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We discuss projective families of lines of ℙ n , and in particular congruences of order one. After giving general results, we obtain a complete classification of the case of ℙ4 in which there is a fundamental curve. Received: 2 August 2000 / Revised version: 11 July 2001  相似文献   

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In this paper, we consider a discrete version of Aleksandrov's projection theorem. We prove that an origin-symmetric convex lattice set, whose lattice's y-coordinates' absolute values are not bigger than 2, can be uniquely determined by its lattice projection counts if its cardinality is not 11. This partly answers a question on the discrete version of Aleksandrov's projection theorem which was proposed by Gardner, Gronchi and Zong in 2005.  相似文献   

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We define a version of the Radon transform for monogenic functions which is based on Szegő kernels. The corresponding Szegő–Radon projection is abstractly defined as the orthogonal projection of a Hilbert module of left monogenic functions onto a suitable closed submodule of functions depending only on two variables. We also establish the inversion formula based on the dual transform.  相似文献   

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We consider the optimal dividend problem for the insurance risk process in a general Lévy process setting. The objective is to find a strategy which maximizes the expected total discounted dividends until the time of ruin. We give sufficient conditions under which the optimal strategy is of barrier type. In particular, we show that if the Lévy density is a completely monotone function, then the optimal dividend strategy is a barrier strategy. This approach was inspired by the work of Avram et al. [F. Avram, Z. Palmowski, M.R. Pistorius, On the optimal dividend problem for a spectrally negative Lévy process, The Annals of Applied Probability 17 (2007) 156–180], Loeffen [R. Loeffen, On optimality of the barrier strategy in De Finetti’s dividend problem for spectrally negative Lévy processes, The Annals of Applied Probability 18 (2008) 1669–1680] and Kyprianou et al. [A.E. Kyprianou, V. Rivero, R. Song, Convexity and smoothness of scale functions with applications to De Finetti’s control problem, Journal of Theoretical Probability 23 (2010) 547–564] in which the same problem was considered under the spectrally negative Lévy processes setting.  相似文献   

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We study the stability of the zero solution to a nonlinear system of ordinary differential equations on the base of its Takagi–Sugeno (TS) representation. As is known, the most constructive stability and stabilization conditions for TS systems stated as linear matrix inequalities are established with the help of a general quadratic Lyapunov function (GQLF). However, such conditions are often too rigid. Using a modification of the Lyapunov direct method, we propose asymptotic stability conditions with weaker requirements to GQLF. They allow an application to a wider class of systems. We also give some illustrative examples.  相似文献   

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In this paper we prove the existence of a nontrivial solution to the nonlinear Schrödinger–Maxwell equations in R3R3, assuming on the nonlinearity the general hypotheses introduced by Berestycki and Lions.  相似文献   

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We classify the rank two BCDL 2003-geometries of O’Nan and show that the maximal rank of a BCDL 2003-geometry for O’Nan is 4. This bound is sharp since it is satisfied by the rank four geometry given by Buekenhout (Contemp Math 45:1–32, 1985).  相似文献   

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We discuss a general class of trigonometric functions whose corresponding Fourier series can be used to calculate several interesting numerical series. Particular cases are presented.  相似文献   

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Restrictions are indicated on a complex-valued measure in the spaceR m ,m 2., under which the n-fold convolution n*,n 2, is uniquely determined by its values on any semispacex 1<r, rR.Translated from Teoriya Funktsii, Funktsional'nyi Analiz i Ikh Prilozheniya, No. 50, pp. 86–90, 1988.  相似文献   

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Faulhuber and Steinerberger conjectured that the logarithmic derivative of ?4 has the property that y2?4(y)/?4(y) is strictly decreasing and strictly convex. In this small note, we prove this conjecture.  相似文献   

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In conversation I was told by Professor R.Brigham the following conjecture [1].Let G(n) be a graph of n vertices.Denote by f(G(n))=t the smallest integer for which the vertices of G(n) can be covered by t cliques. Denote further by h(G(n)) =l the largest integer for which there are l edges of our G(n) no two of Which are in the same clique.Clearly h(G(n)) can be much larger than f(G(n))e.g.if n=2m and G(n) is the complete bipartite graph of m white and m black vertices.Then l(G(n))=m and l(G(n))=m~2. It was conjectured that if G(n).has no isolated vertices then  相似文献   

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We prove and discuss some new (H p ,L p )-type inequalities of weighted maximal operators of Vilenkin-Nörlund means with non-increasing coefficients {q k : k ? 0}. These results are the best possible in a special sense. As applications, some well-known as well as new results are pointed out in the theory of strong convergence of such Vilenkin-Nörlund means. To fulfil our main aims we also prove some new estimates of independent interest for the kernels of these summability results.  相似文献   

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