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In a remark to Green’s conjecture, Paranjape and Ramanan analysed the vector bundle E which is the pullback by the canonical map of the universal quotient bundle \(T_{\mathbb {P}^{g-1}}(-1)\) on \(\mathbb {P}^{g-1}\) and stated a more general conjecture and proved it for the curves with Clifford Index 1 (trigonal and plane quintics). In this paper, we state the conjecture for general linear systems and obtain results for the case of hyper-elliptic curves.  相似文献   

5.
Let A and B be commutative locally convex algebras with unit. A is assumed to be a uniform topological algebra. Let Φ be an injective homomorphism from A to B. Under additional assumptions, we characterize the continuity of the homomorphism Φ?1/Im?Φ by the fact that the radical (or strong radical) of the closure of Im?Φ has only zero as a common point with Im?Φ. This gives an answer to a conjecture concerning some automatic continuity theorems on uniform topological algebras.  相似文献   

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A conjecture of S. Znam [1] is disproved by means of a counterexample.  相似文献   

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A counterexample is given to a conjecture by Tutte on the minimum number of spanning trees that a 3-connected planar graph with a prescribed number of edges may have.  相似文献   

8.
K.L. Ng 《Discrete Mathematics》2009,309(6):1603-1610
For a connected graph G containing no bridges, let D(G) be the family of strong orientations of G; and for any DD(G), we denote by d(D) the diameter of D. The orientation number of G is defined by . Let G(p,q;m) denote the family of simple graphs obtained from the disjoint union of two complete graphs Kp and Kq by adding m edges linking them in an arbitrary manner. The study of the orientation numbers of graphs in G(p,q;m) was introduced by Koh and Ng [K.M. Koh, K.L. Ng, The orientation number of two complete graphs with linkages, Discrete Math. 295 (2005) 91-106]. Define and . In this paper we prove a conjecture on α proposed by K.M. Koh and K.L. Ng in the above mentioned paper, for qp+4.  相似文献   

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This article concerns an old conjecture due to E. T. Whittaker, aiming to describe the group uniformizing an arbitrary hyperelliptic Riemann surface as an index two subgroup of the monodromy group of an explicit second order linear differential equation with singularities at the values .

Whittaker and collaborators in the thirties, and R. Rankin some twenty years later, were able to prove the conjecture for several families of hyperelliptic surfaces, characterized by the fact that they admit a large group of symmetries. However, general results of the analytic theory of moduli of Riemann surfaces, developed later, imply that Whittaker's conjecture cannot be true in its full generality.

Recently, numerical computations have shown that Whittaker's prediction is incorrect for random surfaces, and in fact it has been conjectured that it only holds for the known cases of surfaces with a large group of automorphisms.

The main goal of this paper is to prove that having many automorphisms is not a necessary condition for a surface to satisfy Whittaker's conjecture.

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10.
In 1983 C. Thomassen conjectured that for every k, g∈? there exists d such that any graph with average degree at least d contains a subgraph with average degree at least k and girth at least g. Kühn and Osthus [2004] proved the case g = 6. We give another proof for the case g = 6 which is based on a result of Füredi [1983] about hypergraphs. We also show that the analogous conjecture for directed graphs is true. © 2010 Wiley Periodicals, Inc. J Graph Theory 67:316‐331,2011  相似文献   

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Let K be a totally real algebraic number field of class number hK and L a totally imaginary quadratic extension of K of class number hL. Hecke conjectured that there exists an elementary formula for the first factor hL/hK of the class number of L. The paper develops a theory which allows computation of hL/hK in terms of the periods of certain complex differential forms associated to a manifold defined in a natural way from K. Thus, Hecke's conjecture is reduced to the problem of finding elementary formulas for these periods. The essential idea of the proof consists of establishing a Kronecker limit formula for the non-analytic Eisenstein series for the Hilbert modular group for K.Research supported by NSF Grant GP 20538  相似文献   

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Zbigniew Lonc 《Order》1991,8(1):17-27
Let n and c be positive integers. We show that if n is sufficiently large given c then the Boolean lattice consisting of all subsets of an n-element set can be partitioned into chains of size c except for at most c — 1 elements which also form a chain. This settles a conjecture of Griggs.  相似文献   

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This paper is concerned with a recent conjecture of He (Electron. J. Comb. 14(1), 2007) on the spectral reconstruction of matrices. A counterexample is provided by using Hadamard matrices. We also give some results to the above mentioned conjecture (with slight modifications) in the positive direction.  相似文献   

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In this paper, we prove that formally real fields satisfying some explicit conditions on the v-invariant verify a Lam's conjecture concerning signatures of quadratic forms. In particular, it gives a short proof of a Marshall's conjecture for Pythagorean fields.  相似文献   

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A set D of vertices of a graph is k-dependent if every vertex of D is joined to at most k?1 vertices in D. Let βk(G) be the maximum order of a k-dependent set in G. A set D of vertices of G is k-dominating if every vertex not in D is joined to at least k vertices of D. Let γk(G) be the minimum order of a k-dominating set in G. Here we prove the following conjecture of Fink and Jacobson: for any simple graph G and any positive integer k, γk(G) ≤ βk(G).  相似文献   

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A linear forest is a graph whose connected components are chordless paths. A linear partition of a graph G is a partition of its edge set into linear forests and la(G) is the minimum number of linear forests in a linear partition. It is well known that la(G)=2 when G is a cubic graph and Wormald [N. Wormald, Problem 13, Ars Combinatoria 23(A) (1987) 332-334] conjectured that if |V(G)|≡0 (mod 4), then it is always possible to find a linear partition in two isomorphic linear forests. Here, we give some new results concerning this conjecture.  相似文献   

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We present an affirmative answer to Stanley's zrank conjecture, namely, the zrank and the rank are equal for any skew partition. We show that certain classes of restricted Cauchy matrices are nonsingular and furthermore, the signs are determined by the number of zero entries. We also give a characterization of the rank in terms of the Giambelli-type matrices of the corresponding skew Schur functions. Our approach also applies to the factorial Cauchy matrices and the inverse binomial coefficient matrices.

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18.
Let A be a Banach algebra, and consider A** equipped with the first Arens product. We establish a general criterion which ensures that A is left strongly Arens irregular, i.e., the first topological centre of A** is reduced to A itself. Using this criterion, we prove that for a very large class of locally compact groups, Ghahramani-Lau's conjecture (cf. [Lau 94] and [Gha-Lau 95]) stating the left strong Arens irregularity of the measure algebra M(G), holds true. (Our methods obviously yield as well the right strong Arens irregularity in the situation considered.)Furthermore, the same condition used above implies that every linear left A**-module homomorphism on A* is automatically bounded and w*-continuous. We finally show that our criterion also yields a partial answer to a question raised by Lau-Ülger (Trans. Amer. Math. Soc. 348 (3) (1996) 1191) on the topological centre of the algebra (A*A)*, for A having a right approximate identity bounded by 1.  相似文献   

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We show that the four-dimensional case of Graver's conjecture is not true.  相似文献   

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