Generators info

In theoretical physics, a central charge is an operator Z that commutes with all the other symmetry operators. The adjective “central” refers to the center of the symmetry group — the subgroup of elements that commute with all other elements of the original group — or to the center of a Lie algebra. In some cases, such as two-dimensional conformal field theory, a central charge may also commute with all of the other operators, including operators which are not symmetry generators.

More precisely, the central charge is the charge that corresponds, by Noether’s theorem, to the center of the central extension of the symmetry group.

In theories with supersymmetry, this definition can be generalized to include supergroups and Lie superalgebras. A central charge is any operator which commutes with all the other supersymmetry generators. Theories with extended supersymmetry typically have many operators of this kind. In string theory, in the first quantized formalism, these operators also have the interpretation of winding numbers (topological quantum numbers) of various strings and branes.

In conformal field theory, the central charge is a c-number (commutes with every other operator) term that appears in the commutator of two components of the stress energy tensor.

Narrows Dam is a dam located 6 miles north of Murfreesboro, Arkansas and impounds the water of the Little Missouri River (Arkansas) to create Lake Greeson. Narrows Dam was authorized as a flood control and hydroelectric power project by the Flood Control Act of 1941. The dam is a feature of the comprehensive plan for the Ouachita River Basin. Lake Greeson is operated for hydroelectric power, recreation, and flood control. [1]

The powerhouse of the dam is located adjacent to the east abutment, and it has a total length of 151 feet. The equipment of the powerhouse is three 8,500 KWh generating machines. The powerhouse originally had two generators, but a third was placed in 1969. The average annual output is 28,000,000 KWh.

The dam is named due to its location on the river, The Narrows. During the dam’s construction many cemeteries and graveyards had to be removed due to the creation of the new lake. Narrows Dam is located by the Swaha, or Narrows Dam recreational area.

Lake Greeson is divided into three layers so Narrows Dam can work and operate properly. The bottom portion of the lake always remains full so the powerhouse has enough pressure to operate. The middle layer or “Power Storage” portion is used to regulate the flow of water running into the generators of the dam. The top portion or “Flood Storage” is usually empty unless holding floodwater. A spillway at top of the dam is used to regulate the top portion of the dam, the spillway contains walls to maneuver the flow of the water, and a stilling basin is placed at the foot of the spillway to dissipate erosion from the spillway water hitting the base of the dam. The spillway isn’t used much due to the fact that flooding can be regulated by other means, such as the flood control conduits.

Construction on the dam began on April 1947, the first bucket of concrete was poured in June 1948. The dam was finished in 1950, and dedicated on July 1951.

See also

• List of Arkansas dams and reservoirs

A documentation generator is a programming tool that generates documentation intended for programmers (API documentation) or end users (End-user Guide), or both, from a set of specially commented source code files, and in some cases, binary files.

Document generation can be divided in several type of documents:

Batch documents (all automated documents)
Interactive documents (documents that can not be produced automatically)
Text block correspondence (documents created based on pre defined text blocks)
Forms (forms for websites)

You can place every type of document you come across in one of these categories. A lot of software solutions are offered on the internet that can automate these processes.

See also

• Comparison of documentation generators
• Template processor

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.

The Crystal River 3 Nuclear Generation Station is a nuclear power plant, part of the Crystal River Energy Complex located in Citrus County, Florida near Crystal River, Florida. The site consists of approximately 4,700 acres (19 km²) and contains a single pressurized water reactor sharing the site with 4 fossil-fueled generators. The reactor is rated to produce 842 megawatts of electric power. It is a Babcock and Wilcox pressurized water reactor.

Crystal River 3 was originally owned by Florida Progress Corporation (and operated by its subsidiary, Florida Power Corporation) but, in 2000, it was bought by Carolina Power & Light to form the new company, Progress Energy, which currently runs the plant.

In December 2006, Florida Progress purchased 3,000 acres of land seven miles from the Gulf of Mexico and eight miles north of the existing Crystal River plant in preparation for the potential construction of a new nuclear power reactor. A formal decision has not yet been made. Critics lament the low-lying location of the site. Levy County officials have welcomed the potential plant in an effort to bring jobs to the impoverished county.

External links

• DoE Page
• NukeWorker

• [1]

In mathematics, an automatic group is a finitely generated group equipped with several finite-state automata. These automata can tell if a given word representation of a group element is in a “canonical form” and can tell if two elements given in canonical words differ by a generator.

More precisely, let G be a group and A be a finite set of generators. Then an automatic structure of G with respect to A is a set of finite-state automata:

• the word-acceptor, which accepts for every element of G at least one word in A representing it
• multipliers, one for each <math>a \in A \cup \{1\}</math>, which accept a pair (w_1, w_2), for words w_i accepted by the word-acceptor, precisely when <math>w_1 a = w_2</math> in G.

The property of being automatic does not depend on the set of generators.

Properties

• Automatic groups have word problem solvable in quadratic time. A given word can actually be put into canonical form in quadratic time.

Examples of automatic groups

• Finite groups
• Negatively curved groups
• Euclidean groups
• Coxeter groups
• Braid groups
• Geometrically finite groups

Examples of non-automatic groups

• Baumslag-Solitar groups
• Non-Euclidean nilpotent groups

References

• Epstein, David B. A.; Cannon, James W.; Holt, Derek F.; Levy, Silvio V. F.; Paterson, Michael S.; Thurston, William P. Word processing in groups. Jones and Bartlett Publishers, Boston, MA, 1992. xii+330 pp. ISBN 0-86720-244-0

Fleming’s left hand rule (for electric motors) shows the direction of the thrust on a conductor carrying a current in a magnetic field.

The left hand is held with the thumb, index finger and middle finger mutually at right angles.

• The First finger represents the direction of the Field.

• The Second finger represents the direction of the Current (in the classical direction, from positive to negative).

• The Thumb represents the direction of the Thrust or resultant Motion.

There also exists Fleming’s right hand rule (for generators). The appropriately-handed rule can be recalled by remembering that the letter “g” is in “right” and “generator”.

Both mnemonics are named after British engineer John Ambrose Fleming who invented them.

Other mnemonics also exist that use a left hand rule or a right hand rule for predicting resulting motion from a pre-existing current and field.

Right-handed variant

A right-handed variant of this rule is as follows:
If the current through a wire is in the direction of the thumb of the right hand, and the direction of an external magnetic field on the wire is represented by the fingers, then the force experienced by the wire will be in the direction the palm of the right hand is facing.

Right-handed variants are useful for people who write with their left hand.

See also

• Fleming’s right hand rule
• Right hand rule
• FBI mnemonics

External links

• Overview at ac.wwu.edu (Right Hand - ‘FIB’)
• Diagrams at magnet.fsu.edu. See figure #9. (Left Hand - ‘FBI’)
• Description at starprof.com (Right Hand - ‘IBF’ - palm alternative)

The Korea General Machinery Trading Corporation is a large North Korean machine company. The company is headquartered in the Tongdaewon District near the capital, Pyongyang.

The company imports steel, chemical raw stock and some machine tools and turns out machine tools, metal parts, gears, electric motors, generators, hydroelectric generators, pumps, valves, mining equipment, rolling stock and other machinery.

