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1.
M. B. Nathanson 《Acta Mathematica Hungarica》2000,87(3):179-195
Let A be a set of positive integers with gcd (A) = 1, and let p
A
(n) be the partition function of A. Let c
0 = 2/3. If A has lower asymptotic density and upper asymptotic density , then lim inf log p
A
(n)/c
0 n and lim sup log p
A
(n)/c
0 n . In particular, if A has asymptotic density > 0, then log p
A
(n) c0n. Conversely, if > 0 and log p
A
(n) c
0 n, then the set A has asymptotic density . 相似文献
2.
Dr. Alexander Kovačec 《Monatshefte für Mathematik》1981,92(1):19-35
We shall develop a method to prove inequalities in a unified manner. The idea is as follows: It is quite often possible to find a continuous functional :
n
, such that the left- and the right-hand side of a given inequality can be written in the form (u)(v) for suitable points,v=v(u). If one now constructs a map
n
n
, which is functional increasing (i.e. for each x
n
(which is not a fixed point of ) the inequality (x)<((x)) should hold) one specially gets the chain (u)(
u))(
2(u))...
n
(u)). Under quite general conditions one finds that the sequence {
n
(u)}
n converges tov=v(u). As a consequence one obtains the inequality (u)(v). 相似文献
3.
F. Schipp 《Analysis Mathematica》1990,16(2):135-141
H={h
1,I } — , . : , I ¦(I)¦=¦I¦, ¦I¦ — I. H H
={h
(I),I} . , , . L
p
.
Dedicated to Professor B. Szökefalvi-Nagy on his 75th birthday
This research was supported in part by MTA-NSF Grants INT-8400708 and 8620153. 相似文献
Dedicated to Professor B. Szökefalvi-Nagy on his 75th birthday
This research was supported in part by MTA-NSF Grants INT-8400708 and 8620153. 相似文献
4.
B. F. Skubenko 《Journal of Mathematical Sciences》1984,25(2):1089-1092
Let M be a complete module of a purely algebraic field of degree n3, let be the lattice of this module and let F(X) be its form. By we denote any lattice for which we have = , where is a nondiagonal matrix satisfying the condition ¦-I¦ , I being the identity matrix. The complete collection of such lattices will be denoted by {}. To each lattice we associate in a natural manner the decomposable form F(X). The complete collection of forms, corresponding to the set {}, will be denoted by {F} It is shown that for any given arbitrarily small interval (N–, N+), one can select an such that for each F(X) from {F} there exists an integral vector X0 such that N– < F(X0) < N+.Translated from Zapiski Nauchnykh Seminarov Leningradskogo Otdeleniya Matematicheskogo Instituta im. V. A. Steklova AN SSSR, Vol. 112, pp. 167–171, 1981. 相似文献
5.
Héctor H. Cuenya 《Analysis Mathematica》2000,26(3):175-186
Let (, A, ) be a measure space, a function seminorm on M, the space of measurable functions on , and M
the space {f M : (f) < }. Every Borel measurable function : [0, ) [0, ) induces a function : M M by (f)(x) = (|f(x)|). We introduce the concepts of -factor and -invariant space. If is a -subadditive seminorm function, we give, under suitable conditions over , necessary and sufficient conditions in order that M
be invariant and prove the existence of -factors for . We also give a characterization of the best -factor for a -subadditive function seminorm when is -finite. All these results generalize those about multiplicativity factors for function seminorms proved earlier. 相似文献
6.
, [0, 1], (n+1) n-. . [2]. — (. 5.4 5.6). . 6.4 2 [5]. , [4]. , , [6] [7]. [1]. 相似文献
7.
{p
mn
} -
00>0, (1, 1) (1.1) (1.2). {s
mn
} J
p
- ( bJ
p
-lims
mn
=), (1.3) 0<x,y<1 p
s
(, )/p(x, y) x, y 1-. {r
mn
} - , (1.5) 0<, <1. N
rp
- , (1.6). , bJ
p
-lims
mn
= bJ
q
-lim(N
rps)
mn
=. J
p
- . , . 相似文献
8.
The paper considers control of the heat conduction process ut — u = g from the initial state u(x, 0) to the final state u(x, t1) in a fixed (finite) time t1 via the coefficient (z) in the boundary condition Bu = (u/n) + (x)u. A uniqueness theorem is proved for the problem to find the process—control pair (u, ). The control problem is posed in terms of the coefficient in a boundary condition of the form Bu = (u/n) + (t)u.Translated from Nelineinye Dinamicheskie Sistemy: Kachestvennyi Analiz i Upravlenie — Sbornik Trudov, No. 3, pp. 93–97, 1993. 相似文献
9.
