Showing papers on "Ring (mathematics) published in 2010"
TL;DR: The state of the art of the ring statistics when used to study the structural properties of solids and a new and original method to analyse the connectivity of a topological network using ring statistics is presented.
366 citations
Journal Article•
TL;DR: In this paper, the authors study the Berglund-Hubsch transpose construction W^T for invertible quasihomogeneous potential W. They introduce the dual group G^T and establish the state space isomorphism between the Fan-Jarvis-Ruan-Witten A model of W/G and the orbifold Milnor ring B-model of W^t/G^T.
Abstract: In this article, we study the Berglund--Hubsch transpose construction W^T for invertible quasihomogeneous potential W. We introduce the dual group G^T and establish the state space isomorphism between the Fan-Jarvis-Ruan-Witten A-model of W/G and the orbifold Milnor ring B-model of W^T/G^T. Furthermore, we prove a mirror symmetry theorem at the level of Frobenius algebra structure for G^max. Then, we interpret Arnol'd strange duality of exceptional singularities W as mirror symmetry between W/J and its strange dual W^SD.
168 citations
TL;DR: In this article, a spherically harmonic oscillatory ring-shaped potential is proposed and its exactly complete solutions are presented by the Nikiforov-Uvarov method.
129 citations
TL;DR: In this paper, the prime spectrum of the amalgamated ring along an ideal ideal was studied, and bounds for its Krull dimension were given for the A + X B [X ] and D + M constructions.
126 citations
TL;DR: In this article, the Cox ring of a normal complete variety X with algebraic torus action was investigated in terms of a maximal geometric quotient of X. The Cox ring was shown to be equivalent to the Cox quotient in the sense that the quotient is the product of a set of generators and relations.
114 citations
TL;DR: In this article, a new presentation of the discrete ring theorem for sets of real numbers is given, with special attention given to the relation between the various parameters, and new Marstrand type projection theorems are obtained and formulated either in terms of box or Hausdorff dimension.
Abstract: We give a new presentation of the discrete ring theorem for sets of real numbers [B]. Special attention is given to the relation between the various parameters. As an application, new Marstrand type projection theorems are obtained and formulated either in terms of box or Hausdorff dimension. It is shown that the dimension of the projections satisfies a nontrivial lower bound outside a very sparse set of exceptional directions.
113 citations
TL;DR: In this article, a simple, combinatorial construction of the sl ˆ (n) k -WZNW fusion ring, also known as Verlinde algebra, is given.
98 citations
TL;DR: In this article, the integrability and flatness conditions of D-branes on compact Calabi-Yau manifolds in type II and F-theory compactifications were studied.
97 citations
TL;DR: In this article, a new spectral criterion for Kazhdan's property (T) was established, which is applicable to a large class of discrete groups defined by generators and relations.
Abstract: We establish a new spectral criterion for Kazhdan’s property (T) which is applicable to a large class of discrete groups defined by generators and relations. As the main application, we prove property (T) for the groups EL
n
(R), where n≥3 and R is an arbitrary finitely generated associative ring. We also strengthen some of the results on property (T) for Kac-Moody groups from (Dymara and Januszkiewicz in Invent. Math. 150(3):579–627, 2002).
88 citations
TL;DR: The notion of projective modules over non-noetherian commutative rings was introduced and investigated in this article, where a semidualizing projective module is considered.
Abstract: We introduce and investigate the notion of $\gc$-projective modules over (possibly non-noetherian) commutative rings, where $C$ is a semidualizing module. This extends Holm and J{\o}rgensen's notion of $C$-Gorenstein projective modules to the non-noetherian setting and generalizes projective and Gorenstein projective modules within this setting. We then study the resulting modules of finite $\gc$-projective dimension, showing in particular that they admit $\gc$-projective approximations, a generalization of the maximal Cohen-Macaulay approximations of Auslander and Buchweitz. Over a local (noetherian) ring, we provide necessary and sufficient conditions for a $G_C$-approximation to be minimal.
87 citations
TL;DR: In this article, the authors use the plethystic exponential and the Molien-Weyl formula to compute the Hilbert series (generating functions), which counts gauge invariant operators in N = 1 supersymmetric SU (N c ), Sp (Nc ), SO (N C ) and G 2 gauge theories with 1 adjoint chiral superfield, fundamental chiral chiral fields, and zero classical superpotential.
TL;DR: In this paper, it was shown that the quotient map from K(R-Flat) to K(r-flat)/S always has a right adjoint, i.e., it is equivalent to the Verdier quotient.
