Showing papers on "Ring (mathematics) published in 1990"
Book•
13 Dec 1990
TL;DR: In this paper, the authors propose an algebraic theory of the Laplace transform for linear differential equations over a ring, which is a generalization of the theory of duality in analytic theory.
Abstract: Introduction Multiplication by Xu (Gauss contiguity) Algebraic theory Variation of Wa with g Analytic theory Deformation theory Structure of Hg Linear differential equations over a ring Singularities (Generalities) Non-regular case Modified Laplace transform Algebraic theory of Laplace transform Examples Degenerative parameters Value at the origin Generic case Formal analytic theory Duality Duality-analytic theory Non degeneracy of Oa Fermat surface References Index of notation Index.
539 citations
TL;DR: A probabilistic self-stabilizing algorithm for a ring of identical processes is presented, which results probabilistically in convergence to a normal state with one token if the initial state of the ring is abnormal.
217 citations
TL;DR: Many of the results of this paper are new in the finite case (i.e., G is a finite-dimensional semisimple group over C) as well.
Abstract: Let G be a Kac-Moody group with Borel subgroup B and compact maximal torus T. Analogous to Kostant and Kumar [Kostant, B. & Kumar, S. (1986) Proc. Nati. Acad. Sci. USA 83, 1543-1545], we define a certain ring Y, purely in terms of the Weyl group W (associated to G) and its action on T. By dualizing Y we get another ring 1, which, we prove, is "canonically" isomorphic with the T-equivariant Ktheory KT(G/B) of GIB. Now KT(G/B), apart from being an algebra over KT(pt.) A(T), also has a Weyl group action and, moreover, KT(G/B) admits certain operators {DW},,w similar to the Demazure operators defined on A(T). We prove that these structures on KT(G/B) come naturally from the ring Y. By "evaluating" the A(T)-module W at 1, we recover K(G/B) together with the above-mentioned structures. We believe that many of the results of this paper are new in the finite case (i.e., G is a finite-dimensional semisimple group over C)
207 citations
TL;DR: It is shown that every deformation of GL(n) is equivalent to one in which the comultiplication is unchanged, not merely on elements of degree one but on all elements (settling in the strongest way a decade-old conjecture).
Abstract: We introduce cohomology and deformation theories for a bialgebra A (over a commutative unital ring k) such that the second cohomology group is the space of infinitesimal deformations. Our theory gives a natural identification between the underlying k-modules of the original and the deformed bialgebra. Certain explicit deformation formulas are given for the construction of quantum groups--i.e., Hopf algebras that are neither commutative nor cocommutative (whether or not they arise from quantum Yang-Baxter operators). These formulas yield, in particular, all GLq(n) and SLq(n) as deformations of GL(n) and SL(n). Using a Hodge decomposition of the underlying cochain complex, we compute our cohomology for GL(n). With this, we show that every deformation of GL(n) is equivalent to one in which the comultiplication is unchanged, not merely on elements of degree one but on all elements (settling in the strongest way a decade-old conjecture) and in which the quantum determinant, as an element of the underlying k-module, is identical with the usual one.
152 citations
01 Jan 1990
TL;DR: In this paper, it was shown that the existence of a nonzero Jordan left derivation of R into X implies R is commutative, and this result was used to prove two noncommutative extensions of the Singer-Wermer theorem.
Abstract: Let R be a ring and X be a left R-module. The purpose of this paper is to investigate additive mappings D1: R -* X and D2: R -X that satisfy D, (ab) = aD1 (b) + bD, (a), a, b E R (left derivation) and D2(a2) = 2aD2(a), a E R (Jordan left derivation). We show, by the rather weak assumptions, that the existence of a nonzero Jordan left derivation of R into X implies R is commutative. This result is used to prove two noncommutative extensions of the classical Singer-Wermer theorem.
141 citations
TL;DR: In this paper, it was shown that if P is a prime ideal of a commutative ring R, its nth symbolic power, denoted Pen), is defined to be the ideal of all elements r of R such that there exists an s not in P such that sr is in the ordinary power P\".
103 citations
TL;DR: The finite element code "RING" as discussed by the authors was developed for the analysis of ring rolling and a special feature of the program is the updating procedure in three-dimensional deformation, where a spatially fixed mesh system including deforming region of the workpiece is constructed based on the shape changes of the ring at each time step.
Abstract: The finite element code “RING” was developed for the analysis of ring rolling. A special feature of the program is the updating procedure in three-dimensional deformation. A spatially fixed mesh system including deforming region of the workpiece is constructed based on the shape changes of the ring at each time step. Several simulations are performed with the program “RING”, and the results are compared with experimental data found in the literature. Good agreement between the simulation results and experiments was obtained in terms of geometrical changes of rings in plain ring rolling and T-shaped profiled ring rolling.
