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1.
For an arbitrary variety
of groups and an arbitrary class
of groups that is closed on quotient groups, we prove that a quotient group G/N of the group G possesses an invariant system with
- and
-factors (respectively, is a residually
-group) if G possesses an invariant system with
- and
-factors (respectively, is a residually
-group) and N
(respectively, N is a maximal invariant
-subgroup of the group G). 相似文献
2.
E. S. Dubtsov 《Journal of Mathematical Sciences》2001,107(4):4002-4021
Let K be a compact space, let X be a closed subspace of C(K), and let
be a positive measure on K. The triple
is said to be regular if, for any positive function
and for any
, there exists a function
such that
on K and
. The case where K is the unit sphere in
and the subspace X is invariant with respect to the unitary group is investigated. Sufficient spectral conditions and a necessary condition for the regularity of a triple are obtained. Connections with compactness of certain Hankel operators and applications to interpolation problems are presented. Bibliography: 16 titles. 相似文献
3.
Andrzej Kornacki 《Applications of Mathematics》1997,42(1):71-77
Necessary and sufficient conditions are derived for the inclusions
and
to be fulfilled where
are some classes of invariant linearly sufficient statistics (Oktaba, Kornacki, Wawrzosek (1988)) corresponding to the Gauss-Markov models
, respectively. 相似文献
4.
Let
denote the unit sphere in
and
the geodesic distance in
. A spherical‐basis function approximant is a function of the form
, where
are real constants,
is a fixed function, and
is a set of distinct points in
. It is known that if
is a strictly positive definite function in
, then the interpolation matrix
is positive definite, hence invertible, for every choice of distinct points
and every positive integer M. The paper studies a salient subclass of such functions
, and provides stability estimates for the associated interpolation matrices.
This revised version was published online in June 2006 with corrections to the Cover Date. 相似文献
5.
Ivan Žežula 《Applications of Mathematics》1997,42(1):57-69
We consider a multivariate regression (growth curve) model of the form
, where
and
are unknown scalar covariance components. In the case of replicated observations, we derive the explicit form of the locally best estimators of the covariance components under normality and asymptotic confidence ellipsoids for certain linear functions of the first order parameters {B
ij} estimating simultaneously the first and the second order parameters. 相似文献
6.
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
7.
P. M. Akhmet'ev 《Journal of Mathematical Sciences》2004,119(1):5-9
Pairs B,
of divergence-free vector fields with compact support in
are considered higher-order analog M(B,
c (of order 3) of the Gauss helicity number H(B,
)=
, curl(A)=B; (of order 1) is constructed, which is invariant under volume-preserving diffeomorphisms. An integral expression for M is given. A degree-four polynomial m(B(x1), B(x2),
(
1),
(
2)), x1, x2,
1
2
, is defined, which is symmetric in the first and second pairs of variables separately. M is the average value of m over arbitrary configurations of points. Several conjectures clarifying the geometric meaning of the invariant and relating it to invariants of knots and links are stated. Bibliography: 11 titles. 相似文献
8.
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
9.
Adem Kilicman 《Czechoslovak Mathematical Journal》2001,51(3):463-471
Let
,
be ultradistributions in
and let
and
where
is a sequence in
which converges to the Dirac-delta function
. Then the neutrix product
is defined on the space of ultradistributions
as the neutrix limit of the sequence
provided the limit
exist in the sense that
for all in
. We also prove that the neutrix convolution product
exist in
, if and only if the neutrix product
exist in
and the exchange formula
is then satisfied. 相似文献
10.
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
11.
Ján Jakubík 《Czechoslovak Mathematical Journal》2002,52(3):651-663
Let Int
be the lattice of all intervals of an MV-algebra
. In the present paper we investigate the relations between direct product decompositions of
and (i) the lattice Int
, or (ii) 2-periodic isometries on
, respectively. 相似文献
12.
