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1.
V. V. Kornienko 《Mathematical Notes》2000,68(5-6):576-587
We study the distribution in the complex plane
of the spectrum of the operator
, generated by the closure in
of the operation
originally defined on smooth functions
with values in a Hilbert space
satisfying the Dirichlet conditions
. Here
and A is a model operator acting in
. Criterial conditions on the parameter
for the eigenfunctions of the operator
to form a complete and minimal system as well as a Riesz basis in the Hilbert space H are given. 相似文献
2.
S. Yu. Orevkov 《Mathematical Notes》2000,68(5-6):588-593
Dehornoy constructed a right invariant order on the braid group B
n uniquely defined by the condition
1{\text{ if }}\beta _0 ,\beta _1$$
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are words in
. A braid is called strongly positive if
1$$
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for any
. In the present paper it is proved that the braid
is strongly positive if the word
does not contain
. We also provide a geometric proof of the result by Burckel and Laver that the standard generators of a braid group are strongly positive. Finally, we discuss relations between the right invariant order and quasipositivity. 相似文献
3.
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
4.
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
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 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
7.
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
8.
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
9.
N. A. Shirokov 《Journal of Mathematical Sciences》2005,129(4):4083-4086
Let
n be the unit ball in ℂn, n ≥ 2. Let Tα = {z ∈
n : (z, a) = |a|2} for a ∈
n and denote
for a discrete set A in
n. We find a sharp necessary condition for a set A to be a part of the zero-set for a function in H∞(
n). Bibliography 4 titles.__________Translated from Zapiski Nauchnykh Seminarov POMI, Vol. 303, 2003, pp. 272–278. 相似文献
10.
Let
be the variety of associative (special Jordan, respectively) algebras over an infinite field of characteristic 2 defined by the identity ((((x
1,x
2),x
3), ((x
4,x
5),x
6)), (x
7,x
8)) = 0 (((x
1
x
2 · x
3)(x
4
x
5 · x
6))(x
7
x
8) = 0, respectively). In this paper, we construct infinite independent systems of identities in the variety
(
, respectively). This implies that the set of distinct nonfinitely based subvarieties of the variety
has the cardinality of the continuum and that there are algebras in
with undecidable word problem. 相似文献
11.
Using an analog of the classical Frobenius recursion, we define the notion of a Frobenius
-homomorphism. For
, this is an ordinary ring homomorphism. We give a constructive proof of the following theorem. Let X be a compact Hausdorff space,
the
th symmetric power of X, and
the algebra of continuous complex-valued functions on X with the sup-norm; then the evaluation map
defined by the formula
identifies the space
with the space of all Frobenius
-homomorphisms of the algebra
into
with the weak topology. 相似文献
12.
Let H1(
) be the usual Hardy space on
. We show that the couple (H1(
), L(
) is a Calderón couple. This result immediately follows from the following stronger one: Given any fH1(
) +L(
) there exist two linear operators U and V satisfying the properties: (i) Uf=Nf (Nf being the non-tangential maximal function of f) and U is contractive from H1(
) to L1(
) and also from L(
) to L(
); (ii) V(Nf)=f, V is similtaneously bounded from L1(
) to H1(
) and from L(
) to L(
) and the norms of V on these spaces are controlled by a universal constant. We also have similar results on the couple (Lp(
), BMO (
)) for every 1
相似文献
13.
In this paper, it is proved that for the bilinear operator defined by the operation of multiplication in an arbitrary associative algebra
with unit
over the fields
or
, the infimum of its norms with respect to all scalar products in this algebra (with
) is either infinite or at most
. Sufficient conditions for this bound to be not less than
are obtained. The finiteness of this bound for infinite-dimensional Grassmann algebras was first proved by Kupsh and Smolyanov (this was used for constructing a functional representation for Fock superalgebras). 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 consider equations of the form
, where
is a function with values in the Hilbert space
, the operator B is symmetric, and the operator A is uniformly positive and self-adjoint in
. The linear operator
generating the C
0-semigroup in the energy space
is associated with this equation. We prove that this semigroup is exponentially stable if the operator B is uniformly positive and the operator A dominates B in the sense of quadratic forms. 相似文献
16.
We establish an analog of the Banach—Mazur theorem for real separable linear spaces with asymmetric norm: every such space can be linearly and isometrically embedded in the space of continuous functions f on the interval [0,1] equipped with the asymmetric norm
. This assertion is used to obtain nontrivial representations of an arbitrary convex closed body
, an arbitrary compact set
, and an arbitrary continuous function
. 相似文献
17.
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
18.
V. Yu. Popov 《Algebra and Logic》2005,44(1):46-54
There exist independently based semigroup varieties
and
,
, such that
has no cover in the interval [
;
].Translated from Algebra i Logika, Vol. 44, No. 1, pp. 81–96, January–February, 2005. 相似文献
19.
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
20.
S. N. Chernikov 《Mathematical Notes》1968,4(1):543-545
It is proved that if a periodic group
has an extremal normal divisor
, determining a complete abelian factor group
, then the center of the group
contains a complete abelian subgroup
, satisfying the relation
and intersecting
on a finite subgroup. It is also established with the aid of this proposition that every periodic group of automorphisms of an extremal group
is a finite extension of a contained in it subgroup of inner automorphisms of the group
.Translated from Matematicheskie Zametki, Vol. 4, No. 1, pp. 91–96, July, 1968. 相似文献