共查询到20条相似文献,搜索用时 46 毫秒
1.
V.G. Osmolovskii 《Journal of Mathematical Sciences》2004,122(3):3278-3289
We consider the energy functional of a two-phase elastic medium
with quadratic energy densities
defined for
such that
,where
is a measurable characteristic function. Under some natural conditions on the data of the problem, we prove the existence of an interval (t
-,t
+) of the change of temperature
such that the energy functional has only a minimizer
such that
for
or
such that
t^ + $$
" align="middle" border="0">
. The energy functional has no minimizers
such that
or
if
. We derive two-sided estimates for the numbers
in terms of the characteristics of the two-phase elastic medium and the boundary condition. Bibliography: 3 titles. 相似文献
2.
Introduce the notation:
, is the union of two segments [-1,1] and [-1 +
,1+
],
is a noninteger number,
is the Hölder class with exponent
on
The following result announced by the authors in [J. Math. Sci. 117 (2003), No. 3] is proved. There exist numbers a
1 (
) , b
1 (
)
0 depending only on
such that for any
there exists a polynomial
, such that
. Bibliography: 11 titles. 相似文献
3.
A. P. Scheglova 《Journal of Mathematical Sciences》2005,128(5):3306-3333
We consider the boundary-value problem
where
and n is the unit outward normal. We show that there exist so many nonequivalent positive weak solutions as prescribed under certain conditions on q and R. We construct nonradial solutions for [(n + 1)/2] + 1 ⩽ p < n and some q. Bibliography: 18 titles.__________Translated from Problemy Matematicheskogo Analiza, No. 30, 2005, pp. 121–144. 相似文献
4.
5.
E. G. Emel'yanov 《Journal of Mathematical Sciences》2002,110(6):3078-3090
An extension of a theorem on extremal decomposition of a Riemann surface is obtained. The problem of extremal decomposition is extended from the case of a Riemann surface
with a prescribed set
of distinguished points to the case of the Teichmüller space
corresponding to
under quasiconformal homeomorphisms f. For the functional
of our problem on extremal decomposition of a surface
, we consider a function
expressing the dependence of the extremal value of
on a point
. Differentiation formulas for the function
are derived. These formulas are different and depend on the genus g of the surface
. The case where the function
is pluriharmonic is considered. Bibliography: 8 titles. 相似文献
6.
The following classes of functions analytic in the unit disk are considered:
and
where
is the Nevanlinna characteristic and
is a properly changing positive function on (0,1]. Necessary and sufficient conditions on
are established under which the classes
and
are invariant under the operators of differentiation and integration. Bibliography: 7 titles. 相似文献
7.
The paper deals with the system
where
and
are
-matrix functions;
is a boundary control;
is the solution. The singularities of the fundamental solution corresponding to the controls
(
is the Dirac
-function) are under investigation. In the case of
, the singularities of the fundamental solution are described in terms of the standard scale
. In the presence of points
an interesting effect occurs: singularities of intermediate (fractional) orders appear. Bibliography: 1 title. 相似文献
8.
The paper deals with the problem of recovering the parameters (functions)
and
of the Maxwell dynamical system
(tan is the tangent component;
is a solution) by the response operator
(
is the normal). The parameters determine the velocity
, the c-metric
, and the time
. It is shown that for any fixed
, the operator
determines
and
in
uniquely. Bibliography: 15 titles. 相似文献
9.
D. E. Apushkinskaya H. Shahgholian N. N. Uraltseva 《Journal of Mathematical Sciences》2003,115(6):2720-2730
Let u and solve the problem
where is an open set in
0\} ,n \geqslant 2,H = \Delta - \partial _t \hfill \\ \hfill \\ \end{gathered} $$
" align="middle" border="0">
is the heat operator,
denotes the characteristic function of ,
is the unit cylinder in n+1,
, and the first equation is satisfied in the sense of distributions. We obtain the optimal regularity of the function u, i.e., we show that
. Bibliography: 6 titles. 相似文献
10.
V. A. Zalgaller 《Journal of Mathematical Sciences》2001,104(4):1255-1258
Let
be nonempty convex bodies in
. Let
be vectors in
, let
, and let
. Then
is a convex set, and the family of sets
is concave. Let
. Then for the mean cross-sectional measures W_v (\Phi (\rho )),
, the functions
are concave on D. (Note that % MathType!MTEF!2!1!+-% feaafiart1ev1aaatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn% hiov2DGi1BTfMBaeXafv3ySLgzGmvETj2BSbqefm0B1jxALjhiov2D% aebbnrfifHhDYfgasaacH8srps0lbbf9q8WrFfeuY-Hhbbf9v8qqaq% Fr0xc9pk0xbba9q8WqFfea0-yr0RYxir-Jbba9q8aq0-yq-He9q8qq% Q8frFve9Fve9Ff0dmeaabaqaciGacaGaaeqabaWaaeaaeaaakeaaca% WGxbWaaSbaaSqaaiaaicdaaeqaaOGaaiikaiabfA6agjaacIcacqaH% bpGCcaGGPaGaaiykaiabg2da9iaabAfacaqGVbGaaeiBamaaBaaale% aatCvAUfKttLearyqr1ngBPrgaiuGacqWFRbWAaeqaaOGaeuOPdyKa% aiikaiabeg8aYjaacMcaaaa!4EE7!\[W_0 (\Phi (\rho )) = {\text{Vol}}_k\Phi (\rho )\] is the k-volume.) Bibliography: 2 titles. 相似文献
11.
