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A. Yu. Zaitsev 《Journal of Mathematical Sciences》1984,27(6):3227-3237
Let be the collection of parallelepipeds in R with edges parallel with the coordinate axes and let be the collection of closed sets in R. Let (G, H)=inf {G{A}H{A}+, H{A}G{A}+ for any; L(G, H)= inf {G{A}H{A}+, H{A}G{A}+ for any, where G, H are distributions in
. In the paper one gives the proofs of results announced earlier by the author (Dokl. Akad. Nauk SSSR,253, No. 2, 277–279 (1980)). One considers the problem of the approximation of the distributions of sums of independent random vectors with the aid of infinitely divisible distributions. One obtains estimates for the distances (·, ·), L(·, ·) and. It is proved that, where 0pi1,
; E is the distribution concentrated at zero; Vi(i=1, ..., n) are arbitrary distributions; the products and the exponentials are understood in the sense of convolution.Translated from Zapiski Nauchnykh Seminarov Leningradskogo Otdeleniya Matematicheskogo Instituta im. V. A. Steklova AN SSSR, Vol. 130, pp. 89–103, 1983. 相似文献
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Pawel Hitczenko 《Probability Theory and Related Fields》1988,78(2):223-230
Summary It is shown that for all tangent sequences (d
n) and (e
n) of nonnegative or conditionally symmetric random variables and for every function satisfying the growth condition (2x)(x) the following inequality holds:
. This generalizes results of J. Zinn and proves a conjecture of S. Kwapie and W.A. Woyczyski. 相似文献
5.
Philip Ehrlich 《Algebra Universalis》1988,25(1):7-16
An -universally extending ordered field of power is constructed for each regular power where 0 < On and
. When is inaccessible, the structure is either a (set) model of J. H. Conway's ordered field No or an isomorphic copy of No depending on whether or not is a set or a proper class.Presented by Jan Mycielski. 相似文献
6.
A hyperarithmetic language
is considered, obtained by adding to the arithmetic language a special ternary predicateH
which acts as the universal predicate for
(for some scale of constructive ordinals ). The language
expresses a hierarchy {}< of classes of formulas which is the constructive analog of the initial -section of the classical hyperarithmetic hierarchy. Some properties of this hierarchy are introduced which give a convenient constructive theoryT
. It is shown that the majorizing semantics introduced in [1] (for an equivalent variant see [2]) can be extended to the sentences of the language
for sentences of the arithmetic language. The basis for the construction of the majorant is the idea (stated in [2]) of relating the majorant to deducibility in systems with an -rule.Translated from Zapiski Nauchnykh Seminarov Leningradskogo Otdeleniya Matematicheskogo Instituta im. V. A. Steklova AN SSSR, Vol. 68, pp. 30–37, 1977. 相似文献
7.
Let (E
i
)
iI
be a family of normed spaces and a space of scalar generalized sequences. The -sum of the family (E
i
)
iI
of spaces is
Starting from the topology on and the norm topology on each E
i
, a natural topology on {(E
i
)
iI
} can be defined. We give conditions for {(E
i
)
iI
} to be quasi-barrelled, barrelled or locally complete. 相似文献
8.
Given a real sequence {n}n. Suppose that
is a frame for L2[–, ] with bounds A, B. The problem is to find a positive constant L such that for any real sequence {n}n with ¦n –n¦ <L,
is also a frame for L2[–, ]. Balan [1] obtained
arcsin
. This value is a good stability bound of Fourier frames because it covers Kadec's 1/4-theorem
and is better than
(see Duffin and Schaefer [3]). In this paper, a sharper estimate is given. 相似文献
9.
A. Sh. Abakarov 《Journal of Mathematical Sciences》1984,27(4):2831-2848
This paper deals with the ideals of identities of certain associative algebras over a field F of characteristic zero. An algebra W of matrices of the form
,,,M, where and , are F-algebras with unity and M is a (,)-bimodule, is considered. Under certain natural restrictions on M one obtains the equality of ideals of identities T(W)=T()T(), if [[x1,x2], x3[x4,x5]]T().Translated from Zapiski Nauchnykh Seminarov Leningradskogo Otdeleniya Matematicheskogo Instituta im. V. A. Steklova AN SSSR, Vol. 114, pp. 7–27, 1982. 相似文献
10.
Milan Kučera 《Czechoslovak Mathematical Journal》1999,49(3):449-474
Variational inequalities
are studied, where K is a closed convex cone in
, 3, B
is a × matrix, G is a small perturbation, a real parameter. The assumptions guaranteeing a Hopf bifurcation at some 0 for the corresponding equation are considered and it is proved that then, in some situations, also a bifurcation of periodic solutions to our inequality occurs at some I 0. Bifurcating solutions are obtained by the limiting process along branches of solutions to penalty problems starting at 0 constructed on the basis of the Alexander-Yorke theorem as global bifurcation branches of a certain enlarged system. 相似文献
11.
D. M. Smirnov 《Algebra and Logic》2005,44(2):109-116
Let be the set of all primes,
the field of all algebraic numbers, and Z the set of square-free natural numbers. We consider partially ordered sets of interpretability types such as
, and
, where AD is a variety of -divisible Abelian groups with unique taking of the pth root p(x) for every p ,
is a variety of
-modules over a normal field
, contained in
, and Gn is a variety of n-groupoids defined by a cyclic permutation (12 ...n). We prove that
, and
are distributive lattices, with
and
where
ub and
ubf are lattices (w.r.t. inclusion) of all subsets of the set and of finite subsets of , respectively.Deceased.__________Translated from Algebra i Logika, Vol. 44, No. 2, pp. 198–210, March–April, 2005. 相似文献
12.
