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1.
Pinkall's standard constructions for obtaining a Dupin hypersurface W in N from a Dupin hypersurface M in n , N>n, are studied in the context of Lie sphere geometry. It is shown that a compact Dupin hypersurface W in N with g distinct principal curvatures at each point is reducible to a compact Dupin hypersurface M in n if and only if g=2.This research was supported by NSF Grant No. DMS 87-06015.  相似文献   

2.
In this paper we propose a variable dimension simplicial algorithm for solving the variational inequality problem on the cross product of the nonnegative orthant + m of them-dimensional Euclidean space m and then-dimensional unit simplexS n of n+1. Starting from an arbitrary point (u, v) є + m ×S n, the algorithm generates a piecewise linear path in + m ×S n. The path is traced by making alternately linear programming pivot operations and replacement steps in an appropriate simplicial subdivision of + m ×S n. The algorithm differs from the thus far known algorithm in the number of directions in which it may leave the starting point. More precisely, the algorithm has (n+1)2 m rays to leave the starting point whereas the existing algorithm hasn+m+1 rays. A convergence condition is presented and the accuracy estimation of an approximate solution generated is also given.  相似文献   

3.
A vector optimization problem is given by a feasible setZ n , a vector-valued objective functionf: n l , and an ordering coneC l . We perturb the ordering cone in such a way that the weakly efficient points of the perturbed vector optimization problem given byZ, f, and the perturbed cone are efficient points of the original problem. Especially this means that scalarization methods, which compute in general only weakly efficient points, determine efficient points of the original problem, when they were applied to the perturbed problem.It turns out that the efficient points are the limits of weakly efficient points of the perturbed problems, letting the perturbation tend to zero. On the basis of this, a reference point algorithm is formulated. Finally, we apply this algorithm to a structural optimization problem.  相似文献   

4.
Many global optimization problems can be formulated in the form min{c(x, y): x X, y Y, (x, y) Z, y G} where X, Y are polytopes in p , n , respectively, Z is a closed convex set in p+n, while G is the complement of an open convex set in n . The function c: p+n is assumed to be linear. Using the fact that the nonconvex constraints depend only upon they-variables, we modify and combine basic global optimization techniques such that some new decomposition methods result which involve global optimization procedures only in n . Computational experiments show that the resulting algorithms work well for problems with smalln.  相似文献   

5.
We prove by elementary means a regularity theorem for quasi-isometries of T x n (where T denotes an infinite tree), and of many other metric spaces with similar combinatorial properties, e.g. Cayley graphs of Baumslag–Solitar groups. For quasi-isometries of T x n, it states that the image of {x} x n (xT) is uniformly close to {y} x n for some yT, and there is a well-defined surjection . Even stronger, the image of a quasi-isometric embedding of n+1 in T x n is close to (a geodesic in T)T)x n.  相似文献   

6.
It is proved in this article that any generalized solution of a sufficiently general class of elliptic-type differential inequalities in  n that is non-negative almost everywhere in  n and vanishes almost everywhere on an open set n is trivial in  n .  相似文献   

7.
In this article semilinear hyperbolic first order systems in two variables are considered, whose nonlinearity satisfies a global Lipschitz condition. It is shown that these systems admit unique global solutions in the Colombeau algebraG(2). In particular, this provides unique generalized solutions for arbitrary distributions as initial data. The solution inG(2) is shown to be consistent with the locally integrable or the distributional solutions, when they exist.  相似文献   

8.
Let {V(k) :K1} be a sequence of independent, identically distributed random vectors in d with mean vector . The mappingg is a twice differentiable mapping from d to 1. Setr=g(). A bivariate central limit theorem is proved involving a point estimator forr and the asymptotic variance of this point estimate. This result can be applied immediately to the ratio estimation problem that arises in regenerative simulation. Numerical examples show that the variance of the regenerative variance estimator is not necessarily minimized by using the return state with the smallest expected cycle length.This research was supported by Army Research Office Contract DAAG29-84-K-0030. The first author was also supported by National Science Foundation Grant ECS-8404809 and the second author by National Science Foundation Grant MCS-8203483.  相似文献   

9.
Summary We present an algorithm which enables us to calculate one particular subgradient of a convex functionf: 2 at a given point. Such a calculation is required in many existing numerical methods for convex nondifferentiable optimization. The novelty of our approach lies in the assumption that only the values off are computable and no analytical formula for the subdifferential is known. We include some numerical examples.  相似文献   

