共查询到20条相似文献,搜索用时 15 毫秒
1.
Holger Boche 《manuscripta mathematica》1998,95(1):137-147
The behaviour of multidimensional Shannon sampling series for continuous functions is examined. A continuous functiong
1 εC
0[0,1]2 with support in the rectangle [0,1]×[0,1/2] is indicated in the paper for which the two dimensional Shannon sampling series
diverge almost everywhere in the rectangle [0,1]×[1/2,1]. This shows that the localization principle for Shannon sampling
series cannot hold in two dimensions and in higher dimensions. The result solves a problem formulated by P.L. Butzer. 相似文献
2.
Jean-Pierre Gabardo 《Journal of Fourier Analysis and Applications》2000,6(3):277-298
We characterize the Hilbert spaces H whose elements are distributions supported on the interval [0, 1] and which have the
property that the system of exponentials {e2πinx}n∈Z
forms a complete orthogonal system for H, generalizing in this way the classical situation where H=L2([0, 1]) and the system is actually orthonormal. This characterization is extended to the more general setting of spectral pairs
and is used to obtain sampling results in various related spaces of functions, that generalize the classical Shannon sampling
theorem. 相似文献
3.
In this paper, we are concerned with the following nth-order ordinary differential equation $$x^{(n)}(t)+f(t,x(t),x'(t),\ldots,x^{(n-1)}(t))=0,\quad t\in (0,1),$$ with the nonlinear boundary conditions $$\begin{array}{l}x^{(i)}(0)=0,\quad i=0,1,\ldots,n-3,\\[3pt]g(x^{(n-2)}(0),x^{(n-1)}(0),x(\xi_1),\ldots,x(\xi_{m-2}))=A,\\[3pt]h(x^{(n-2)}(1),x^{(n-1)}(1),x(\eta_1),\ldots,x(\eta_{l-2}))=B,\end{array}$$ here A,B∈R, f:[0,1]×R n →R is continuous, g:[0,1]×R m →R is continuous, h:[0,1]×R l →R is continuous, ξ i ∈(0,1), i=1,…,m?2, and η j ∈(0,1), j=1,…,l?2. The existence result is given by using a priori estimate, Nagumo condition, the method of upper and lower solutions and Leray-Schauder degree. We also give an example to demonstrate our result. 相似文献
4.
Marcin Szyszkowski 《Quaestiones Mathematicae》2018,41(2):165-171
We characterize sets A0, A1 for which there is a DB1 function f with [f = 0] = A0 and [f = 1] = A1. This characterization is a conjunction of necessary conditions for Darboux and for Baire 1 functions. We also characterize sets A?, A+ for which there is a DB1 function with [f < 0] = A? and [f > 0] = A+. The same characterzations are provided for approximately continuous functions. 相似文献
5.
A. Hajnal 《Combinatorica》1985,5(2):137-139
We prove (in ZFC) that for every infinite cardinal ϰ there are two graphsG
0,G
1 with χ(G
0)=χ(G
1)=ϰ+ and χ(G
0×G
1)=ϰ. We also prove a result from the other direction. If χ(G
0)≧≧ℵ0 and χ(G
1)=k<ω, then χ(G
0×G
1)=k. 相似文献
6.
Eugene Wesley 《Israel Journal of Mathematics》1973,14(1):104-114
Using the method of forcing of set theory, we prove the following two theorems on the existence of measurable choice functions:
LetT be the closed unit interval [0,1] and letm be the usual Lebesgue measure defined on the Borel subsets ofT. Theorem1. LetS⊂T×T be a Borel set such that for alltεT,S
t
def={x|(t,x)εS} is countable and non-empty. Then there exists a countable series of Lebesgue-measurable functionsf
n: T→T such thatS
t={fn(t)|nεω} for alltε[0,1],W
x={y|(x,y)εW} is uncountable. Then there exists a functionh:[0,1]×[0,1]→W with the following properties: (a) for each xε[0,1], the functionh(x,·) is one-one and ontoW
x and is Borel measurable; (b) for eachy, h(·, y) is Lebesgue measurable; (c) the functionh is Lebesgue measurable. 相似文献
7.
8.
9.
Der-Shin Chang Yuang-Chin Chiang 《Annals of the Institute of Statistical Mathematics》1980,32(1):275-281
Consider a realization of the process
on the intervalT=[0,1] for functionsf
1(t),f
2(t),...,f
n
(t) inH(R), the reproducing kernel Hilbert space with reproducing kernelR(s,t) onT×T, whereR(s,t)=E[ξ(s)ξt)] is assumed to be continuous and known. Problems of the selection of functions {f
k
(t)}
k=1
n
to be ϕ-optimal design are given, and an unified approach to the solutions ofD-,A-,E- andD
s-optimal design problems are discussed. 相似文献
10.
