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Topic: Affine chain

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affine transformations

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	Simplex - Wikipedia, the free encyclopedia
		Such a general simplex is often called an affine n-simplex, to emphasize that the canonical map is an affine transformation.
		Note that each face of an n-simplex is an affine n-1-simplex, and thus the boundary of an n-simplex is an affine n-1-chain.
		The boundary operation commutes with the mapping because, in the end, the chain is defined as a set and little more, and the set operation always commutes with the map operation (by definition of a map).
	en.wikipedia.org /wiki/Simplex (833 words)

	ASCII version of Phys. Rev. A 44, 2730
		Growth processes resulting in self affine interfaces have attracted particular interest during the last few years because of their relevance to a number of phenomena of practical importance, including thin film growth by vapor deposition, two phase viscous flow in porous media, formation of biological patterns, and sedimentation of granular materials (see, e.g., Refs.
		A single valued standard self affine function h (x) satisfies the relation h (x) apeq lambda^{-H}h (lambda x), where lambda is a parameter and H is the Houmllder or roughness exponent.
		These self affine functions are obtained by plotting the displacement h (x) of a particle randomly walking in one dimension as a function of time (denoted here by x).
	www.nd.edu /~alb/paper/PRA44_2730 (2199 words)

	Simplex -- Facts, Info, and Encyclopedia article (Site not responding. Last check: 2007-10-15)
		Such a general simplex is often called an affine n-simplex, to emphasize that the canonical map is an ((mathematics) a transformation that is a combination of single transformations such as translation or rotation or reflection on an axis) affine transformation.
		Note that each face of an n-simplex is an affine n-1-simplex, and thus the (The line or plane indicating the limit or extent of something) boundary of an n-simplex is an affine n-1-chain.
		More generally, a simplex (and a chain) can be embedded into a (A pipe that has several lateral outlets to or from other pipes) manifold by means of smooth, differentiable map.
	www.absoluteastronomy.com /encyclopedia/S/Si/Simplex.htm (1261 words)

	4/18/98 Chapter 2 Polymer Physics
		Birefringence in polymers is a measure of the conformational distribution of chains since it is based on the birefringence of the chain's
		The presence of other chains serves to form an oddly shaped "tube" in which the polymer chain is confined, especially at a single snapshot of time.
		The undeformed chain can be described as a series of subunits of length "a", the tube diameter" which are randomly arranged in space.
	www.eng.uc.edu /~gbeaucag/Classes/Physics/Chapter3.html (1658 words)

	Affine 2D Analogue
		This flow is what all the the literature on affine evolutions claim to be the affine analogue of the curve shortening flow in Euclidean space.
		Now, in affine geometry, the claimed analogue is the functional is affine length and the fastest way to shrink it is the evolution in the affine normal direction which corresponds to an Euclidean curvature deformation in the Euclidean normal direction.
		We have argued that the affine curve evolution is not necessarily the fastest way to shrink the affine perimeter.
	www.cim.mcgill.ca /~mdesco/shape_report/report/node4.html (794 words)

	Algebraic Topology: Homology
		A chain complex (C,d) is a graded Abelian group C with fixed differential d of degree -1.
		A morphism of chain complexes (a chain map) is a morphism of graded Abelian groups that commutes with the differential.
		A chain homotopy from f to g is a homomorphism e : C -> D of degree 1 such that f - g = de + ed.
	www.win.tue.nl /~aeb/at/algtop-6.html (3450 words)

	Phycologia: Identification of Alexandrium affine and A. margalefii (Dinophyceae) using DNA sequencing and LSU ... (Site not responding. Last check: 2007-10-15)
		We report on the identification of A. affine and A. margalefii from Bahia Concepcion, Mexico, by RFLP and DNA sequencing.
		Sequences of the D1-D2 domains of the LSU rDNA of A. affine and A. margalefii were compared with those of 18 other Alexandrium isolates, using maximum likelihood and maximum parsimony analyses.
		Because A. margalefii has not been identified previously in Mexico, and A. affine has only recently been reported, it was important to confirm the identification of these species and to establish linkages to other populations globally.
	www.findarticles.com /p/articles/mi_qa3850/is_200305/ai_n9275996 (1371 words)

