set S containing x that generates G, still generates G when x is removed from S. In the integers with addition, the only non-generator is 0. The set of all non-generators forms a subgroup of G, the Frattini subgroup.

Examples

The group of units U(Z₉) is the group of all integers relatively prime to 9 under multiplication mod 9 (U₉ ={1,2,4,5,7,8}). All arithmetic here is done modulo 9. Seven is not a generator of U(Z₉), since

<math>\{7^i\pmod{9}\ |\ i \in \mathbb{N}\} = \{7,4,1\}.</math>

while 2 is, since:

<math>\{2^i\pmod{9}\ |\ i \in \mathbb{N}\} = \{2,4,8,7,5,1\}.</math>

On the other hand, the symmetric group of size n is not cyclic, so it is not generated by any one element. However, it is generated by the two permutations (1 2) and (1 2 3 … n). For example, for S₃ we have:

e = (1 2)(1 2)

(1 2) = (1 2)

(2 3) = (1 2)(1 2 3)

(1 3) = (1 2 3)(1 2)

(1 2 3) = (1 2 3)

(1 3 2) = (1 2)(1 2 3)(1 2)

Infinite groups can also have finite generating sets. The additive group of integers has 1 as a generating set. The element 2 is not a generating set, as the odd numbers will be missing. The two-element subset {3, 5} is a generating set, since (-5) + 3 + 3 = 1 (in fact, any pair of coprime numbers is, as a consequence of Bézout’s identity).

See also

• Cayley graph
• Generating set for related meanings in other structures
• Presentation of a group

External links

• Mathworld: Group generators

BIC TCP (Binary Increase Congestion control) is an implementation of TCP with an optimized congestion control algorithm for high speed networks with high latency (LFN: Long Fat Networks).

BIC TCP is implemented and used by default in Linux kernels 2.6.8 and above. The default implementation was again changed to CUBIC TCP in the 2.6.19 version.

See Also

• TCP congestion avoidance algorithm
• Transmission Control Protocol#Development_of_TCP

External Links

• BIC TCP Home Page.

Modern Screen was a popular American magazine for over 50 years featuring articles, pictorials and interviews with movie stars (and later television and music personalities.)
Modern Screen debuted in November 1930 (some sources say December 1930) and quickly became Photoplay magazine’s main competition among dozens of monthly movie magazines published during the era, selling millions of copies each month during the 1930s and 1940s with one of the highest circulations of any magazine in America. By 1933 the magazine was able to boast “The Largest Circulation of Any Screen Magazine” and used the line on its magazine covers. During the early 1930s, the magazine featured artwork portraits of film stars on the cover, by 1940 it had gone to featuring natural color photographs on the cover.

Modern Screen remained a major success through the 1950s but the swift downturn in movie ticket sales at the end of the decade led to a sales decline although the magazine remained popular well into the late 1970s. In the early 1980s, however, the popularity of general interest celebrity publications like People Magazine proved to be the end of old-fashioned movie magazines and Modern Screen quit being published in 1985 after several years of being a bimonthly magazine.

The magazine was published by the Dell Magazines, from New York City. Modern Screen had many different editors in chief over the years, including Richard Heller and Mark Bego, the latter of whom edited the book The Best of Modern Screen (St. Martin’s Press, 1986).

Trivia

• Jean Harlow is seen reading a copy of Modern Screen in the film Dinner at Eight.

• Lily Tomlin released a comedy album in 1975 that was a parody of celebrity magazines and titled in “Modern Scream”.

Gernot Hummer, better known under the alias CharNode, is an independent electronic music artist from Austria. He has been active since 2004, making music in the electronica, techno and trance genres.

External links

• Official CharNode website
• Remixwars page

Diffusion capacitance is the capacitance due to the injected charge carriers which diffuse from anode to cathode in forward bias mode of a diode or from emitter to base (forward biased junction in active region) for a transistor. Current in the base of transistors is due to diffusion; therefore there is a delay in the movement of charge carriers. This causes a lag of current and causes a capacitance to exist.

Back to Electronics

Electronic test equipment (sometimes called ‘testgear’) is used to create stimulus signals and capture responses from electronic Devices Under Test (DUTs). In this way, the proper operation of the DUT can be proven or faults in the device can be traced and repaired. Use of electronic test equipment is essential to any serious work on electronics systems.