We introduce the notion of hyper-self-duality for Bose-Mesner algebras as a strengthening of formal self-duality. Let
denote a Bose-Mesner algebra on a finite nonempty set X. Fix p X, and let
and
denote respectively the dual Bose-Mesner algebra and the Terwilliger algebra of
with respect to p. By a hyper-duality of
, we mean an automorphism of
such that
for all
; and
is a duality of
.
is said to be hyper-self-dual whenever there exists a hyper-duality of
. We say that
is strongly hyper-self-dual whenever there exists a hyper-duality of
which can be expressed as conjugation by an invertible element of
. We show that Bose-Mesner algebras which support a spin model are strongly hyper-self-dual, and we characterize strong hyper-self-duality via the module structure of the associated Terwilliger algebra. 相似文献
12.
In the metastable range, a class of mappings yielding a negative solution of the isotopic realization problem (posed by E. V. Shchepin in 1993) and satisfying an additional technical condition is described in algebraic terms. Namely, one constructs an obstruction to isotopic realization of a discretely realizable continuous mapping f of an n-polyhedron to an orientable PL m-manifold; the completeness of this obstruction is established for
in the case where f is discretely realizable by skeleta. Also, for
, a series of mappings
(with singular set consisting of a p-adic solenoid,
, and a point) is presented for which the problem is solved in the negative. Furthermore, it is shown that the problem is solved in the affirmative in the metastable range if stabilization with codimension one is allowed, as well as in the case of a mapping
, under the condition that f is discretely realizable by skeleta and the configuration singular set
is acyclic in dimension
(in the sense of the SteenrodSitnikov homology). Bibliography: 31 titles. 相似文献
13.
O. L. Vinogradov 《Journal of Mathematical Sciences》2001,107(4):3987-4001
In what follows, C is the space of
-periodic continuous real-valued functions with uniform norm,
is the first continuity modulus of a function
with step h, H
n is the set of trigonometric polynomials of order at most n,
is the set of linear positive operators
(i.e., of operators such that
for every
),
is the space of square-integrable functions on
,
It is proved that
coincides with the smallest eigenvalue of some matrix of order n+1. The main result of the paper states that, for every
does not exceed and, for
, is equal to the minimum of the quadratic functional
over the unit sphere of
. Then it is calculated that
Bibliography: 19 titles. 相似文献
14.
15.
The systems of bases are constructed for the spaces of cusp forms
and
. Formulas are obtained for the number of representations of a positive integer by the sum of k binary quadratic forms of the kind
, of the kind
and of the kind
. 相似文献
16.
Judita Lihová 《Czechoslovak Mathematical Journal》1999,49(1):67-80
Let
be a partially ordered set, Int
the system of all (nonempty) intervals of
partially ordered by the set-theoretical inclusion
. We are interested in partially ordered sets
with Int
isomorphic to Int
. We are going to show that they correspond to couples of binary relations on A satisfying some conditions. If
is a directed partially ordered set, the only
with Int
isomorphic to Int
are
corresponding to direct decompositions
of
(
denotes the dual of
. The present results include those presented in the paper [11] by V. Slavík. Systems of intervals, particularly of lattices, have been investigated by many authors, cf. [1]–[11]. 相似文献
17.
We prove a local limit theorem for large deviations of the sums
, where
, is a Markov Gaussian random field,
is a bounded vector-valued function, and
. This paper generalizes the paper [13]. 相似文献
18.
A. Cossidente J. W. P. Hirschfeld G. Korchmáros F. Torres 《Compositio Mathematica》2000,121(2):163-181
The number N of rational points on an algebraic curve of genus g over a finite field
satisfies the Hasse–Weil bound
. A curve that attains this bound is called maximal. With
and
, it is known that maximalcurves have
. Maximal curves with
have been characterized up to isomorphism. A natural genus to be studied is
and for this genus there are two non-isomorphic maximal curves known when
. Here, a maximal curve with genus g
2 and a non-singular plane model is characterized as a Fermat curve of degree
. 相似文献
19.
G. V. Kuz'mina 《Journal of Mathematical Sciences》2003,118(1):4880-4894
We apply a variant of the method of the extremal metric to some problems concerning extremal decompositions and related problems. Let
be a system of distinct points on
and let
be the family of all systems
of nonoverlapping simply connected domains on
such that
. Let
where
is the reduced module of the domain
with respect to the point
. At present, the problem concerning the value
was solved completely for
. In this work, we continue the previous author's investigations and consider the case
. In addition, we consider the problem concerning the maximum of the sum
in the family
introduced above, where
, are arbitrary points of the circle
, and is a positive number. We prove that if
, then the maximum is attained only for systems of equidistant points of the circle
. For
, this result was obtained earlier by Dubinin who applied the method of symmetrization. It is shown that if
, where
is an even number, then equidistant points of the circle
do not realize the indicated maximum. Bibliography: 11 titles. 相似文献
20.
M. S. Lyapina 《Journal of Mathematical Sciences》2004,120(2):1109-1116
A bi-Lipschitz continuous mapping of a space X is a bijection
such that
, where
. We write
if f is a Lipschitz (bi-Lipschitz) mapping of X into itself and denote by
the set of all bi-Lipschitz mappings of X that are not isometry. Thus,
if
and blip
. For X we consider a standard Cantor set K on the real line (with standard metric). The main result of this paper is formulated as follows:
where
Bibliography: 2 titles. 相似文献