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Topic: Linear system of divisors

	Linear system - Wikipedia, the free encyclopedia (Site not responding. Last check: 2007-09-07)
		For time-invariant systems this is the basis of the impulse response or the frequency response methods (see LTI system theory), which describe a general input function x(t) in terms of unit impulses or frequency components.
		Typical differential equations of linear time-invariant systems are well adapted to analysis using the Laplace transform in the continuous case, and the Z-transform in the discrete case (especially in computer implementations).
		A common use of linear models is to describe a nonlinear system by linearization.
	en.wikipedia.org /wiki/Linear_system (246 words)

	Linear system of divisors - Wikipedia, the free encyclopedia
		A linear system in general is part of, but not necessarily the whole of, an equivalence class for linear equivalence.
		Such classes are parametrised by a projective space, and the definition of a linear system is as the divisors corresponding to a linear subspace of that projective space.
		Linear systems are still at the heart of contemporary algebraic geometry; but they are typically introduced by means of the ample line bundle language.
	en.wikipedia.org /wiki/Linear_system_of_divisors (595 words)

	Linear Equivalence of Divisors
		If C is a curve defined over a finite field, then this returns an abelian group isomorphic to its divisor class group, a map of representatives from the class group to the divisor group and the homomorphism from the divisor group onto the class group.
		If D is a divisor on C then colloquially speaking the Riemann--Roch space L(D) is the finite dimensional vector subspace of the function field of C consisting of functions with poles no worse that D (and at least as many zeros as the negative part of D if D is not effective).
		This is the map determined by (a basis of the) Riemann--Roch space of the canonical divisor K_C.
	www.umich.edu /~gpcc/scs/magma/text1033.htm (1090 words)

	[No title] (Site not responding. Last check: 2007-09-07)
		An electromagnetic system for the measurement of relative positions is a transducer that will convert a relative physical position and angular rotation between two bodies to a signal that can be interpreted as their relative po- sition and rotation.
		A system for position measurement according to claim 5-6, c h a r a c t e r i z e d in that the second transmission coil comprises a return conductor placed at the said center-line.
		A system for position measurement according to claims 1-8, c h a r a c t e r i z e d in that the first detector comprises a first and a second detector coil, the latter being displaced by half the width of the pat- tern of the first transmitter coil.
	www.wipo.int /cgi-pct/guest/getbykey5?KEY=00/02013.000113&ELEMENT_SET=DECL (4320 words)

	First Steps in Numerical Analysis (Site not responding. Last check: 2007-09-07)
		In simple cases, there are two or three variables; in complex systems (for example, in a linear model of the economy of a country) there may be several hundred variables.
		A linear system of n equations in n variables with coefficient matrix A and non-zero constants vector b has a unique solution, if and only if the determinant of A is not zero.
		Mathematically speaking, it should be clear to the student that performing elementary operations on a system of linear equations leads to equivalent systems with the same solutions.
	kr.cs.ait.ac.th /~radok/math/mat7/step11.htm (1267 words)

	[No title]
		Finally, a criterion is given for reachability of the abstract systems introduced, giving thus a unified proof of known reachability results for discrete-time, continuous-time, and delay-differential systems.
		Systems will be defined as interconnections of a basic systemo - e.g., an integrator, unit delay, or any fixed linear system - with coefficients in a fixed operator ring - representing themselves lumped or distributed elements.
		A system 2: is said to be of minimal rank when it has smallest rank among all Z with the same result.
	www.math.rutgers.edu /~sontag/FTP_DIR/finitary.txt (3457 words)

	A New Program for Computing the P-Linear System Cardinality that Determines the Group of Weil Divisors of a Zariski ...
		Previously an algorithm and associated computer program for determining the group of Weil divisors of a normal Zariski surface, Xg, given by zp=g(x,y), where p>0 is the characteristic of a fixed algebraically closed field, k, containing g(x,y), has been presented.
		The algorithm generates a p-linear system of equations that has a set of solutions isomorphic to the divisor class group of the surface.
		The divisor class group, which is an abelian group and a geometric invariant, assists in the classification of algebraic surfaces over a fixed algebraically closed field.
	library.wolfram.com /infocenter/Articles/1039 (251 words)