P. Révész 《Probability Theory and Related Fields》1992,93(1):21-37
Summary We say that the discD()R
2, of radius , located around the origin isp-covered in timeT by a Wiener processW(·) if for anyzD() there exists a 0tT such thatW(t) is a point of the disc of radiusp, located aroundz. The supremum of those 's (0) is studied for which,D() isp-covered inT. 相似文献
10.
U — [0, 1] Y — . X=[1–U
1/v
/Y], U Y. 相似文献
11.
Yu. A. Neretin 《Journal of Mathematical Sciences》2005,126(2):1077-1094
The matrix of a permutation is a particular case of Markov transition matrices. In the same way, a measure-preserving bijection of a space (A, ) with a finite measure is a particular case of Markov transition operators. A Markov transition operator can also be considered as a map (polymorphism) (A, ) (A, ), which spreads points of (A, ) into measures on (A, ). Denote by * the multiplicative group of positive real numbers, and by the semigroup of measures on *. In this paper, we discuss *-polymorphisms and -polymorphisms, which are analogs of Markov transition operators (or polymorphisms) for the groups of bijections (A, ) (A, ) leaving the measure quasi-invariant; two types of polymorphisms correspond to the cases where A has finite and infinite measure, respectively. In the case where the space A itself is finite, the *-polymorphisms are some -valued matrices. We construct a functor from -polymorphisms to *-polymorphisms; it is described in terms of summations of -convolution products over matchings of Poisson configurations. Bibliography: 33 titles.Published in Zapiski Nauchnykh Seminarov POMI, Vol. 292, 2002, pp. 62–91.This revised version was published online in April 2005 with a corrected cover date and article title. 相似文献
12.
13.
Fan Xianling 《数学学报(英文版)》1996,12(3):254-261
In this paper the regularity of the Lagrangiansf(x, )=||(x)(1<
1(x)2< +) is studied. Our main result: If(x) is Holder continuous, then the Lagrangianf(x, )=f(x, )=||(x) is regular. This result gives a negative answer to a conjecture of V. Zhikov.Supported by the National Natural Science Foundation of China. 相似文献
14.
Summary Let be a natural exponential family on and (V, ) be its variance function. Here, is the mean domain of andV, defined on , is the variance of . A problem of increasing interest in the literature is the following: Given an open interval and a functionV defined on , is the pair (V, ) a variance function of some natural exponential family? Here, we consider the case whereV is a polynomial. We develop a complex-analytic approach to this problem and provide necessary conditions for (V, ) to be such a variance function. These conditions are also sufficient for the class of third degree polynomials and certain subclasses of polynomials of higher degree. 相似文献
15.
, (n), - (P
n
), P
n
(A
n
)>0P
n
(A
n
)0,n. [15] - , . , P
n
P
n
T
n
T
n
. 相似文献
16.
The paper is a study of the limiting behaviour of the [n t]-th iterates of the well-known Post-Widder operatorsL
n, x used in the real inversion of the Laplace transform. It is shown that the limiting operators constitute a semigroup T
t;t0 of class (C
0) on a family C
,; , >0 of Banach spaces. Applications of the semigroup structure lead to a pointwise saturation theorem forL
n, x and a characterization of convex functions inC
, through an inequality involving the action ofL
n, x. 相似文献
17.
V. F. Kolchin 《Mathematical Notes》1977,21(5):386-394
It is shown that the conditional distributions of a number of characteristics of a branching process (t), (0)=m, under the condition that the number of total progeny m in this process is equal to n, coincide with the distributions of the corresponding characteristics of a generalized scheme of arrangement of particles in cells. In the case where the number of offsprings of a particle has the Poisson distribution, the characteristics of the branching process (t), (0)=1, under the condition that 1=n+1, coincide with the characteristics of a random tree. By using these connections we obtain in this article a series of limit theorems as n for characteristics of random trees and branching processes under the conditions that m=n.Translated from Matematicheskie Zametki, Vol. 21, No. 5, pp. 691–705, May, 1977. 相似文献
18.
Nieminen Juhani 《manuscripta mathematica》1972,7(1):13-21
Let L be a distributive lattice characterized by a ternary operation (, ,), where (a,b,c)=(ab)(bc)(ac)=(ab)(ac)(bc), a,b,cL. The note considers convex sublattices of L, called generalized ideals of L generated by the operation (, ,). Some remarks have been stated about the graph of a distributive lattice. 相似文献
19.
J. Mogyoródi 《Analysis Mathematica》1981,7(3):185-197
, , . . . [1], , . , , ., , L logL. , , . . . . [5]. , . 相似文献
20.
Tomasz Łuczak 《Order》1991,8(3):291-297
Let =(n,p) be a binary relation on the set [n]={1, 2, ..., n} such that (i,i) for every i and (i,j) with probability p, independently for each pair i,j [n], where i<j. Define as the transitive closure of and denote poset ([n], ) by R(n, p). We show that for any constant p probability of each first order property of R(n, p) converges as n . 相似文献