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We investigate the indecomposable decomposition of the modular standard modules of two families of association schemes of finite order. First, we show that, for each prime number p, the standard module over a field F of characteristic p of a residually thin scheme S of p-power order is an indecomposable FS-module. Second, we describe the indecomposable decomposition of the standard module over a field of positive characteristic of a wreath product of finitely many association schemes of rank 2.  相似文献   

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S. Sharma  M. Rana 《Discrete Mathematics》2018,341(7):1903-1914
This paper provides the combinatorial interpretations of twelve mock theta functions in terms of (n+t)-color partitions with attached weights. We further find combinatorial interpretations of the generalized versions of all these mock theta functions and present these into six families.  相似文献   

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The main purpose of this work is to introduce noncommutative relative schemes and establish some of basic properties of schemes and scheme morphisms. In particular, we prove an analogue of the canonical bijection: ((X, O), Spec(A)) Hom (A, (X, O)). We define a noncommutative version of the ech cohomology of an affine cover and show that the ech cohomology can be used to compute higher direct images. This fact is applied here to compute cohomology of invertible sheaves on skew projective spaces and in [LR3] to study D-modules on quantum flag varieties.  相似文献   

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LetY = (X, {R i } oid) denote aP-polynomial association scheme. By a kite of lengthi (2 i d) inY, we mean a 4-tuplexyzu (x, y, z, u X) such that(x, y) R 1,(x, z) R 1,(y, z) R 1,(u, y) R i–1,(u, z) R i–1,(u, x) R i. Our main result in this paper is the following.  相似文献   

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Summary Singularly perturbed boundary value ordinary differential problems are considered, where the problem defining the reduced solution is singular. For numerical approximation, families of symmetric difference schemes, which are equivalent to certain collocation schemes based on Gauss and Lobatto points, are used. Convergence results, previously obtained for the regular singularly perturbed case, are extended. While Gauss schemes are extended with no change, Lobatto schemes require a small modification in the mesh selection procedure. With meshes as prescribed in the text, highly accurate solutions can be obtained with these schemes for singular singularly perturbed problems at a very reasonable cost. This is demonstrated by examples.This research was completed while the author was visiting the Department of Applied Mathematics, Weizmann Inst., Rehovot, Israel. The author was supported in part under NSERC grant A4306  相似文献   

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This paper studies finite volume schemes for scalar hyperbolic conservation laws on evolving hypersurfaces of \(\mathbb {R}^3\) . We compare theoretical schemes assuming knowledge of all geometric quantities to (practical) schemes defined on moving polyhedra approximating the surface. For the former schemes error estimates have already been proven, but the implementation of such schemes is not feasible for complex geometries. The latter schemes, in contrast, only require (easily) computable geometric quantities and are thus more useful for actual computations. We prove that the difference between approximate solutions defined by the respective families of schemes is of the order of the mesh width. In particular, the practical scheme converges to the entropy solution with the same rate as the theoretical one. Numerical experiments show that the proven order of convergence is optimal.  相似文献   

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The notion of a balanced set of vectors is defined, and the classification of such sets suggested. A slightly stronger condition is considered for association schemes, with the following result. LetX be ad-class symmetric association scheme with Bose-Mesner algebraM and Krein parametersq ij h , and let E = Et (0 t d) be any primitive idempotent ofM. For eachx X letx E denote the diagonal matrix withy, y entryE xy(y X). Define the representation diagramD E on the nodes 0, 1, ...,d by drawing an undirected arc between any nodesh, j for whichq tj h > 0. CallD E an augmented tree if it has a single loop, whose removal yields a tree. Writexy = i ifx, y X are ith associates (0 i d).  相似文献   

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Estimates of stability of weighted differences in norms of Banach spaces are constructed. On the basis of these, corresponding estimates of stability in the norms of the spaces Ch and Lph, 1 P < , are obtained for difference schemes which approximate an initial-boundary value problem for the heat equation with boundary conditions of the first, second, and third kinds. In addition, the estimates of resolvents of difference elliptic operators in Ch and Lph, 1 P < , obtained in this article are used in an essential way.Translated from Ukrainskii Matematicheskii Zhurnal, Vol. 42, No. 9, pp. 1254–1258, September, 1990.  相似文献   

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《Discrete Mathematics》2024,347(1):113658
Bent partitions are partitions of an elementary abelian group, which have similarities to partitions from spreads. In fact, a spread partition is a special case of a bent partition. In particular, bent partitions give rise to a large number of (vectorial) bent functions. Examples of bent partitions, which generalize the Desarguesian spread, have been presented by Anbar, Meidl and Pirsic, 2021, 2022. Bent partitions, which generalize some other classes of (pre)semifield spreads, have been presented by Anbar, Kalaycı, Meidl 2023. In this article, it is shown that these bent partitions induce (pk+1)-class amorphic associations schemes on Fpm×Fpm, where k is a divisor of m with special properties. This implies a construction of amorphic association schemes from some classes of (pre)semifields.  相似文献   

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Let be a self-dual P-polynomial association scheme. Then there are at most 12 diagonal matricesT such that (PT)3 =I. Moreover, all of the solutions for the classical infinite families of such schemes (including the Hamming scheme) are classified.This work was supported by NSF grant DMS-9400510.  相似文献   

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A perfect secret-sharing scheme is a method of distributing a secret among a set of participants such that only qualified subsets of participants can recover the secret and the joint shares of the participants in any unqualified subset is statistically independent of the secret. The set of all qualified subsets is called the access structure of the scheme. In a graph-based access structure, each vertex of a graph \(G\) represents a participant and each edge of \(G\) represents a minimal qualified subset. The information ratio of a perfect secret-sharing scheme is defined as the ratio between the maximum length of the share given to a participant and the length of the secret. The average information ratio is the ratio between the average length of the shares given to the participants and the length of the secret. The infimum of the (average) information ratios of all possible perfect secret-sharing schemes realizing a given access structure is called the (average) information ratio of the access structure. Very few exact values of the (average) information ratio of infinite families of access structures are known. Csirmaz and Tardos have found the information ratio of all trees. Based on their method, we develop our approach to determining the exact values of the average information ratio of access structures based on trees.  相似文献   

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