M. Bildhauer 《Journal of Mathematical Sciences》2003,115(6):2747-2752
Uniqueness is proved for solutions of the dual problem that is associated with the minimum problem
among the mappings
with prescribed Dirichlet boundary data and for smooth strictly convex integrands f of linear growth. No further assumptions on f or its conjugate function
are imposed, in particular,
is not assumed to be strictly convex. A special solution of the dual problem is seen to be a mapping into the image of
, which immediately implies uniqueness. Bibliography: 13 titles. 相似文献
13.
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
14.
15.
In this paper geodesically corresponding metricsg and
on a manifoldM, dim 5, under the assumption that the tensorsR andS of the metricg satisfyR.R=Q(S, R), are considered. It is stated that the corresponding tensors
and
of
not necessarily must satisfy
. Certain relations between the curvatures ofg and
are obtained.Supported by a post-doctoral fellowship of the researchcouncil of the KU Leuven; Bitnet FGBDA3O at BLEKUL11 相似文献
16.
O. V. Sarafanov 《Journal of Mathematical Sciences》2004,120(2):1195-1239
The C
*-algebra
generated by the operators of pseudodifferential boundary value problems on a manifold
with smooth closed disjoint edges and boundary
is studied. The operators act in the space L
2(
)
L
2(
). The goal of this paper is to describe all (up to an equivalence) irreducible representations of the algebra
Bibliography: 12 titles. 相似文献
17.
Hendrik Grundling 《Acta Appl Math》1997,46(2):107-145
Given an inductive limit group
where each
is locally compact, and a continuous two-cocycle
, we construct a C*-algebra
group algebra
is imbedded in its multiplier algebra
, and the representations of
are identified with the strong operator continuous
of G. If any of these representations are faithful, the above imbedding is faithful. When G is locally compact,
is precisely
, the twisted group algebra of G, and for these reasons we regard
in the general case as a twisted group algebra for G. Applying this construction to the CCR-algebra over an infinite dimensional symplectic space (S,\,B),we realise the regular representations as the representation space of the C*-algebra
, and show that pointwise continuous symplectic group actions on (S,\, B) produce pointwise continuous actions on
, though not on the CCR-algebra. We also develop the theory to accommodate and classify 'partially regular' representations, i.e. representations which are strong operator continuous on some subgroup H of G (of suitable type) but not necessarily on G, given that such representations occur in constrained quantum systems. 相似文献
18.
D. M. Smirnov 《Algebra and Logic》2003,42(2):136-146
We continue to study interrelations between permutative varieties and the cyclic varieties defined by cycles of the form
. A criterion is given determining whether a cyclic variety
is interpretable in
. For a permutation
without fixed elements, it is stated that a set of primes
for which
is interpretable in
in the lattice
is finite. It is also proved that for distinct primes
, the Helly number of a type
in
coincides with dimension of the dual type
and equals
. 相似文献
19.
In the canonical smooth fiber bundles
endowed with the metric tensor fields of relevant structure, we consider natural representations of the Galilean groups
and construct
-invariant generalizations of differentiable connections. In both regular and special cases of the representations of the relevant groups
, we found all the affine nonholonomic
-,
-, and
-connections of the first order (see [1]–[3]) possessing the local Lie groups of transformations
and also described the respective
-invariant planar connections. 相似文献
20.
Real valued M-estimators
in a statistical model 1 with observations
are replaced by
-valued M-estimators
in a new model with observations
where
are regressors,
is a structural parameter and
a structural function of the new model. Sufficient conditions for the consistency of
are derived, motivated by the sufficiency conditions for the simpler parent estimator
The result is a general method of consistent estimation in a class of nonlinear (pseudolinear) statistical problems. If F
has a natural exponential density ex–b( x ) then our pseudolinear model with u = (g o )–1 reduces to the well known generalized linear model, provided () = db()/d and g is the so-called link function of the generalized linear model. General results are illustrated for special pairs and leading to some classical M-estimators of mathematical statistics, as well as to a new class of generalized -quantile estimators. 相似文献