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	Constant - Wikipedia, the free encyclopedia
		Constants are by convention usually denoted by lower-case letters from the beginning of the English alphabet, such as a, b, and c.
		In a polynomial (or a generalisation of a polynomial, such as a Taylor series or Fourier expansion), the constant term is associated to the exponent zero.
		For some purposes, the constant is taken to be the value of f(0), but this depends on the function being defined at 0; it would not work for f(x)=1-1/x.
	en.wikipedia.org /wiki/Constant (539 words)

	Constant - LearnThis.Info Enclyclopedia (Site not responding. Last check: 2007-10-07)
		Constants are usually denoted by lower-case letters from the beginning of the English alphabet, such as a, b, and c.
		In a polynomial (or a generalisation of a polynomial, such as a Taylor expansion or Fourier expansion), the constant term is associated to the exponent zero.
		There is only one function with that domain (given any codomain), the empty function, and any formula can be used to define the empty function, since the formula won't apply to anything and will therefore never be wrong.
	encyclopedia.learnthis.info /c/co/constant.html (713 words)

	Constant function -- Facts, Info, and Encyclopedia article (Site not responding. Last check: 2007-10-07)
		Constant functions can be characterized with respect to (additional info and facts about function composition) function composition in two ways.
		Every constant function whose (Territory over which rule or control is exercised) domain and (additional info and facts about codomain) codomain are the same is (additional info and facts about idempotent) idempotent.
		Every constant function between ((mathematics) any set of points that satisfy a set of postulates of some kind) topological spaces is (additional info and facts about continuous) continuous.
	www.absoluteastronomy.com /encyclopedia/c/co/constant_function.htm (294 words)

	Locally constant function - Wikipedia, the free encyclopedia
		In mathematics, a function f from a topological space A to a set B is called locally constant, iff for every a in A there exists a neighborhood U of a, such that f is constant on U.
		To be more definite, the locally constant integer-valued functions on X form a sheaf in the sense that for each open set U of X we can form the functions of this kind; and then verify that the sheaf axioms hold for this construction, giving us a sheaf of abelian groups (even commutative rings).
		This can be referred to a constant sheaf, meaning exactly sheaf of locally constant functions taking their values in the (same) group.
	en.wikipedia.org /wiki/Locally_constant_function (343 words)

	PlanetMath: constant function (Site not responding. Last check: 2007-10-07)
		The composition of a constant function with any function (for which composition is defined) is a constant function.
		A constant map between topological spaces is continuous.
		This is version 2 of constant function, born on 2003-09-11, modified 2003-09-12.
	planetmath.org /encyclopedia/ConstantMapping.html (66 words)

	[No title]
		Functions f(x) = C are antiderivatives of the function 0, where C is some constant number.
		The antiderivatives of the constant function 0 is a constant number.
		C is the antiderivative of the constant function 0.
	www.mtholyoke.edu /~mpeterso/classes/math101/jitt25ans.html (414 words)

	Functions
		Functions in the GCL are rules for taking objects of specified data types, and using them to construct and return an object of a (possibly different) specified data type.
		Functions return a value, which may in turn be used as a parameter to another function call, allowing more complex computations to be expressed.
		Since a function may have multiple signatures, it is conceivable that a function call might be ambiguous, in the sense that its parameters match more than one signature for that function.
	econweb.tamu.edu /gambit/doc/manual-0.97.0.6/x706.html (2528 words)

	XEXPR - XML Expression Language (Site not responding. Last check: 2007-10-07)
		This function is used to signal early exit from a function.
		Constant functions are provided as a way to bind constants to a function.
		In addition, the content of the constant functions is limited to the valid syntactic structures of the constant type.
	www.w3.org /TR/xexpr (2769 words)

	[No title]
		A function is specified as const both in its declaration and in its definition by inserting the keyword const after the function's parameter list, and, in the case of the function definition, before the left brace that begins the function body.
		When an operator function is implemented as a member function, the leftmost operand (or the only operand) must be a class object (or a reference to a class object) of the operator's class.
		Operator member functions are called only when: The left operand of a binary operator is specifically an object of that class, or The single operand of a unary operator is an object of that class.
	www.cecs.csulb.edu /~pompei/cecs475/lect_int.doc (3058 words)

	math lessons - Arbitrary constant of integration
		If a function f is defined on an interval and F is an antiderivative of f, then the set of all antiderivatives of f is given by the functions F(x) + C, with C an arbitrary constant.
		Consequently, the kernel of d/dx is the space of all constant functions.
		For example, if we were to ask for functions defined on the union of intervals [0,1] and [2,3], and if a were 0, then it would not be possible to integrate from 0 to 3, because the function is not defined between 1 and 2.
	www.mathdaily.com /lessons/Arbitrary_constant_of_integration (953 words)

