共查询到20条相似文献,搜索用时 15 毫秒
1.
M. Skałba 《Archiv der Mathematik》2005,84(6):485-495
Let S(x) denote the number of primes p < x which divide both 2n–3 and 3n–2 for some
We prove that
Received: 8 April 2004 相似文献
2.
Tomasz Człapiński 《Czechoslovak Mathematical Journal》1999,49(4):791-809
We consider the mixed problem for the hyperbolic partial differential-functional equation of the first order
where
is a function defined by z
(x,y)(t, s) = z(x + t, y + s), (t, s) [–, 0] × [0, h]. Using the method of bicharacteristics and the method of successive approximations for a certain integral-functional system we prove, under suitable assumptions, a theorem of the local existence of generalized solutions of this problem. 相似文献
3.
This paper deals with the concept of exponentiability for a special class of multivalued maps. To be more precise, we discuss
the exponentiability of a multivalued map F: X⇉X expressible in the form F(x) = {Ax:A ∈ Ξ}, with Ξ denoting a collection of linear continuous operators defined on a Banach space X. Among other results, we prove that, under suitable assumptions on Ξ, the Painlevé–Kuratowski limit
exists for all x ∈ X, and it admits the representation [expF](x) = {e
A
x:A ∈ clco(Ξ)}. The operation of exponentiation has therefore a convexification effect on Ξ. By exploiting the above-mentioned representation formula, we derive general properties for the semigroup {S
F
(t)}
t⩾0 defined by
By way of application, we obtain a formula of exponential type for the reachable set associated to the differential inclusion
相似文献
4.
Y. -F. S. Pétermann 《Monatshefte für Mathematik》1987,103(2):145-157
Let denote the sum-of-divisors function, and set
. Gronwall and Wigert proved (independently) in 1913 and 1914, respectively, thatE
1 (x)= (x log logx). In this paper we obtain the more preciseE
1 (x)=–(x log logx). The method consists in averaging
over suitable arithmetic progressions, and was suggested by the work ofP. Erdös andH. N. Shapiro [Canad. J. Math. 3–4, 375–385 (1951)] on the error term corresponding to Euler's functions,
. 相似文献
5.
Paolo Cubiotti 《Set-Valued Analysis》1993,1(1):81-87
In this paper, we deal with the following generalized quasi-variational inequality problem: given a closed convex subsetX
n
, a multifunction :X 2
n
and a multifunction :X 2
X
, find a point (
) X ×
n
such that
We prove an existence theorem in which, in particular, the multifunction is not supposed to be upper semicontinuous. 相似文献
6.
The dimension of a graphG=(V, E) is the minimum numberd such that there exists a representation
and a thresholdt such thatxy E iff
. We prove that d(G)n–x(G) and
wheren=|V| andx(G) is the chromatic number ofG; we present upper bounds for the dimension of graphs with a large girth and we show that the complement of a forest can be represented by unit vectors inR
6. We prove that d(G)1/15n for most graphs and that there are 3-regular graphs with d(G)c logn/log logn. 相似文献
7.
Jia Chaohua 《数学学报(英文版)》1996,12(4):433-445
LetP(x) denote the greatest prime factor of
n. In this paper, we shall prove thatP(x)>x
0.728 holds true for sufficiently largex.Project supported by the Tian Yuan Item in the National Natural Science Foundation of China. 相似文献
8.
There are many studies on the asymptotic behavior of solutions of differential equations. In the present paper, we consider another aspect of this problem, namely, the rate of the asymptotic convergence of solutions. Let ϕ (t) be a scalar continuous monotonically increasing positive function tending to ∞ as t → ∞. It is established that if all solutions of a differential system satisfy the inequality
then the solution x(t; t
0, x
0) of this differential system tends to 0 faster than
.__________Published in Ukrains’kyi Matematychnyi Zhurnal, Vol. 57, No. 1, pp. 137–142, January, 2005. 相似文献
9.
O. Naselli 《Journal of Optimization Theory and Applications》1996,91(1):81-90
In this paper, we present a class of functions:f:X such that inf
xX
f(x)=
, whereX is a nonempty, finitely compact and convex set in a vector space andB
x
={xX: y aff(X){x:[x, y]X={x}. Our main tool is a recent minimax theorem by Ricceri (Ref. 1). 相似文献
10.
Summary LetX be a diffusion in natural scale on (0,1], with 1 reflecting, and letc(x)(H
x
) andv(x)var (H
x
), whereH
x
=inf{t: X
t
=x}. Let
x
=sup{t:X
t
=x}. The main results of this paper are firstly that (i)c is slowly varying; (ii)
are all equivalent: and secondly that (v)
are all equivalent, and are implied by the condition
. Other partial results for more general limit theorems are proved, and new results on regular variation are established. 相似文献
11.