Taean Heavy Machine Complex

An important part of Korea General Machinery is the Taean Heavy Machine Complex in Tongdaewon. This is where its hydroelectric generators and other thermal power generating equipment is manufactured, including turbines, motors, transformers, etc. Taean manufactures different sizes classes of hydroelectric equipment in its Tongsuse Class including a 50,000 kVA generator. The factory complex is up-to-date in its computerization.

Huichon Machine Tool Factory

Huichon Tool-Machine Factory|Huichon Machine Tool Factory in Huichon is North Korea’s leading manufacturer of heavy-duty machine tools for domestic use and for export. The 50-year old factory group is involved in machine tool production processes including steel-making, casting, processing, assembly, painting and packing. Product is produced on serial basis and small lot basis.

Its output of precision machine tools includes an assortment of spline-grinding machines and industrial lathes.

See Also

• Economy of North Korea

External link

• Naenara, North Korea’s Web Portal

A linear alternator is essentially a linear motor used as a “generator”. (An “alternator” is a type of AC “electric generator”.) The devices are often physically equivalent. The principal difference is in how they are used and which direction the energy flows. An alternator converts mechanical energy to electrical energy, whereas a motor converts electrical energy to mechanical energy. Like most electric motors and electric generators, the linear alternator works by the principle of electromagnetic induction. However, most alternators work with rotary motion, whereas “linear” alternators work with “linear” motion (i.e. motion in a straight line).

When a magnet moves in relation to a coil of wire, this changes the magnetic flux passing through the coil, and thus induces the flow of an electric current, which can be used to do work. A linear alternator is most commonly used to convert reciprocating motion directly into electric energy. This short-cut eliminates the need for a crank or linkage that would otherwise be required to convert a reciprocating motion to a rotary motion in order to be compatible with a rotary generator.

The simplest type of Linear alternator is a torch (UK) or flashlight (USA) which contains a coil and a permanent magnet. When the appliance is shaken back and forth, the magnet oscillates through the coil and induces an electric current. This current is used to charge a capacitor, thus storing energy for later use. The appliance can then produce light, usually from a light-emitting diode, until the capacitor is discharged. It can then be re-charged by further shaking.

Other devices are under development which use linear alternators to generate electricity; these devices include the opposed-piston free-piston engine and the free-piston Stirling engine.

See also

• Alternator
• Faraday Flashlight
• Linear motor
• Stelzer engine

Links

• [1]

In category theory, the concept of an injective cogenerator is drawn from examples such as Pontryagin duality. Generators are objects which cover other objects as an approximation, and (dually) cogenerators are objects which envelope other objects as an approximation. When working with unfamiliar algebraic objects, one can use these to approximate with the more familiar.

More precisely:

• A generator of a category with a zero object is some object G so that every non-zero object H has some non-zero morphism f:G → H.

• A cogenerator is an object C such that every other nonzero object H has some nonzero morphism f:H → C. (Note the reversed order).

The abelian group case

Assuming one has a category like that of abelian groups, one can in fact form direct sums of copies of G until the morphism

f: Sum(G) →H

is surjective; and one can form direct products of C until the morphism

f:H→ Prod(C)

is injective.

For example, the integers are a generator of the category of abelian groups (since every abelian group is a quotient of a free abelian group). This is the origin of the term generator. The approximation here is normally described as generators and relations.

As an example of a cogenerator in the same category, we have Q/Z, the rationals modulo the integers, which is a divisible abelian group. Given any abelian group A, there is an isomorphic copy of A contained inside the product of |A| copies of Q/Z. This approximation is close to what is called the divisible envelope - the true envelope is subject to a minimality condition.

General theory

In topological language, we try to find covers of unfamiliar objects.

Finding a generator of an abelian category allows one to express every object as a quotient of a direct sum of copies of the generator. Finding a cogenerator allows one to express every object as a subobject of a direct product of copies of the cogenerator. One is often interested in projective generators (even finitely generated projective generators, called progenerators) and minimal injective cogenerators. Both examples above have these extra properties.

The cogenerator Q/Z is quite useful in the study of modules over general rings. If H is a left module over the ring R, one forms the (algebraic) character module H* consisting of all abelian group homomorphisms from H to Q/Z. H* is then a right R-module. Q/Z being a cogenerator says precisely that H* is 0 if and only if H is 0. Even more is true: the * operation takes a homomorphism

f:H → K

to a homomorphism

f*:K* → H*,

and f* is 0 if and only if f is 0. It is thus a faithful contravariant functor from left R-modules to right R-modules.

Every H* is very special in structure: it is pure-injective (also called algebraically compact), which says more or less that solving equations in H* is relatively straightforward. One can often consider a problem after applying the * to simplify matters.

All of this can also be done for continuous modules H: one forms the topological character module of continuous group homomorphisms from H to the circle group R/Z.

In general topology

The Tietze extension theorem can be used to show that an interval is an injective cogenerator in a category of topological spaces subject to separation axioms.

AWM could stand for:

• Appliance Wiring Material, a wire category.
• Adult Web Master
• Advantage West Midlands, a UK regional development agency
• Angry White Male
• Arctic Warfare Magnum, a sniper rifle
• Ardent Window Manager
• The National Rail code for Ashwell and Morden railway station, United Kingdom
• Australian War Memorial
• Arab World Ministries, a Christian missionary society
• Association for Women in Mathematics
• Advanced Wave Memory, a system for using sampled waveforms in synthesizers and tone generators developed by Yamaha (manufacturer)
• AlliedWarMachine.com, an online gaming community

In theoretical physics, a central charge is an operator Z that commutes with all the other symmetry operators. The adjective “central” refers to the center of the symmetry group — the subgroup of elements that commute with all other elements of the original group — or to the center of a Lie algebra. In some cases, such as two-dimensional conformal field theory, a central charge may also commute with all of the other operators, including operators which are not symmetry generators.

More precisely, the central charge is the charge that corresponds, by Noether’s theorem, to the center of the central extension of the symmetry group.

In theories with supersymmetry, this definition can be generalized to include supergroups and Lie superalgebras. A central charge is any operator which commutes with all the other supersymmetry generators. Theories with extended supersymmetry typically have many operators of this kind. In string theory, in the first quantized formalism, these operators also have the interpretation of winding numbers (topological quantum numbers) of various strings and branes.

In conformal field theory, the central charge is a c-number (commutes with every other operator) term that appears in the commutator of two components of the stress energy tensor.

Unit Generators (or ugens) are the basic formal unit in many MUSIC-N-style computer music programming languages. They are sometimes called opcodes (particularly in Csound), though this expression is not accurate in that these are not machine-level instructions.

Unit Generators form the building blocks for designing synthesis and signal processing algorithms in software. For example, a simple unit generator called OSC could generate a sinusoidal waveform of a specific frequency (given as an input or argument to the function or class that represents the unit generator). ENV could be a unit generator that delineates a breakpoint function. Thus ENV could be used to drive the amplitude envelope of the oscillator OSC through the equation OSC*ENV. Unit generators often use predefined arrays of values for their functions (which are filled with waveforms or other shapes by calling a specific generator function).

The Unit Generator theory of sound synthesis was first developed and implemented by Max Mathews and his colleagues at Bell Labs in the 1950s.

