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1.
Hypersurfaces in a Unit Sphere Sn+1(1) with Constant Scalar Curvature   总被引:3,自引:0,他引:3  
The paper considers n-dimensional hypersurfaces with constantscalar curvature of a unit sphere Sn–1(1). The hypersurfaceSk(c1)xSnk(c2) in a unit sphere Sn+1(1) is characterized,and it is shown that there exist many compact hypersurfaceswith constant scalar curvature in a unit sphere Sn+1(1) whichare not congruent to each other in it. In particular, it isproved that if M is an n-dimensional (n > 3) complete locallyconformally flat hypersurface with constant scalar curvaturen(n–1)r in a unit sphere Sn+1(1), then r > 1–2/n,and (1) when r (n–2)/(n–1), if then M is isometric to S1xSn–1(c),where S is the squared norm of the second fundamental form ofM; (2) there are no complete hypersurfaces in Sn+1(1) with constantscalar curvature n(n–1)r and with two distinct principalcurvatures, one of which is simple, such that r = (n–2)/(n–1)and   相似文献
2.
In this paper, we prove that n-dimensional complete and connected submanifolds with parallel mean curvature vector H in the (n+p)-dimensional Euclidean space E n + p are the totally geodesic Euclidean space E n , the totally umbilical sphere S n (c) or the generalized cylinder S n − 1 (c) ×E 1 if the second fundamental form h satisfies <h>2n 2|H|2/ (n− 1). Received: 28 November 2000 / Revised version: 7 May 2001  相似文献
3.
Given a complete k-partite graph G=(V1,V2,…,Vk;E) satisfying |V1|=|V2|=?=|Vk|=n and weights of all  k-cliques of G, the  k-dimensional assignment problem finds a partition of vertices of G into a set of (pairwise disjoint) n k-cliques that minimizes the sum total of weights of the chosen cliques. In this paper, we consider a case in which the weight of a clique is defined by the sum of given weights of edges induced by the clique. Additionally, we assume that vertices of G are embedded in the d-dimensional space Qd and a weight of an edge is defined by the square of the Euclidean distance between its two endpoints. We describe that these problem instances arise from a multidimensional Gaussian model of a data-association problem.We propose a second-order cone programming relaxation of the problem and a polynomial time randomized rounding procedure. We show that the expected objective value obtained by our algorithm is bounded by (5/2−3/k) times the optimal value. Our result improves the previously known bound (4−6/k) of the approximation ratio.  相似文献
4.
In semilinear elliptic equations, we prove that the necessary and sufficient condition for the comparison theorem of positive solutions to be valid is that the nonlinear term is sublinear. Our theorem needs neither any regularity of the nonlinear term nor the smoothness of the boundary. Applying this theorem, we prove the uniqueness of positive solutions for the Dirichlet problem. Received: 9 April 2008  相似文献
5.
The univariate generalized beta- and generalized F-distributions are frequently in recent statistical modellings and applications. They have richer properties than the standard beta- and Snedecor F-distributions and provide more flexibility than these distributions, of which they are natural extensions. Their connection with the Gauss hypergeometric function and Lauricella functions leads to further generalizations and important properties. This article gives a unified and up-to-date treatment of these two generalized distributions using only simple arguments. Proofs are given for some original results and a complete reference to their source is provided for established ones. The important problem of parameter estimation is also studied.  相似文献
6.
An algorithm for suppressing the chaotic oscillations in non-linear dynamical systems with singular Jacobian matrices is developed using a linear feedback control law based upon the Lyapunov–Krasovskii (LK) method. It appears that the LK method can serve effectively as a generalised method for the suppression of chaotic oscillations for a wide range of systems. Based on this method, the resulting conditions for undisturbed motions to be locally or globally stable are sufficient and conservative. The generalized Lorenz system and disturbed gyrostat equations are exemplified for the validation of the proposed feedback control rule.  相似文献
7.
We study a complex 3-dimensional family of classical Schottky groups of genus 2 as monodromy groups of the hypergeometric equation. We find non-trivial loops in the deformation space; these correspond to continuous integer-shifts of the parameters of the equation.

  相似文献

8.
In an article by Sasaki and Yoshida (2000), we encountered Schottky groups of genus 2 as monodromy groups of the hypergeometric equation with purely imaginary exponents. In this paper we study automorphic functions for these Schottky groups, and give a conjectural infinite product formula for the elliptic modular function .

  相似文献

9.
Let G be a weighted graph with n vertices and m edges. We address the d-cycle problem, i.e., the problem of finding a subgraph of minimum weight with given cyclomatic number d. Hartvigsen [Minimum path bases, J. Algorithms 15 (1993) 125–142] presented an algorithm with running time O(n2m) and O(n2d−1m2) for the cyclomatic numbers d=1 and d2, respectively. Using a (d+1)-shortest-paths algorithm, we develop a new more efficient algorithm for the d-cycle problem with running time O(n2d−1+n2m+n3logn).  相似文献
10.
Spaces with radially symmetric curvature at base point are shown to be diffeomorphic to space forms. Furthermore, they are either isometric to or under a radially symmetric metric, to with Riemannian universal covering of equipped with a radially symmetric metric, or else have constant curvature outside a metric ball of radius equal to the injectivity radius at .

  相似文献

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