	Write-up 1 (Site not responding. Last check: 2007-10-07)
		The greatest integer function is also often called the floor function, which is why the brackets only have the bottom hooks, like a supporting floor.
		Similar to the constant b in the linear function, c shifts the graph up or down as it changes the y-intercept point, as can be seen in these graphs.
		Notice that the constants within the greatest integer function brackets each affect the graph in two ways and their responsibilities match those of the linear function’s constants and the greatest integer function’s constants a and d.
	www.auburn.edu /~byrddem/4040/writeup1 (3122 words)

	SCATMECH: dielectric_function
		For the case of a table of values, the optical constant is linearly interpolated between the tabulated points.
		Function which returns the optical_constant of the material at wavelength l.
		This function forces the material to be non-absorbing by setting the imaginary part of the index of refraction to zero.
	physics.nist.gov /Divisions/Div844/facilities/scatmech/html/dielfunc.htm (484 words)

	SCATMECH: dielectric_stack
		It provides member functions that return the reflection and transmission coefficients of the stack.
		This example represent four layers, the first layer (nearest to substrate) having optical constants given in a file named silicon and thickness 2.00 (in whatever units the calculations are carried out).
		Function that adds a new layer on top of existing layers, with a specified epsilon and thickness.
	physics.nist.gov /Divisions/Div844/facilities/scatmech/html/dielstack.htm (667 words)

	function (Site not responding. Last check: 2007-10-07)
		The inverse of a function, a mapping from the function's outputs to its inputs, may be a relation rather than another function.
		A function which takes no arguments is a constant function, or simply, a constant.
		Since a function must return the same value for each input and the input cannot change (since it has no arguments), it must always return the same value.
	www.nist.gov /dads/HTML/function.html (294 words)

	Anti-derivatives
		The difference in our two examples is that in the first case the domain of the function g is an interval, and in the second case it was not.
		Certainly one part of this theorem we already knew: If f is a constant function on an interval then f is continuous, f has a derivative, and the derivative is everywhere in the interval.
		The interval part is important, as we could have a function whose domain is only the positive integers, and constant, but it cannot be differentiated.
	www.uwm.edu /~ericskey/226S99/CLN/node21.html (379 words)

	unit03-sect03-les01-lessona (Site not responding. Last check: 2007-10-07)
		You met the constant function in earlier mathematics courses.
		The basic shape of the constant function is a horizontal line.
		To construct the graph of any constant function we can simply draw a horizontal line through one point that satisfies the function.
	www.cdli.ca /courses/math3103/unit03/section03/lesson01/3-lesson-a.htm (341 words)

	Math Forum - Ask Dr. Math (Site not responding. Last check: 2007-10-07)
		Date: 11/08/2001 at 19:07:59 From: Masha Albrecht Subject: Degree of constant function Dear Dr Math, I teach at Galileo High School in San Francisco and we teachers are stumped on this question: First, we agree that F(x) = 1 is a polynomial function of degree 0.
		It's important to distinguish between a discontinuity like that of x^-1 at x = 0, where the function is actually undefined and the discontinuity is not removable, and one like x^0, where it is only indeterminate and can be removed by a proper definition.
		Even if there were no consensus on doing this with 0^0 in general, there would be no problem with calling a constant function a degree-zero polynomial, because the difficulty is so easily dealt with.
	mathforum.org /library/drmath/view/54602.html (314 words)

	PHP: Constants - Manual
		A valid constant name starts with a letter or underscore, followed by any number of letters, numbers, or underscores.
		Constants and (global) variables are in a different namespace.
		When you define a constant, it becomes fixed at that point and is immutable.
	www.php.net /manual/en/language.constants.php (1673 words)

	Non-constant Function (Site not responding. Last check: 2007-10-07)
		Take the 'log' of both sides gives: log{[f(x)^a]} = log{af(x)} Using the properties of the 'log' function* that: log{x^a} = a* log{x} and log{ax} = log {a} + log{x} gives: alog{f(x)} = log{a} + log{f(x)} Subtracting log{f(x)} from both sides gives: a*log{f(x)} - log{f(x)} = log{a}.
		If a is a constant, then f(x) is a constant.
		In this problem, the only constant value of a that will work for a non-constant f(x) is a=1.
	www.newton.dep.anl.gov /askasci/math99/math99101.htm (410 words)

