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1.
Let t be the flow (parametrized with respect to arc length) of a smooth unit vector field v on a closed Riemannian manifold M n , whose orbits are geodesics. Then the (n-1)-plane field normal to v, v, is invariant under d t and, for each x M, we define a smooth real function x (t) : (1 + i (t)), where the i(t) are the eigenvalues of AA T, A being the matrix (with respect to orthonormal bases) of the non-singular linear map d2t , restricted to v at the point x -t M n.Among other things, we prove the Theorem (Theorem II, below). Assume v is also volume preserving and that x ' (t) 0 for all x M and real t; then, if x t : M M is weakly missng for some t, it is necessary that vx 0 at all x M.  相似文献   

2.
Given a square matrixM of ordern and a vectorq n , the linear complementarity problem is the problem of either finding aw n and az n such thatwMz=q,w0,z0 andw T z=0 or showing that no such (w, z) exists. This problem is denoted asLCP(q, M). We say that a solution (w, z) toLCP(q, M) is degenerate if the number of positive coordinates in (w, z) is less thann. As in linear programming, degeneracy may cause cycling in an adjacent vertex following methods like Lemke's algorithm. Moreover, ifLCP(0,M) has a nontrivial solution, a condition related to degeneracy, then unless certain other conditions are satisfied, the algorithm may not be able to decide about the solvability of the givenLCP(q, M). In this paper we review the literature on the implications of degeneracy to the linear complementarity theory.  相似文献   

3.
Let be the uniform triangulation generated by the usual three-directional mesh of the plane and let 1 be the unit square consisting of two triangles of . We study the space of piecewise polynomial functions in C k (R 2) with support 1 having a sufficiently high degree n, which are symmetrical with respect to the first diagonal of 1. Such splines are called 1-splines. We first compute the dimension of this space in function of n and k. Then, for any fixed k0, we prove the existence of 1-splines of class C k and minimal degree. These splines are not unique. Finally, we describe an algorithm computing the Bernstein–Bézier coefficients of these splines, and we give an example.  相似文献   

4.
LetG n ()be the semi-direct product of the symmetric groupS n by the Steinberg groupSt n ()of a ringWe first prove thatG n ()has a Coxeter-type presentation. The canonical morphism St n () GL n ()extends to a group homo Gn() GL n ()We next determine the kernel of for n = We also give an expression for the generator of the algebraic K group K 2(Z)of the integers in terms of permutation matrices.  相似文献   

5.
Complete Subobjects of Fuzzy Sets Over MV-Algebras   总被引:2,自引:1,他引:1  
A subobjects structure of the category -FSet of -fuzzy sets over a complete MV-algebra is investigated, where an -fuzzy set is a pair A = (A, ) such that A is a set and : A × A is a special map. Special subobjects (called complete) of an -fuzzy set A which can be identified with some characteristic morphisms A * = (L × L, ) are then investigated. It is proved that some truth-valued morphisms are characteristic morphisms of complete subobjects.  相似文献   

6.
In this paper we consider the problem of determining and constructing E- and MV-optimal block designs to use in experimental settings where treatments are applied to experimental units occurring in b blocks of size k, k. It is shown that some of the well-known methods for constructing E- and MV-optimal unequally replicated designs having k fail to yield optimal designs in the case where . Some sufficient conditions are derived for the E- and MV-optimality of block designs having and methods for constructing designs satisfying these sufficient conditions are given.  相似文献   

7.
We derive Sobolev inequalities for Besov spaces B p,p (F), 0<<1, 1p< on d-sets F in R n , dn, from a metric property of the Bessel capacity on R n . We first extend Kaimanovitch's result on the equivalence of Sobolev and capacitary inequalites for contractive p-norms in a general setting allowing unbounded Lévy kernels. A simple part of the Jonsson–Wallin trace theorem for Besov spaces and some basic properties of Bessel and Besov capacities on R n are then utilized in getting the desired inequalities. When p=2, the Besov space being considered is a non-local regular Dirichlet space and gives rise to a jump type symmetric Markov process M over the d-set. The upper bound of the transition function of M and metric properties of M -polar sets are then exhibited.  相似文献   

8.
We study the class of bounded C 0-semigroups T=(T t ) t0 on a Banach space X satisfying the asymptotic finite dimensionality condition: codim X 0(T)<, where X 0(T):={x X:limt T t x=0}. We prove a theorem which provides some necessary and sufficient conditions for asymptotic finite dimensionality.  相似文献   

9.
M. Käärik  K. Pärna 《Acta Appl Math》2003,78(1-3):175-183
Let P be a probability distribution on a separable metric space (S,d). We study the following problem of approximation of a distribution P by a set from a given class A2 S : W(A,P) S (d(x,A))P(dx)min AA , where is a nondecreasing function. A special case where A is a parametric class A={A():T} is considered in detail. Our main interest is to obtain convergence results for sequences {A * n }, where A * n is an optimal set for a measure P n satisfying P n P, as n.  相似文献   

10.
We express the real connective K-theory groups o4k–1(B Q ) ofthe quaternion group Q of order = 2 j 8 in terms of therepresentation theory of Q by showing o4k–1(B Q ) = Sp(S 4k+3/Q )where is any fixed point free representation of Q in U(2k + 2).  相似文献   

