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Topic: Fixed point (mathematics)

	Egwald Mathematics — Geometry, Linear Algebra, Optimal Control, Statistics and Econometrics, Nonlinear Dynamics, ...
		In Hopf bifurcations, a stable limit cycle emerges — growing from a fixed point (supercritical Hopf bifurcation), or an unstable limit cycle disappears — diminishing towards a fixed point.
		Fixed points occur at the intersection(s) of the system's nullclines.
		Use index theory to detect the presence and characteristics of fixed points.
	www.egwald.ca /mathematics (1464 words)

	Fixed Point Math
		The idea behind fixed point math is that we pretend that there is a decimal point.
		Addition and subtraction work are basically the same with fixed point numbers are they do with integer or floats.
		Fixed point math is something that has applications in many, many areas of computer graphics.
	members.aol.com /form1/fixed.htm (461 words)

	Fixed point (mathematics) (Site not responding. Last check: )
		In mathematics, a fixed point (sometimes shortened to fixpoint) of a function is a point that is mapped to itself by the function.
		In graphical terms, a fixed point means the point (x, f(x)) is on the line y = x, or in other words the graph of f has a point in common with that line.
		Attractive fixed points are a special case of a wider mathematical concept of attractors.
	www.guideofpills.com /Fixed_point_%28mathematics%29.html (731 words)

	Search Results for "Mathematics"
		...e, in mathematics, in mathematics, irrational number occurring widely in mathematics and science, approximately equal to the value 2.71828; it is the base of natural,...
		...proof, in mathematics, in mathematics, finite sequence of propositions each of which is either an axiom or follows from preceding propositions by one of the rules...
		...cone, in mathematics, or conical surface, in mathematics, surface generated by a moving line (the generator) that passes through a given fixed point (the vertex)...
	www.bartleby.com /cgi-bin/texis/webinator/sitesearch?query=Mathematics&filter=colReference (265 words)

	Doing It Fast, fixed point arithmetic techniques and fast 3d transforms (Site not responding. Last check: )
		A fixed point number is called fixed point because the decimal point (I'm going to use decimal numbers in the first part of this discussion) is in a fixed location in the number.
		For example, you might have a table of sines in 2.30 binary fixed point format (in a binary format the numbers are the number of bits, not the number of digits) that you want to multiply by numbers in an 18.14 format.
		The integer square root of a fixed point number divided by the square root of 2 to the F power where F is the number of bits of fraction in the fixed point number is the square root of the original fixed point number.
	www.gameprogrammer.com /4-fixed.html (4813 words)

	Fixed Point Mathematics Library for Z180/64180 CPUs
		The fixed point number format is 8.24 bits: There are 8 bits to the left of the decimal point, and 24 to the right of it.
		For this reason, this calling convention was dropped halfway through the project and all the fixed point mathematical functions were rewritten to follow a new calling convention, designed specifically to overcome this particular problem while providing the same facilities to the programmer.
		The fixed point function then uses a subroutine named lightweight_marshal_parameters_arity_2 (or _arity_1 for single parameter functions) to convert the indexes and variable area base pointer to the actual pointers to variables within the variable area.
	www.jwhitham.org.uk /em180/mcp (1534 words)

	SPHERE Scripting for Dummies
		Obviously one of the largest limitations to the SPHERE language is its lack of ability to use decimal points, and the agony involved with that.
		The solution is to use fixed point math, which is a type of math in which a certain portion of each number is dedicated to the decimal places, and a certain part is dedicated to the integer part of the number.
		When a mathematical operation is completed on the current value, the result of that operation becomes the new current value.
	www.cs.rit.edu /~djr7581/view.php?file=decimal_points (917 words)

	The Brouwer-Kakutani Fixed Point Theorem
		That is, self-replicating molecules are an instantiation of the Fixed Point Theorem where the map is the one determined by the laws of Physics and Chemistry.
		Evolution is evidently the process of moving to ever stabler fixed points, working against the force of Entropy (the destroyer) which leads back to decay and disorder.
		Nevertheless, such a Fixed Point does seem to be a point of attraction of the Advance of Civilization, so the best way for an individual to lead society in that direction is by setting an example that is worthy of imitation.
	underground.musenet.org:8080 /utnebury/fixed.point.html (1029 words)

	Mathematics
		Mathematics 17, "An Introduction to Mathematics Beyond Calculus", is a course designed for students interested in learning about some of the aspects of mathematics not usually encountered in the first years of mathematical studies.
		In the second course, Mathematics 2, the study of calculus will be continued so that by the end of the sequence the students will have been introduced to the algebra and calculus of the exponential and logarithm functions and the trigonometric functions and to differential equations.
		Prerequisite: Mathematics 8, or Mathematics 3 and 6.
	www.dartmouth.edu /~reg/courses/desc/math.html (7962 words)