Carding may refer to :

• A carder is someone who “cards” or combs material in order to align the fibres as in carding wool. Carders used large steel combs, cards, to align the fibres of raw sheep fleeces to enable them to be further processed. This process combs out some of the dirt, organizes the fibers, and fluffs up the wool with air so the ’spinner’ can use it easily.

• A carder is a criminal who engages in carding, a form of identity theft. Carders use lists of credit and debit card information to perpetrate multiple acts of fraud (by web or by phone), by making purchases without the consent of the original cardholder.

Carders may obtain card numbers by various means:

• • Hacking servers operated by online merchants who store unencrypted card information.
  • Extracting card information from data keyed into consumer machines infected with a keystroke logging virus.
  • Trading or purchasing lists of cards from other online criminals.
  • Engaging in phishing scams to intercept card information.

Carders may also use card generators. These are programs that extrapolate sequences of potentially valid new card numbers from a single card that is known to be valid. Card generators are generally ineffective following the adoption of expiry, AVS, CVV and PIN validation.

Carders may also veer into other forms of identity theft, such as obtaining the credentials (username and password) of consumers with online payment accounts, such as PayPal.

Carding is a form of wire fraud, and is a federal offense in the United States.

Computer random number generators are important in mathematics, cryptography and gambling. This list includes all common types, regardless of quality.

Pseudorandom number generators (PRNGs)

The following algorithms are pseudorandom number generators:

• Blum Blum Shub
• Inversive congruential generator
• ISAAC (cipher)
• Lagged Fibonacci generator
• Linear congruential generator - the most common type in computer programming languages
• Linear feedback shift register
• Multiply-with-carry
• Mersenne twister

Cryptographic PRNGs

Cipher algorithms and cryptographic hashes can also be used as pseudorandom number generators. These include

• Block ciphers in counter mode
• Cryptographic hashes in counter mode
• Stream ciphers

True random number generators

The following include some source of information entropy, allowing them to be considered true random number generators.

• CryptGenRandom - Microsoft Windows
• Fortuna
• SecureRandom class in the Java programming language
• Yarrow - Mac OS X and FreeBSD
• /dev/random - Linux and Unix

See also

• Diceware
• Hardware random number generator
• Random number generator attack
• Randomness

External links

• Random Number Generation in the GNU Scientific Library Reference Manual
• Diehard tests - statistical test suite for random number generators.

In mathematics, the Frattini subgroup Φ(G) of a group G is the intersection of all proper maximal subgroups of G, or, if G has no proper maximal subgroups, then Φ(G) is defined to be G itself. It is analogous to the Jacobson radical in the theory of commutative rings, and intuitively can be thought of as the subgroup of “small elements” (see the “non-generator” characterization below). It is named after Giovanni Frattini, who defined the concept in a paper published in 1885.

Some facts

• If G is finite, Φ(G) is equal to the set of all non-generators or non-generating elements of G. A non-generating element of G is an element that can always be removed from a generating set; that is, an element a of G such that whenever X is a generating set of G, X − {a} is also a generating set of G.
• Φ(G) is always a characteristic subgroup of G; in particular, it is always a normal subgroup of G.
• If G is finite, then Φ(G) is nilpotent.
• If G is a finite p-group, then the Frattini subgroup is the smallest (with respect to inclusion) normal subgroup N such that the quotient group G/N is an elementary abelian group i.e. isomorphic to a direct sum of cyclic groups of order p. Moreover, if the quotient group G/Φ(G) (also called the Frattini quotient of G) has order p^k, then k is the smallest number of generators for G (that is the smallest cardinality of a generating set for G). In particular a finite p-group is cyclic if and only if its Frattini quotient is cyclic (of order p). A finite p-group is elementary abelian if and only if its Frattini subgroup is the trivial group, Φ(G) = 1.

An example of a group with nontrivial Frattini subgroup is the cyclic group G of order p², where p is prime, generated by a, say; here, Φ(G) = < a^p >.

See also

• Fitting subgroup

In mathematics, a (B, N) pair is a structure on groups of Lie type
that allows one to give uniform proofs of many results, instead of giving a large number of
case-by-case proofs. Roughly speaking, it shows that all such groups are similar to the
general linear group over a field. They were invented by the mathematician Jacques Tits, and are also sometimes known as Tits systems.

Definition

A (B, N) pair is a pair of subgroups B and N of a group G such that the following axioms hold:

• G is generated by B and N.
• The intersection H of B and N is a normal subgroup of N.
• The group W = N/H is generated by a set of elements w_i of order 2, for i in some non-empty set I.
• If w_i is one of the generators of W and w is any element of W, then w_iBw is contained in the union of Bw_iwB and BwB.
• No generator w_i normalizes B.

The idea of this definition is that B is an analogue of the upper triangular matrices of
the general linear group GL_n(K), H is an analogue of the diagonal matrices,
and N is an analogue of the normalizer of H.

The subgroup B is sometimes called the Borel subgroup, H is sometimes called the Cartan subgroup, and W is called the Weyl group.

The number of generators w_i is called the rank.

Examples

• Suppose that G is any doubly transitive permutation group on a set X with more than 2 elements. We let B be the subgroup of G fixing a point x, and we let N be the subgroup fixing or exchanging 2 points x and y. The subgroup H is then the set of elements fixing both x and y, and W has order 2 and its nontrivial element is represented by anything exchanging x and y.

• Conversely, if G has a BN pair of rank 1, then the action of G on the cosets of B is doubly transitive. So BN pairs of rank 1 are more or less the same as doubly transitive actions on sets with more than 2 elements.

• Suppose that G is the general linear group GL_n(K) over a field K. We take B to be the upper triangular matrices, H to be the diagonal matrices, and N to be the matrices with exactly one non-zero element in each row and column. There are n-1 generators w_i, represented by the matrices obtained by swapping two adjacent rows of a diagonal matrix.

• More generally, any group of Lie type has the structure of a BN-pair.

Properties of groups with a BN pair.

The map taking w to BwB is an isomorphism from the set of elements of W to the set of double cosets of B; this is the Bruhat decomposition G = BWB.

The subgroups of G containing B are called parabolic subgroups. There are exactly 2ⁿ of them, and they correspond to subsets of I.

Applications

BN-pairs can be used to prove that most groups of Lie type are simple. More precisely, if G has a BN-pair such that B is a solvable group, the intersection of all conjugates of B is trivial, and the set of generators of W cannot be decomposed into two non-empty commuting sets, then G is simple whenever it is a perfect group. In practice all of these conditions except for G being perfect are easy to check. Checking that G is perfect needs some slightly messy calculations (and in fact there are a few small groups of Lie type which are not perfect or simple). But showing that a group is perfect is usually far easier than showing it is simple.

References

The standard reference for BN pairs is:

• Bourbaki, Nicolas, Lie Groups and Lie Algebras: Chapters 4-6 (Elements of Mathematics), ISBN 3-540-42650-7

Functional verification, in electronic design automation, is the task of verifying that the logic design conforms to specification. In everyday terms, functional verification attempts to answer the question “Does this proposed design do what is intended?” This is a complex task, and takes the majority of time and effort in most large electronic system design projects.