	Other works
		A function relating the length of the chain, the amplitude of links and the fractal dimension of the set are obtained.
		In this chapter we study links of a symbolic chain that assigns positive elements to a subset of the natural numbers with integer square roots and negative elements to the rest of them.
		In this chapter we study chains generated with basic stairs which are repeated one after the other.
	math.bu.edu /people/smarotta/Otherworks.htm (1597 words)

	Abstract (Site not responding. Last check: 2007-10-15)
		Instead, each chain uses a different (and smaller) set of dynamic variables: the location of each entanglement, and the number of Kuhn steps in chain strands between entanglements.
		In the language of reptation, the model exhibits chain connectivity, chain-length fluctuations, chain stretching, and tube dilation.
		Because of the affinity assumption and lack of constraint release, the model should be expected to approximate well a linear chain in a matrix of fixed obstacles, and somewhat less accurately a polymer melt.
	www.iit.edu /~schieber/Schieber_Publications11.html (247 words)

	Introduction
		Under assumptions such as the affine deformation of junction points and the additivity of individual strand entropy, the end-to-end distribution fuction directly leads to the network elasticity through either a finite-chain average or a network average [1, 8, 9].
		However, their agreement with experiments is incomplete, and many alternative theoretical models of elasticity have been proposed, ranging from the constrained fluctuation [10] and primitive path [11, 12] to sliplink [13, 14] and tube models [15, 16].
		The gradual breakdown of the affine assumption with increasing strain accounts for the eventual failure of the affine model and the necessity of other alternative ones.
	www.tcm.phy.cam.ac.uk /~ym101/rubber/node1.html (547 words)

	Titles of Talks (Site not responding. Last check: 2007-10-15)
		Abstract: A spin chain based on the XXZ model is constructed, with staggered disposition of the spectral parameter and of the anisotropy parameter.
		Considering affine Toda theories as perturbed non-affine Toda theories and using reflection relations which relate different fields with the same conformal dimension, we deduce the vacuum expectation values of local fields for all dual pairs of non-simply laced affine Toda field theories.
		For single p-merized Hubbard chains doping is shown to affect the position at which plateaux appear, leading to the emergence of plateaux at irrational values of the magnetization.
	www.lpt.ens.fr /tmrT2000/abs.html (4618 words)

	Research/Chain Geometry
		The aim of the project is to investigate various aspects of chain geometry, in particular the (generalized) chain geometries arising from the projective line P(R) over a ring R containing a field F which is not necessarily commutative.
		The corresponding chain geometry is an algebraic model for the Euclidean Möbius plane, i.e., the Euclidean plane with one extra "point at infinity".
		Havlicek: The Dual of a Chain Geometry, J.
	www.geometrie.tuwien.ac.at /havlicek/proj303.html (1606 words)

	[No title]
		Of course we insist that each c_i be distinct from c_(i-1) (and if we want to avoid self-intersecting chains of dodecahedra, we do so locally precisely by prescribing for each c which of the other six color c' may follow.) One may phrase this in purely group-theoretic terms as follows.
		The short answer is that the reason no such product of affine motions can ever be the identity map is that every application of R picks up some more 5's in denominators; it will take a little while to set this up properly.
		Since we have a coordinate system picked out, we may represent the affine maps with matrices: a function of the form v -> M.v + w for some fixed 3x3 matrix M and 3x1 vector w is represented by the 4x4 matrix [ M w ] [ 0 1 ].
	www.math.niu.edu /~rusin/known-math/98/dodec_prf (2722 words)

	Baxter 2000 Workshop Program
		With a view to establishing an exact representation of the ground state energy of the finite size XXZ spin chain in terms of elementary functions, we concentrate on the crossing-parameter $\eta$- dependence around $\eta=\pi/3$ for which the ground state energy is known.
		Quantum (affine) superalgebras have recently played a prominent role in the construction and analysis of one-dimensional integrable models of strongly correlated fermions.
		The Wakimoto construction for the quantum affine algebra $U_q(\slthten)$ admits a reduction to the $q$-deformed parafermion algebras.
	wwwmaths.anu.edu.au /events/Baxter2000/abstracts.html (3973 words)