Practical electronics engineering and assembly requires the use of many different kinds of electronic test equipment ranging from the very simple and inexpensive (such as a test light consisting of just a light bulb and a test lead) to extremely complex and sophisticated such as Automatic Test Equipment.

Generally, more advanced test gear is necessary when developing circuits and systems than is needed when doing production testing or when troubleshooting existing production units in the field.

Types of test equipment

Basic equipment

The following items are used for basic measurement of voltages, currents, and components in the circuit under test.

• Voltmeter (Measures voltage)
• Ohmmeter (Measures resistance)
• Ammeter, e.g. Galvanometer or Milliameter (Measures current)
• Multimeter e.g., VOM (Volt-Ohm-Milliameter) or DVM (Digital “Volt” Meter) (Measures all of the above)

The following are used for stimulus of the circuit under test:

• Power supplies
• Signal generator
• Pulse generator

The following analyze the response of the circuit under test:

• Oscilloscope (Measures all of the above as they change over time)
• Frequency counter (Measures frequency)

And connecting it all together:

• Test probes

Advanced or less commonly used equipment

Meters

• Solenoid voltmeter (Wiggy)
• Clamp meter (current transducer)
• Wheatstone bridge (Precisely measures resistance)
• Capacitance meter (Measures capacitance)
• EMF Meter (Measures Electric and Magnetic Fields)
• Electrometer (Measures charge)

Probes

• RF probe
• Signal tracer

Analysers

• Logic analyzer (Tests digital circuits)
• Spectrum analyzer (SA) (Measures spectral energy of signals)
• Vector signal analyzer (VSA) (Like the SA but it can also perform many more useful digital demodulation functions)
• Time-domain reflectometer for testing integrity of long cables

Signal-generating devices

• Signal generator
• Frequency synthesiser
• Function generator
• Pulse generator
• Signal injector

Miscellaneous devices

• Continuity tester
• Cable tester
• Hipot tester
• Network analyzer (used to characterize components or complete computer networks)
• Test light
• Transistor tester

Manufacturers

• Aeroflex
• Agilent Technologies
• Amperis Products
• Anaheim Scientific Corporation
• Anritsu
• Applied Instruments
• B&K Precision Corporation
• Boonton Electronics
• Chauvin Arnoux
• ETS-Lindgren
• Extech Instruments
• Fluke
• Keithley Instruments
• Lambda Americas
• Leader Instruments
• Philips
• Rohde & Schwarz
• Sorensen/Elgar Electronics Corporation/PowerTen
• Tektronix
• Valhalla Scientific
• Wavetek
• Tabor Electronics

A second stage manufacturer, known in the industry as “body-builder,” builds such products as bus and truck bodies, ambulances, motor homes, and other specialized vehicles.

Neither their product, nor the first stage portion, called an incomplete motor vehicle, are fully-compliant with all of the requirements for a complete motor vehicle without the other.

Cutaway van chassis are one of the more popular incomplete motor vehicles for second stage manufacturers to use as a platform for their products. A large portion of small school buses, minibuses, and recreational vehicles are based upon cutaway van chassis.

The A Device is a decoration of the United States military which is presented as an attachment to the American Defense Service Medal and the Air Force Overseas Service Ribbon. The A Device is a bronze colored letter “A”, pinned to the center of both awards.

Atlantic Device in World War II

The American Defense Service Medal was the first decoration to use the A Device and the award was originally known as the “Atlantic Device” and also as the “Axis Device”. The A Device was awarded to any member of the United States Navy who, while deployed to the Atlantic Ocean between June 22 and December 7, 1941, engaged in armed conflict, or potential armed conflict, with naval forces of the German Kriegsmarine. Those having done so were awarded the American Defense Service Medal with A Device, the intent being to recognize those who had participated in the “undeclared war” when the United States of America was assisting Britain with war convoys and German U-Boat interdiction.

USAF Arctic Device

The A Device became obsolete after the Second World War and did not appear again until the year 2002. At that time, the United States Air Force declared that the A Device would be awarded to those who had received the Air Force Overseas Short Tour Service Ribbon for tours of duty in arctic locations such as Northern Greenland and Alaska*.

Now known as the “Arctic Device”, the A Device is awarded as an attachment to the Air Force Overseas Short Tour Service Ribbon. The A Device is not authorized for any other United States military decorations.