101 citations
TL;DR: In this article, a finite general linear group is defined and the monoid ℛ plays the same role for M that the Weyl group W does for G. In particular, there is a length function on ℓ which extends the length functions on W and a C-algebra which includes Iwahori's "Hecke algebra" and shares many of its properties.
Abstract: Let G=GL
n
(F
q
) be the finite general linear group and let M=M
n
(F
q
) be the monoid of all n×n matrices over F
q
. Let B be a Borel subgroup of G, let W be the subgroup of permutation matrices, and let ℛ⊃W be the monoid of all zero-one matrices which have at most one non-zero entry in each row and each column. The monoid ℛ plays the same role for M that the Weyl group W does for G. In particular there is a length function on ℛ which extends the length function on W and a C-algebra H
C
(M, B) which includes Iwahori's ‘Hecke algebra’ H
C
(G, B) and shares many of its properties.
84 citations
TL;DR: In this article, Conexity of level sets for solutions to elliptic ring problems is investigated in the context of Partial Differential Equations (PDE) and level sets are used to solve ring problems.
Abstract: (1990). Conexity Of Level Sets For Solutions To elliptic Ring Problems. Communications in Partial Differential Equations: Vol. 15, No. 4, pp. 541-556.
70 citations
01 Oct 1990
TL;DR: In this article, the authors present computer simulations and measured results describing a dual-mode filter cell implemented by using a single microstrip ring resonator and a procedure is presented to predict the position in frequency of the transmission zeros.
Abstract: The general behavior of microstrip ring resonators has been known for some time. In particular, the possibility of exciting two degenerate resonances on a single ring has already been established. In the technical literature, however, one can not find (to the authors knowledge) a complete and detailed description of actual microwave filters implemented by explicitly using the dual-mode nature of the microstrip ring. In this paper we present computer simulations and measured results describing a dual-mode filter cell implemented by using a single microstrip ring resonator. The microstrip dual-mode filter presented allows the implementation of two transmission poles and two transmission zeros using only one dual-mode ring resonator. This result is of particular interest because it has already been demonstrated experimentally that a similar behavior can be also obtained with circular-waveguide resonators. The presence or the absence of the transmission zeros is explained in simple terms. In addition, a procedure is presented to predict the position in frequency of the transmission zeros.
66 citations
TL;DR: In this paper, the Chow ring of stable curves of genus 4 was shown to have a dimension at least 13 and a single relation between the fourteen generators which still can exist in the moduli space.
Abstract: ring of the moduli space of stable curves of genus 4. These results are not complete. We find generators for the Chow ring of 4 and for the Chow groups in codimension 1 and 2 of -W4. For A2(G'4) we find fourteen generators. Using test surfaces we prove that the dimension of A 2(4/'4) is at least 13 and explicitly determine the single relation between the fourteen generators which still can exist. Finally, we have two proofs that this relation does indeed hold, so that the dimension of A2( 4/4) equals 13. This enables us to determine the Chow ring of ,4'4. Our original proof is based on a rather delicate argument; the second proof uses a result of Ran (see [R]) and is much simpler.
TL;DR: This work associates the stability of the ring with repulsive forces which it is shown are present between two-dimensional rotors, and the observed minimal distance for repulsion agrees with the stable radius of the vortex ring.
01 May 1990
TL;DR: In this article, an embedding of the Jacobian variety of a curve of genus 2 is given, together with an explicit set of defining equations, for which the induced formal group is defined over the same ring as the coefficients of.
Abstract: An embedding of the Jacobian variety of a curve of genus 2 is given, together with an explicit set of defining equations. A pair of local parameters is chosen, for which the induced formal group is defined over the same ring as the coefficients of . It is not assumed that has a rational Weierstrass point, and the theory presented applies over an arbitrary ground field (of characteristic ╪ 2, 3, or 5).
01 Jan 1990
TL;DR: In this paper, the performance of a number of slotted-ring protocols supporting integration of synchronous and asynchronous traffic in high-speed local area networks (HSLANs) is evaluated.