	Affine Circle Geometry over Quaternion Skew Fields (ResearchIndex)
		Abstract: We investigate the ane circle geometry arising from a quaternion skew eld and one of its maximal commutative sub elds.
		0.3: The Dual of a Chain Geometry - Andrea Blunck Hans (2001)
		The Dual of a Chain Geometry - Andrea Blunck Hans (2001)
	citeseer.ist.psu.edu /630396.html (324 words)

	Markus Stroppel: Research Interests
		For instance, an affine plane is an incidence structure if we put P the set of points, L the set of lines, and stipulate that (p,l) belongs to F if the point p lies on the line l.
		The length of such a chain is defined as the number of elements minus 1.
		A nice example is the action of the group of all linear bijections on the affine plane: one has to delete the origin, but the rest of the structure has a description as indicated.
	servix.mathematik.uni-stuttgart.de /~stroppel/interests.shtml (1549 words)

	Affine Homography (Site not responding. Last check: 2007-10-15)
		We first look at the case when the transformation between two views is affine.
		The general projective homography relating two different views of the same planar shape can be reasonably approximated by an affine homography.
		This approximation seems to be a practical one as most real life configurations of imaging a scene from multiple view points, possess structure that are very close that of affine homographies.
	www.cs.columbia.edu /~sujit/Papers/Html/PlrShapeRecIcpr02/node3.html (471 words)

	Homework 9 (Site not responding. Last check: 2007-10-15)
		For the hamburger chain in Problem 5 on page 368, write a matrix equation for the dynamic system representing the probability that a person will go to each hamburger chain.
		Your model for underclassmen should be a first-order affine system and your model for upperclassmen should be a second-order affine system.
		If there are 400 freshmen in year 0, find the particular solution to the underclassmen system and use this to express the number of upperclassmen as a first order nonhomogeneous dynamic system.
	ite.gmu.edu /~klaskey/syst201/homework9.html (248 words)

	[No title]
		is a proper chain of closed irreducible subsets of
		Since the original chain had maximal length, one of these inclusions must be an equality.
		is a proper chain of prime ideals, we have
	odin.mdacc.tmc.edu /~krc/agathos/dimen.html (969 words)

	Copyright (c) 1996, 1997, 1998 Thomas E. Burge. All rights reserved.
		The libraries such as Pixar's librib.a, BMRT's libribout.a, or the Affine Toolkit's libsribw.a provide a set of RI calls that could be used if the desired action is to simply print the parsed data.
		The Affine Toolkit was designed for filtering RIBs and being used in plugins to import and export RIBs.
		The function uses a table created by a utility called tokentbl, which is included in the Affine Toolkit.
	www.affine.com /coding.html (3585 words)

	[No title]
		The ilEltImg differs from the above chain (if directly specified by the application) in that it provides an optimized hardware pass as well as roam and zoom look- ahead support.
		The second warp is an affine warp and changes the geometric relationship between the rectified image plane and the display plane.
		When performing a window paint operation, the fast path first determines which tiles are required in the second (draw) texture to satisfy the request.
	www.sgi.com /products/software/imagevision/man/man3/ilEltImg.html (4780 words)

	[No title] (Site not responding. Last check: 2007-10-15)
		Affine Capture The first technique implemented is the Affine Capture technique in [2].
		Affine Capture Example a) Part of the reference frame b) The part marked for tracking c) One of the frames used for motion capture.
		It corresponds to the third image on the top row in d) d) Output during affine capture of the left leg Rotation Capture The affine capture presented in the previous section is not stable.
	www.dgp.toronto.edu /~paulyang/csc2530/project_report.doc (2811 words)

	Recognition of Human Gaits
		The parameters of the chain are set by hand by clicking on the desired joints in the first image of the sequence.
		The resulting joint angles are a photometric and view invariant representation of the motion [1].
		Vector of affine invariant moments computed on the binary silhouette of the moving body, computed by background subtraction techniques.
	www.cs.ucla.edu /~bissacco/gaitrec.html (616 words)

	Network Average
		is the average number of chain strands per unit volume.
		Equation (14) gives the full tensorial free energy with the finite extensibility effect, and it can be viewed as an extension of the previous work on uniaxial deformations [9].
		Due to the breakdown of affine assumption at slightly large strains and experimental errors at low strains, quantitative comparison of eq.(18) with experiments is difficult at this stage.
	www.tcm.phy.cam.ac.uk /~ym101/rubber/node3.html (644 words)