Note, however, that the two representations of the A Device are different. The Atlantic Device does not have “feet”, but the Arctic Device does (see the AFPC website for representation of this version: http://www.afpc.randolph.af.mil/Awardsnet/devices.aspx?Mode=Graphics)

*Although Alaska has locations within the Arctic circle, there are currently no bases within that region. Only Thule Air Base qualifies for this device, as of 8 February 2007.

In military telecommunications, the term Electronic Support (ES) is the division of electronic warfare involving actions taken under direct control of an operational commander to search for, intercept, identify, and locate sources of radiated electromagnetic energy for the purpose of immediate threat recognition. Thus, Electronic Support (ES) provides a source of information required for immediate decisions involving Electronic Protection (EP), Electronic Attack (EA), avoidance, targeting, and other tactical employment of forces. Electronic Support data can be used to produce signals intelligence (SIGINT), both communications intelligence (COMINT) and electronics intelligence (ELINT).

Teaching in-Role is a method of teaching in which the teacher takes on a role and creates a drama around the students. This approach allows the teacher to take on the role of someone who does not know the answers, act in ways that the teacher would not, or to demonstrate appropriate playing within the drama.

See also

• First-person interpretation

Brock

is a village in west central Saskatchewan, Canada. It is located 165 km south-west of Saskatoon.

Sestamibi is a radiopharmaceutical used in nuclear medicine imaging. It is also known as methoxyisobutylisonitrile or MIBI. The radioisotope attached to the sestamibi molecule is technetium-99m, forming ⁹⁹Tc^m-sestamibi (or Tc99m MIBI).

Its main use is for imaging the myocardium (heart muscle). It is also used in the work-up of primary hyperparathyroidism to identify parathyroid adenomas, for radioguided surgery of the parathyroid and in the work-up of possible breast malignancies.

Cardiac imaging

Technetium-99m sestamibi is a lipophilic cation which, when injected intravenously into a patient, distributes in the myocardium proportionally to the myocardial blood flow. As opposed to Thallium-201, MIBI does not undergo significant redistribution. Single photon emission computed tomography (SPECT) imaging of the heart is performed using a gamma camera to detect the gamma rays emitted by the technetium-99m sestamibi as it decays. Two sets of images are acquired. For one set, the Tc99m MIBI is injected whilst the patient is at rest and then the myocardium is imaged. In the second set, the patient is stressed either by exercising on a treadmill or pharmacologically. The Tc99m MIBI is injected at peak stress and then imaging is performed . The resulting two sets of images are compared with each other to distinguish ischaemic from infarcted areas of the myocardium. This imaging technique is also known as myocardial perfusion imaging (MPI).

Parathyroid imaging

In hyperparathyroidism, one or more of the four parathyroid glands have developed a benign tumor called an adenoma. The affected gland takes up Tc99m MIBI following an intravenous injection. The patient’s neck is imaged with a gamma camera to show the tumor.

Breast imaging

Tc99m MIBI is also used in the evaluation of breast nodules. Malignant breast tissues concentrate MIBI to a much greater extent and more frequently than benign disease. As such, limited characterization of breast anomalies is possible. Scintimammography has the highest specificity for breast cancer of any imaging test, but its sensitivity is too low to allow for routine use.

Radioguided surgery of the parathyroids

Following the administration of Tc99m MIBI it collects in overactive parathyroid glands. During surgery, the surgeon can use a probe sensitive to gamma rays to locate the overactive parathyroid before removing it.

References

• Cardiolite.com
• Parathyroid.com
• Myoview.com
• Miraluma

Good News from the Next World was a Simple Minds album, released in 1995. It had two hit singles, “She’s a River” and “Hypnotised”. The album garnered moderate commercial success, and critically, it was not badly received in the United States. In the UK, however, it was critically panned; the album “approximates the noise that would be made if the entire contents of a music shop were strapped to an Empire transport ship from Star Wars,” wrote Melody Maker, but “[f]or all it’s cod-Wagnerian vastness, there are no tunes.” [1]

Track listing

All songs written by Jim Kerr and Charlie Burchill

1. “She’s a River” – 5:32
2. “Night Music” – 5:24
3. “Hypnotised” – 5:53
4. “Great Leap Forward” – 5:56
5. “7 Deadly Sins” – 5:11
6. “And the Band Played On” – 5:32
7. “My Life” – 5:16
8. “Criminal World” – 5:03
9. “This Time” – 4:58

X-12-ARIMA is the U.S. Census Bureau’s software package for seasonal adjustment. It can be used together with gretl, which provides a graphical user interface for X-12-ARIMA.

