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1.
Letq be a prime power. It is shown that for any hypergraph = {F 1,...,F d(q–1)+1} whose maximal degree isd, there exists Ø 0 , such that 0 (modq).  相似文献   

2.
We obtain asymptotic estimates of meromorphic solutions to the differential equationP n (z, , )=P n–1 (z, , ,..., (m) ) in the angular domain P={z: arg z · }. Here Pn(z, w, w) is a polynomial in all variables, and of degree n with respect to w and w; Pn–1(z, w, w, ..., w(m)) is a polynomial in all variables, and of degree n –1 with respect to w, w, ..., w(m) In the particular case, when the solutions are entire functions, these estimates are more precise than the known estimates that are obtained by using the method of Wiman-Valiron, which cannot be applied to meromorphic solutions in the domain P.Translated from Ukrainskii Matematicheskii Zhurnal, Vol. 44, No. 4, pp. 514–523, April, 1992.  相似文献   

3.
Let w be an element of the Weyl group of sl n + 1. We prove that for a certain class of elements w (which includes the longest element w0 of the Weyl group), there exist a lattice polytope R l(w) , for each fundamental weight i of sl n + 1, such that for any dominant weight = i = 1 n a i i , the number of lattice points in the Minkowski sum w = i = 1 n a i i w is equal to the dimension of the Demazure module E w (). We also define a linear map A w : R l(w) P Z R where P denotes the weight lattice, such that char E w () = e eA(x) where the sum runs through the lattice points x of w .  相似文献   

4.
LetX be the solution of the SDE:dX t = (X t)dB t +b(X t)dt, with andb C b (R) such that >0 for some constant , andB a real Brownian motion. Let be the law ofX onE=C([0, 1],R) andk E* – {0}, whereE* is the topological dual space ofE. Consider the classical form: k (u, v)=u / kv / kd, whereu andv are smooth functions onE. We prove that, if k is closable for anyk in a dense subset ofE* and if the smooth functions are contained in the domain of the generator of the closure of k , must be a constant function.  相似文献   

5.
For a bounded regular Jordan domain in R 2, we introduce and study a new class of functions K() related on its Green function G. We exploit the properties of this class to prove the existence and the uniqueness of a positive solution for the singular nonlinear elliptic equation u+(x,u)=0, in D(), with u=0 on and uC(), where is a nonnegative Borel measurable function in ×(0,) that belongs to a convex cone which contains, in particular, all functions (x,t)=q(x)t ,>0 with nonnegative functions qK(). Some estimates on the solution are also given.  相似文献   

6.
In this paper we introduce left linear theories of exponentN (a set) on the setL as mapsL ×L N (l, ) l · L such that for alll L and , L N the relation (l · ) =l( · ) holds, where · L N is given by ( · )(i) = (i),i N. We assume thatL has a unit, that is an element L N withl · =l, for alll L, and · = , for all L N . Next, left (resp. right)L-modules andL-M-bimodules and their homomorphisms are defined and lead to categoriesL-Mod, Mod-L, andL-M-Mod. These categories are algebraic categories and their free objects are described explicitly. Finally, Hom(X, Y) andX Y are introduced and their properties are investigated.Herrn Professor Dr. D. Pumplün zum 60. Geburtstag gewidmet  相似文献   

7.
n (D) — ,s n (D), v (v=1, 2, ...,s/2) — . m={0x 0<x 1<...<x 2m–1<2,x 2m =x 0+2} , x j +1–x j <(4s max v )–1,j=0, 1, ..., 2m –1, ( ) 2- - n,m 2m , m . , L q - (1q) W ( n )={f 2 :f (n–1)AC 2 , n (D)f 1} 2- - (s n f), m . , - - n,m .

The author expresses his gratitude to Yu. N. Subbotin for a useful discussion on the results of this paper.  相似文献   

8.
LetG be a domain inC n ,EG, mes E=0 for (r)=r 2n–1(r), where (r) is a nondecreasing non-negative function (r>0). Iff(z) is holomorphic inGE and (,f, GE)(), C=const, thenf(z) is holomorphic inG.The impossibility of the relaxation of the stipulations on () and(r) is also established.The statement above is a corollary to a more general result about the representation of a holomorphic function from a certain class in the form of an integral with respect to -measure, extended over the set of singular points of the function.  相似文献   

9.
Improving Bruck's Completion-Theorem for nets, we show that a net of order k and degree k + 1 – can be extended to an affine plane, if 3k > 83 – 182 + 8 + 4. As applications we obtain the following two theorems: A maximal partial t-spread in PG(2t + 1, q), q not a square, with deficiency > 0 satisfies 83 – 182 + 8 + 4 3q 2. There exists an absolute constant c such that every linear space with constant point degree n + 1 and minimum line degree n + 1 – a can be embedded in a protective plane of order n provided that n > ca 3.  相似文献   

10.
Let s 0 and let + s be the set of functions x defined on a finite interval I and such that, for all collections of s + 1 pairwise different points t 0,..., t s I, the corresponding divided differences [x; t 0,...,t s ] of order s are nonnegative. Let + s B p + s B p, 1 p where B p is a unit ball in the space L p, and let + s L q + s L q, 1 q . For every s 3 and 1 q p , we determine the exact orders of the shape-preserving Kolmogorov widths {x - y} \right\ L_q , $$]]>, where M n is the collection of all affine linear manifolds M n in L q such that dim M n n and M n + s L q .Translated from Ukrainskyi Matematychnyi Zhurnal, Vol. 56, No. 7, pp. 901–926, July, 2004.  相似文献   

