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1.
Ryoichi Shimizu 《Annals of the Institute of Statistical Mathematics》1986,38(1):195-204
Summary LetX be a positive random variable with the survival function
and the densityf. LetX have the moments μ=E(X) and μ2=E(X
2) and put ε=|1-μ2/2μ2|. Put
and
. It is proved that the following inequalities hold:
, for allx>0, ifq(x) is monotone and that
, ifq
1
(x) is monotone. It is also shown that Brown's inequality
which holds wheneverq
1
(x) is increasing is not valid in general whenq
1 is decreasing.
The Institute of Statistical Mathematics 相似文献
2.
A. Ya. Khelemskii 《Mathematical Notes》1977,21(1):51-54
Let
and
be algebras of local and quasilocal observable spin systems corresponding to the group Zr,
be a differentiation invariant with respect to displacements. The question of representation of D in the form of formal Hamiltonian
formed by the displacements of an elementx ε
is considered. It is shown that such a representation exists if the condition
holds, where
means an element obtained from the elements [TkX,a] by some r-multiple process of summation.
Translated from Matematicheskii Zametki, Vol. 21, No. 1, pp. 93–98, January, 1977. 相似文献
3.
L. V. Kritskov 《Mathematical Notes》1999,65(4):454-461
Suppose thatА is a nonnegative self-adjoint extension to {
} of the formal differential operator−Δu+q(x)u with potentialq(x) satisfying the condition {
} or the condition {
} in which the nonnegative function itχ(r) is such that {
}. For each α∈(0, 2], we establish an estimate of the generalized Fourier transforms of an arbitrary function {
} of the form {
} If, in addition, {
}, then, along with this estimate, a similar lower bound is established.
Translated fromMatematicheskie Zametki, Vol. 65, No. 4, pp. 542–551, April, 1999. 相似文献
4.
Cristóbal González 《Journal d'Analyse Mathématique》2000,82(1):21-54
We consider the differential operator
in a symmetric intervalJ ofR, where ϕ is the density function of a finite measure supported inJ satisfying a certain regularizing property. Using as main tools left symmetrization with respect to the weight ϕ, and certain
measure preserving transformations, we prove differential inequalities involving the differential operators
. As applications, we give comparison results for solutions to non-linear differential equations related to the
operator, and with Neumann boundary data, generalizing in different ways results by C. Borell in [Bor 85b].
Research supported in part by a Grant from El Ministerio de Educación y Cultura (Spain) PB97-1081, and from La Junta de Andalucía. 相似文献
5.
A. N. Skiba 《Mathematical Notes》1999,65(3):326-330
It is proved that, if
is a singly generated composition formation, where
, then
is a composition formation.
Translated fromMatematicheskie Zametki, Vol. 65, No. 3, pp. 389–395, March, 1999. 相似文献
6.
M. I. Anokhin 《Mathematical Notes》1997,61(1):3-8
LetF be a free group with at most countable system
of free generators, letR be its normal subgroup recursively enumerable with respect to
, and let
be a variety of groups that differs from
and for which the corresponding verbal subgroupV of the free group of countable rank is recursive. It is proved that the word problem inF/V(R) is solvable if and only if this problem is solvable inF/R, and if
, then there exists anR such, that the conjugacy problem inF/R is solvable, but this problem is unsolvable inF/V(R) for any Abelian variety
(all algorithmic problems are regarded with respect to the images of
under the corresponding natural epimorphisms).
Translated fromMatematicheskie Zametki, Vol. 61, No. 1, pp. 3–9, January, 1997.
Translated by M. I. Anokhin 相似文献
7.
A. V. Glushak 《Mathematical Notes》1996,60(3):269-273
The stability of the uniform correctness of the Cauchy problem
,t>0,u(0)=u
0,u′(0)=0 fork>0 with respect to perturbations of the operator
is studied.
Translated fromMatematickeskie Zameiki, Vol. 60, No. 3, pp. 363–369, September, 1996. 相似文献
8.
This paper deals with the problem of small oscillations in a liquid layer of finite depth under the assumption that the bottom
is an elastic medium. The system of equations corresponding to the problem is written out and explained. The main aim of the
paper is to recast these equations in the form
, where
and
are positive operators in the function space naturally corresponding to the problem. The further aim is to investigate the
spectrum of the linear pencil
, which determines the dynamics of the problem.
Translated fromMatematicheskie Zametki, Vol. 68, No. 1, pp. 66–81, July, 2000. 相似文献
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9.
Karl-Hermann Neeb 《Semigroup Forum》1996,53(1):230-261
We say that an invariant convex coneW in a Lie algebras
is elliptic if its interior consists of elliptic elements of
. If such a cone exists, then
has a compactly embedded Cartan subalgebra. The first main result, of this paper is a characterization of those Lie algebras,
which contain elliptic invariant cones. If
is an invariant domain in such a cone, then we characterize the invariant locally convex functions onD by their restrictions to
where
is a compactly embedded Cartan subalgebra. 相似文献
10.
Yu. F. Korobeinik 《Mathematical Notes》2000,67(4):448-458
LetF ⊂ ℂ be a dense-in-itself set that has a nonempty connected interior and contains the origin, and let
be the space of infinitely differentiable complex-valued functions onF. For some classes of such setsF, we prove that for an arbitrary sequence
of complex numbers there exists a functionf ε
withf
(n)(0)=d
n,n=0, 1, 2, ..., and study the analyticity properties off. The functionf is constructed in the form of various function series, namely, a power series, a series of simple fractions, and an exponential
series. Analytic solutions of the multidimensional Borel problem are also considered.