	Recent Advances in the Theory of Quantum Integrable Systems
		In a vertex algebraic context, we present an explicit description of the twisted Wakimoto realizations of the affine Lie algebras in correspondence with an arbitrary finite order automorphism and a compatible integral gradation of a complex simple Lie algebra.
		Bulk scattering is non trivial, provided that the bulk scattering matrix depends separately on the spectral parameters of the colliding particles, and not only on their difference.
		There is an approach due to Bazhanov and Reshetikhin for solving integrable RSOS models which consists of solving the functional relations which result from the truncation of the fusion hierarchy.
	wwwlapp.in2p3.fr /lapth/RAQIS03/program2.html (2337 words)

	G.E.C. - Publications (Site not responding. Last check: 2007-10-15)
		We assessed the ability of a generalized affine gap cost model to reliably detect remote protein homology and to produce high-quality alignments.
		Generalized affine gap alignment with optimal gap parameters performed as well as the traditional affine gap model in remote homology detection.
		We conclude that generalized affine gap costs should be used when alignment accuracy carries more importance than aligned sequence length.
	threeplusone.com /pubs (3041 words)

	Algebraic Geometry (Site not responding. Last check: 2007-10-15)
		Projective spaces are typically regarded as a union of affine spaces, with affine coordinates.
		A projective variety is a consideration how to fit the algebraic variety and affine variety together, to make an algebraic variety in projective space.
		An affine variety is a k-space which is isomorphic to a closed subspace of an affine space over k.
	www.risberg.ws /Hypertextbooks/Mathematics/Geometry/algebraic.htm (1388 words)

	[No title]
		So they are connected * by a chain* of weak equivalences by proposition 2 (see also remark 6 for the notion of weak equival* *ence).
		X * is representable, affine* and faithfully flat because P and P 0are.
		As P is affine i* t is in particular quasi-compact, hence fpqc, and thus of effective cohomological descent for quas *i-coherent modules, [LM-B ],13.5.5,i).
	hopf.math.purdue.edu /Naumann/comodlandweber.txt (5917 words)

	Infinite Analysis Seminar Tokyo 2002
		Abstract: A spin chain defined on a finite lattice might have an infinite dimensional symmetry, and the degree of the degeneracy might increase exponentially with repect to the lattice size.
		In fact, it is shown in Ref. [1] that if the anisotropic parameter \Delta =(q+1/q)/2 is given by a root of unity, q, then it is the case: the (inhomogeneous) transfer matrix of the the XXZ spin chain under the P.B.C.s (anti-)commutes with the sl_2 loop algebra.
		In this talk, we discuss a generalization of the six-vertex (XXZ) result to the eight-vertex model (i.e., the XYZ spin chain), where some degenerate eigenvectors were constructed first by R.J. Baxter in 1972.
	www.ms.u-tokyo.ac.jp /~takebe/iat/seminar2002.html (1147 words)

	Quantum Grops in 2D Physics
		Chapters 4 and 5 serve to introduce the reader to some mathematical tools not generally known to practicing physicists, while discussing the algebraic Bethe ansatz solution to the eight-vertex model and, thus motivated, the face models.
		The trigonometric solution to the latter is presented in the general framework of the Temperley--Lieb--Jones algebra, complemented by an appendix on knot theory and another one on finite-dimensional subfactors.
		In chapter 7, we turn to the representation theory of quantum groups at roots of unity, and present several physical applications thereof, with an emphasis on explicit calculations.
	mpej.unige.ch /~ruiz/book.html (416 words)

	An integrable system of coupled non-linear evolution equations and its supersymmetric version (Site not responding. Last check: 2007-10-15)
		In particular, systems which are embedded in a bi-Hamiltonian structure draw more attention of the physicists because they ensure the existence of an infinite number of independent, commuting conserved quantities.
		Wilson [8], on the other hand, established the fact that one may obtain different coupled equations from affine algebra associated with the calculations of two-dimensional Toda lattice (2DTL).
		We have given first few Hamiltonians of the infinite chain which in turn give rise to an infinite hierarchy of coupled equations each of which is a Hamiltonian system.
	www.sif.it /cimento/toca/110.03/07/07.html (790 words)

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