See also

• ARIMA
• CSPro
• AnSWR
• WinIDAMS
• U.S. Census Bureau

External links

• Census Bureau’s X-12-ARIMA page
  
• Flowchart of algorithm

Tom McKitterick is an American actor. He starred in The Warriors, playing Cowboy. After The Warriors, McKitterick left for stage until 1981. When he left stage and acting, he became a photojournalist and was represented by Impact Visuals, a progressive photo agency in New York. Eventually, in addition to news, he shot sports - tennis in particular: a decade of shooting grand slams, Masters and Davis Cup. After twenty years, McKitterick changed careers once again. He returned to the show business, and is currently producing Period of Adjustment, a play by Tennessee Williams in conjunction with the Almeida Theatre in London. He hopes to bring it to Broadway in the fall of 2006.

Height: 5′6″

A meta-algorithm is an algorithm that can be usefully considered to have other significant algorithms, not just elementary operations and simple control structures, as its constituents; also an algorithm that has subordinate algorithms as variable and replaceable parameters. Thus a meta-algorithm defines a class of concrete algorithms.

This term is inappropriate for simple structural composition, e.g. using an algorithm for addition as a step of an algorithm for square root; it is usually employed for general strategies and design patterns applicable to different underlying algorithms and problems.

Evolutionary computation is a typical example of a family of meta-algorithms: it needs a model of the search space, a model of solution quality, an algorithm for initialization, an algorithm to evolve new attempts from old attempts and an algorithm for termination, all of which are problem-dependent but conform to the general architecture of evaluating a succession of tentative solutions somehow related to previous attempts.

Other examples of meta-algorithms include boosting, Simulated annealing, Bootstrap aggregating (bagging), AdaBoost and Random-restart hill climbing.

In probability theory, Markov’s inequality gives an upper bound for the probability that a non-negative function of a random variable is greater than or equal to some positive constant. It is named after the Russian mathematician Andrey Markov, although it appeared earlier in the work of Pafnuty Chebyshev (Markov’s teacher).

Markov’s inequality (and other similar inequalities) relate probabilities to expectations, and provide (frequently) loose but still useful bounds for the cumulative distribution function of a random variable.

Statement

In the language of measure theory, Markov’s inequality states that if (X,Σ,μ) is a measure space, f is a measurable extended real-valued function, and t > 0, then

<math> \mu(\{x\in X|\,|f(x)|\geq t\}) \leq {1\over t}\int_X |f|\,d\mu.</math>

For the special case where the space has measure 1 (i.e., it is a probability space), it can be restated as follows: if X is any random variable and a > 0, then

<math>\textrm{Pr}(|X| \geq a) \leq \frac{\textrm{E}(|X|)}{a}.</math>

Proofs

We separate the case in which the measure space is a probability space from the more general case because the probability case is more accessible for the general reader.

Special case: probability theory

For any event E, let I_E be the indicator random variable of E, that is, I_E = 1 if E occurs and = 0 otherwise. Thus I_{(|X| ≥ a)} = 1 if the event |X| ≥ a occurs, and I_{(|X| ≥ a)} = 0 if |X| < a. Then, given a>0,

<math>aI_{(|X| \geq a)} \leq |X|.\,</math>

Therefore

<math>\operatorname{E}(aI_{(|X| \geq a)}) \leq \operatorname{E}(|X|).\,</math>

Now observe that the left side of this inequality is the same as

<math>a\operatorname{E}(I_{(|X| \geq a)})=a\Pr(|X| \geq a).\,</math>

Thus we have

<math>a\Pr(|X| \geq a) \leq \operatorname{E}(|X|)\,</math>

and since a > 0, we can divide both sides by a.

General case: measure theory

For any measurable set A, let 1_A be its indicator function, that is, 1_A(x) = 1 if x ∈ A, and 0 otherwise. If A_t is defined as A_t = {x ∈ X| |f(x)| ≥ t}, then

<math>0\leq t\,1_{A_t}\leq |f|1_{A_t}\leq |f|.</math>

Therefore

<math>\int_X t\,1_{A_t}\,d\mu\leq\int_{A_t}|f|\,d\mu\leq\int_X |f|\,d\mu.</math>

Now, note that the left side of this inequality is the same as

<math>t\int_X 1_{A_t}\,d\mu=t\mu(A_t).</math>

Thus we have

<math>t\mu(\{x\in X|\,|f(x)|\geq t\}) \leq \int_X|f|\,d\mu,</math>

and since t > 0, both sides can be divided by t, obtaining

<math>\mu(\{x\in X|\,|f(x)|\geq t\}) \leq {1\over t}\int_X|f|\,d\mu.</math>

Q.E.D.