11.
For unbounded domains with external power-type peaks, we propose a method for the approximation of functionsf(x) w p r () by polynomial splines in the metricw p r (), 1pq, and present the corresponding estimates.Translated from Ukrainskii Matematicheskii Zhurnal, Vol. 46, No. 9, pp. 1224–1233, September, 1994.  相似文献   

12.
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Consider the parametric linear complementarity problem w=Mz+q+p, w0, z0, w T z=0, where p0, 0q0, and 0. We show that a necessary condition for every complementary map z() to be isotone for every nonzero q0 and every p is that M be either a P-matrix or a -matrix. The Cottle necessary and sufficient conditions for strong and uniform isotonicity for P-matrices are restated, with slight modifications, for -matrices.  相似文献   

13.
For 0<1 and graphsG andH, we writeGH if any -proportion of the edges ofG span at least one copy ofH inG. As customary, we writeC k for a cycle of lengthk. We show that, for every fixed integerl1 and real >0, there exists a real constantC=C(l, ), such that almost every random graphG n, p withp=p(n)Cn –1+1/2l satisfiesG n,p1/2+ C 2l+1. In particular, for any fixedl1 and >0, this result implies the existence of very sparse graphsG withG 1/2+ C 2l+1.The first author was partially supported by NSERC. The second author was partially supported by FAPESP (Proc. 93/0603-1) and by CNPq (Proc. 300334/93-1). The third author was partially sopported by KBN grant 2 1087 91 01.  相似文献   

14.
Summary This paper studies annihilating properties of operators generated by spherical convolution over the unit sphere 2q of Cq. Its specific aim is to answer the following question: given a complex number , ||1, to determine what functions of L2(2q) have zero average over every section w,q :={ z 2q: <z,w> = } of 2q . Here, <.,.>stands for the usual inner product of Cq.  相似文献   

15.
Given two finite sets of points X + and X in n , the maximum box problem consists of finding an interval (box) B = {x : l x u} such that B X = , and the cardinality of B X + is maximized. A simple generalization can be obtained by instead maximizing a weighted sum of the elements of B X +. While polynomial for any fixed n, the maximum box problem is -hard in general. We construct an efficient branch-and-bound algorithm for this problem and apply it to a standard problem in data analysis. We test this method on nine data sets, seven of which are drawn from the UCI standard machine learning repository.  相似文献   

16.
This paper is concerned with the existence and boundedness of the solutions to the linear complementarity problemw=Mz+q,w0,z0,w T z=0, for eachq n . It has been previously established that, ifM is copositive plus, then the solution set is nonempty and bounded for eachq n iffM is aQ-matrix. This result is shown to be valid also forL 2-matrices,P 0-matrices, nonnegative matrices, andZ-matrices.  相似文献   

17.
We give necessary and sufficient conditions for infinite matrices to map a sequence space X into a sequence space Y where X = l 1 and Y = w p , w p , w 0 p (1 p < ), or X = w 0, w, w and Y = l p (1 p ), or X = w 0, w, w and Y = w 0 p , w p , w p (1 p < ). Furthermore the Hausdorff measure of noncompactness is applied to give necessary and sufficient conditions for a linear operator between these spaces to be compact.  相似文献   

18.
LetG=a 1,b 1, ...,a q ,b q | (W 1 (a 1,b 1) ...W q (a q b q ))=1,q1, 2,W j (a j ,b j )1. We solve the isomorphism problem forG inasmuch as we can decide in finitely many steps, if any arbitrary one-relator group is isomorphic toG or not. FurthermoreG turns out to have a finitely generated automorphism group. Forq=1 this was proved byS. J. Pride. Forq2 the proof is based onNielsen's reduction method. There are some other interesting results on subgroup problems for one-relator groups obtained by this method.  相似文献   

19.
In an attempt to find a q-analogue of Weber and Schafheitlin's integral 0 x J (ax) J (bx) dx which is discontinuous on the diagonal a = b the integral 0 x J (2) (a(1 – q)x; q)J (1) (b(1 – q)x; q) dx is evaluated where J (1) (x; q) and J (2) (x; q) are two of Jackson's three q-Bessel functions. It is found that the question of discontinuity becomes irrelevant in this case. Evaluations of this integral are also made in some interesting special cases. A biorthogonality formula is found as well as a Neumann series expansion for x in terms of J (2) +1+2n ((1 – q)x; q). Finally, a q-Lommel function is introduced.  相似文献   

20.
The solvability of the following class of nonlinear variational inequality (NVI) problems based on a class of iterative procedures, which possess an equivalence to a class of projection formulas, is presented.Determine an element x * K and u * T(x *) such that u *, xx * 0 for all x K where T: K P(H) is a multivalued mapping from a real Hilbert space H into P(H), the power set of H, and K is a nonempty closed convex subset of H. The iterative procedure adopted here is represented by a nonlinear variational inequality: for arbitrarily chosen initial points x 0, y 0 K, u 0 T(y 0) and v 0 T(x 0), we have u k + x k+1y k , xx k+1 0, x K, for u k T(y k ) and for k 0where v k + y k x k , xy k 0, x K and for v k T(x k ).  相似文献   

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