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1.
In this paper, we suggest a new functional approach to the study of group classes which enables us to describe all formations and Fitting classes of finite groups in the language of functions. The notions of
-fibered formation and of
-fibered Fitting class with direction are introduced. A direction is defined as a mapping of the set
of all primes into the set of all nonempty Fitting formations. The existence of infinitely many mappings of this kind makes it possible to construct new forms of formations and Fitting classes for a given nonempty set
. In particular, an
-local formation is an
-fibered formation with a direction such that
for any prime p. In the paper we study some basic properties of
-fibered formations and of
-fibered Fitting classes with direction and obtain the structure of their minimal satellites for a given . 相似文献
2.
We introduce the notions of a Gibbs measure with the corresponding potential with association
(where
is a subset of the set
) of a Markov random field with memory
and measure with association
. It is proved that these three notions are equivalent. 相似文献
3.
We construct the trajectory attractor
of a three-dimensional Navier--Stokes system with exciting force
. The set
consists of a class of solutions to this system which are bounded in
, defined on the positive semi-infinite interval
of the time axis, and can be extended to the entire time axis
so that they still remain bounded-in-
solutions of the Navier--Stokes system. In this case any family of bounded-in-
solutions of this system comes arbitrary close to the trajectory attractor
. We prove that the solutions
are continuous in t if they are treated in the space of functions ranging in
. The restriction of the trajectory attractor
to
,
, is called the global attractor of the Navier--Stokes system. We prove that the global attractor
thus defined possesses properties typical of well-known global attractors of evolution equations. We also prove that as
the trajectory attractors
and the global attractors
of the
-order Galerkin approximations of the Navier--Stokes system converge to the trajectory and global attractors
and
, respectively. Similar problems are studied for the cases of an exciting force of the form
depending on time
and of an external force
rapidly oscillating with respect to the spatial variables or with respect to time
. 相似文献
4.
For a given homogeneous elliptic partial differential operator
with constant complex coefficients, two Banach spaces
and
of distributions in
, and compact sets
and
in
, we study joint approximations in the norms of the spaces
and
(the spaces of Whitney jet-distributions) by the solutions of the equation
in neighborhoods of the set
. We obtain a localization theorem, which, under certain conditions, allows one to reduce the above-cited approximation problem to the corresponding separate problems in each of the spaces. 相似文献
5.
We prove the absolute continuity of the spectrum of the Schrödinger operator in
,
, with periodic (with a common period lattice
) scalar
and vector
potentials for which either
,
, or the Fourier series of the vector potential
converges absolutely,
, where
is an elementary cell of the lattice
,
for
, and
for
, and the value of
is sufficiently small, where
and
otherwise,
, and
. 相似文献
6.
We consider the series
and
whose coefficients satisfy the condition
for
, where the sequence
can be expressed as the union of a finite number of lacunary sequences. The following results are obtained. If
as
, then the series
is uniformly convergent. If
for all
, then the sequence of partial sums of this series is uniformly bounded. If the series
is convergent for
and
as
, then this series is uniformly convergent. If the sequence of partial sums of the series
for
is bounded and
for all
, then the sequence of partial sums of this series is uniformly bounded. In these assertions, conditions on the rates of decrease of the coefficients of the series are also necessary if the sequence
is lacunary. In the general case, they are not necessary. 相似文献
7.
Let
be a closed orientable surface of genus
, endowed with the structure of a Riemann manifold of constant negative curvature. For the universal covering
, there is the notion of absolute, each of whose points determines an asymptotic direction of a bundle of parallel equidirected geodesics. In the paper it is proved that there is a set
on the absolute having the cardinality of the continuum and such that if an arbitrary flow on
has a semitrajectory whose covering has asymptotic direction defined by a point from
, then this flow is not analytical and has infinitely many stationary points. 相似文献
8.
An urn contains colored balls,
~balls of each of
different colors. The balls are drawn sequentially and equiprobably, one ball at a time, and then each drawn ball drawn is either returned to the urn (sampling with replacement) or left outside the urn (sampling without replacement). The drawing continues until some
colors are drawn at least
~times each. Observable statistics are the numbers
,
, of colors that have appeared precisely
~times each by the stopping time. The asymptotic behavior as
of these values for each of the two sampling models is studied; the possibility of their use for identifying the model is discussed. 相似文献
9.