	Oberstar Consulting - Whitepapers
		Fixed Point Representation and Fractional Math - The purpose of this paper is to investigate the issues relating to algorithm implementation utilizing fixed-point rather than floating-point mathematics.
		Issues relating to sampling rate, fixed point mathematics, and signal reconstruction were observed and investigated.
		Issues relating to algorithm optimization, fixed point mathematics, sampling rate, and signal reconstruction were observed and investigated.
	www.superkits.net /whitepapers.htm (352 words)

	News \| TimesDaily.com \| TimesDaily \| Florence, AL
		In mathematics, a fixed-point theorem is a result saying that a function F will have at least one fixed point (a point x for which F(x) = x), under some conditions on F that can be stated in general terms.
		Every lambda expression has a fixed point, and a fixed point combinator is a "function" which takes as input a lambda expression and produces as output a fixed point of that expression.
		Every closure operator on a poset has many fixed points; these are the "closed elements" with respect to the closure operator, and they are the main reason the closure operator was defined in the first place.
	www.timesdaily.com /apps/pbcs.dll/section?category=NEWS&template=wiki&text=fixed-point_theorem (470 words)

	Mathematical Programming Glossary Page 2
		For each theorem, X is assumed to be nonempty, f denotes a function from X to X, and F a point-to-set map from X to subsets of X. A fixed point of f is x in X such that f(x)=x.
		A fixed point of F is x in X such that x is in F(x).
		If f is a contractor, it has a unique fixed point, and successive approximation, x^(k+1)=f(x^k), converges to it from any starting point (x^0).
	orion.math.uwaterloo.ca /~hwolkowi/mirror.d/glossary/second.php?page=fixedpts.html (374 words)

	Aristotle and Mathematics (Stanford Encyclopedia of Philosophy)
		From his examples (points and lines for geometry), it would seem that the genus is to be understood loosely as the fundamental entities in the science.
		Mathematical examples: ‘line’ is in the definition of triangle, ‘point’ is in the definition of line.
		The objects studied by mathematical sciences are perceptible objects treated in a special way, as a perceived representation, whether as a diagram in the sand or an image in the imagination.
	plato.stanford.edu /entries/aristotle-mathematics (9432 words)

	fixed-point from FOLDOC (Site not responding. Last check: )
		The fixed point of a function, f is any value, x for which f x = x.
		The fixed point combinator, written as either "fix" or "Y" will return the fixed point of a function.
		Apart from that, fixed-point representation has the advantage of having uniform density, i.e., the smallest resolvable difference of the representation is B throughout the representable range, in sharp contrast to floating-point representations.
	ftp.sunet.se /foldoc/foldoc.cgi?fixed-point (173 words)

	Model of Fixed Point Arithmetic
		For decimal fixed point types, the attribute T'Round may be used to imply explicit conversion with rounding (see 3.5.10).
		A multiplication P * Q of an operand of a fixed point type F by an operand of an integer type I, or vice-versa, and a division P / Q of an operand of a fixed point type F by an operand of an integer type I, are also allowed.
		The possibility of overflow in the result of a predefined arithmetic operation or conversion yielding a result of a fixed point type T is analogous to that for floating point types, except for being related to the base range instead of the safe range.
	www.adapower.com /rm95/RM-G-2-3.html (958 words)

	Fixed Gear Bicycles for the Road
		When you ride a fixed gear, the need to push hard to get up the hills forces you to ride at a higher intensity than you otherwise might.
		The most common use for a flip-flop hub is to have a fixed sprocket on one side, and a single-speed freewheel on the other side.
		The idea is that, most of the time you would ride the fixed gear, but if you found your self far from home and getting tired, or were in unusually hilly terrain, you would turn the wheel around and use the freewheel.
	sheldonbrown.com /fixed.html (5069 words)

	Mathematics Applied to Physics/Engineering
		A problem to minimize (optimization) the time taken to walk from one point to another is presented.
		This applet helps you explore the cycloid which is the curve traced by a fixed point on the circumference of a circle as the circle rolls along a line in a plane.
		This is simple example where mathematics is used in communication systems.
	www.analyzemath.com /appliedmath.html (312 words)

	Geometric Fixed Point Principles - Mathematics and the Liberal Arts
		The Mathematics and the Liberal Arts pages are intended to be a resource for student research projects and for teachers interested in using the history of mathematics in their courses.
		When the mathematical review (MR) number and reviewer are known to the author of these pages, they are given as part of the bibliographic citation.
		One of her examples is her own (apparently new) observation that if one has three circles intersecting in pairs, the three chords joining the points of intersection meet in a point; a proof is given in the article
	math.truman.edu /~thammond/history/FixedPoints.html (254 words)

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