F. Morits 《Mathematical Notes》1975,17(2):127-133
Let {Xi}
–
be a sequence of random variables, E(Xi) 0. If 1, estimates for the -th moments
can be derived from known estimates
of the -th moment. Here we generalized the Men'shov-Rademacher inequality for =2 for orthonormal Xi, to the case 1 and dependent random variables. The Men'shov-Payley inequality >2 for orthonormal Xi) is generalized for >2 to general random variables. A theorem is also proved that contains both the Erdös -Stechkin theorem and Serfling's theorem withv > 2 for dependent random variables.Translated from Matematicheskie Zametki, Vol. 17, No. 2, pp. 219–230, February, 1975.This article was written while the author was working in the V. A. Steklov Mathematics Institute, Academy of Sciences of the USSR. 相似文献
13.
Hermann Hähl 《Geometriae Dedicata》1987,23(3):319-345
We study 16-dimensional locally compact translation planes in which, for an affine point o, the stabilizer
of the affine collineation group
contains a subgroup locally isomorphic to SU4 (). If has only one affine fixed point o, then it is shown that either the plane is the classical Moufang plane over the Cayley numbers, or else must be normal in the stabilizer
and
has dimension at most 37. This also comprises the proof of the fact that if
contains a subgroup locally isomorphic to SU4() × SL2() then the plane is the classical Cayley plane. The case that has more affine fixed points in dealt with as well; then, except for a well-known family of planes admitting Spin7() as a group of collineations,
has dimension at most 34. 相似文献
14.
Min Ho Lee 《Monatshefte für Mathematik》2004,141(3):187-196
Let
be an equivariant holomorphic map of symmetric domains associated to a homomorphism
of semisimple algebraic groups defined over
. If
and
are torsion-free arithmetic subgroups with
, the map induces a morphism :
of arithmetic varieties and the rationality of is defined by using symmetries on
and
as well as the commensurability groups of and . An element
determines a conjugate equivariant holomorphic map
of which induces the conjugate morphism
of . We prove that is rational if is rational. 相似文献
15.
Let X be an open subset of
n and (f1, ...,fp): X
p be a holomorphic mapping. We prove that if (x0,0, 0) T* ×
p does not belong to the characteristic variety of the
X []-module
X[]f, then there exists a conic neighborhood V × of (x0, 0) such the function
is rapidely decreasing in | Im | for with Re bounded, for any (n,n)-form of class C with compact support in V. The following partial converse of this result is also established: if
for all (n,n)-forms of class C with compact support in X, then
. 相似文献
16.
We prove that, in a locally -solvable group G = AB with locally normal subgroups A and B, there exist pairwise-permutable Sylow - and p-subgroups A
, A
p
and B
, B
p
, p , of the subgroups A and B, respectively, such that A
B
is a Sylow -subgroup of the group G and, for an arbitrary nonempty set
,
are Sylow - and -subgroups, respectively, of the group G. 相似文献
17.
Let (, , ) be a complete measure space, L0 the vector lattice of -measurable real functions on , : L0 [0, )] a lattice semimodular,
the corresponding modular space, S0 the ideal generated by
and
0,{\text{ }}\exists {\text{ }}s \in {\text{ }}S_{\text{0}} {\text{ such that }}\rho \left( {\frac{{x - s}}{\user1{\lambda }}} \right) < \infty } \right\}$$
" align="middle" border="0">
. In X consider the distance
0:\rho \left( {\frac{{x - y}}{\user1{\lambda }}} \right) \leqq \user1{\lambda }} \right\}$$
" align="middle" border="0">
and, if is convex, the distances dL, do subordinated to the Luxemburg and Amemiya-Orlicz norms, respectively. We give necessary and sufficient conditions for H(So) in order to be proximinal in X with the distances d, dL and do. 相似文献
18.
G. A. Mikhalin 《Mathematical Notes》1974,16(3):803-805
We show that if a sequence {j} is such that 1>2 3...,
then for any bounded sequence {Sn} the equation
implies the equation
. This theorem generalizes a theorem of N. A. Davydov [2].Translated from Matematicheskie Zametki, Vol. 16, No. 3, pp. 361–364, September, 1974.In conclusion the author thanks N. A. Davydov for useful advice in the writing of this paper. 相似文献
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Suppose that A is an n × n nonnegative matrix whose eigenvalues are = (A), 2, ..., n. Fiedler and others have shown that \det( I -A) n - n, for all > with equality for any such if and only if A is the simple cycle matrix. Let a
i be the signed sum of the determinants of the principal submatrices of A of order i × i, i=1, ..., n - 1. We use similar techniques to Fiedler to show that Fiedler's inequality can be strengthened to:
for all . We use this inequality to derive the inequality that:
. In the spirit of a celebrated conjecture due to Boyle-Handelman, this inequality inspires us to conjecture the following inequality on the nonzero eigenvalues of A: If 1 = (A), 2,...,k
are (all) the nonzero eigenvalues of A, then
. We prove this conjecture for the case when the spectrum of A is real. 相似文献