Examples

• Markov’s inequality is used to prove Chebyshev’s inequality.
• If X is a non-negative integer valued random variable, as is often the case in combinatorics, then taking a = 1 in Markov’s inequality gives that <math>\textrm{Pr}(X \neq 0) \leq \textrm{E}(X).</math> If X is the cardinality of some set, then this proves that that set is not empty. Thus one gets existence proofs.

Universal Games is a Nevada company that produced such board games as Merger, Titanic: The Board Game, and the Apollo 13 edition of Solarquest.

In 1965, their address was in Houston, Texas. Universal Games released Merger, a financial game for 2-4 players. This game simulated automobile production and stock manipulation. Each player is a plant manager. The goal of the game is to make the most money. The game is similar is style to many of the 3M bookshelf games.

Pulse Global is a family of radio stations, exclusively playing new, unsigned, and emerging artists over the internet. The following franchises are currently operating:-

• Pulse Rated - operating from the UK and covering Europe and the rest of the world, Pulse Rated broadcasts over the internet at http://uk.pulserated.com.
• Pulse Rated (Americas) - operates from Los Angeles, this station covers the North America region, broadcasting over the internet at http://usa.pulserated.com.

Company profile:

Over the last 2 years, Pulse has firmly established itself as the world’s leading internet & satellite radio broadcaster playing only the very best music from new, unsigned, and emerging artists from around the world.

Pulse exists to provide a unique, and importantly free, resource for the promotion and support of talented new artists by making sure they are heard by the largest possible audience.

The two stations currently feature and promote over 2,300 acts from a total of 39 countries, all of whom have been through the stringent Pulse selection and legal process in order to grant Pulse specific non-exclusive rights.

Corporate operations are currently managed from the UK division, who franchise the brand name and services out to various territories.

Libelle is a German cipher system, developed by the Federal Office for Information Security. The algorithm is not publicised, in an attempt to make cryptanalysis more difficult. Some experts think this security through obscurity is a bad approach, because public scrutiny of an algorithm would uncover potential weaknesses. In order to keep the algorithm secret, it is only distributed as a microchip named Pluto and not as a piece of software.

It is possible to have a secret cipher algorithm while still reaping the benefits of public cryptography research: one way is to make a non-weakening change to a public algorithm, like changing the Nothing up my sleeve numbers, or chaining the public cipher with an unrelated secret cipher. This is likely the case, as the unusual keylength of 168 bit heavily suggests 3DES as the core cipher.

See also

• Skipjack

In telecommunication, the term chirping has the following meanings:

1. The rapid changing, as opposed to long-term drifting, of the frequency of an electromagnetic wave.

Chirping is most often observed in pulsed operation of a source.

2. A pulse compression technique that uses (usually linear) frequency modulation during the pulse.

3. A trademarked term in mobile communications used by Nextel and Boost Mobile for sending voice messages to a private number in push-to-talk or walkie-talkie mode.

4. To make fun of someone from afar or to make fun of a good friend at anytime about things that are only “inside jokes”. It can be used in context as either a positive compliment or a negative retort.

See also: chirp.

! colspan=”5″ style=”background-color:silver;text-align:center;” id=”001″| 104001–104100 [ edit]

! colspan=”5″ style=”background-color:silver;text-align:center;” id=”101″| 104101–104200 [ edit]

! colspan=”5″ style=”background-color:silver;text-align:center;” id=”201″| 104201–104300 [ edit]

! colspan=”5″ style=”background-color:silver;text-align:center;” id=”301″| 104301–104400 [ edit]

! colspan=”5″ style=”background-color:silver;text-align:center;” id=”401″| 104401–104500 [ edit]

! colspan=”5″ style=”background-color:silver;text-align:center;” id=”501″| 104501–104600 [ edit]

! colspan=”5″ style=”background-color:silver;text-align:center;” id=”601″| 104601–104700 [ edit]

! colspan=”5″ style=”background-color:silver;text-align:center;” id=”701″| 104701–104800 [ edit]

! colspan=”5″ style=”background-color:silver;text-align:center;” id=”801″| 104801–104900 [ edit]

! colspan=”5″ style=”background-color:silver;text-align:center;” id=”901″| 104901–105000 [ edit]

In mathematics, a free Boolean algebra is a Boolean algebra with a distinguished set of elements, called generators, such that:

1. Each element of the Boolean algebra can be expressed as a finite combination of generators, using the Boolean operations, and
2. The generators are as independent as possible, in the sense that there are no relationships among them (again in terms of finite expressions using the Boolean operations) that do not hold in every Boolean algebra no matter which elements are chosen.