E. G. Coffman Jr. Bjorn Poonen Peter Winkler 《Probability Theory and Related Fields》1995,102(1):105-121
Summary Letn random intervalsI
1, ...,I
n be chosen by selecting endpoints independently from the uniform distribution on [0.1]. Apacking is a pairwise disjoint subset of the intervals; itswasted space is the Lebesgue measure of the points of [0,1] not covered by the packing. In any set of intervals the packing with least wasted space is computationally easy to find; but its expected wasted space in the random case is not obvious. We show that with high probability for largen, this best packing has wasted space
. It turns out that if the endpoints 0 and 1 are identified, so that the problem is now one of packing random arcs in a unit-circumference circle, then optimal wasted space is reduced toO(1/n). Interestingly, there is a striking difference between thesizes of the best packings: about logn intervals in the unit interval case, but usually only one or two arcs in the circle case. 相似文献
11.
Michel Talagrand 《Probability Theory and Related Fields》2005,131(2):145-153
A simple packing of a collection of rectangles contained in [0,1]2 is a disjoint subcollection such that each vertical line meets at most one rectangle of the packing. The wasted space of the packing is the surface of the area of the part of [0,1]2 not covered by the packing. We prove that for a certain number L, for all N2, the wasted space WN in an optimal simple packing of N independent uniformly distributed rectangles satisfiesWork partially supported by an N.S.F. grant.Mathematics Subject Classification (2000): 60D05 相似文献
12.
本文考虑形如的非线性四阶微分方程非局部边值问题,这里a,b∈L~1[0,1],g:(0,1)→[0,∞)在(0,1)上连续、对称,且可能在t=0和t=1处奇异.f:[0,1]×[0,∞)→[0,∞)连续且对所有x∈[0,∞],f(·,x)在[0,1]上对称.在某些适当的增长性条件下,应用Krasnoselskii不动点定理证明了对称正解的存在性和多重性. 相似文献
13.
Allan M Krall 《Journal of Differential Equations》1977,24(2):253-267
This article discusses linear differential boundary systems, which include nth-order differential boundary relations as a special case, in np[0,1] × np[0,1], 1 ? p < ∞. The adjoint relation in nq[0,1] × nq[0,1], , is derived. Green's formula is also found. Self-adjoint relations are found in n2[0,1] × n2[0,1], and their connection with Coddington's extensions of symmetric operators on subspaces of np[0,1] × n2[0,1] is established. 相似文献
14.
Savita Bhatnagar 《Proceedings Mathematical Sciences》2005,115(4):383-389
The aim of this paper is to study the algebraAC
p
of absolutely continuous functionsf on [0,1] satisfying f(0) = 0,f ’ ∈ Lp[0, 1] and the multipliers ofAC
p
. 相似文献
15.
16.
Abraham Berman 《Linear and Multilinear Algebra》2013,61(5):439-456
Let A be an n?×?n real matrix. A is called {0,1}-cp if it can be factorized as A?=?BB T with bij =0 or 1. The smallest possible number of columns of B in such a factorization is called the {0,1}-rank of A. A {0,1}-cp matrix A is called minimal if for every nonzero nonnegative n?×?n diagonal matrix D, A-D is not {0,1}-cp, and r-uniform if it can be factorized as A=BB T, where B is a (0,?1) matrix with r 1s in each column. In this article, we first present a necessary condition for a nonsingular matrix to be {0,1}-cp. Then we characterize r-uniform {0,1}-cp matrices. We also obtain some necessary conditions and sufficient conditions for a matrix to be minimal {0,1}-cp, and present some bounds for {0,1}-ranks. 相似文献
17.
Consider the shortest tour throughn pointsX
1,...,X
n
independently uniformly distributed over [0,1]2. Then we show that for some universal constantK, the number of edges of length at leastun
–1/2 is at mostKnxp(–u)2/K)with overwhelmingprobability.This research is in part supported by an NSF grant. 相似文献
18.
In this paper, we consider the following sequential fractional differential equation with initial value problem: where 0<????1 and f:[0,1]×?×???? is continuous. Existence and uniqueness results of solutions are established. 相似文献
19.
It is shown that the space X[0,1], of continuous maps [0,1]X with the compact-open topology, is not locally compact for any space X having a nonconstant path of closed points. For a T1-space X, it follows that X[0,1] is locally compact if and only if X is locally compact and totally path-disconnected.
Mathematics Subject Classifications (2000) 54C35, 54E45, 55P35, 18B30, 18D15. 相似文献
20.
This paper deals with the solutions defined for all time of the KPP equation ut = uxx + f(u), 0 < u(x,t) < 1, (x,t) ∈ ℝ2, where ƒ is a KPP‐type nonlinearity defined in [0,1]: ƒ(0) = ƒ(1) = 0, ƒ′(0) > 0, ƒ′(1) < 0, ƒ > 0 in (0,1), and ƒ′(s) ≤ ƒ′(0) in [0,1]. This equation admits infinitely many traveling‐wave‐type solutions, increasing or decreasing in x. It also admits solutions that depend only on t. In this paper, we build four other manifolds of solutions: One is 5‐dimensional, one is 4‐dimensional, and two are 3‐dimensional. Some of these new solutions are obtained by considering two traveling waves that come from both sides of the real axis and mix. Furthermore, the traveling‐wave solutions are on the boundary of these four manifolds. © 1999 John Wiley & Sons, Inc. 相似文献