Functional verification is very difficult - it is equivalent to program verification, and is NP-hard or even worse - and no solution has been found that works well in all cases. However, it can be attacked by many methods. None of them are perfect, but each can be helpful in certain circumstances:

• Logic simulation simulates the logic before it is built.
• Simulation acceleration applies special purpose hardware to the logic simulation problem.
• Emulation builds a version of system using programmable logic. This is expensive, and still much slower than the real hardware, but orders of magnitude faster than simulation. It can be used, for example, to boot the operating system on a processor.
• Formal verification attempts to prove mathematically that certain requirements (also expressed formally) are met, or that certain undesired behaviors (such as deadlock) cannot occur.
• HDL-specific versions of lint, and other heuristics, are used to find common problems.

Simulation based verification (also called ‘dynamic verification’) is widely used to “simulate” the design, since this method scales up very easily. Stimulus is provided to exercise each line in the HDL code. A test-bench is built to functionally verify the design by providing meaningful scenarios to check that given certain input, the design performs to specification.

A simulation environment is typically composed of several types of components:

• The generator (or irritator) generates input vectors. Modern generators generate random, biased, and valid stimuli. The randomness is important to achieve a high distribution over the huge space of the available input stimuli. To this end, users of these generators intentionally under-specify the requirements for the generated tests. It is the role of the generator to randomly fill this gap. This mechanism allows the generator to create inputs that reveal bugs not being searched for directly by the user. Generators also bias the stimuli toward design corner cases to further stress the logic. Biasing and randomness serve different goals and there are tradeoffs between them, hence different generators have a different mix of these characteristics. Since the input for the design must be valid (legal) and many targets (such as biasing) should be maintained, many generators use the Constraint Satisfaction Problem (CSP) technique to solve the complex testing requirements. The legality of the design inputs and the biasing arsenal are modeled. The model-based generators use this model to produce the correct stimuli for the target design.
• The drivers translate the stimuli produced by the generator into the actual inputs for the design under verification. Generators create inputs at a high level of abstraction, namely, as transactions or assembly language. The drivers convert this input into actual design inputs as defined in the specification of the design’s interface.
• The simulator produces the outputs of the design, based on the design’s current state (the state of the flip-flops) and the injected inputs. The simulator has a description of the design net-list. This description is created by synthesizing the HDL to a low gate level net-list.
• The monitor converts the state of the design and its outputs to a transaction abstraction level so it can be stored in a ’score-boards’ database to be checked later on.
• The checker validates that the contents of the ’score-boards’ are legal. There are cases where the generator creates expected results, in addition to the inputs. In these cases, the checker must validate that the actual results match the expected ones.
• The arbitration manager manages all the above components together.

Different coverage metrics are defined to assess that the design has been adequately exercised. These include function coverage (has every function been exercised?), statement coverage (has each line of HDL been exercised?), and branch coverage (has each direction of every branch been exercised?). None of these are sufficient to prove a design works, but all are helpful in pointing out areas of the HDL that have not been tested.

External links

Certess, Inc. product’s : Certitude

ResMed is a manufacturer of products for the treatment of sleep disorders, particularly obstructive sleep apnea.

ResMed was formed in 1989, its primary purpose was to commercialise a device for treating obstructive sleep apnea with nasal continuous positive airway pressure (CPAP). CPAP treatment was commercialised by Peter Farrell and Professor Colin Sullivan.

In March 2007, the company recalled all of its flagship S8 models worldwide due to electrical safety problems.

See also

• Sleep and breathing#Abnormal sleep and breathing (Sleep related breathing disorders)

References

Product recall

The Crystal River 3 Nuclear Generation Station is a nuclear power plant, part of the Crystal River Energy Complex located in Citrus County, Florida near Crystal River, Florida. The site consists of approximately 4,700 acres (19 km²) and contains a single pressurized water reactor sharing the site with 4 fossil-fueled generators. The reactor is rated to produce 842 megawatts of electric power. It is a Babcock and Wilcox pressurized water reactor.

Crystal River 3 was originally owned by Florida Progress Corporation (and operated by its subsidiary, Florida Power Corporation) but, in 2000, it was bought by Carolina Power & Light to form the new company, Progress Energy, which currently runs the plant.

In December 2006, Florida Progress purchased 3,000 acres of land seven miles from the Gulf of Mexico and eight miles north of the existing Crystal River plant in preparation for the potential construction of a new nuclear power reactor. A formal decision has not yet been made. Critics lament the low-lying location of the site. Levy County officials have welcomed the potential plant in an effort to bring jobs to the impoverished county.

External links

• DoE Page
• NukeWorker

• [1]

The Korea General Machinery Trading Corporation is a large North Korean machine company. The company is headquartered in the Tongdaewon District near the capital, Pyongyang.

The company imports steel, chemical raw stock and some machine tools and turns out machine tools, metal parts, gears, electric motors, generators, hydroelectric generators, pumps, valves, mining equipment, rolling stock and other machinery.

Taean Heavy Machine Complex

An important part of Korea General Machinery is the Taean Heavy Machine Complex in Tongdaewon. This is where its hydroelectric generators and other thermal power generating equipment is manufactured, including turbines, motors, transformers, etc. Taean manufactures different sizes classes of hydroelectric equipment in its Tongsuse Class including a 50,000 kVA generator. The factory complex is up-to-date in its computerization.

Huichon Machine Tool Factory

Huichon Tool-Machine Factory|Huichon Machine Tool Factory in Huichon is North Korea’s leading manufacturer of heavy-duty machine tools for domestic use and for export. The 50-year old factory group is involved in machine tool production processes including steel-making, casting, processing, assembly, painting and packing. Product is produced on serial basis and small lot basis.

Its output of precision machine tools includes an assortment of spline-grinding machines and industrial lathes.

See Also

• Economy of North Korea

External link

• Naenara, North Korea’s Web Portal

A diversion dam is the term for a dam that diverts all or a portion of the flow of a river from its natural course. Diversion dams do not generally impound water in a reservoir. Instead, the water is diverted into an artificial water course or canal, which may be used for irrigation or return to the river after passing through hydroelectric generators, flow into a different river or be itself dammed forming a reservoir.

A vortex generator is an aerodynamic surface, consisting of a small vane that creates a vortex. They can be found in many devices, but the term is most often used in aircraft design.

Vortex generators are added to the leading edge of a swept wing in order to maintain steady airflow over the control surfaces at the rear of the wing. They are typically rectangular or triangular, tall enough to protrude above the boundary layer, and run in spanwise lines near the thickest part of the wing. They can be seen on the wings and vertical tails of many airliners. Vortex generators are positioned in such a way that they have an angle of attack with respect to the local airflow.

A vortex generator creates a tip vortex which draws energetic, rapidly-moving air from outside the slow-moving boundary layer into contact with the aircraft skin. The boundary layer normally thickens as it moves along the aircraft surface, reducing the effectiveness of trailing-edge control surfaces; vortex generators can be used to remedy this problem, among others, by re-energizing the boundary layer. Vortex generators delay flow separation and aerodynamic stalling; they improve the effectiveness of control surfaces (e.g Embraer 170 and Symphony SA-160); and, for swept-wing transonic designs, they alleviate potential shock-stall problems (e.g. Harrier, Blackburn Buccaneer, Gloster Javelin).

Many aircraft carry vane vortex generators from time of manufacture, but there are also after-market suppliers who sell VG kits to improve the STOL performance of some light aircraft.

Air jet vortex generators work on a different principle. They direct a jet of air into the boundary layer, thereby re-energising it.

