Showing papers on "Ring (mathematics) published in 1991"

A Lower Bound on Probabilistic Algorithms for Distributive Ring Coloring

Abstract: Suppose that n processors are arranged in a ring and can communicate only with their immediate neighbors. It is shown that any probabilistic algorithm for 3 coloring the ring must take at least $\frac{1}{2}\log^* n - 2$ rounds, otherwise the probability that all processors are colored legally is less than $\frac{1}{2}$. A similar time bound holds for selecting a maximal independent set. The bound is tight (up to a constant factor) in light of the deterministic algorithms of Cole and Vishkin [Inform, and Control, 70 (1986), pp. 32–53] and extends the lower bound for deterministic algorithms of Linial [Proc. 28th IEEE Foundations of Computer Science Symposium, 1987, pp. 331–335].

N=2 LANDAU-GINZBURG VS. CALABI-YAU σ-MODELS: NON-PERTURBATIVE ASPECTS

Abstract: We discuss some nonperturbative aspects of the correspondence between N=2 Landau-Ginzburg orbifolds and Calabi-Yau σ-models. We suggest that the correct framework is Deligne’s theory of mixed Hodge structures (closely related to catastrophe theory). We derive a general topological formula for the chiral ring OPE coefficients of any Landau-Ginzburg model, including the absolute normalization. This follows from the identification of spectral flow with Grothendieck’s local duality. Wherever the LG model has a CY interpretation, its OPE coefficients are equal to those of the σ-model as given by intersection theory, including normalization. We discuss at length the tricky case of a number of LG fields greater than c/3+2, presenting explicit examples. In passing, we get many results about the geometry of moduli spaces for such conformal theories. We explain the beautiful algebraic geometry connected with a remarkable model pointed out by Vafa, and its relations with moduli space geometry.

Asymptotically fast triangularization of matrices over rings

Abstract: This paper considers the problems of triangularizing and diagonalizing matrices over rings, with particular emphasis on the integral case. It begins with a description of fast algorithms for the computation of Hermite and Smith normal forms of integer matrices. Then it shows how to apply fast matrix multiplication techniques to the problem of triangularizing a matrix over a ring using elementary column operations. These general results lead to an algorithm for triangularizing integer matrices that has a faster running time than the known Hermite normal form algorithms. The triangular matrix that is computed has small entries like the Hermite normal form, and will suffice for many applications.

When is a multiplicative derivation additive

Abstract: Our main objective in this note is to prove the following Suppose R is a ring having an idempotent element e ( e ≠ 0 , e ≠ 1 ) which satisfies: ( M 1 ) x R = 0 implies x = 0 ( M 2 ) e R x = 0 implies x = 0 ( and hence R x = 0 implies x = 0 ) ( M 3 ) e x e R ( 1 − e ) = 0 implies e x e = 0 If d is any multiplicative derivation of R , then d is additive

Ground Rings and Their Modules in 2D Gravity with $c\le 1$ Matter

Abstract: All solvable two-dimensional quantum gravity models have non-trivial BRST cohomology with vanishing ghost number. These states form a ring and all the other states in the theory fall into modules of this ring. The relations in the ring and in the modules have a physical interpretation. The existence of these rings and modules leads to nontrivial constraints on the correlation functions and goes a long way toward solving these theories in the continuum approach.

Annihilator ideals, associated primes and kasch-mccoy commutative rings

Abstract: If R is a ring, and A right annulet(= annihilator right ideal) then A[X] is a right annulet of the polynomial ring R[X]. (In factX can be any set of variables.). An annulet I of R[X] of this form is said to be be extended. Not all annulets of R[X] are extended, since e.g., the ascending chain on right annulets (= acc ┴) is not inherited by R[X], as, Kerr [Ke] observed. Nevertheless, maximal (minimal) annulets of a polynomial ring R[X] are extended, as a theorem of McCopy on annihilators in R[X] readily shows (see Introduction).

On Rings of Continuous Functions on Topological Spaces

Abstract: This paper is related to studies byM.H.Stone [2] and to the above paper by G.E. Shilov. In contrast to the latter, we consider the ring of continuous functions on a topological space as a purely algebraic object without defining any topological relations in it. It turns out that in the case of bicompact spaces, considered by M.H. Stone, and also in some much more general cases, even the purely algebraic structure of the ring of continuous functions determines the topological space to within a homeomorphism.

