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Page "Homomorphism" ¶ 29
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function and which
This is the primary function of the imagination operating in the absence of the original experiential stimulus by which the images were first appropriated.
But because it is the function of the mind to turn the one into the other by means of the capacities with which words endow it, we do not unwisely examine the type of distinction, in the sphere of politics, on which decisions hang.
It was this fear which explained the development of a priestly caste whose function in society was to mollify and appease the angry deities.
A primary function is the operation of a Government Bid Center, which receives bids daily from the Federal Government's principal purchasing agencies.
Furthermore, one can find a neighborhood of Q in which the difference function is monotone, for since it is analytic it can have only a finite number of extrema in any interval.
The values Af are the ordinary values at Af of a multi-valued function g{t} which has components corresponding to those of f{t}.
Closely related to this function is the fact that the religious system provides a body of ultimate ends for the society, which are compatible with the supreme eternal ends.
Tone languages use for linguistic contrasts speech parameters which also function heavily in nonlinguistic use.
The form of the industry demand function is one which makes quantity demanded vary inversely with the product price, and vary directly with the level of Aj.
The extent to which the public-limit price is raised by a given increase in the basic wage rate is itself a function of three things: the passage of time, the level of GNP, and the size of the wage increase.
We are abstracting from the fact of strikes here, but it should be obvious that the extent to which the public-limit price is raised by a given increase in the basic wage rate is also a function of the show of resistance put up by the industry.
Moreover, whereas in Interstate Commerce Commission parlance `` variable cost '' means a cost deemed to vary in direct proportion to changes in rate of output, in the type of analysis now under review `` variable cost '' has been used more broadly, so as to cover costs which, while a function of some one variable ( such as output of energy, or number of customers ), are not necessarily a linear function.
271 - 307 ) indicate, that the concept of function in sociology has been built up from physiological and biological models, in which the notions of teleology, i.e., metaphysical purpose, are central.
In a properly ordered society the massive force of public law performs the function which in natural law theory ineptly is left altogether to a small voice so often still.
Extreme caution should be used, however, to avoid the conflicting usage of an index word or electronic switch which may result from the assignment of more than one name or function to the same address.
The specification of the objective function of which the optimization is desired.
The objective function, which is to be maximized, is some function, usually piecewise continuous, of the product state.
An optimal policy is an admissible policy Af which maximizes the objective function P.
We thus have an optimal policy which maximizes the expected value of the objective function for a given Af.
As retinal images are conceded to be an integral function of the brain it seems logical to suppose that the nerves, between the inner brain and the eyes, carry the direct drive for cooperation from the various brain centers -- rather than to theorize on the transmission of an image which is already in required location.
A local church which conceives its function to be entirely that of ministering to the conscious desires and concerns of its members tends to look on everything ecumenical as an extra, not as a normal aspect of its own life as a church.
Exceptions are Lambertian surfaces, which scatter radiation in all directions according to a cosine function, so their albedo does not depend on the incident distribution.

function and preserves
Consequently, a function satisfying the Cauchy – Riemann equations, with a nonzero derivative, preserves the angle between curves in the plane.
Hence G is also a transformation group ( and an automorphism group ) because function composition preserves the partitioning of A.
A function which preserves operation should have this property: f ( a + b ) =
This specificity preserves the integrity of other proteins such as hormones, and therefore the biological system continues to function normally.
In addition to being an isomorphism of sets, the logarithm function also preserves certain operations.
In mathematics, a linear map, linear mapping, linear transformation, or linear operator ( in some contexts also called linear function ) is a function between two modules ( including vector spaces ) that preserves the operations of module ( or vector ) addition and scalar multiplication.
In mathematics, an injective function is a function that preserves distinctness: it never maps distinct elements of its domain to the same element of its codomain.
In mathematics, a monotonic function ( or monotone function ) is a function between ordered sets that preserves the given order.
In calculus, a function f defined on a subset of the real numbers with real values is called monotonic ( also monotonically increasing, increasing or non-decreasing ), if for all x and y such that x ≤ y one has f ( x )f ( y ), so f preserves the order ( see Figure 1 ).
In mathematics, a conformal map is a function which preserves angles.
is conformal if and only if it is holomorphic and its derivative is everywhere non-zero on U. If f is antiholomorphic ( that is, the conjugate to a holomorphic function ), it still preserves angles, but it reverses their orientation.
Additionally, in group theory of the 1930s, a meromorphic function ( or simply a meromorph ) was a function from a group G into itself which preserves the product on the group.
In algebra an additive function ( or additive map ) is a function that preserves the addition operation:
A morphism of magmas is a function mapping magma to magma, that preserves the binary operation:
In advanced mathematics, a linear function means a function that is a linear map, that is, a map between two vector spaces that preserves vector addition and scalar multiplication.
Modern English preserves a case distinction for pronouns, but it has conflated the accusative and dative into a single oblique case, the object pronouns him, her, me, etc., which may function either as direct or indirect objects.
In mathematics, more specifically topology, a local homeomorphism is intuitively a function, f, between topological spaces that preserves local structure.