Abstract: The performance of a number of slotted-ring protocols supporting integration of synchronous and asynchronous traffic in high-speed local area networks (HSLANs) is evaluated. They are the Cambridge fast ring, a variant of the Cambridge fast ring, and Orwell. The performance of their basic access mechanisms is compared and contrasted with that of the multiple-token ring. The effect of a uniframe scheme for supporting synchronous traffic is examined. A delay analysis of the integrated-services slotted-ring protocols is presented. >
TL;DR: In this paper, it was shown that the existence of symmetric bi-derivation on a prime ring of characteristic different from two and three, such that the mappingx → D(x, y) is a derivation, for any fixedy ∈ R, then eitherD1 = 0 orD2 = 0.
Abstract: LetR be a ring. A bi-additive symmetric mappingD(.,.): R × R → R is called a symmetric bi-derivation if, for any fixedy ∈ R, the mappingx → D(x, y) is a derivation. The purpose of this paper is to prove two results concerning symmetric bi-derivations on prime rings. The first result states that, ifD1 andD2 are symmetric bi-derivations on a prime ring of characteristic different from two and three such thatD1(x, x)D2(x,x) = 0 holds for allx ∈ R, then eitherD1 = 0 orD2 = 0. The second result proves that the existence of a nonzero symmetric bi-derivation on a prime ring of characteristic different from two and three, such that [[D(x, x),x],x] ∈ Z(R) holds for allx ∈ R, whereZ(R) denotes the center ofR, forcesR to be commutative.
TL;DR: A ring R is a quasi-Frobenius (QF) ring if and only if every right R-module is embeddable in a projective module as discussed by the authors.
01 Jan 1990
TL;DR: In this article, the authors investigated the foundational questions concerning convergent cohomology using the language and techniques of Grothendieck topologies, and defined the concept of convergent topos (X/W)conv.
Abstract: The purpose of this note is to investigate some of the foundational questions concerning convergent cohomology as introduced in [?] and [?], using the language and techniques of Grothendieck topologies. In particular, if X is a scheme of finite type over a perfect field k of characteristic p and with Witt ring W, we define the “convergent topos (X/W)conv,” and we study the cohomology of its structure sheaf OX/W and of KX := Q ⊗ OX/W. Since the topos (X/W)conv is not noetherian, formation of cohomology does not commute with tensor products, and these are potentially quite different.
TL;DR: In this article, it was shown that the coordinate ring of Grassmannians in Plucker coordinates gives wonderful rings, where Grassmannian embeddings by high enough trists on ample sheaf on projective schemes give wonderful rings.
TL;DR: In this paper, the authors continue their investigation of loops which give rise to alternative loop rings, and describe many properties of this class, including diverse examples of Moufang loops which are united by the fact that they have loop rings which are alternative, and discuss analogues in loop theory of a number of important group theoretic constructions.
Abstract: In this paper, the authors continue their investigation of loops which give rise to alternative loop rings. If the coefficient ring has characteristic 2, these loops turn out to form a surprisingly wide class, in contrast to the situation of characteristic ≠ 2. This paper describes many properties of this class, includes diverse examples of Moufang loops which are united by the fact that they have loop rings which are alternative, and discusses analogues in loop theory of a number of important group theoretic constructions.
TL;DR: In this article, the authors constructed stable stable operations for the version of elliptic cohomology where the coefficient ring Ell ∗ agrees with the ring of modular forms for SL2(Z) which are meromorphic at ∞, and Tn restricts to the nth Hecke operator Tn on Ell∗.
TL;DR: Bergen and Passman as discussed by the authors showed that the Δ-methods of J. A. Bergen and D. S. Passman can be used to handle U(L) in all characteristics and u(L), if the latter ring is prime.
TL;DR: In this paper, the propagation velocity, size, shape, orientation, and swirl velocity of Gulf Stream warm core rings are estimated by fitting idealized warm core ring feature models to observed surface fronts in the satellite imagery, to expendable bathythermograph survey data, and to satellite-tracked drifting buoy data.
Abstract: Analysis techniques were developed to track and estimate the propagation velocity, size, shape, orientation, and swirl velocity of Gulf Stream warm core rings. The methods involve fitting idealized warm core ring feature models to observed surface fronts in the satellite imagery, to expendable bathythermograph survey data, and to satellite-tracked drifting buoy data. The ring feature models are analytic structure functions with adjustable parameters. In this case the ring is modeled as an isolated translating elliptic paraboloid with a swirl velocity that increases linearly with distance from the center. Use of the feature models is illustrated with data collected from warm core ring 83-E. Gradient currents based on the bathythermograph survey of ring 83-E and the feature model agree well with currents measured by expendable current profilers. A comparison of the time series of ring 83-E feature model parameters indicates that not only is the feature model analysis of the buoy track an effective method for tracking and monitoring the evolution of Gulf Stream rings, it also provides useful forecasts of ring locations based simply on a persisted propagation velocity. These techniques were used to provide real time support for exploratory deepwater drilling operations off the U.S. east coast.