10.
Summary Given strong uniqueness for an Itô's stochastic equation with discontinuous coefficients, we prove that its solution can be constructed on any probability space by using, for example, Euler's polygonal approximations. Stochastic equations in d and in domains in d are considered.Research supported by the Hungarian National Foundation of Scientific Research No. 2990.Supported in part by NSF Grant DMS-9302516  相似文献   

11.
In this paper we introduce the inverse Gaussian and Wishart distributions on the cone of real (n, n) symmetric positive definite matricesH n + () and more generally on an irreducible symmetric coneC. Then we study the convergence of random continued fractions onH n + () andC by means of real Lagrangians forH n + () and by new algebraic identities on symmetric cones forC. Finally we get a characterization of the inverse Gaussian distribution onH n + () andC.  相似文献   

12.
We study homogenization in the small period limit for a periodic parabolic Cauchy problem in d and prove that the solutions converge in L 2(d) to the solution of the homogenized problem for each t > 0. For the L2(d)-norm of the difference, we obtain an order-sharp estimate uniform with respect to the L 2(d)-norm of the initial value.Translated from Funktsionalnyi Analiz i Ego Prilozheniya, Vol. 38, No. 4, pp. 86–90, 2004Original Russian Text Copyright © by T. A. SuslinaSupported by RFBR grant No. 02-01-00798.  相似文献   

13.
A sequence of independent and identically distributed random vectorsX n on k is said to belong to the generalized domain of attraction of a nondegenerate random vectorY on k provided that there exist linear operatorsA n on k and nonrandom constantsb n k such that the centered and normalized partial sumsA n (X 1++X n b n converge in distribution toY. In this paper we show that the sequence of norming operatorsA n can always be chosen to vary regularly.Partially supported by NSF Grant DMS-91-03131 at Albion College.  相似文献   

14.
Given a metrizable compact convex setX of a locally convex Hausdorff space, a positive projectionT:C(X, )C(X, ) and a continuous function :X[0, 1], it is shown that under suitable assumptions there exists a positive contraction semigroup onC(X, ) that can be represented in terms of the Lototsky-Schnabl operators associated withT and . Several properties of this semigroup are investigated. In particular, its infinitesimal generator is determined in a core of its domain. WhenX p for somep1, then the generator is shown to be a degenerate elliptic second order differential operator.Dedicated to Professor George Maltese on the occasion of his 60th birthday  相似文献   

15.
Summary We investigate the fundamentality of the set of all continuous ridge functions in the spaceC( n ) as well as inC(X) for a general Banach space,X. Both positive and negative results are obtained. Necessary and sufficient conditions for the fundamentality are given for certain sets of ridge functions inC( n ).  相似文献   

16.
Elementary self-adjoint perturbations of the Laplacian supported by curves with singular angle points in 3 and 4 are studied. The perturbations are shown to be semibounded in 3 and not semibounded in 4. In the latter case semiboundedness may take place in subspaces with a given symmetry, as simple examples illustrate.Translated from Teoreticheskaya i Matematicheskaya Fizika, Vol. 105, No. 1, pp. 3–17, October, 1995.  相似文献   

17.
Let x=g(t,x(t),u(t)) be the governing equation of an optimal control problem with two-point boundary conditions h 0(x(a))+h 1(x(b)) = 0, where x: [a,b] n is continuous, u: [a,b] k-n is piecewise continuous and left continuous, h0,h1: n q are continuously differentiable, and g:[a,b]× k n is continuous. The paper finds functions i C1([a,b]× n ) such that (x(t),u(t)) is a solution of the governing equation if and only if
  相似文献   

18.
ForC 4-embedded manifoldsS 3 which are differmorphic to the standard sphere in 3 the existence of non-constant minimal surfaces bounded byS and intersectingS orthogonally along their boundaries is deduced.This research was supported by the Sonderforschungsbereich 72 of the Deutsche-Forschungs-Gemeinschaft  相似文献   

19.
All Convex Polytopes in 4 the Facets of Which Are Regular Tetrahedra. Continuing in n (n4) the study of convex polytopes the facets of which are regular, it is proved: Regular polytopes and the two bipyramids over the tetrahedron and the icosahedron are the only convex polytopes in 4 the facets of which are regular tetrahedra.  相似文献   

20.
A linear autonomous control system in n is said to be completely controllable iff there existsT>0 such that eachx n can be steered to anyy n in timeT. This paper presents a geometric characterization of this property in the case in which there are constraints on the values which the control maps can assume. A necessary and sufficient condition to get instant controllability (i.e., complete controllability for anyT>0) is also derived. This condition generalizes the well-known Kalman condition to the constrained case.  相似文献   

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