11.
Let ( t ) t0 be a -semistable convolution semigroup of probability measures on a Lie groupG whose idempotent 0 is the Haar measure on some compact subgroupK. Then all the measures 1 are supported by theK-contraction groupC K() of the topological automorphism ofG. We prove here the structure theoremC K()=C()K, whereC() is the contraction group of . Then it turns out that it is sufficient to study semistable convolution semigroups on simply connected nilpotent Lie groups that have Lie algebras with a positive graduation.  相似文献   

12.
Roozbeh Hazrat 《K-Theory》2002,27(4):293-328
Employing Bak's dimension theory, we investigate the nonstable quadratic K-group K 1,2n (A, ) = G 2n (A, )/E 2n (A, ), n 3, where G 2n (A, ) denotes the general quadratic group of rank n over a form ring (A, ) and E 2n (A, ) its elementary subgroup. Considering form rings as a category with dimension in the sense of Bak, we obtain a dimension filtration G 2n (A, ) G 2n 0(A, ) ; G 2n 1(A, ) ... E 2n (A, ) of the general quadratic group G 2n (A, ) such that G 2n (A, )/G 2n 0(A, ) is Abelian, G 2n 0(A, ) G 2n 1(A, ) ... is a descending central series, and G 2n d(A)(A, ) = E 2n (A, ) whenever d(A) = (Bass–Serre dimension of A) is finite. In particular K 1,2n (A, ) is solvable when d(A) < .  相似文献   

13.
In this paper we present a study of spaces of splines in C k (R 2) with supports the square 1 and the lozenge 1 formed respectively by four and eight triangles of the uniform four directional mesh of the plane. Such splines are called 1 and 1-splines. We first compute the dimension of the space of 1-splines. Then we prove the existence of a unique 1-spline of minimal degree for any fixed k0. By using this last result, we also prove the existence of a unique 1-spline of minimal degree. Finally, we describe algorithms allowing to compute the Bernstein–Bézier coefficients of 1-spline and 1-spline of minimal degree.  相似文献   

14.
In this article we prove a Liouville type theorem for p-harmonic morphisms. We show that if : MNis a p-harmonic morphism (p2) from a complete noncompact Riemannian manifold Mof nonnegative Ricci curvature into a Riemannian manifold Nof nonpositive scalar curvature such that the p-energy E p (), or (2p–2)-energy E 2p–2() is finite, then is constant.  相似文献   

15.
In the previous part of this paper, we constructed a large family of Hecke algebras on some classical groups G defined over p-adic fields in order to understand their admissible representations. Each Hecke algebra is associated to a pair (J , ) of an open compact subgroup J and its irreducible representation which is constructed from given data = (, P0, ). Here, is a semisimple element in the Lie algebra of G, P0 is a parahoric subgroup in the centralizer of in G, and is a cuspidal representation on the finite reductive quotient of P0. In this paper, we explicitly describe those Hecke algebras when P0 is a minimal parahoric subgroup, is trivial and is a character.  相似文献   

16.
Let be a class of groups. Given a group G, assign to G some set of its subgroups =(G). We say that is a G-covering system of subgroups for (or, in other words, an -covering system of subgroups in G) if G whenever either =Ø or Ø and every subgroup in belongs to . We find the systems of subgroups in the class of finite soluble groups G which are simultaneously the G-covering systems of subgroups for the classes of p-supersoluble and p-nilpotent groups.  相似文献   

17.
Lie theory renders a concept of curvature for the geometries (,) introduced by W. Benz [1]. Among regular curves in the chains of (, ) are characterized by =0.  相似文献   

18.
The following statement is proved. Letu be a subharmonic function in the region and u the associated measure. Then there exists a functionf holomorphic in and such that if f is the associated measure of the function in ¦f¦, then ¦u(z)–ln¦f(z)¦ A¦ln s¦+B¦ln diam¦+ s(¦lns¦+1)+C. hold at every point z for which the setsD(z, t)={w: ¦w–z¦},t(0,s) lie in and satisfy(D(z, t))t both for= u and for= f . In the case where is an unbounded region, In diam should be replaced by ln ¦z¦. The constants, , do not depend on andu.

. . .  相似文献   

19.
Kolesov  A. Yu.  Rozov  N. Kh. 《Mathematical Notes》2001,69(5-6):790-798
We consider the boundary-value problem u tt + u t + (1 + cos2)sin u =2 u xx, u x|x=0=ux|x==0, where 0<1, =(1+)t, ,> 0, and the sign of is arbitrary. It is proved that for an appropriate choice of the external parameters and and for sufficiently small the number of exponentially stable solutions 2-periodic in can be made equal to an arbitrary predefined number.  相似文献   

20.
We exhibit new invariants of the contact structure E(), the contact flow F and the transverse symplectic geometry of a contact manifold (M, ). The invariant of contact structures generalizes to transversally oriented foliations. We focus on the particular cases of orientations of smooth manifolds and transverse orientations of foliations. We define the transverse Calabi invariants and determine their kernels.Supported in part by NSF grants DMS 90-01861 and DMS 94-03196.  相似文献   

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