It is proved that the following conditions are equivalent for an arbitrary commutative Moufang loop
:1) the loop
is finite over the center;2) every subloop of
defines a finite conjugacy class of subloops;3) every associative subloop of
defines a finite conjugacy class of subloops;4) every infinite associative subloop of
defines a finite conjugacy class of subloops. 相似文献
10.
Suppose that
is an arbitrary finite complex Borel measure on the interval
is its Poisson integral,
and
are the conjugate harmonics of
, and
is the nontangential limiting value of the analytic function
as
. In this paper, we consider the problem of representing the analytic function
in terms of its boundary values
. 相似文献
11.
We study a version of the Gauss map
for a surface
immersed in
and prove an analog of the Ruh--Vilms theorem which states that this map is harmonic iff
has a constant mean curvature. As a corollary, we conclude that an embedded flat torus
with constant mean curvature is a spherical Delonay surface. 相似文献
12.
We study trigonometric sums in finite fields
. The Weil estimate of such sums is well known:
, where f is a polynomial with coefficients from F(Q). We construct two classes of polynomials f,
, for which
attains the largest possible value and, in particular,
. 相似文献
13.
Let
be a sequence of complex numbers such that
as
. For
close to the imaginary axis, upper bounds of the indicator of a nonzero entire function of exponential type with minimal growth vanishing on
is obtained. These bounds give sufficient conditions for the system of exponents
to be incomplete in an unbounded domain in
. 相似文献
14.
Two numerical characteristics of a nonrectifiable arc
generalizing the notion of length are introduced. Geometrically, this notion can naturally be generalized as the least upper bound of the sums
, where
are the lengths of segments of a polygonal line inscribed in the curve
and
is a given function. On the other hand, the length of
is the norm of the functional
in the space
; its norms in other spaces can be considered as analytical generalizations of length. In this paper, we establish conditions under which the generalized geometric rectifiability of a curve
implies its generalized analytic rectifiability. 相似文献
15.
In this paper, we generalize Bernstein's theorem characterizing the space
by means of local approximations. The closed interval
is partitioned into disjoint half-intervals on which best approximation polynomials of degree
divided by the lengths of these half-intervals taken to the power
are considered. The existence of the limits of these ratios as the lengths of the half-intervals tend to zero is a criterion for the existence of the
th derivative of a function. We prove the theorem in a stronger form and extend it to the spaces
. 相似文献
16.
We obtain sufficient conditions for the continuity of the general nonlinear superposition operator (generalized Nemytskii operator) acting from the space
of differentiable functions on a bounded domain
to the Lebesgue space
. The values of operators on a function
are locally determined by the values of both the function
itself and all of its partial derivatives up to order
inclusive. In certain particular cases, the sufficient conditions obtained are proved to be necessary as well. The results are illustrated by several examples, and an application to the theory of Sobolev spaces is also given. 相似文献
17.
A nondegenerate null-pair of the real projective space
consists of a point and of a hyperplane nonincident to this point. The manifold of all nondegenerate null-pairs
carries a natural Kählerian structure of hyperbolic type and of constant nonzero holomorphic sectional curvature. In particular,
is a symplectic manifold. We prove that
is endowed with the structure of a fiber bundle over the projective space
, whose typical fiber is an affine space. The vector space associated to a fiber of the bundle is naturally isomorphic to the cotangent space to
. We also construct a global section of this bundle; this allows us to construct a diffeomorphism
between the manifold of nondegenerate null-pairs and the cotangent bundle over the projective space. The main statement of the paper asserts that the explicit diffeomorphism
is a symplectomorphism of the natural symplectic structure on
to the canonical symplectic structure on
. 相似文献
18.
It is proved that if a normal semifinite weight on a von Neumann algebra
satisfies the inequality
for any selfadjoint operators
in
, then this weight is a trace. Several similar characterizations of traces among the normal semifinite weights are proved. In particular, Gardner's result on the characterization of traces by the inequality
is refined and reinforced. 相似文献
19.
It is proved that systems of exponentials orthogonal to measures of a special kind form bases in
, for which an analog of the Riesz theorem on the projection from
is valid. 相似文献
20.
Quasiconcave functions
and
belong to the same scale if there exist quasiconcave functions
and
and numbers
such that
and
. We establish a criterion for such functions to belong to the same scale up to equivalence. This criterion is obtained in terms of nodes of the corresponding linear-constant step-functions. It turns out that nodes must be equivalent to sequences. 相似文献