Abstract: Let R be a ring. In a previous paper [11] we found a new description for the category K(R-Proj); it is equivalent to the Verdier quotient K(R-Flat)/S, for some suitable S C K(R-Flat). In this article we show that the quotient map from K(R-Flat) to K(R-Flat)/S always has a right adjoint. This gives a new, fully faithful embedding of K(R-Proj) into K(R-Flat). Its virtue is that it generalizes to nonaffine schemes.
Journal Article•
TL;DR: This work first analyzes the structure of the ring [FORMULA] and defines linear codes over this ring which turns out to be a ring that is not finite chain or principal ideal contrary to the rings that have hitherto been studied in coding theory.
Abstract: In this work, we investigate linear codes over the ring [FORMULA] . We first analyze the structure of the ring and then define linear codes over this ring which turns out to be a ring that is not finite chain or principal ideal contrary to the rings that have hitherto been studied in coding theory. Lee weights and Gray maps for these codes are defined by extending on those introduced in works such as Betsumiya et al. (Discret Math 275:43-65, 2004) and Dougherty et al. (IEEE Trans Inf 45:32-45, 1999). We then characterize the [FORMULA] -linearity of binary codes under the Gray map and give a main class of binary codes as an example of [FORMULA] -linear codes. The duals and the complete weight enumerators for [FORMULA] -linear codes are also defined after which MacWilliams-like identities for complete and Lee weight enumerators as well as for the ideal decompositions of linear codes over [FORMULA] are obtained.
TL;DR: In this article, the authors numerically studied a vortex ring impacting a flat wall with an angle of incidence θ ≥ 0° (i.e., the angle at which the vortex hits the wall).
Abstract: We numerically study a vortex ring impacting a flat wall with an angle of incidence θ ≥ 0°) in three dimensions by using the lattice Boltzmann equation. The hydrodynamic behaviour of the ring–wall interacting flow is investigated by systematically varying the angle of incidence θ in the range of 0° ≤ θ ≤ 40° and the Reynolds number in the range of 100 ≤ Re ≤ 1000, where the Reynolds number Re is based on the translational speed and initial diameter of the vortex ring. We quantify the effects of θ and Re on the evolution of the vortex structure in three dimensions and other flow fields in two dimensions. We observe three distinctive flow regions in the θ–Re parameter space. First, in the low-Reynolds-number region, the ring–wall interaction dissipates the ring without generating any secondary rings. Second, with a moderate Reynolds number Re and a small angle of incidence θ, the ring–wall interaction generates a complete secondary vortex ring, and even a tertiary ring at higher Reynolds numbers. The secondary vortex ring is convected to the centre region of the primary ring and develops azimuthal instabilities, which eventually lead to the development of hairpin-like small vortices through ring–ring interaction. And finally, with a moderate Reynolds number and a sufficiently large angle of incidence θ, only a secondary vortex ring is generated. The secondary vortex wraps around the primary ring and propagates from the near end of the primary ring, which touches the wall first, to the far end, which touches the wall last. The rings develop a helical structure. Our results from the present study confirm some existing experimental observations made in the previous studies.
TL;DR: It is proved that cyclic codes over the ring are principally generated, and the generator polynomial of cyclic Code 2+2+vF+2 is given.
Abstract: In this paper, we investigate the structure and properties of cyclic codes over the ring F 2+vF 2 . We first study the relationship between cyclic codes over F 2+vF 2 and binary cyclic codes. Then we prove that cyclic codes over the ring are principally generated, and give the generator polynomial of cyclic codes over the ring. Finally, we obtain the unique idempotent generators for cyclic codes of odd length and determine the number of cyclic codes for a given length n over F 2+vF 2.
TL;DR: The notion of generalized lower and upper approximations with respect to an ideal of a ring which is an extended notation of rough ideal introduced lately by Davvaz is proposed and some significant properties of them are discussed.
Posted Content•
TL;DR: In this article, a symmetric monoidal structure on the localizing motivator Mot of dg categories was constructed, and a simple construction of the Chern character maps from non-connective algebraic K-theory to negative and periodic cyclic homology was given.
Abstract: In this article we further the study of non-commutative motives. Our main result is the construction of a symmetric monoidal structure on the localizing motivator Mot of dg categories. As an application, we obtain : (1) a computation of the spectra of morphisms in Mot in terms of non-connective algebraic K-theory; (2) a fully-faithful embedding of Kontsevich's category KMM of non-commutative mixed motives into the base category Mot(e) of the localizing motivator; (3) a simple construction of the Chern character maps from non-connective algebraic K-theory to negative and periodic cyclic homology; (4) a precise connection between Toen's secondary K-theory and the Grothendieck ring of KMM ; (5) a description of the Euler characteristic in KMM in terms of Hochschild homology.