Motivation and example

The generators of a free Boolean algebra can represent independent propositions. For example, we might consider the two propositions “John is tall” and “Mary is rich”. These generate a Boolean algebra with four atoms, namely

1. John is tall, and Mary is rich
2. John is tall, and Mary is not rich
3. John is not tall, and Mary is rich
4. John is not tall, and Mary is not rich

Other elements of the Boolean algebra are then logical disjunctions of the atoms, such as “John is tall and Mary is not rich, or John is not tall and Mary is rich”. In addition there is one more element, FALSE, which is not a disjunction of atoms (though it can be thought of as the empty disjunction; that is, the disjunction of no atoms).

This example yields a Boolean algebra with 16 elements; in general, for finite n, the free Boolean algebra with n generators has 2ⁿ atoms, and therefore <math>2^{2^n}</math> elements.

For infinitely many generators the situation is very similar, except that there are no atoms. Each element of the Boolean algebra is a combination of finitely many of the generating propositions; two such elements are considered to be the same if they are logically equivalent.

Category-theoretic definition

More formally, using concepts from category theory, a free Boolean algebra on a set of generators S is an ordered pair (π,B), where

1. π: S → B is a mapping,
2. B is a Boolean algebra,

and which is universal with respect to this property. This means that for any Boolean algebra B₁ and mapping π₁: S → B₁, there is a unique homomorphism f: B → B₁ such that

<math> \pi_1 = f \circ \pi. </math>

This universality property can also be formulated as an initiality property in so-called comma categories.

The uniqueness up to isomorphism is a property that follows immediately from the universal property. Note that the mapping π can be shown to be injective. Thus any free Boolean algebra B has the property that there is a subset S of B, called the set of generators of B, such that any map from S into a Boolean algebra B₁ extends uniquely to a homomorphism from B into B₁.

Topological realization

For any desired number κ of generators, finite or infinite, the free Boolean algebra with κ generators may be realized as the collection of all clopen subsets of {0,1}^κ, given the product topology assuming that {0,1} has the discrete topology. The generators may be enumerated as follows: for each α<κ the α’th generator is the set of all elements of {0,1}^κ whose α’th coordinate is 1. In particular, the free Boolean algebra with <math>\aleph_0</math> generators is the collection of all clopen subsets of Cantor space. Perhaps surprisingly, there are only countably many of these. In fact, while for finite n the free Boolean algebra with n generators has cardinality <math>2^{2^n}</math>, for infinite κ the corresponding cardinality is just κ.

For the wider context of this topological realization, see the article on Stone’s representation theorem for Boolean algebras.

References

Saunders Mac Lane (1999) Algebra. 3d. edition, American Mathematical Society. ISBN 0-821-81646-2.

“Release Technique” can also refer to an alternative therapy system related to “The Sedona Method”

Release Technique is a dance technique which would more accurately be described as an anti-technique, as the fundamental principle of it is to use the body’s natural channels of moving and functioning to access dance movement - as opposed to other formal dance techniques that encourage some degree, at least, of distortion of the body’s natural alignments or ‘normal’ mechanics.

Release Technique focuses on a lack of tension, and utilises breath and momentum to facilitate movement, rather than brute force or other artificial techniques.

See also

• Skinner releasing technique^TM

Spira may refer to:

A surname:

• Elijah Spira
• Harry Spira
  

Other:

• Spira (Final Fantasy), the world in which the computer role-playing games Final Fantasy X and Final Fantasy X-2 are based
• Spira mirabilis, the mathematical logarithmic spiral
• Spira Footwear, a controversial brand of running shoe
• Cadbury Spira, a Cadbury chocolate bar in a spiral shape

Endogenous preferences are preferences that cannot be taken as given, but are affected by individual internal responses to the external state of affairs. They are interdependent, in part determined by social institutions, marketed advertisement, and subject to learning (experience and observation) and habit formation (past-experience).