共查询到20条相似文献,搜索用时 510 毫秒
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.
V. N. Sudakov 《Mathematical Notes》1973,14(4):886-888
Let X and Y be locally compact-compact topological spaces, F X×Y is closed, and P(F) is the set of all Borel probability measures on F. For us to find, for the pair of probability measures (x, y P (X)×P(Y), a probability measure P(F) such that
X
=
X
–1
,
Y
=
Y
–1
it is necessary and sufficient that, for any pair of Borel sets A X, B Y for which (A× B) F=Ø, the condition
XA+
YB 1 holds.Translated from Matematicheskie Zametki, Vol. 14, No. 4, pp. 573–576, October, 1973. 相似文献
3.
4.
M. Milman 《Analysis Mathematica》1978,4(3):215-223
X(Y) f -:X(Y)={fM(×): fX(Y)=f(x,.)YX< . =(0, ), M (×) — , ×, X, Y, Z— . X(Y) Z(×). 相似文献
5.
Rangachari Venkataraman 《Monatshefte für Mathematik》1985,100(1):47-66
An abelian topological group is an group if and only if it is a locally -compactk-space and every compact subset in it is contained in a compactly generated locally compact subgroup. Every abelian groupG is topologically isomorphic to G
0 where 0 andG
0 is an abelian group where every compact subset is contained in a compact subgroup. Intrinsic definitions of measures, convolution of measures, measure algebra,L
1-algebra, Fourier transforms of abelian groups are given and their properties are studied. 相似文献
6.
A Strong Maximum Principle for some quasilinear elliptic equations 总被引:37,自引:0,他引:37
J. L. Vázquez 《Applied Mathematics and Optimization》1984,12(1):191-202
In its simplest form the Strong Maximum Principle says that a nonnegative superharmonic continuous function in a domain
n
,n 1, is in fact positive everywhere. Here we prove that the same conclusion is true for the weak solutions of – u + (u) = f with a nondecreasing function ,(0)=0, andf0 a.e. in if and only if the integral((s)s)
–1/2
ds diverges ats=0+. We extend the result to more general equations, in particular to –
p
u + (u) =f where
p
(u) = div(|Du|
p-2
Du), 1 <p < . Our main result characterizes the nonexistence of a dead core in some reaction-diffusion systems.This work was partly done while the author was visiting the University of Minnesota as a Fulbright Scholar. 相似文献
7.
Jean Michel Morel 《manuscripta mathematica》1985,54(1-2):165-185
In this paper, we describe a method for extending (in some approximated sense) solutions of a nonlinear P.D.E. on a domain , to solutions in a domain containing . Such an extension property, the Runge property, is well known for a large class of linear problems including elliptic equations. We prove here the Runge property for semilinear problems of the kind -u+g(u)=f, with f L
loc
1
(N). (As a consequence, we get infinitely many solutions for these problems). The proof is based on a homotopy method, and requires a refinement of the linear results: We prove that the Runge extension v on of a solution u in for a linear elliptic equation Lu=f can be choosen in order to depend continuously on u and the coefficients of L. 相似文献
8.
L
p
, 0<<1, . 相似文献
9.
Chang -Pao Chen 《Analysis Mathematica》1996,22(2):99-112
f(x,y)
jk
. , {c
jk} , f(x, )(, ) [0,1)х[0,1) , - (0,0). , , f, - f. , , , [1] . . - [5] [6].
This research is supported by National Science Council, Taipei, R.O.C. under Grant #NSC 84-2121-M-007-026. 相似文献
This research is supported by National Science Council, Taipei, R.O.C. under Grant #NSC 84-2121-M-007-026. 相似文献
10.
, [0, 1], (n+1) n-. . [2]. — (. 5.4 5.6). . 6.4 2 [5]. , [4]. , , [6] [7]. [1]. 相似文献
11.
Osvaldo Marrero 《Aequationes Mathematicae》1977,16(3):195-220
This work is an attempt to give a complete survey of all known results about pseudo (v, k, )-designs. In doing this, the author hopes to bring more attention to his conjecture given in Section 6; an affirmative answer to this conjecture would settle completely the existence and construction problem for a pseudo (v, k, )-design in terms of the existence of an appropriate (v, k, )-design. 相似文献
12.
