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91.
We consider compact hyperbolic Coxeter polytopes whose Coxeter diagram contains a unique dotted edge. We prove that such a polytope in d-dimensional hyperbolic space has at most d+3 facets. In view of results by Kaplinskaja [I.M. Kaplinskaya, Discrete groups generated by reflections in the faces of simplicial prisms in Lobachevskian spaces, Math. Notes 15 (1974) 88-91] and the second author [P. Tumarkin, Compact hyperbolic Coxeter n-polytopes with n+3 facets, Electron. J. Combin. 14 (2007), R69, 36 pp.], this implies that compact hyperbolic Coxeter polytopes with a unique pair of non-intersecting facets are completely classified. They do exist only up to dimension 6 and in dimension 8. 相似文献
92.
Emmanuel Rio 《Journal of Theoretical Probability》2009,22(1):146-163
We obtain precise constants in the Marcinkiewicz-Zygmund inequality for martingales in
for p>2 and a new Rosenthal type inequality for stationary martingale differences for p in ]2,3]. The Rosenthal inequality is then extended to stationary and adapted sequences. As in Peligrad et al. (Proc. Am.
Math. Soc. 135:541–550, [2007]), the bounds are expressed in terms of
-norms of conditional expectations with respect to an increasing field of sigma algebras. Some applications to a particular
Markov chain are given.
相似文献
93.
Rasul A. Khan 《Journal of Theoretical Probability》2009,22(2):348-364
The Dubins–Savage inequality is generalized by using the pth (1<p≤2) conditional moment of the martingale differences. This inequality is further extended under suitable conditions when p>2. Another martingale inequality due to Freedman is also generalized when 0<p≤2. Implications of these inequalities for strong convergence are discussed. Some general exponential inequalities are also
given for martingales (supermartingales) under suitable conditions.
相似文献
94.
We present a multivariate generating function for all n×n nonnegative integral matrices with all row and column sums equal to a positive integer t, the so called semi-magic squares. As a consequence we obtain formulas for all coefficients of the Ehrhart polynomial of
the polytope B
n
of n×n doubly-stochastic matrices, also known as the Birkhoff polytope. In particular we derive formulas for the volumes of B
n
and any of its faces. 相似文献
95.
96.
97.
S. S. Tameroğlu 《基于设计的结构力学与机械力学》2013,41(3):381-413
Abstract ABSTRACT This paper presents a new solution method for several types of buckling and bending problems of beams and plates. The method is based on the use of a non-orthogonal series expansion, consisting of some specially chosen trigonometric functions for the elastic curve y of a beam or the deflection surface w of a plate. The calculations are performed using the Euler and Bernoulli polynomials, under realistic approximations of limiting values of the boundary conditions. In this method, it is not necessary to use the solution of the differential equation of the problem, Results obtained using the method are shown to be consistent with known solutions. 相似文献
98.
99.
100.
《Optik》2014,125(24):7198-7202
In the present paper, laser pulse distortion/breakup and the effect of the plasma channel on the laser propagation through the collisional plasma have been studied by using moment theory approach. Second order nonlinear differential equations of the beam width parameter have been derived for the propagation of the laser through uniform homogenous plasma and preformed plasma channel having parabolic density profile. Differential equations of beam width parameter have been solved numerically using Runge Kutta method. It has been observed from analysis that when the laser pulse propagates through the homogenous plasma, the low intensity front and rear parts of the laser get defocused/diffracted and the high intensity central/main portion of the laser pulse gets self-guided. As a result of this, the laser pulse gets distorted. This distortion of the laser has not been observed when the laser pulse is propagated through the plasma channel having density minimum at the axis and maximum at the edges. The laser pulse is guided as a whole, even the low intensity front and rear parts of the laser are also guided. Therefore, the plasma channel is useful to prevent the distortion/breakup of the laser. 相似文献