TL;DR: In this article, it was shown that if G is a connected, simply connected, semisimple algebraic group over an algebraically closed field of sufficiently large characteristic, then all the blocks of the restricted enveloping algebra (Ug)0 of the Lie algebra g of G can be endowed with a Koszul grading.
Abstract: In this article we prove that if G is a connected, simply connected, semisimple algebraic group over an algebraically closed field of sufficiently large characteristic, then all the blocks of the restricted enveloping algebra (Ug)0 of the Lie algebra g of G can be endowed with a Koszul grading (extending results of Andersen, Jantzen, and Soergel). We also give information about the Koszul dual rings. In the case of the block associated to a regular character λ of the Harish-Chandra center, the dual ring is related to modules over the specialized algebra (Ug)λ with generalized trivial Frobenius character. Our main tool is the localization theory developed by Bezrukavnikov, Mirkovic, and Rumynin
01 Jun 2010
TL;DR: In this paper, the authors give a self-contained and elementary proof of Gordon's theorem on the diagonal coinvariant ring, with r>1, for the rational Cherednik algebra of type G(r,p,n).
Abstract: The goal of this paper is to lay the foundations for a combinatorial study, via orthogonal functions and intertwining operators, of category O for the rational Cherednik algebra of type G(r,p,n). As a first application, we give a self-contained and elementary proof of the analog for the groups G(r,p,n), with r>1, of Gordon's theorem (previously Haiman's conjecture) on the diagonal coinvariant ring. We impose no restriction on p; the result for p
TL;DR: Four different approaches to account for heterogeneity in observer distribution in spatial analyses of ring re-encounter data are reviewed, which could improve the understanding of bird movements considerably.
Abstract: Ring re-encounter data, in particular ring recoveries, have made a large contribution to our understanding of bird movements. However, almost every study based on ring re-encounter data has struggled with the bias caused by unequal observer distribution. Re-encounter probabilities are strongly heterogeneous in space and over time. If this heterogeneity can be measured or at least controlled for, the enormous number of ring re-encounter data collected can be used effectively to answer many questions. Here, we review four different approaches to account for heterogeneity in observer distribution in spatial analyses of ring re-encounter data. The first approach is to measure re-encounter probability directly. We suggest that variation in ring re-encounter probability could be estimated by combining data whose re-encounter probabilities are close to one (radio or satellite telemetry) with data whose re-encounter probabilities are low (ring re-encounter data). The second approach is to measure the spatial variation in re-encounter probabilities using environmental covariates. It should be possible to identify powerful predictors for ring re-encounter probabilities. A third approach consists of the comparison of the actual observations with all possible observations using randomization techniques. We encourage combining such randomisations with ring re-encounter models that we discuss as a fourth approach. Ring re-encounter models are based on the comparison of groups with equal re-encounter probabilities. Together these four approaches could improve our understanding of bird movements considerably. We discuss their advantages and limitations and give directions for future research.
TL;DR: In this article, the authors investigated the problem of extension of ring Q-homeomorphisms between domains in metric spaces with measures to the boundary, and established conditions for the function Q(x) and the boundary of the domain under which any ring Q -homeomorphism admits a continuous or a homeomorphic extension.
Abstract: We investigate the problem of extension of so-called ring Q-homeomorphisms between domains in metric spaces with measures to the boundary. We establish conditions for the function Q(x) and the boundary of the domain under which any ring Q-homeomorphism admits a continuous or a homeomorphic extension to the boundary. The results are applicable, in particular, to Riemannian manifolds, Lowner spaces, and Carnot and Heisenberg groups.
TL;DR: For characteristic zero and algebraically closed field k, Larsen and Lunts as discussed by the authors showed that the converse is true when dim X ≤ 1o rX is a smooth connected projective surface or if X contains only finitely many rational curves.
Abstract: Let K0(Var k) be the Grothendieck ring of algebraic varieties over a field k .L et X, Y be two algebraic varieties over k which are piecewise isomorphic (i.e. X and Y admit finite partitions X1 ,..., Xn, Y1 ,..., Yn into locally closed subvarieties such that Xi is iso- morphic to Yi for all i ≤ n), then (X )=( Y ) in K0(Var k). Larsen and Lunts ask whether the converse is true. For characteristic zero and algebraically closedfield k, we answer positively this question when dim X ≤ 1o rX is a smooth connected projective surface or if X contains only finitely many rational curves.
TL;DR: In this paper, the (S,ω)-Armendariz condition on R was studied, which is a generalization of the standard Armendariz conditions from polynomials to skew generalized power series.