René L. Schilling 《Journal of Theoretical Probability》1998,11(2):303-330
Let {X
t}
t0 be a Feller process generated by a pseudo-differential operator whose symbol satisfiesÇn|q(Ç,)|c(1=)()) for some fixed continuous negative definite function (). The Hausdorff dimension of the set {X
t:tE}, E [0, 1] is any analytic set, is a.s. bounded above by dim E. is the Blumenthal–Getoor upper index of the Levy Process associated with (). 相似文献
13.
14.
Fabio Cipriani 《Potential Analysis》1994,3(2):203-218
We give a general criterion for the intrinsic ultracontractivity of Dirichlet Laplacians –
D
on domainsD ofR
d d 3, based on the Lieb's formula. It applies to various classes of domains (e.g. John, Hölder andL
p-averaging domains) and gives new conditions for intrinsic ultracontractivity in terms of the Minkowski dimension of the boundary D. In particular, isotropic self-similar fractals and domains satisfying a c-covering condition are considered. 相似文献
15.
M. Truszczyński 《Periodica Mathematica Hungarica》1988,19(4):273-286
A family of subtrees of a graphG whose edge sets form a partition of the edge set ofG is called atree decomposition ofG. The minimum number of trees in a tree decomposition ofG is called thetree number ofG and is denoted by(G). It is known that ifG is connected then(G) |G|/2. In this paper we show that ifG is connected and has girthg 5 then(G) |G|/g + 1. Surprisingly, the case wheng = 4 seems to be more difficult. We conjecture that in this case(G) |G|/4 + 1 and show a wide class of graphs that satisfy it. Also, some special graphs like complete bipartite graphs andn-dimensional cubes, for which we determine their tree numbers, satisfy it. In the general case we prove the weaker inequality(G) (|G| – 1)/3 + 1. 相似文献
16.
The number of subgroups of type and cotype in a finite abelian p-group of type is a polynomialg
with integral coefficients. We prove g
has nonnegative coefficients for all partitions and if and only if no two parts of differ by more than one. Necessity follows from a few simple facts about Hall-Littlewood symmetric functions; sufficiency relies on properties of certain order-preserving surjections that associate to each subgroup a vector dominated componentwise by . The nonzero components of (H) are the parts of , the type of H; if no two parts of differ by more than one, the nonzero components of – (H) are the parts of , the cotype of H. In fact, we provide an order-theoretic characterization of those isomorphism types of finite abelian p-groups all of whose Hall polynomials have nonnegative coefficients. 相似文献
17.
Wolfgang Adamski 《Monatshefte für Mathematik》1987,103(3):169-176
LetE be a vector lattice of real-valued functions defined on a setX, and (E):={{f1}:fE}. Among others, it is shown that, under some additional assumptions onE, every measure that integrates all functionsfE is (E)--smooth iffX is (E)-complete. An application of this general result to various topological situations yields some new measure-theoretic characterizations of realcompact, Borel-complete andN-compact spaces, respectively. 相似文献
18.
Let x(w), w=u+iv B, be a minimal surface in 3 which is bounded by a configuration , S consisting of an arc and of a surface S with boundary. Suppose also that x(w) is area minimizing with respect to , S. Under appropriate regularity assumptions on and S, we can prove that the first derivatives of x(u, v) are Hölder continuous with the exponent =1/2 up to the free part of B which is mapped by x(w) into S. An example shows that this regularity result is optimal. 相似文献
19.
Р. С. Юлмухаметов 《Analysis Mathematica》1985,11(3):257-282
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
. . . 相似文献
20.
Periodic solutions of differential equations in Banach spaces 总被引:2,自引:0,他引:2
Klaus Deimling 《manuscripta mathematica》1978,24(1):31-44
Let X be a Banach space, DX, f: [0,)xDX continuous and -periodic. In this paper we consider various conditions on D and f sufficient for existence of an -periodic solution of the differential equation u=f(t,u). In the main, we shall assume that D is closed bounded and convex and f satisfies a boundary condition at D such that D is flow invariant for u=f(t,u). The map f is assumed to be either compact or dissipative or a certain perturbation of such maps. 相似文献