Fast algorithms for computing one- and two-dimensional convolution in integer polynomial rings

1997 ◽  
Vol 16 (1) ◽  
pp. 121-139
Author(s):  
H. Krishna Garg ◽  
C. C. Ko
Keyword(s):  
Fast Algorithms ◽  
Polynomial Rings ◽  
Two Dimensional ◽  
Integer Polynomial

scholarly journals Prime ideals in two-dimensional polynomial rings

1989 ◽  
Vol 107 (3) ◽  
pp. 577-577 ◽  
Author(s):  
William Heinzer ◽  
Sylvia Wiegand
Keyword(s):  
Polynomial Rings ◽  
Prime Ideals ◽  
Two Dimensional

scholarly journals Prime ideals in birational extensions of two-dimensional polynomial rings

2005 ◽  
Vol 201 (1-3) ◽  
pp. 142-153 ◽  
Author(s):  
A. Serpil Saydam ◽  
Sylvia Wiegand
Keyword(s):  
Polynomial Rings ◽  
Prime Ideals ◽  
Two Dimensional

Homomorphisms of two-dimensional linear groups over Laurent polynomial rings and Gaussian domains

1991 ◽  
Vol 109 (2) ◽  
pp. 287-297 ◽  
Author(s):  
Yu Chen
Keyword(s):  
Commutative Ring ◽  
Linear Group ◽  
Unit Group ◽  
Commutative Rings ◽  
Laurent Polynomial ◽  
Polynomial Rings ◽  
Linear Groups ◽  
Two Dimensional ◽  
Euclidean Domain ◽  
Invertible Matrices

Let GL2(R) be the general linear group of 2 × 2 invertible matrices in M2(R) over a commutative ring R with 1 and SL2(R) be the special linear group consisting of 2 × 2 matrices over R with determinant 1. In this paper we determine the homomorphisms from GL2 and SL2, as well as their projective groups, over Laurent polynomial rings to those groups over Gaussian domains, i.e. unique factorization domains (cf. Theorems 1, 2, 3 below). We also consider more generally the homomorphisms of non-projective groups over commutative rings containing a field which are generated by their units (cf. Theorems 4 and 5). So far the homomorphisms of two-dimensional linear groups over commutative rings have only been studied in some specific cases. Landin and Reiner[7] obtained the automorphisms of GL2(R), where R is a Euclidean domain generated by its units. When R is a type of generalized Euclidean domain with a degree function and with units of R and 0 forming a field, Cohn[3] described the automorphisms of GL2(R). Later, Cohn[4] applied his methods to the case of certain rings of quadratic integers. Dull[6] has considered the automorphisms of GL2(R) and SL2(R), along with their projective groups, provided that R is a GE-ring and 2 is a unit in R. McDonald [9] examined the automorphisms of GL2(R) when R has a large unit group. The most recent work of which we are aware is that of Li and Ren[8] where the automorphisms of E2(R) and GE2(R) were determined for any commutative ring R in which 2, 3 and 5 are units.

Fast Algorithms on Center Location of Two Dimensional Gaussian Distribution Spot

2012 ◽  
Vol 32 (5) ◽  
pp. 0512002 ◽  
Author(s):  
冯新星 Feng Xinxing ◽  
张丽艳 Zhang Liyan ◽  
叶南 Ye Nan ◽  
杨博文 Yang Bowen
Keyword(s):  
Gaussian Distribution ◽  
Fast Algorithms ◽  
Two Dimensional ◽  
Center Location

scholarly journals Fusion of interfaces in Landau-Ginzburg models: a functorial approach

2021 ◽  
Vol 2021 (4) ◽  
Author(s):  
Nicolas Behr ◽  
Stefan Fredenhagen
Keyword(s):  
Topological Defects ◽  
Polynomial Rings ◽  
Two Dimensional ◽  
Minimal Models ◽  
Actual Computation ◽  
Category Of Modules ◽  
Chiral Superfields ◽  
Functorial Approach

Abstract We investigate the fusion of B-type interfaces in two-dimensional supersymmetric Landau-Ginzburg models. In particular, we propose to describe the fusion of an interface in terms of a fusion functor that acts on the category of modules of the underlying polynomial rings of chiral superfields. This uplift of a functor on the category of matrix factorisations simplifies the actual computation of interface fusion. Besides a brief discussion of minimal models, we illustrate the power of this approach in the SU(3)/U(2) Kazama-Suzuki model where we find fusion functors for a set of elementary topological defects from which all rational B-type topological defects can be generated.

scholarly journals REVERSIBLE SKEW LAURENT POLYNOMIAL RINGS AND DEFORMATIONS OF POISSON AUTOMORPHISMS

2009 ◽  
Vol 08 (05) ◽  
pp. 733-757 ◽  
Author(s):  
DAVID A. JORDAN ◽  
NONGKHRAN SASOM
Keyword(s):  
Laurent Polynomial ◽  
Polynomial Rings ◽  
Two Dimensional ◽  
Coordinate Ring ◽  
Base Field ◽  
Poisson Algebras ◽  
Enveloping Algebra ◽  
Period 2 ◽  
Solvable Lie Algebra ◽  
Laurent Polynomial Ring

A skew Laurent polynomial ring S = R[x±1;α] is reversible if it has a reversing automorphism, that is, an automorphism θ of period 2 that transposes x and x-1 and restricts to an automorphism γ of R with γ = γ-1. We study invariants for reversing automorphisms and apply our methods to determine the rings of invariants of reversing automorphisms of the two most familiar examples of simple skew Laurent polynomial rings, namely a localization of the enveloping algebra of the two-dimensional non-abelian solvable Lie algebra and the coordinate ring of the quantum torus, both of which are deformations of Poisson algebras over the base field 𝔽. Their reversing automorphisms are deformations of Poisson automorphisms of those Poisson algebras. In each case, the ring of invariants of the Poisson automorphism is the coordinate ring B of a surface in 𝔽3 and the ring of invariants Sθ of the reversing automorphism is a deformation of B and is a factor of a deformation of 𝔽[x1, x2, x3] for a Poisson bracket determined by the appropriate surface.

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