	Linear system - TheBestLinks.com - Algebraic geometry, Continuous function, Differential equation, Digital signal ... (Site not responding. Last check: 2007-09-07)
		In mathematics, automatic control and digital signal processing, a linear system is a model comprising a system of linear functions such that the behaviour of the resulting system can be described as a sum of the linear parts, as opposed to nonlinear systems, which may contain nonlinear functions.
		The mathematical properties of linear systems will typically include differential equations, which make them fit for analysis using the laplace transform in the continuous case, and Z-transform in the discrete case (especially in computer implementations).
		See also: linear system of divisors in algebraic geometry.
	www.thebestlinks.com /Linear_system.html (168 words)

	Monocosm: a linear solution to the effective four-dimensionality problem, a topos-theoretic look at the foundations of ...
		Given two systems X and Y, we can consider a system Z (the union of X and Y) whose states are all states of X and all states of Y.
		For two systems X and Y with common states there is a system Z (the intersection of X and Y) whose states are their common states.
		Two systems interact if states of one system depend on states of the other one, which is described as a function in set theoretical terms.
	home.netcom.com /~trifonov (2849 words)

	Divisors
		To any ideal $I$ in the homogeneous coordinate ring $S_X$ of $X$ we associate the effective divisor that is the sum of the pure codimension $1$ components of $I$, each taken with the multiplicity it has in the primary decomposition of $I$.
		A divisor $D$ is principal iff $L(D)$ has dimension one, and the zero locus of its generator is the empty set.
		We wish to compute homomorphisms from the canonical module into $S_X$, and take the divisor whose first ideal is the image of a homomorphism of non-negative degree, and whose second ideal is an arbitrary nonzero element of $S_X$ whose degree is equal to the degree of the homomorphism.
	www.math.umn.edu /systems_guide/Macaulay2/html/0585.html (2642 words)

	History of Mathematics - The First Mathematicians
		The study of linear and quadratic equations led to form of primitive numerical algebra.
		The Babylonian system of writing was called cuneiform and was based on a series of straight lined symbols.
		However, a drawback of this system is the lack of a proper 0.
	members.aol.com /bbyars1/first.html (673 words)

	ABSTRACT ALGEBRA ON LINE: Integers
		Any two nonzero integers a and b have a greatest common divisor, which can be expressed as the smallest positive linear combination of a and b.
		Moreover, an integer is a linear combination of a and b if and only if it is a multiple of their greatest common divisor.
		The greatest common divisor of two numbers can be computed by using a procedure known as the Euclidean algorithm.
	www.math.niu.edu /~beachy/aaol/integers.html (950 words)

	sec1.html
		An attempt to generate in a computer-algebra system a substantial part of this table, as well as extend it further, faces several complications, including the following.
		In the first stage we start from an integrand symbolically factored into possibly complex linear factors, permitting explicit formulas for reduction by one-parameter recurrence relations to a set of basic integrals somewhat different from the classical ones.
		On the other hand an integrand containing only linear factors with symbolic coefficients can be integrated in terms of canonical R-functions with no assumptions about the numerical values of the symbols; for this purpose Legendre's canonical forms are unsuitable.
	www.getnet.com /~cherry/tthgold/jsc/sec1.html (974 words)

	The Banyan--Sharon Grant
		As their system developed, the clay tablets were not merely places to record numbers of livestock and merchandise but we find computational tables and calculations of areas.
		This sexagesimal, base 60 system, probably was an attempt to unify their systems of measure.
		Not only was their influence great during their time, but to their credit they left behind a legacy of value-placed mathematics, measurement systems still in place today, as well as a legal code still studied in law schools around the globe.
	depts.clackamas.cc.or.us /banyan/1.2/grant.htm (1340 words)

