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1.
In this paper we define partially ordered quasi-uniform spaces (X,
, ≤) (PO-quasi-uniform spaces) as those space with a biconvex quasi-uniformity
on the poset (X, ≤) and give a construction of a (transitive) biconvex compatible quasi-uniformity on a partially ordered topological space
when its topology satisfies certain natural conditions. We also show that under certain conditions on the topology
of a PO-quasi-uniform space (X,
, ≤), the bicompletion
of (X,
) is also a PO-quasi-uniform space (
, ⪯) with a partial order ⪯ on
that extends ≤ in a natural way.
相似文献
2.
V. D. Lyakhovsky 《Theoretical and Mathematical Physics》2006,148(1):968-979
In accordance with the quantum duality principle, the twisted algebra
is equivalent to the quantum group
and has two preferred bases: one inherited from the universal enveloping algebra
and the other generated by coordinate functions of the dual Lie group
. We show howthe transformation
can be explicitly obtained for any simple Lie algebra and a factorable chain
of extended Jordanian twists. In the algebra
, we introduce a natural vector grading
, compatible with the adjoint representation of the algebra. Passing to the dual-group coordinates allows essentially simplifying
the costructure of the deformed Hopf algebra
, considered as a quantum group
. The transformation
can be used to construct new solutions of the twist equations. We construct a parameterized family of extended Jordanian
deformations
and study it in terms of
; we find new realizations of the parabolic twist.
Dedicated to the birthday of my teacher, Yurii Novozhilov
__________
Translated from Teoreticheskaya i Matematicheskaya Fizika, Vol. 148, No. 1, pp. 112–125, July, 2006. 相似文献
3.
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
4.
R. E. Maiboroda 《Ukrainian Mathematical Journal》1998,50(7):1067-1079
For a process X(t)=Σ
j=1
M
g
j
(t)ξ
j
(), where gj(t) are nonrandom given functions, is a stationary vector-valued Gaussian process, Eξk(t) = 0, and Eξk(0) Eξl(τ) = r
kl(τ), we construct an estimate for the functions r
kl(τ) on the basis of observations X(t), t ∈ [0, T]. We establish conditions for the asymptotic normality of as T → ∞. We consider the problem of the optimal choice of parameters of the estimate depending on observations.
Translated from Ukrainskii Matematicheskii Zhurnal, Vol. 50, No. 7, pp. 937–947, July, 1998. 相似文献
5.
We establish new properties of C
1 (0, + ∞)-solutions of the linear functional differential equation
in the neighborhoods of the singular points t = 0 and t = + ∞.
__________
Translated from Ukrains’kyi Matematychnyi Zhurnal, Vol. 57, No. 12, pp. 1668–1676, December, 2005. 相似文献
6.
Let E be a non empty set, let P : = E × E,
:= {x × E|x ∈ E},
:= {E × x|x ∈ E}, and
:= {C ∈ 2
P
|∀X ∈
: |C ∩ X| = 1} and let
. Then the quadruple
resp.
is called chain structure resp. maximal chain structure. We consider the maximal chain structure
as an envelope of the chain structure
. Particular chain structures are webs, 2-structures, (coordinatized) affine planes, hyperbola structures or Minkowski planes.
Here we study in detail the groups of automorphisms
,
,
,
related to a maximal chain structure
. The set
of all chains can be turned in a group
such that the subgroup
of
generated by
the left-, by
the right-translations and by ι the inverse map of
is isomorphic to
(cf. (2.14)). 相似文献
7.
José M. Isidro 《Central European Journal of Mathematics》2007,5(3):512-522
Let G be the Banach-Lie group of all holomorphic automorphisms of the open unit ball
in a J*-algebra
of operators. Let
be the family of all collectively compact subsets W contained in
. We show that the subgroup F ⊂ G of all those g ∈ G that preserve the family
is a closed Lie subgroup of G and characterize its Banach-Lie algebra. We make a detailed study of F when
is a Cartan factor.
相似文献
8.
Friedrich W. Bauer 《Journal of Mathematical Sciences》2008,148(2):175-191
In a category with homotopy
(Definition 1.1), one can define a natural concept of (co)fibrations and weak equivalences (Sec. 2) such that some properties
of a closed model category hold. If
is a complete and cocomplete category (with respect to finite limits) with simplicial homotopy (Definition 1.3), one achieves a full closed model structure in
(Theorem 4.6). For each category with homotopy
, there exists a category with simplicial homotopy
(see Sec. 5) (the simplicial envelope of
). If
is already a complete category with simplicial homotopy, then
is Quillen equivalent to
(Theorem 5.9).
__________
Translated from Sovremennaya Matematika i Ee Prilozheniya (Contemporary Mathematics and Its Applications), Vol. 41, Topology
and Its Applications, 2006. 相似文献
9.
Kazem Khashyarmanesh 《Archiv der Mathematik》2007,88(5):413-418
Let (
) be a commutative Noetherian local ring with non-zero identity,
an ideal of R and M a finitely generated R-module with
. Let D(–) := Hom
R
(–, E) be the Matlis dual functor, where
is the injective hull of the residue field
. We show that, for a positive integer n, if there exists a regular sequence
and the i-th local cohomology module H
i
a
(M) of M with respect to
is zero for all i with i > n then
The author was partially supported by a grant from Institute for Studies in Theoretical Physics and Mathematics (IPM) Iran
(No. 85130023).
Received: 9 August 2006 相似文献
10.
Let
, n = 1, 2, ..., be the supercritical branching random walk in which the family sizes may be infinite with positive probability.