01 Jul 1990
TL;DR: The theory of Gröbner basis of the ring of differential operators and its applications to the following problems: zero recognition of an expression that contains special functions or binomial coefficients etc., i.e. formula verification by a computer.
Abstract: It is well known that Grobner basis is a fundamental and powerful tool to solve problems of polynomials ([Buch*],[JSC] etc). Recently, it is revealed that we can use Grobner basis of Weyl algebra to solve the problems of integrations and formula verifications of transcendental functions ([Zei*], [Tak*], [AZ], [WZ*]).The purpose of the paper is to survey the theory of Grobner basis of the ring of differential operators and its applications to the following problems:Computation of differential equations for a definite integral with parameters.Zero recognition of an expression that contains special functions or binomial coefficients etc., i.e. formula verification by a computer.Derivations of some of special functions identities.Solving a definite integral or obtaining an asymptotic expansion of a definite integral with parameters.
TL;DR: In this paper, the problem of finding a minimal free resolution of S/I t, over arbitrary base ring R = Z, the ring of integers, has been studied in the Noetherian commutative ring setting.
Abstract: Let R be a Noetherian commutative ring with, unit element, and X ij be variables with 1 ≤ i ≤ m and 1 ≤ j ≤ n . Let S = R[x ij ] be the polynomial ring over R , and I t be the ideal in S , generated by the t × t minors of the generic matrix (x ij ) ∈ M m, n (S) . For many years there has been considerable interest in finding a minimal free resolution of S/I t , over arbitrary base ring R . If we have a minimal free resolution P. over R = Z, the ring of integers, then R′ ⊗ z P . is a resolution of S/I t over the base ring R′ .
TL;DR: In this paper, it was shown that a semiprime (right) Goldie ring must be an order in a semisimpleural Artinian ring if it has an infinite ascending chain of annihilator ideals.
TL;DR: In this article, the authors investigated solvable groups of finite Morley rank and proved that G = G' > T for some T and the ring Z[T]/annG' is intepretable in G.
Abstract: We investigate solvable groups of finite Morley rank. We find conditions on G for G' to split in G. In particular, if G' is abelian and Z (G) = 1 we prove that G = G' > T for some T and the ring Z[T]/annG' is intepretable in G. We exploit the methods used in proving these results to find more information about solvable groups.
TL;DR: In this article, the authors use invariant theory to detect unexpected multiplicative relations in H*(Z',, F2) for n > 16. The complexity of the numerical evidence which they present explains the absence of complete calculations for n ≥ 16.
Abstract: Some time ago Nakaoka IN] determined the additive structure of H*(Z.,F2). Around the same time, the ring structure of H*(274, F2) was calculated and it was assumed that the same type of simple multiplicative relations would appear for n > 4. Since then, most work has concentrated on the embedding 2;. ~ ,~o, using the polynomial ring structure of H*(Xo~, F2). In particular, most of the recent work in [HI was explicitly or implicitly described in [ M M ] more than a decade ago, and provides no new information on the multiplicative structure of the mod 2 cohomology of finite symmetric groups. In this paper we use invariant theory to detect unexpected multiplicative relations in H*(Z',, F2). The complicated nature of the numerical evidence which we present explains the absence of complete calculations for n > 16. The rings of invariants which we study are at the core of any computation of H*(2;., F2). They build up sucessively, yielding relations rich in symmetry but of a highly convoluted type. The following problem lies at the heart of all this. Let P. be a polynomial ring k over F2 on n variables, and let P..k = (~P"" Then Ek acts by permuting blocks of generators. 1
TL;DR: General expressions for the circulating (resonant) and output fields and intensities of various configurations of such fiber loop and ring resonators are derived and tabulated.
Abstract: The theory of optical fiber loop and ring resonators with multiple couplers is generalized. In Part 1 of the paper, general expressions for the circulating (resonant) and output fields and intensities of various configurations of such fiber loop and ring resonators are derived and tabulated. Computed results are presented as graphs. Special characteristics and possible applications of these loop and ring resonators are discussed. For example, they can be used as frequency selective beam splitters. Performance parameters of these loops and rings such as finesses, peak transmission, and contrast, etc. are treated in Part 2 of the paper.
TL;DR: In this article, it was shown that Lusztig's homomorphism from an affine Hecke algebra to the direct sum-mand of its asymptotic algebra corresponding to the lowest two-sided cell is related to the homomorphisms constructed by Chriss and Ginzburg using equivariant K-theory.