Vortex generators are also being used in automotive vehicles. In one form they are used as in aircraft to influence the boundary layer of air flow primarily for drag reduction. In another form they are installed in the engine’s air intake hose. Manufacturers claim that the vortex generator creates a swirling motion within the air intake pipe, and within the combustion chamber causing improved burning of the fuel, increasing horsepower and fuel efficiency.

See also

• Turbulator
• Boundary layer suction

External links

• Aeronautical Testing Service, Inc. Manufacturer of Vortex Generator Kits

Lemon is an LALR parser generator for C or C++. It does the same job as GNU bison and yacc. But lemon is not another bison or yacc clone. It uses a different grammar syntax which is designed to reduce the number of coding errors. Lemon also uses a parsing engine that is both reentrant and thread-safe. Furthermore, Lemon implements features that can be used to eliminate resource leaks, making it suitable for use in long-running programs such as graphical user interfaces or embedded controllers.

Lemon was written by Dr. Richard Hipp and resides in the public domain.

External links

• The Lemon Parser Generator
• Calculator with Lemon and Lex in C++ Example

The Armstrong oscillator is an oscillator used to produce a sine-wave output of constant amplitude and of fairly constant frequency within the RF range. It is generally used as a local oscillator in receivers, as a source in signal generators, and as a radio-frequency oscillator in the medium- and high-frequency range. The oscillator was name after its inventor Edwin Armstrong.

A turbo generator is a turbine directly connected to an electric generator for the generation of electric power. Large Steam powered turbo generators (steam turbine generators) provide the majority of the world’s electricity and are also used by steam powered, turbo-electric ships.

Smaller turbo-generators with gas turbines are often used as auxiliary power units. For base loads diesel generators are usually preferred, since they offer much better fuel-efficiency and are also more reliable, but on the other hand they are much heavier and need more space.

The efficiency of larger gas turbine plants can be enhanced, if the hot exhaust gases are used to generate steam which drives another turbo generator.

Turbo generators were also used on steam locomotives as a power source for coach lighting and heating systems.

External Links

• http://www.srdrives.com/turbo-generator.shtml

Pulse generators can either be internal circuits or pieces of electronic test equipment used to generate pulses.

Features

Simple pulse generators usually allow control of the pulse repetition rate (frequency), pulse width, delay with respect to an internal or external trigger and the high- and low-voltage levels of the pulses. More-sophisticated pulse generators may allow control over the rise time and fall time of the pulses. Pulse generators may use digital techniques, analog techniques, or a combination of both techniques to form the output pulses. For example, the pulse repetition rate and duration may be digitally controlled but the pulse amplitude and rise and fall times may be determined by analog circuitry in the output stage of the pulse generator. With correct adjustment, pulse generators can also produce a 50% duty cycle square wave. Pulse generators are generally single-channel providing one frequency, delay, width and output. To produce multiple pulses, these simple pulse generators would have to be ganged in series or in parallel.

A new family of pulse generators can produce multiple-channels of independent widths and delays and independent outputs and polarities. Often called digital delay/pulse generators, the newest designs even offer differing repetition rates with each channel. These digital delay generators are useful in synchronizing, delaying, gating and triggering multiple devices usually with respect to one event.

Pulse generators are generally voltage sources, with true current pulse generators being available only from a few suppliers.

Applications

These pulses can then be injected into a device under test and used as a stimulus or clock signal or analyzed as they progress through the device, confirming the proper operation of the device or pinpointing a fault in the device. Pulse generators are also used to drive devices such as switches, lasers and optical components, modulators, intensifiers as well as resistive loads.

The output of a pulse generator may also be used as the modulation signal for a signal generator.

In mathematics, a (B, N) pair is a structure on groups of Lie type
that allows one to give uniform proofs of many results, instead of giving a large number of
case-by-case proofs. Roughly speaking, it shows that all such groups are similar to the
general linear group over a field. They were invented by the mathematician Jacques Tits, and are also sometimes known as Tits systems.

Definition

A (B, N) pair is a pair of subgroups B and N of a group G such that the following axioms hold:

• G is generated by B and N.
• The intersection H of B and N is a normal subgroup of N.
• The group W = N/H is generated by a set of elements w_i of order 2, for i in some non-empty set I.
• If w_i is one of the generators of W and w is any element of W, then w_iBw is contained in the union of Bw_iwB and BwB.
• No generator w_i normalizes B.

The idea of this definition is that B is an analogue of the upper triangular matrices of
the general linear group GL_n(K), H is an analogue of the diagonal matrices,
and N is an analogue of the normalizer of H.

The subgroup B is sometimes called the Borel subgroup, H is sometimes called the Cartan subgroup, and W is called the Weyl group.

The number of generators w_i is called the rank.

Examples

• Suppose that G is any doubly transitive permutation group on a set X with more than 2 elements. We let B be the subgroup of G fixing a point x, and we let N be the subgroup fixing or exchanging 2 points x and y. The subgroup H is then the set of elements fixing both x and y, and W has order 2 and its nontrivial element is represented by anything exchanging x and y.

• Conversely, if G has a BN pair of rank 1, then the action of G on the cosets of B is doubly transitive. So BN pairs of rank 1 are more or less the same as doubly transitive actions on sets with more than 2 elements.

• Suppose that G is the general linear group GL_n(K) over a field K. We take B to be the upper triangular matrices, H to be the diagonal matrices, and N to be the matrices with exactly one non-zero element in each row and column. There are n-1 generators w_i, represented by the matrices obtained by swapping two adjacent rows of a diagonal matrix.

• More generally, any group of Lie type has the structure of a BN-pair.

Properties of groups with a BN pair.

The map taking w to BwB is an isomorphism from the set of elements of W to the set of double cosets of B; this is the Bruhat decomposition G = BWB.

The subgroups of G containing B are called parabolic subgroups. There are exactly 2ⁿ of them, and they correspond to subsets of I.

Applications

BN-pairs can be used to prove that most groups of Lie type are simple. More precisely, if G has a BN-pair such that B is a solvable group, the intersection of all conjugates of B is trivial, and the set of generators of W cannot be decomposed into two non-empty commuting sets, then G is simple whenever it is a perfect group. In practice all of these conditions except for G being perfect are easy to check. Checking that G is perfect needs some slightly messy calculations (and in fact there are a few small groups of Lie type which are not perfect or simple). But showing that a group is perfect is usually far easier than showing it is simple.

References

The standard reference for BN pairs is:

• Bourbaki, Nicolas, Lie Groups and Lie Algebras: Chapters 4-6 (Elements of Mathematics), ISBN 3-540-42650-7

In theoretical physics, a central charge is an operator Z that commutes with all the other symmetry operators. The adjective “central” refers to the center of the symmetry group — the subgroup of elements that commute with all other elements of the original group — or to the center of a Lie algebra. In some cases, such as two-dimensional conformal field theory, a central charge may also commute with all of the other operators, including operators which are not symmetry generators.

More precisely, the central charge is the charge that corresponds, by Noether’s theorem, to the center of the central extension of the symmetry group.

In theories with supersymmetry, this definition can be generalized to include supergroups and Lie superalgebras. A central charge is any operator which commutes with all the other supersymmetry generators. Theories with extended supersymmetry typically have many operators of this kind. In string theory, in the first quantized formalism, these operators also have the interpretation of winding numbers (topological quantum numbers) of various strings and branes.