P. Cubiotti 《Journal of Optimization Theory and Applications》1997,92(3):457-475
In this paper, we deal with the following problem: given a real normed space E with topological dual E*, a closed convex set XE, two multifunctions :X2X and
, find
such that
We extend to the above problem a result established by Ricceri for the case (x)X, where in particular the multifunction is required only to satisfy the following very general assumption: each set (x) is nonempty, convex, and weakly-star compact, and for each yX–:X the set
is compactly closed. Our result also gives a partial affirmative answer to a conjecture raised by Ricceri himself. 相似文献
12.
Given a finite setX of vectors from the unit ball of the max norm in the twodimensional space whose sum is zero, it is always possible to writeX = {x1, , xn} in such a way that the first coordinates of each partial sum
lie in [–1, 1] and the second coordinates lie in [–C, C] whereC is a universal constant. 相似文献
13.
Let Q be the lexicographic sum of finite ordered sets Q
x over a finite ordered set P. For some P we can give a formula for the jump number of Q in terms of the jump numbers of Q
x and P, that is,
, where s(X) denotes the jump number of an ordered set X. We first show that
where w(X) denotes the width of an ordered set X. Consequently, if P is a Dilworth ordered set, that is, s(P) = w(P)–1, then the formula holds. We also show that it holds again if P is bipartite. Finally, we prove that the lexicographic sum of certain jump-critical ordered sets is also jump-critical. 相似文献
14.
Martin Goldstern 《Monatshefte für Mathematik》1993,116(3-4):237-243
IfC is a Polish probability space,
a Borel set whose sectionsW
x ( have measure one and are decreasing
, then we show that the set
x
W
x
has measure one. We give two proofs of this theorem—one in the language of set theory, the other in the language of probability theory, and we apply the theorem to a question on completely uniformly distributed sequences.Supported by DFG grant Ko 490/7-1. 相似文献
15.
Let
We show that for every function
satisfying the conditional equation
either there exists a solution
of the Goab-Schinzel equation
such that
(i.e., f(x) = g(x) for
) or there is x0 > 0 with f(x0) < –1 and f(x) = 0 for x x0 . In particular we determine the solutions
of the conditional equation that are continuous at a point, Lebesgue measurable or Baire measurable (i.e., have the Baire property). In this way we solve some problems raised by the first author.Received: 2 March 2004 相似文献
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16.
A. Leibman 《Geometric And Functional Analysis》1994,4(6):648-659
We prove that ifX is a compact space andT
1, ...,T
t are homeomorphisms ofX generating a nilpotent group, then there existx X andn
1,n
2, ... N such that
for eachj=1, ...t.Supported by British Technion Society. 相似文献
17.
Kiyômi Kataoka 《Inventiones Mathematicae》1985,81(2):305-340
A functionk(x, u) of the(n+n)-variables is said to be a positive Hermite kernel if
, and the matrix(k(x
i, xj))i,j is positive semi-definite for every integerN and everyx
1, ..., xN. In this paper, we prove that this positive structure can be microlocalized in the category of microfunctions. Further we obtain a useful theorem concerning the positivity of pseudo-differential operators. This theory will play important roles in the study of analytic singularities of solutions of boundary value problems. 相似文献
18.
V. Ostrik 《Transformation Groups》1997,2(3):279-287
We study the tensor category
of tilting modules over a quantum groupU
q
with divided powers. The setX
+ of dominant weights is a union of closed alcoves
numbered by the elementswW
f
of a certain subset of affine Weyl groupW. G. Lusztig and N. Xi defined a partition ofW
f
into canonical right cells and the right order
R
on the set of cells. For a cellAW
f
we consider a full subcategory
formed by direct sums of tilting modulesQ() with highest weights
. We prove that
is a tensor ideal in
, generalizing H. Andersen's theorem about the ideal of negligible modules which in our notations is nothing else then
. The proof is an application of a recent result by W. Soergel who has computed the characters of tilting modules.This material is based upon work supported by the U.S. Civilian Research and Development Foundation under Award No. RM1-265. 相似文献
19.
J. F. B. M. Kraaijevanger 《Numerische Mathematik》1986,48(3):303-322
Summary This paper deals with polynomial approximations ø(x) to the exponential function exp(x) related to numerical procedures for solving initial value problems. Motivated by positivity and contractivity requirements imposed on these numerical procedures we study the smallest negative argument, denoted by –R(ø), at which ø is absolutely monotonic. For given integersp1,m1 we determine the maximum ofR(ø) when ø varies over the class of all polynomials of a degree m with
(forx0). 相似文献
20.
We show that a Banach space valued random variableX such that
t} \right\} = 0$$
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satisfies the central limit theorem if and only if the following criterion on small balls is fulfilled:
t} \right\} = 0$$
" align="middle" vspace="20%" border="0"> 相似文献
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