Assume that a natural martingale related to
converges almost surely and in the mean to a random variable W. For a large subclass of nonnegative and concave functions ƒ, we provide a criterion for the finiteness of
Wf(W). The main assertions of the present paper generalize some results obtained recently in Kuhlbusch’s Ph.D. thesis as well
as previously known results for the Galton-Watson processes. In the process of the proof, we study the existence of the ƒ-moments of perpetuities.
Published in Ukrains’kyi Matematychnyi Zhurnal, Vol. 58, No. 4, pp. 451–471, April, 2006. 相似文献
11.
We study the boundary-value problemu
tt
-u
xx
=g(x, t),u(0,t) =u (π,t) = 0,u(x, t +T) =u(x, t), 0 ≤x ≤ π,t ∈ ℝ. We findexact classical solutions of this problem in three Vejvoda-Shtedry spaces, namely, in the classes of, and-periodic functions (q and s are natural numbers). We obtain the results only for sets of periods, and which characterize the classes of π-, 2π -, and 4π-periodic functions.
Translated from Ukrainskii Matematicheskii Zhurnal, Vol. 51, No. 2, pp. 281–284, February, 1999. 相似文献
12.
Dorothee Schueth 《Geometriae Dedicata》2004,105(1):77-83
A nonflat Einstein solvmanifold (
, g) is said to be of standard type if in the associated metric Lie algebra
, the orthogonal complement
of the derived algebra is Abelian. It is an open question whether the standard condition is automatically satisfied for all
nonflat Einstein solvmanifolds. We derive certain properties of the metric Lie algebra
of a nonflat Einstein solvmanifold (
, g) under the assumption
. In particular, we obtain some new sufficient conditions which imply standard type. 相似文献
13.
V. D. Lyakhovsky 《Journal of Mathematical Sciences》2006,136(1):3596-3606
Using a graphic presentation of the dual Lie algebra
# (r) for a simple algebra
, it is possible to show that there always exist solutions rech of the classical Yang—Baxter equation with a parabolic carrier. To get a closed-form expression for rech, we find dual coordinates in which the adjoint action of the carrier
c
is reducible. This allows us to find the structure of Jordanian r-matrices rJ which are candidates for enlarging the initial full chain rfch and realize the desired solution rech in the factorized form rech ≈ rfch + rJ. We obtain a unique transformation: the canonical chain has to be replaced by a special kind of peripheric r-matrices, rfch → rrfch. To illustrate the method, the case of
=sl(11) is considered in the full detail. Bibliography: 11 titles.
To my friend Petr Petrovich Kulish
__________
Translated from Zapiski Nauchnykh Seminarov POMI, Vol. 317, 2004, pp. 122–141. 相似文献
14.
For any partial groupoid
, let Fr
be the free extension of
to a total groupoid. We show that
implies
and that the theory of Fr
is uniformly recursive in the theory of
. These results fail if “groupoid” is replaced by “semigroup”, “commutative semigroup”, “group”, “abelian group”, “semilattice”,
“K-lattice” for any nontrivial varietyK of lattices, or “Boolean algebra”.
Research supported in part by NSF Grant MCS78-01867. We thank the referee for his valuable comments.
Presented by B. Jónsson. 相似文献
15.
We establish the validity of the inclusion G/N∈
X for groups G ∈
X under certain restrictions on N ⊴ G, where X is one of the following classes, the class of locally graded groups, the class of RI-groups, or the class for a fixed group variety .
Translated from Ukrainskii Matematicheskii Zhurnal, Vol. 50, No. 11, pp. 1545–1553, November, 1998. 相似文献
16.
I. V. Kal’chuk 《Ukrainian Mathematical Journal》2007,59(9):1342-1363
We obtain asymptotic equalities for the upper bounds of approximations by Weierstrass operators on the functional classes
and
in the metrics of the spaces Ĉ and
respectively.
__________
Translated from Ukrains’kyi Matematychnyi Zhurnal, Vol. 59, No. 9, pp. 1201–1220, September, 2007. 相似文献
17.
For an arbitrary self-adjoint operator B in a Hilbert space
, we present direct and inverse theorems establishing the relationship between the degree of smoothness of a vector
with respect to the operator B, the rate of convergence to zero of its best approximation by exponential-type entire vectors of the operator B, and the k-modulus of continuity of the vector x with respect to the operator B. The results are used for finding a priori estimates for the Ritz approximate solutions of operator equations in a Hilbert space.
__________
Translated from Ukrains'kyi Matematychnyi Zhurnal, Vol. 57, No. 5, pp. 633–643, May, 2005. 相似文献
18.
A group G has finite rank r if every finitely generated subgroup of G is at most r-generator. If C is a class of groups then we let C* denote the class of groups G in which every proper subgroup of G is either of finite rank or in C. We let denote the class of soluble groups and the class of soluble groups of derived length at most d, where d is a positive integer. We let λ denote the set of closure operations
and let denote the λ-closure of the class of periodic locally graded groups. Amongst other results we prove that a soluble -group is either of finite rank or of derived length at most d and also that a group in the class is either locally soluble, or has finite rank, or is isomorphic to one of or for suitable locally finite fields .
The second author would like to thank the Department of Mathematics at Bucknell University for its hospitality while part
of this work was being done. 相似文献
19.
A. V. Syrtsov 《Journal of Mathematical Sciences》2006,139(4):6792-6802
The class of Magnus
-groups is closed under the operation of the
-product.
__________
Translated from Fundamentalnaya i Prikladnaya Matematika, Vol. 10, No. 3, pp. 199–213, 2004. 相似文献