	CSE 150 Lecture Notes, February 3, 2003
		The function-symbol father is the name of a function that maps semantic objects to semantic objects.
		This means that if we have the constant 13 and the function father, then father(13) is a well-formed term that designates some object.
		When you write down knowledge formally, the real knowledge is in the interrelationships between predicates and functions, not in the names of the predicates and functions, because constant-symbols, function-symbols, and predicate-symbols are uninterpreted.
	www-cse.ucsd.edu /~elkan/150/feb03.html (633 words)

	constant function (Site not responding. Last check: 2007-10-07)
		Definition: A function that always gives the same value.
		Note: A 0-ary or nullary function that is pure (no state or interactions with external variables) must be a constant function.
		Paul E. Black, "constant function", from Dictionary of Algorithms and Data Structures, Paul E. Black, ed., NIST.
	www.nist.gov /dads/HTML/constantfunc.html (91 words)

	[No title]
		Normally, constant addresses which are the sum of a `symbol_ref' and an integer are stored inside a `const' RTX to mark them as constant.
		For example, suppose an address that is equal to the sum of a register and a constant is used twice in the same basic block.
		X is the RTL expression for the constant to output, and MODE is the machine mode (in case X is a `const_int').
	www.mit.edu /afs/sipb/project/bounds/info/gcc.info-23 (6868 words)

	Math Forum - Ask Dr. Math (Site not responding. Last check: 2007-10-07)
		Two functions are said to be orthogonal over a given interval if integrating their product (over that interval) equals zero.
		Thus the "right angle" is not seen in the graphs of the functions, but in an infinite-dimensional space, each "point" of which represents a function.
		Now, the zero function will be orthogonal to all functions in exactly the same sense that the zero vector is orthogonal to all vectors; the dot product is zero because the length is zero, but it really says nothing about the direction of the other vector, since the zero vector has no direction.
	mathforum.org /library/drmath/view/52141.html (333 words)

	Physics Help and Math Help - Physics Forums - Derivative of constant function - proof
		Yep,you're right.Differentiation should always be looked upon as process of evaluating a limit from a ratio.When the numerator is zero,as a difference between 2 identical constants,then the limit is identically zero,being a ratio bewteen zero and a positive/negative quantity,very,very,very small,but still nonnull.
		The formula for the derivative of a constant is the most simple,i guess u know that.In all other cases,u really need to compute that limit involved by the definition.
		For any linear function, its graph is a straight line- it is its own "tangent line" and so its derivative is a constant: its slope.
	www.physicsforums.com /printthread.php?t=57525 (594 words)

	Graph of parabola
		It is called a constant function, because to every value of x there corresponds the same value of y: 3.
		In the absolute value function, the negative values of y in the identity function are reflected into the positive side.
		The graph of the square root function is related to y = x².
	www.themathpage.com /aPreCalc/graph-of-parabola.htm (461 words)

	Elasticity of Substitution
		This expression for the elasticity of substitution in the constant returns to scale case was precisely the form in which it was first introduced by John Hicks (1932: p.117, 245).
		Thus the elasticity of substitution of a constant returns to scale production function can be expressed as the elasticity of output per capita with respect to the marginal product of labor.
		A special class of production functions, known as Constant Elasticity of Substitution (CES) production functions, were introduced by Arrow, Chenery, Minhas and Solow (1961) (thus it is also known as the ACMS function).
	cepa.newschool.edu /het/essays/product/elastic.htm (2257 words)

	072MVT.LBZ
		If the function is not a constant, we can use the fact that differentiable functions are automatically continuous in combination with the theorem I showed on Monday to claim that f(x) must have at least one max or min between a and b.
		be a differentiable function on an interval [a,b].
		This function will be the function whose graph is the line connecting the points (a,f(a)) and (b,f(b)).
	www.lawrence.edu /fast/greggj/math140/072/072MVT.html (689 words)

	Admissible prime constellations
		From these definitions it follows that s(x) is a piecewise-constant function (continuous on the right) that jumps from k-1 to k when x reaches l(k).
		where C(0,a_2,...,a_k) is a non-zero constant for admissible constellations, to reduce the expected size of the first x that makes P(x;0,a_2,...,a_k) nonzero, it is crucial to either make C(0,a_2,...,a_k) as large as possible or to make k as small as possible.
		It also appears that the absolute value of the error is bounded from above by the square root of k multiplied by a constant close to one (shaded area), at least for small values of k.
	www.ieeta.pt /~tos/apc.html (1090 words)

	[Gs-code-review] Fix for SF bug "[ #228714 ] ShadingType 1 can mis-identify the function as constant" - ...
		For sampled functions this may be done analytically.
		Evaluate the function for each pixel in device space, but "tune" the > function evaluation logic to be fast.
		Convert the constant color to device color, and fill mesh with regular 'fill'.
	www.ghostscript.com /pipermail/gs-code-review/2001-March/000399.html (652 words)

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