In conformal field theory, the central charge is a c-number (commutes with every other operator) term that appears in the commutator of two components of the stress energy tensor.

In abstract algebra, the Weyl algebra is the ring of differential operators with polynomial coefficients (in one variable),

<math>

 f_n(X) \partial_X^n + \cdots + f_1(X) \partial_X + f_0(X).

</math>

More precisely, let F be a field, and let F[X] be the ring of polynomials in one variable, X, with coefficients in F. Then each f_i lies in F[X]. ∂_X is the derivative with respect to X. The algebra is generated by X and ∂_X.

The Weyl algebra is an example of a simple ring that is not a matrix ring over a division ring. It is also a noncommutative example of a domain, and an example of an Ore extension.

You can also construct the Weyl algebra as a quotient of the free algebra on two generators, X and Y, by the ideal generated by the single relation

YX − XY − 1.

The Weyl algebra is the first in an infinite family of algebras, also known as Weyl algebras. The n-th Weyl algebra, A_n, is the ring of differential operators with polynomial coefficients in n variables. It is generated by X_i and <math>\part_{X_i}</math>.

Weyl algebras are named after Hermann Weyl, who introduced them to study the Heisenberg uncertainty principle in quantum mechanics. It is a quotient of the universal enveloping algebra of the Lie algebra of the Heisenberg group, by setting the element 1 of
the Lie algebra equal to the unit 1 of the universal enveloping algebra.

One may give an abstract construction of the algebras A_n in terms of generators and relations.
We do so in a more sophisticated way: Start with an
abstract vector space V (of dimension 2n) equipped with a symplectic form <math>\omega</math>.
Define the Weyl algebra W(V) to be

<math>W(V) := T(V) / (\!( v \otimes w - w \otimes v - \omega(v,w), \text{ for } v,w \in V )\!),</math>

where the notation <math>(\!( )\!)</math> means “the ideal generated by”. In other words, <math>W(V)</math> is the algebra generated by V subject
only to the relation <math>vw - wv = \omega(v,w)</math>. Then, W(V) is isomorphic to <math>A_{n}\,</math> (it does not depend on the choice
of <math>\omega</math>). In this form, one sees that W(V)
is a quantization of the symmetric algebra Sym(V). If V is over a field of characteristic zero,
then W(V) is naturally isomorphic to the symmetric algebra Sym(V) equipped with the deformed Moyal product (considering the symmetric
algebra to be polynomial functions on <math>V^*</math>, where the variables span the vector space V, and replacing <math>i \hbar</math> in
the Moyal product formula with 1). The isomorphism is given by
the symmetrization map from Sym(V) to W(V):
<math>a_1 \cdots a_n \mapsto \frac{1}{n!} \sum_{\sigma \in S_n} a_{\sigma(1)} \otimes \cdots \otimes a_{\sigma(n)}</math>. If one prefers to have the
<math>i \hbar</math> and work over the complex numbers, one could have instead defined the Weyl algebra above as generated by X_i and
<math>i \hbar \part_{X_i}</math> (as is frequently done in quantum mechanics).

Thus, the Weyl algebra is a quantization of the symmetric algebra, which is essentially the same as the Moyal quantization (if for the latter one restricts to polynomial functions), but
the former is in terms of generators and relations (considered to be differential operators) and the latter is in terms of a deformed multiplication.
In the case of exterior algebras, the analogous quantization to the Weyl one is the Clifford algebra.

For more details about this quantization in the case <math>n=1</math> (and an extension using the Fourier transform to integrable (”most”)
functions, not just polynomial functions), see Weyl quantization.

References

• M. Rausch de Traubenberg, M. J. Slupinski, A. Tanasa, Finite-dimensional Lie subalgebras of the Weyl algebra, (2005) (Classifies subalgebras of the one dimensional Weyl algebra over the complex numbers; shows relationship to SL(2,C))

A chemical oxygen generator is a device that releases oxygen created by a chemical reaction. The oxygen source is usually an inorganic superoxide, chlorate or perchlorate. A promising group of oxygen sources are ozonides. The generators are usually ignited mechanically, by a firing pin, and the chemical reaction is usually exothermic, making the generator a potential fire hazard. Potassium superoxide was used as an oxygen source on early manned USSR space missions, and for firefighters and mine rescue.

Chemical oxygen generator in commercial airliners

Commercial aircraft provide emergency oxygen to passengers to protect them from drops in cabin pressure. Chemical oxygen generators are not used for the cockpit crew. For each row of seats there are overhead masks and oxygen generators. If a decompression occurs, the panels are opened either by an automatic pressure switch or by a manual switch, and the masks are released. When the passengers pull down on the mask they remove the retaining pins and trigger the production of oxygen.

The oxidizer core is sodium chlorate (NaClO₃), which is mixed with less than 5
percent barium peroxide (BaO₂) and less than 1 percent potassium perchlorate (KClO₄). The explosives in the percussion cap are a lead styphnate and tetracene mixture. The chemical reaction is exothermic and the exterior temperature of the canister will reach 260 °C (500°F). It will produce oxygen for 15 to 20 minutes. The two-mask generator is approximately 63 mm (2.5″) in diameter and 223 mm (8.8″) long. The three-mask generator is approximately 70 mm (2.8″) in diameter and 250 mm (10″) long.

Accidental activation of improperly shipped expired generators caused the ValuJet Flight 592 crash.

Oxygen candle

A chlorate candle, or an oxygen candle, is a cylindrical chemical oxygen generator containing a mix of sodium chlorate and iron powder. When ignited, the mixture smolders at about 600 °C (1100°F), producing sodium chloride, iron oxide, and about 6.5 man-hours of oxygen per kilogram of the mixture. It releases oxygen at a fixed rate. The mixture has an indefinite shelf life if stored properly; candles stored for 20 years have shown no decrease in oxygen output. The oxygen is released by thermal decomposition. The heat is supplied by the burning iron. The candle has to be wrapped in thermal insulation to maintain the reaction temperature and to protect surrounding equipment.

Potassium and lithium chlorate, and sodium, potassium and lithium perchlorates can also be used in oxygen candles.

It is thought that an explosion caused by one of these candles led to the deaths of two British Navy sailors on HMS Tireless, a nuclear-powered submarine, under the Arctic in March 2007.’Oxygen candle’ caused explosion

Solid oxygen generator from Mir

The TGK generator contains a replaceable cartridge, a thin walled steel tube with a three-part block of oxygen-releasing mixture based on lithium perchlorate. Two parts are tablets of the chemical mixture and the third one is the igniter tablet with a flash igniter. The igniter is struck by a firing pin when the device is activated. One cartridge releases 600 liters (159 gallons) of oxygen and burns for 5-20 minutes at 450-500 °C. (840-930°F)Oxygen Generators The oxygen is cooled and filtered from dust and odors, and released into the space station atmosphere.

On 23 February 1997, during the exchange of an air filter, a failed chemical oxygen generator spewed a torch-like jet of a molten metal and sparks across one of the Mir space station modules, burning for 14 minutes and blocking the escape route to one of the Soyuz spacecraft. The accident was caused by a leak of the lithium perchlorate from one of the canisters.