function and addition
Ackermann's three-argument function,, is defined such that for p = 0, 1, 2, it reproduces the basic operations of addition, multiplication, and exponentiation as
One interesting aspect of the Ackermann function is that the only arithmetic operations it ever uses are addition and subtraction of 1.
In addition, if all human hemoglobin were free in the plasma rather than being contained in RBCs, the circulatory fluid would be too viscous for the cardiovascular system to function effectively.
He proposed a reform of the Latin alphabet by the addition of three new letters, two of which served the function of the modern letters W and Y.
Partial application makes it easy to define these functions, for example by creating a function that represents the addition operator with 1 bound as its first argument.
* Keypad-consists of keys used to input numbers and function commands ( addition, multiplication, square-root, etc.
In addition, classes in many languages define an indivisible unit that must be used as a whole — if you want to use a String concatenation function, you must import and compile against all of String.
The addition ( or loss ) of species which are ecologically similar to those already present in an ecosystem tends to only have a small effect on ecosystem function.
This allows one to succinctly express, for example, the successor function as the addition operator partially applied to the natural number one.
In addition to the mass, momentum, and energy conservation equations, a thermodynamical equation of state giving the pressure as a function of other thermodynamic variables for the fluid is required to completely specify the problem.
In addition, there are several genetic disorders that can affect the shape and function of the feet, including a club foot or flat feet.
For example, a ring possesses both addition and multiplication, and a homomorphism from the ring to the ring is a function such that
While almost none of this math goes beyond the basic functions of addition, subtraction, multiplication, and division ( certain obscure and completely optional situations may call for a logarithmic function ), this can seem daunting to newcomers.
In addition, the low-rate mesh supports multicasting, reliable broadcasting, portability support, trace route and energy saving function, and the high rate mesh supports multihop time-guaranteed service.
In addition of performing at games and pep rallies, members function as goodwill ambassadors of the team, participating in corporate, community and charitable events in the Jacksonville metropolitan area where they sign autographs and pose for pictures.
In addition, countercurrent exchange by the vessels carrying the blood supply to the nephron is essential for enabling this function.
Déjacque wrote that: ‘ By government I understand all delegation, all power outside the people ,’ for which must be substituted, in a process whereby politics is transcended, the ‘ people in direct possession of their sovereignty ,’ or the ‘ organised commune .’ For Déjacque, the communist anarchist utopia would fulfil the function of inciting each proletarian to explore his or her own human potentialities, in addition to correcting the ignorance of the proletarians concerning ‘ social science .’"
The addition of long chain soap-like molecules leads to a series of new phases that show a variety of liquid crystalline behavior both as a function of the inorganic-organic composition ratio and of temperature.
In Haskell syntax, "" prepends an element to a list, returns a list without its first element, and uses a specified function ( in this case addition ) to combine corresponding elements of two lists to produce a third.
Other goddesses known to have similar hills are Áine and Grian of County Limerick who, in addition to a tutelary function, also have solar attributes.
In addition to describing the motion of atomic level phenomena, quantum mechanics is useful in understanding some large scale phenomenon such as superfluidity, superconductivity, and biological systems, including the function of smell receptors and the structures of proteins.

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