	Citebase - On Shokurov's Log Flips: The 3-dimensional Case
		The main idea is to choose a good reduced Cartier divisor H on Z such that it contains all singularities of Z and sin gularities of the push down of the boundary on Z. And moreover that the components of ∗ H on any model W of Z generate the Neron-Severi group of W.
		DW = i=1 di Di, such that Di is a divisor on W, is the trace of D on W where W is a birational model of Y.
		The bounded family in the conjecture corresponds to that bounded family of divisors, because each of those divisors is free on a model depending on the divisor.
	www.citebase.org /cgi-bin/citations?id=oai:arXiv.org:math/0303210 (3698 words)

	Mathematics Department Courses (Site not responding. Last check: 2007-09-07)
		Topics: system of linear equations in two or more variables, trigonometry of the right triangle, radicals, the system of complex numbers, graphs of conic sections, and graphs of trigonometric functions.
		Topics: linear inequalities in one variable, graphic and algebraic solutions of simultaneous linear equations, geometry and topology, probability, statistics, computers, and calculators.
		The student will find the number of divisors of a natural number, the sum of the divisors, the product of the divisors, and the means of the divisors; become acquainted with perfect, multiple perfect, amicable and sociable numbers; analyze various theorems related to perfect numbers; study Euler's function; solve simple diophantine equations; and study congruences.
	www.hostos.cuny.edu /oaa/mat/courses.htm (1112 words)

	Abstracts
		The theme is that arbitrary big line bundles display a surprising number of properties analogous to those of ample divisors.
		One offshoot of this new approach is that one can solve a large system of equations by finding the solution components of its subsystems and then intersecting these.
		It also allows one to find the intersection of two components of the two possibly identical polynomial systems, which is not possible with any previous numerical continuation approach.
	mathnt.mat.jhu.edu /JAMI/jami2004/Abstracts.htm (324 words)

	[No title] (Site not responding. Last check: 2007-09-07)
		Cartier divisor $D$) is numerically equivalent to $0$ iff one has $C \cdot D = 0$ for all Cartier divisors $D$ (resp.
		Since a divisor whose ideal sheaf is generated by its global sections is numerically effective, one has $\tilde{P} (Z/X) \subset P(Z/X)$.
		The linear system ${\cal F}_{0}$ contains the pencil generated by ${\cal C}_{0}$ and $3L'$ where $L'$ is the tangent line to ${\cal C}_{0}$ at $Q_{1}$.
	home.imf.au.dk /esn/preprints/045 (2038 words)

	Stony Brook Math Calendar
		In this talk, after a brief introduction to Prym varieties and their theta divisors, I will discuss a theorem for Prym varieties which is analogous to the Riemann singularity theorem for Jacobians.
		In many contexts in complex projective geometry it is of interest to produce an irreducible element of a linear system.
		Bertini's classical second theorem describes the linear systems for which this is impossible, i.e.
	www.math.sunysb.edu /cal/scott.php?LocationID=1&Date=2004-10-01 (800 words)

	Introduction to Maple
		In this tutorial, we discuss the general properties of a computer algebra system as Maple and illustrate some of the basic commands.
		A computer algebra system is a program that will perfom mathematical calculations in exact, symbolic form.
		From MacKichan Software, Inc. : "A computer algebra system is a math engine that helps you to quickly perform the symbolic computations fundamental to algebra, trigonometry, and calculus: evaluating, factoring, combining, expanding, and simplifying terms and expressions containing integers, fractions, and real and complex numbers.
	archives.math.utk.edu /mathtech/intro (588 words)

	New Page 1
		Application of the Theory of Matrices to the Investigation of Systems of Linear Differential Equations.
		Linear Least Squares with Linear Equality Constraints Using a Basis of the Null Space.
		Linear Algebra for Signal Processing, IMA Volumes in Mathematics and Its Applications, Springer-Verlag, New York.
	www.cs.cornell.edu /cv/Books/GVL/MCRefs.htm (1541 words)

	Inferno's COLOUR(6)
		The implementation supports only pixel sizes that are either divisors or multiples of 8 bits.
		Properly gamma-corrected displays with adequate low-intensity resolution pack the high-intensity parts of the colour cube with colours whose differences are almost imperceptible.
		Finally, the right value for gamma correction is determined in part by the characteristics of the physical display device, and correction should be done on output.
	www.vitanuova.com /inferno/man/6/colour.html (861 words)