References

Uses

Chemical oxygen generators are used in aircraft, breathing apparatus for firefighters and mine rescue crews, submarines, and everywhere where a compact emergency oxygen generator with long shelf life is needed. They usually contain a device for absorption of carbon dioxide, often a filter filled with lithium hydroxide; a kilogram of LiOH absorbs about half a kilogram of CO₂.

Self-contained self-rescue devices (SCSRs) are used to facilitate escape from mines.

On the International Space Station, chemical oxygen generators are located aboard the Elektron module. Each canister can produce enough oxygen for one crewmember for one day.

ASEA (Allmänna Svenska Elektriska Aktiebolaget) was a Swedish industry company. It merged with the Swiss BBC Brown Boveri in 1988 to form Asea Brown Boveri. ASEA still exists, but only as a holding company owning 50% of ABB Group.

History

ASEA was founded 1883 by Ludvig Fredholm in Stockholm as manufacturer of electrical light and generators. By a merging with Wennström’s & Granström’s Electrical Power Company (Wenströms & Granströms Elektriska Kraftbolag) the name was change to Allmänna Svenska Elektriska Aktiebolaget, literally the “General Swedish Electrical Limited Company”, or a ASEA for short.

• 1889 - the partner Jonas Wenström creates 3-phased generators, engines and transformers.
• 1933 - The company removes a swastika from the logotype, due to the symbol’s association with Nazi Germany.
• 1953 - ASEA creates the first industrial diamonds.
• 1954 - HVDC Gotland project, first static high-voltage DC system
• 1960s - ASEA builds 9 of 12 nuclear plants in Sweden.
• 1974 - Industrial robots are introduced by ASEA
• 1987 - Acquires Finnish Oy Strömberg Ab
• 1988 - Merges with BBC Brown Boveri

See also

• Sigfrid Edström
• Uno Lamm
• ABB Group

Berkeley Yacc is a reimplementation of the Unix parser generator Yacc, originally written by Robert Corbett in 1990. It has the advantages of being written in ANSI C and being public domain software.

Installation

A very simple tutorial that explains how to compile and install Berkeley Yacc on Linux can be found here.

A prismatic surface is a surface generated by all the lines that are parallel to a given line and intersect a broken line that is not in the same plane as the given line. The broken line is the directrix of the surface; the parallel lines are its generators (or elements). If the broken line is close (i.e. a closed polygon), then the surface is a closed prismatic surface.

Narrows Dam is a dam located 6 miles north of Murfreesboro, Arkansas and impounds the water of the Little Missouri River (Arkansas) to create Lake Greeson. Narrows Dam was authorized as a flood control and hydroelectric power project by the Flood Control Act of 1941. The dam is a feature of the comprehensive plan for the Ouachita River Basin. Lake Greeson is operated for hydroelectric power, recreation, and flood control. [1]

The powerhouse of the dam is located adjacent to the east abutment, and it has a total length of 151 feet. The equipment of the powerhouse is three 8,500 KWh generating machines. The powerhouse originally had two generators, but a third was placed in 1969. The average annual output is 28,000,000 KWh.

The dam is named due to its location on the river, The Narrows. During the dam’s construction many cemeteries and graveyards had to be removed due to the creation of the new lake. Narrows Dam is located by the Swaha, or Narrows Dam recreational area.

Lake Greeson is divided into three layers so Narrows Dam can work and operate properly. The bottom portion of the lake always remains full so the powerhouse has enough pressure to operate. The middle layer or “Power Storage” portion is used to regulate the flow of water running into the generators of the dam. The top portion or “Flood Storage” is usually empty unless holding floodwater. A spillway at top of the dam is used to regulate the top portion of the dam, the spillway contains walls to maneuver the flow of the water, and a stilling basin is placed at the foot of the spillway to dissipate erosion from the spillway water hitting the base of the dam. The spillway isn’t used much due to the fact that flooding can be regulated by other means, such as the flood control conduits.

Construction on the dam began on April 1947, the first bucket of concrete was poured in June 1948. The dam was finished in 1950, and dedicated on July 1951.

See also

• List of Arkansas dams and reservoirs

In group theory, Tietze transformations are used to transform a given presentation of a group into another, often simpler presentation of the same group. These transformations are named after Heinrich Franz Friedrich Tietze who introduced them in a paper in 1908.

A presentation is in terms of generators and relations; formally speaking the presentation is a pair of a set of named generators, and a set of words in the free group on the generators that are taken to be the relations. Tietze transformations are built up of elementary steps, each of which individually rather evidently takes the presentation to a presentation of an isomorphic group. These elementary steps may operate on generators or relations, and are of four kinds.

1. Adding a Relation

If a relation can be derived from the existing relations then it may be added to the presentation without changing the group. Let G=< x | x³=1 > be a finite presentation for the cyclic group of order 3. Multiplying x³=1 on both sides by x³ we get x⁶ = x³ = 1 so x⁶ = 1 is derivable from x³=1. Hence G=< x | x³=1, x⁶=1 > is another presentation for the same group.

2. Removing a Relation

If a relation in a presentation can be derived from the other relations then it can be removed from the presentation without affecting the group. In G=< x | x³=1, x⁶=1 > the relation x⁶ = 1 can be derived from x³=1 so it can be safely removed. Note, however, that if x³=1 is removed from the presentation the group G=< x | x⁶=1 > defines the cyclic group of order 6 and does not define the same group. Care must be taken to show that any relations that are removed are consequences of the other relations.

3. Adding a Generator

Given a presentation it is possible to add a new generator that is expressed as a word in the original generators. Starting with G=< x | x³=1 > and letting y=x² the new presentation G=< x,y | x³=1, y=x² > defines the same group.

4. Removing a Generator

If a relation can be formed where one of the generators is a word in the other generators then that generator may be removed. In order to do this it is necessary to replace all occurrences of the removed generator with its equivalent word. The presentation for the elementary abelian group of order 4, G=< x,y,z | x = yz, y²=1, z²=1, x=x^-1 > can be replaced by G=< y,z | y²=1, z²=1, (yz)=(yz)^-1 > by removing x.

Examples

Let G=< x,y | x³=1, y²=1, (xy)²=1 > be a presentation for the symmetric group of degree three. The generator x corresponds to the permutation (1,2,3) and y to (2,3). Through Tietze transformations this presentation can be converted to G=< y, z | (zy)³=1, y²=1, z²=1>, where z corresponds to (1,2).

x,y,z

References

• Roger C Lyndon, Paul E Schupp, Combinatorial Group Theory, Springer, 2001. ISBN 3-540-41158-5.

Natural Docs is a multi-language documentation generator. It is written in Perl and is available as free software under the terms of the GNU General Public License. It attempts to keep the comments written in source code just as readable as the generated documentation. It is written and maintained by Greg Valure.

Theoretically, it can generate documentation from any language that can support comments, or from plain text files. When executed, it can automatically document functions, variables, classes, and inheritance from ActionScript 2.0, C#, and Perl regardless of existing documentation in the source code. In all other languages, these need to be explicitly documented for them to be generated. It can generate documentation in HTML, either with frames or without.