Translated fromMatematicheskie Zametki, Vol. 67, No. 4, pp. 525–538, April, 2000. 相似文献
11.
A. Yu. Karlovich 《Mathematical Notes》1998,64(3):330-341
We consider the Banach algebra
of singular integral operators with matrix piecewise continuous coefficients in the reflexive Orlicz spaceL
M
n
(Γ). We assume that Γ belongs to a certain wide subclass of the class of Carleson curves; this subclass includes curves with
cusps, as well as curves of the logarithmic spiral type. We obtain an index formula for an arbitrary operator from the algebra
in terms of the symbol of this operator.
Translated fromMatematicheskie Zametki, Vol. 64, No. 3, pp. 383–396, September, 1998. 相似文献
12.
We obtain an expansion of
in powers of a small parameter, wherex
t
is a random process satisfying the stochastic differential equation
.Translated fromTeoriya Sluchaínykh Protsessov, Vol. 14, pp. 28–37, 1986. 相似文献
13.
D. N. Dudin 《Mathematical Notes》1968,3(1):42-44
For an algebra
of subsets of a set X there is constructed a set
and an algebra of its subsets so that the mapping
is a one-to-one correspondence between
and
and for each additive measure on
the measure
on
defined by the equation
is countably additive.Translated from Matematicheskie Zametki, Vol. 3, No. 1, pp. 71–76, January, 1968.The author wishes to express his deep appreciation to S. V. Fomin, under whose guidance this paper was written. 相似文献
14.
In the open disk
of the complex plane, we consider the following spaces of functions: the Bloch space
; the Hardy--Sobolev space
; and the Hardy--Besov space
. It is shown that if all the poles of the rational function R of degree n,
, lie in the domain
, then
, where
and
depends only on
. The second of these inequalities for the case of the half-plane was obtained by Semmes in 1984. The proof given by Semmes was based on the use of Hankel operators, while our proof uses the special integral representation of rational functions. 相似文献
15.
T. Levasseur 《Transformation Groups》1998,3(4):337-353
Let
u
be a compact Lie algebra and let
u
be its complexification. Let ζ−1/2 be the inverse on the set of regular elements of
u
of a square root of the discriminant of
. Generalizing a result of W. Lichtenstein in the case
u
=
(n, ℂ) or
(nℝ), we prove that ∂(q).ζ1/2 is non zero for all harmonic polynomialsq ∈S(
) \ {0}. This fact is deduced from results about equivariantD-modules supported on the nilpotent cone of
. 相似文献
16.
For measuresμ on the circleT the quantities
,
need not be equal; it is shown, however, that they are continuous with respect to each other whenμ varies on bounded subsets ofM(T), the space of measures onT. It is also shown that measuresμ which areɛ-almost idempotent (i.e.
) are the sum of an idempotent measure and of a measureυ satisfying
providedɛ is small enough (as a function of ‖μ‖). 相似文献
17.
A. G. Babenko 《Mathematical Notes》1996,60(3):248-263
In this paper we prove the Jackson-Stechkin inequalityE
n−1(f)<ω
n
(f, 2τ
n
,λ),n≥1,m≥5,r≥1, f ∈L2(
),f ≢ const, which is sharp for eachn=2, 3, ...; hereE
n−1
(f) is the best approximation of a functionf by spherical polynomials of degree ≤n−1, ω
n
(f, τ) is theτth modulus of continuity off based on the translations
,t ∈ ℝ,x ∈
,
,
is the measure of the unit Euclidean sphere
,
, andτ
n
,λ is the first positive zero of the Gegenbauer cosine polynomial
(cost).
Translated fromMatematicheskie Zametki, Vol. 60, No. 3, pp. 333–355, September, 1996.
The present paper was discussed at Ural State University in a seminar headed by Professor Arestov. The author is grateful
to Professor Arestov and Associate Professor Popov for useful conversations.
This research was supported by the State Commission for Higher Education of the Russian Federation under grant No. 2-16-5-31
and by the Russian Foundation for Basic Research under grant No. 93-011-196. 相似文献
18.
We obtain a set of necessary and sufficient conditions for
to imply
for 1 <k ≤ s < ∞. Using this result we establish several inclusion theorems as well as conditions for the equivalence of
and
. 相似文献
19.
I. I. Mel'nik 《Mathematical Notes》1973,14(5):962-966
On the lattice of manifolds of all algebras L we study the operator of nilpotent closure
, where
is a nilpotent manifold of -algebras. With a given system of identities defining, we construct a system *, giving the manifold
It is proved that if does not contain
, then the lattice of submanifolds of
is the double of the lattice of submanifolds of. We describe the free and subdirect indecomposable manifolds of algebras
. Let
and A be adense retract of B. We denote by (B) the lattice of congruences on B. The theorem is proved: (B) is a complemented lattice if and only if (A) is a complemented lattice.Translated from Matematicheskie Zametki, Vol. 14, No. 5, pp. 703–712, November, 1973. 相似文献
20.
Let
and
be adjoint nilpotent orbits in a real semisimple Lie algebra. Write
≥
if
is contained in the closure of
. This defines a partial order on the set of such orbits, known as the closure ordering. We determine this order for the split
real form of the simple complex Lie algebra, E
8. The proof is based on the fact that the Kostant-Sekiguchi correspondence preserves the closure ordering. We also present
a comprehensive list of simple representatives of these orbits, and list the irreeducible components of the boundaries
and of the intersections
. 相似文献