	[No title] (Site not responding. Last check: 2007-09-07)
		Barnett, Matrices, polynomials and linear time-invariant systems, IEEE Trans.
		Emre and L.M. Silverman, New criteria and system theoretic interpretations for relatively prime polynomial matrices, IEEE Trans.
		H.A. Nour-Eldin, A new stability criterion for linear stationary sampled-data systems, Sci.
	www.elsevier.com /homepage/sac/cam/mcnamee/10.htm (4459 words)

	MAT 091 Course Guideline (Site not responding. Last check: 2007-09-07)
		Topics include the real number system and operations with real numbers and algebraic expressions, linear equations and inequalities, polynomials, factoring, and introduction to quadratic equations.
		Story problems appear as a main topic under Linear Equations; they should, however, be integrated into the course whenever appropriate.
		be able to graph linear equations with two variables in the rectangular coordinate system.
	rock.uwc.edu /facultypages/galexand/devmath/091Guide.htm (251 words)

	[No title]
		We present the argument in a manner such that precalculus level mathematics is sufficient for understanding (and enjoying) the introductory arguments, while elementary calculus and linear algebra are sufficient prerequisites for much of the paper.
		Then the expected number of real zeros of the system is $$\sqrt{\prod_{k=1}^m d_k}.$$ The result has also been generalized to underdetermined systems of equations \cite{Ko1}.
		This number is called the {\it degree} of the embedding (or of the {\it complete linear system of divisors}, if we wish to emphasize the intersections).
	www.ams.org /bull/pre-1996-data/199501/199501001.tex.html (10717 words)

	Rational Solutions of Singular Linear Systems - Mulders, Storjohann (ResearchIndex) (Site not responding. Last check: 2007-09-07)
		Abstract: A deterministic algorithm is presented for computing a particular solution to a linear system of equations with polynomial coefficients.
		Given an A 2 F [x] n\Thetam and b 2 F [x] n, where F is a field, the algorithm will either return a particular solution v 2 F (x) m to the system Av = b or determine that the system is inconsistent.
		The cost of the algorithm is O((n +m)r 2 d 1+ffl) field operations from F, where r is the rank of A and d \Gamma 1 is a bound for the degrees of...
	citeseer.ist.psu.edu /322324.html (497 words)

	Graduate Course Descriptions
		Theorems on stability and instability in terms of eigenvalues of the linearized system.
		Some special subjects of study which may be included are: the role of the condition number in numerical analysis as a complexity measure, linear programming over the rationals and reals, the location of zeros of systems of polynomial equations in n-variables, dynamical systems related to numerical algorithms, algebraic complexity theory and topological lower bounds.
		Linear algebra and a first course in ODEs (one that includes linear stability implies stability for systems).
	www.math.toronto.edu /graduate/courses/descriptions.html (4174 words)

	(WO 00/02013) POSITION MEASUREMENT SYSTEM (Site not responding. Last check: 2007-09-07)
		The first inductive system comprises a transmitting coil and a first detector, with the attribute that the pattern of conductors that form the coil extends along a longitudinal axis.
		A second inductive system comprises a second transmitting coil and a second detector, with the attribute that the coil extends essentially in the longitudinal direction.
		Using said detectors, it is possible to accurately determine the linear and/or angular position(s) of two bodies relative to each other.
	wipo.int /cgi-pct/guest/getbykey5?KEY=00/02013.000113&ELEMENT_SET=DECL (176 words)

	Math Forum - Ask Dr. Math Archives: College Linear Algebra (Site not responding. Last check: 2007-09-07)
		Converting an arbitrary vector to a transformation matrix for a left- handed coordinate system.
		Explaining Cramer's Rule by applying it to a system of equations.
		Given an autonomous system defined by a pair of differential equations, I know how to find critical points and the Jacobian matrix, but how do I determine if the critical point is a saddle point?
	mathforum.org /library/drmath/sets/college_linearalg.html (881 words)

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