Group-theoretical descriptions of ring-theoretical invariants of group algebras

Abstract: Let F be a field, and let G be a finite group. Then the elements of G form a distinguished basis of the group algebra FG of G over F. In this paper we shall be concerned with the following two closely related questions: Which invariants of the ring FG can be described in terms of the group basis G of FG? Which invariants of the group G are determined by the structure of the ring FG?

Preform design in ring rolling processes by the three-dimensional finite element method

Abstract: Perform design by the three-dimensional finite element method has been carried out for plain ring rolling and T-section profiled ring rolling. The application of the backward tracing scheme for perform design in ring rolling processes demonstrates, for the first time, the extension of the scheme into three dimensions. The preform design in plain ring rolling aims at obtaining a preform which simulates a final plain ring product with uniform axial height. Loading simulations were carried out for two progressively modified preforms derived from the result of loading simulations with a rectangular-shaped ring. Then, backward tracing was applied to obtain a final preform for the specified product configuration of uniform axial height. The preform in the T-section profiled ring rolling process was to be designed to simulate a final profiled ring product with complete filling in the groove and uniform axial height. The final preform shape for plain ring rolling was selected as a trial preform in T-section profiled ring rolling. A more satisfactory preform was obtained from the backward tracing results. It was shown by forward simulation that the final preform was good enough to satisfy the design criteria.

Towards optimal simulations of formulas by bounded-width programs

Abstract: We show that, over an arbitrary ring, for any fixed ∈>0, all balanced algebraic formulas of sizes are computed by algebraic straight-line programs that employ a constant number of registers and have lengthO (s 1+∈). In particular, in the special case where the ring isGF(2), we obtain a technique for simulating balanced Boolean formulas of sizes by bounded-width branching programs of lengthO(s 1+∈), for any fixed ∈>0. This is an asymptotic improvement in efficiency over previous simulations in both the Boolean and algebraic settings.

Products of idempotent integer matrices

Abstract: Let E denote the set of non-identity idempotent matrices in the full matrix ring Mn(R) over a principal ideal domain R. A necessary and sufficient condition is found for the subsemigroup generated by E to be the set of all matrices in Mn(R) of rank less than n. The condition is satisfied when R is a discrete valuation ring and when R is the ring of integers. Thus every n × n matrix of rank less than n is a product of idempotent integer matrices.

On rings for which homogeneous maps are linear

Abstract: Let R be the collection of all rings R such that for every Rmodule G, the centralizer near-ring MR(G) = {f: G -GIf(rx) = rf(x), r E R, x E G} is a ring. We show R E 9 if and only if MR(G) = EndR(G) for each R-module G. Further information about R is collected and the Artinian rings in R are completely characterized.

An experimental study of the molecular mixing process in an axisymmetric laminar vortex ring

Abstract: Results are presented from an experimental study of the molecular mixing of a dynamically passive conserved scalar quantity in an axisymmetric laminar vortex ring. The experiments are based on highly resolved laser‐induced fluorescence imaging measurements of the scalar field ζ(x,t) in the diametral plane of the ring, from which the evolution of the molecular mixing rate field ∇ζ⋅∇ζ(x,t) can be directly examined. In particular, the structure and dynamics of the mixing process are addressed during the three characteristic stages in the ring evolution, namely, (i) the ring generation stage, (ii) the ring pinch‐off stage, and (iii) the asymptotic stage of the ring. Results show a layering of the mixing process in which the diffusional cancellation term ∇(∇ζ):∇(∇ζ) plays a major role in setting the overall mixing rate achieved. The scalar field measurements are also used to extract detailed information about the underlying velocity field in the ring.

Linear stability of a self-gravitating ring

Abstract: Stability of a self-gravitating ring about a central body is considered. The purpose is to derive a bound on the mass of the ring in order that the system will be linearly stable. Our bound will, in some cases, be the best possible bound. The bound is also expanded as an asymptotic series. Comparisons of our result are made with respect to previous analyses performed by Tisserand, Pendse and Willerding.