Unlike Javadoc, it is not considered an industry standard for documenting in any language, although Javadoc compatibility is being developed for certain languages. Javadoc Support on NaturalDocs.org It is used by some hobbyists and companies, such as CNET Networks, Inc. and Iron Realms Entertainment.CNET’s Global Framework by CNET Networks, Inc. and generated documentation using Natural DocsRapture by Iron Realms Entertainment and generated documentation using Natural Docs It has gained popularity amongst ActionScript 2.0 developers because no other free documentation generator exists that fully supports ActionScript 2.0 and because it generates higher-quality output than similar generators that partially support the language, such as ROBODoc.

Example

This is an example of the documentation style:

/*
 * Function: Multiply
 *
 * Multiplies two integers.
 *
 * Parameters:
 *    x - The first integer.
 *    y - The second integer.
 *
 * Returns:
 *    The two integers multiplied together.
 *
 * See Also:
 *    <Divide>
 */

int Multiply (int x, int y)
   {  return x * y;  };

For comparison, this is how the same thing would be documented with Javadoc:

/**
 * Multiplies two integers.
 *
 * @param x The first integer.
 * @param y The second integer.
 * @return The two integers multiplied together.
 * @see Divide
 */ 	 

int Multiply (int x, int y)
   { return x * y; };

See also

• Comparison of documentation generators

Notes and references

Further reading

• Natural Docs Home Page
• List of features
• List of supported languages

Orion Platinum is a music production suite developed by Synapse Audio Software.

The software supports all stages of music production, from composing/arranging music to mixing and mastering it. It includes multitrack audio recording, generators, effects and a mixing desk with sub busses. It supports both traditional linear sequencing and pattern-based sequencing. Supported external interfaces include VST, DX and ReWire. Audio output resolutions range from 16 Bit/44.1kHz up to 32 Bit/192 kHz, Stereo.

Features

Generators

Orion Platinum comes with the following internal generators (as of version 7):

Toxic III

Licensed by Maxx Claster

Toxic II

Licensed by Maxx Claster. Despite Toxic III being introduced in v7, Toxic II is still included.

Tomcat

Sampler

Ultran

Wasp XT

History

Wasps roots come from a free standalone software-synth, the TS-404. It was coded by Richard Hoffman (who is now the main driving force behind Synapse Audio), and was later licensed to Image-Line Software for FL Studio. The TS-404 was later developed into the first version of Wasp. Wasp was included in early versions Orion and also licensed to Image Line who sold it as an add on plugin for Fruity Loops and as a separate VSTi plugin.

Wasp was continually developed by Synapse Audio / Sonic Syndicate as part of Orion. A major update to Wasp, Wasp XT, was released with the first version of Orion Platinum in 2002. Image-Line didn’t update their version of Wasp until FL Studio v6 was released in early 2006 (also changing the name to Wasp XT). It is not clear whether the later Image-Line version uses the same code as the Synapse-Audio version.

Drums

Monobass

Emulation of TB-303

XR-909

Emulation of Roland TR-909

Wavefusion

Screamer

Plucked String

MIDI Out

External links

• Orion Platinum
• Synapse Audio Software

In abstract algebra, a free algebra is the noncommutative analogue of a polynomial ring (which may be regarded as a free commutative algebra).

Let R be a commutative ring. The free algebra on n indeterminates, {X₁, …, X_n}, is the ring spanned by all linear combinations of products of the variables. This ring is denoted R<X₁, …, X_n>. With the obvious scalar multiplication R<X₁, …, X_n> forms an algebra over R. Unlike in a polynomial ring, the variables do not commute. For example X₁X₂ does not equal X₂X₁.

More generally, one can construct the free algebra R<E> on any set E of generators. Since rings may be regarded as Z-algebras, a free ring on E can be defined as the free algebra Z<E>.

Over a field, the free algebra on n indeterminates can be constructed as the tensor algebra on an n-dimensional vector space. For a more general coefficient ring, the same construction works if we take the free module on n generators.

The construction of the free algebra on E is functorial in nature and satisfies an appropriate universal property. The free algebra functor is left adjoint to the forgetful functor from the category of R-algebras to the category of sets.

See also

• Tensor algebra
• Free object

References

Berkeley Yacc is a reimplementation of the Unix parser generator Yacc, originally written by Robert Corbett in 1990. It has the advantages of being written in ANSI C and being public domain software.

Installation

A very simple tutorial that explains how to compile and install Berkeley Yacc on Linux can be found here.

In electrical engineering, Millman’s Theorem (or the parallel generator theorem) is a useful method to simplify the solution of a circuit. It is named after Jacob Millman, who proved the theorem. A similar method, known as Tank’s method, had already been commonly used before Millman’s proof.

Explanation

Millman’s theorem gives a very quick method to compute the voltage at the ends of a circuit made up of only branches in parallel.

Let e_k be the voltage generators and a_m the current generators.

Let R_i be the resistances on the branches with no generator.

Let R_k be the resistances on the branches with voltage generators.

Let R_m be the resistances on the branches with current generators.

Then Millman states that the voltage at the ends of the circuit is given by:

<math>v=\frac{\sum_{}\frac{\pm e_{k}}{R_{k}}+\sum_{}\pm a_{m}}{\sum_{}\frac{1}{R_{k}}+\sum_{}\frac{1}{R_{i}}}</math>

It can be proved by considering the circuit as a single supernode. Then, according to Ohm and Kirchhoff, the voltage between the ends of the circuit is equal to the total current entering the supernode divided by the total equivalent conductance of the supernode.

The total current is the sum of the currents flowing in each branch.

The total equivalent conductance of the supernode is the sum of the conductance of each branch, since all the branches are in parallel. When computing the equivalent conductance all the generators have to be switched off, so all voltage generators become short circuits and all current generators become open circuits. That’s why the resistances on the branches with current generators do not appear in the expression of the total equivalent conductance.

See also

• Analysis of resistive circuits

Lemon is an LALR parser generator for C or C++. It does the same job as GNU bison and yacc. But lemon is not another bison or yacc clone. It uses a different grammar syntax which is designed to reduce the number of coding errors. Lemon also uses a parsing engine that is both reentrant and thread-safe. Furthermore, Lemon implements features that can be used to eliminate resource leaks, making it suitable for use in long-running programs such as graphical user interfaces or embedded controllers.

Lemon was written by Dr. Richard Hipp and resides in the public domain.

External

links

• The Lemon Parser Generator
• Calculator with Lemon and Lex in C++ Example

Cushman Dam No. 2 is a hydroelectric dam on the North Fork of the Skokomish River in Mason County, Washington, United States, forming Lake Kokanee. Built in 1930, its three 27,000 kilowatt generators provide 233 million kilowatt-hours annually to the Tacoma Power system.

See also

• Cushman Dam No. 1

Epydoc is a documentation generator that renders its own lightweight markup language Epytext for Python documentation strings. As opposed to freeform Python docstrings, reStructured Text (both also supported) and other markup languages for docstrings, Epytext supports linking between different pieces of documentation.

There are several tools for rendering Epytext. Most commonly, the epydoc program is used to render Epytext as a series of HTML documents for display on the Internet, or as a PDF document for printing. Epydoc also supports viewing the rendered documentation within Python using a GUI. The syntax is uncomplicated enough for the programmer to read the raw Epytext docstrings embedded in the source code directly.

See also

• Comparison of documentation generators

External link

• Epydoc website

‘Tohatsu Corporation’ of Tokyo, Japan, was founded in 1932. It manufactures and sells outbo