Abstract: Let R be a ring, S a strictly ordered monoid, and ω:S→End(R) a monoid homomorphism. The skew generalized power series ring R[[S,ω]] is a common generalization of (skew) polynomial rings, (skew) power series rings, (skew) Laurent polynomial rings, (skew) group rings, and Mal’cev–Neumann Laurent series rings. We study the (S,ω)-Armendariz condition on R, a generalization of the standard Armendariz condition from polynomials to skew generalized power series. We resolve the structure of (S,ω)-Armendariz rings and obtain various necessary or sufficient conditions for a ring to be (S,ω)-Armendariz, unifying and generalizing a number of known Armendariz-like conditions in the aforementioned special cases. As particular cases of our general results we obtain several new theorems on the Armendariz condition; for example, left uniserial rings are Armendariz. We also characterize when a skew generalized power series ring is reduced or semicommutative, and we obtain partial characterizations for it to be reversible or 2-primal.
Book•
29 Jan 2010TL;DR: In this article, a method of dealing with questions connected with anchor rings was developed, and two sets of solutions may be found by differentiating I and d I/d z any number of times with respect to c.
Abstract: In this Paper I have developed a method of dealing with questions connected with Anchor Rings. If r, θ, ϕ be the coordinates of any point outside an anchor ring, whose central circle is of radius c , then ∫π dϕ/√(r2+c2 - 2cr sinθ cosϕ ) is a solution of Laplace’s equation, finite at all external points and vanishing at infinity. Let this be called I. Then dI/dz is another solution; and two sets of solutions may be found by differentiating I and d I/ d z any number of times with respect to c . These solutions are symmetrical with respect to the axis of the ring. In the first set z is involved only in even powers; in the second set in odd powers.
TL;DR: In this article, the authors studied compactly generated t-structures on a commutative Noetherian ring R generated by complexes in D fg − (R ) and proved that they are exactly the compactly constructed t-structure on D ( R ) and described them in terms of decreasing filtrations by supports of Spec ( R ).
TL;DR: In this article, the authors compare and contrast relative cohomology theories that arise from resolutions involving semidualizing modules, and demonstrate the failure of the naive version of balance one might expect for these functors.
Abstract: We compare and contrast various relative cohomology theories that arise from resolutions involving semidualizing modules. We prove a general balance result for relative cohomology over a Cohen-Macaulay ring with a dualizing module, and we demonstrate the failure of the naive version of balance one might expect for these functors. We prove that the natural comparison morphisms between relative cohomology modules are isomorphisms in several cases, and we provide a Yoneda-type description of the first relative Ext functor. Finally, we show by example that each distinct relative cohomology construction does in fact result in a different functor.
TL;DR: In this article, the topological Hochschild homology of ring spectra arising as Thom spectra for loop maps f : X! BF, where BF denotes the classifying space for stable spherical fibrations, has been investigated.
Abstract: We describe the topological Hochschild homology of ring spectra that arise as Thom spectra for loop maps f : X! BF, where BF denotes the classifying space for stable spherical fibrations. To do this, we consider sym- metric monoidal models of the category of spaces over BF and corresponding strong symmetric monoidal Thom spectrum functors. Our main result identi- fies the topological Hochschild homology as the Thom spectrum of a certain stable bundle over the free loop space L(BX). This leads to explicit calcula- tions of the topological Hochschild homology for a large class of ring spectra, including all of the classical cobordism spectra MO, MSO, MU, etc., and the Eilenberg-Mac Lane spectra HZ/p and HZ.
TL;DR: Test results demonstrate that the ring artifacts can be more effectively suppressed using the proposed iterative center weighted median filter as compared to other ring removal techniques reported in the literature.
TL;DR: In this article, direct integration is used to solve the closed amplitudes of multicut matrix models with polynomial potentials, where the gap conditions up to genus four are used to fix the holomorphic ambiguity.
Abstract: We show how direct integration can be used to solve the closed amplitudes of multicut matrix models with polynomial potentials. In the case of the cubic matrix model, we give explicit expressions for the ring of nonholomorphic modular objects that are needed to express all closed matrix model amplitudes. This allows us to integrate the holomorphic anomaly equation up to holomorphic modular terms that we fix by the gap condition up to genus four. There is an onedimensional submanifold of the moduli space in which the spectral curve becomes the Seiberg-Witten curve and the ring reduces to the nonholomorphic modular ring of the group Γ(2). On that submanifold, the gap conditions completely fix the holomorphic ambiguity and the model can be solved explicitly to very high genus. We use these results to make precision tests of the connection between the large order behavior of the 1/N expansion and nonperturbative effects due to instantons. Finally, we argue that a full understanding of the large genus asymptotics in the multicut case requires a new class of nonperturbative sectors in the matrix model.