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1.
Dong Zhe 《Czechoslovak Mathematical Journal》2006,56(2):287-298
In this paper we investigate finite rank operators in the Jacobson radical
of Alg(
), where
are nests. Based on the concrete characterizations of rank one operators in Alg(
) and
, we obtain that each finite rank operator in
can be written as a finite sum of rank one operators in
and the weak closure of
equals Alg(
) if and only if at least one of
is continuous. 相似文献
2.
Furstenberg family and chaos 总被引:3,自引:0,他引:3
Jin-cheng XlONG~ Jie L Feng TAN School of Mathematical Sciences South China Normal University Guangzhou China 《中国科学A辑(英文版)》2007,50(9):1325-1333
A Furstenberg family F is a family,consisting of some subsets of the set of positive integers,which is hereditary upwards,i.e.A■B and A∈F imply B∈F.For a given system (i.e.,a pair of a complete metric space and a continuous self-map of the space) and for a Furstenberg family F, the definition of F-scrambled pairs of points in the space has been given,which brings the well-known scrambled pairs in Li-Yorke sense and the scrambled pairs in distribution sense to be F-scrambled pairs corresponding respectively to suitable Furstenberg family F.In the present paper we explore the basic properties of the set of F-scrambled pairs of a system.The generically F-chaotic system and the generically strongly F-chaotic system are defined.A criterion for a generically strongly F-chaotic system is showed. 相似文献
3.
For a big number of varieties
of groups close to Engelian, it is proved that a variety of lattice-ordered groups generated by all linearly ordered groups
in the class
does not coincide with the variety
of all o-approximable lattice-ordered groups.
Supported by FP “Universities of Russia” grant No. UR.04.01.001.
__________
Translated from Algebra i Logika, Vol. 45, No. 1, pp. 20–27, January–February, 2006. 相似文献
4.
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
5.
The following assertion is proved. Let
be the set of integers the number of the prime power of which is
. Let
be the size of
. Then for each irrational
, uniformly in
, \begin{equation*} \frac{1}{\pi_k(x)} \bigg|\sum _{\alul{n\le x}{n\in\cN_k}} f(n) e^{2\pi in\alpha}\bigg|\to 0, \end{equation*}
where
is an arbitrary multiplicative function with
,
is a positive constant.
This revised version was published online in June 2006 with corrections to the Cover Date. 相似文献
6.
We compute in this paper the distribution of the area
swept under the occupation process of an M/M/1 queue during a busy period. For this purpose, we use the expression of the Laplace transform
of the random variable
established in earlier studies as a fraction of Bessel functions. To get information on the poles and the residues of
, we take benefit of the fact that this function can be represented by a continued fraction. We then show that this continued
fraction is the even part of an S fraction and we identify its successive denominators by means of Lommel polynomials. This allows us to numerically evaluate
the poles and the residues. Numerical evidence shows that the poles are very close to the numbers
as
. This motivated us to formulate some conjectures, which lead to the derivation of the asymptotic behaviour of the poles and
the residues. This is finally used to derive the asymptotic behaviour of the probability survivor function
. The outstanding property of the random variable
is that the poles accumulate at 0 and its tail does not exhibit a nice exponential decay but a decay of the form
for some positive constants c and
, which indicates that the random variable
has a Weibull-like tail.
This revised version was published online in June 2006 with corrections to the Cover Date. 相似文献
7.
Let ℂ denote the complex numbers and
denote the ring of complex-valued Laurent polynomial functions on ℂ\{0}. Furthermore, we denote by
the subsets of Laurent polynomials whose restriction to the unit circle is real, nonnegative, respectively. We prove that
for any two Laurent polynomials
, which have no common zeros in ℂ\{0} there exists a pair of Laurent polynomials
satisfying the equation Q
1
P
1 + Q
2
P
2 = 1. We provide some information about the minimal length Laurent polynomials Q
1 and Q
2 with these properties and describe an algorithm to compute them. We apply this result to design a conjugate quadrature filter
whose zeros contain an arbitrary finite subset Λ⊂ℂ\{0} with the property that for every
implies
and
.
This revised version was published online in June 2006 with corrections to the Cover Date. 相似文献
8.
Hidetoshi Maeda 《Archiv der Mathematik》2007,88(5):419-424
Let
be an ample vector bundle of rank n – 1 on a smooth complex projective variety X of dimension n≥ 3 such that X is a
-bundle over
and that
for any fiber F of the bundle projection
. The pairs
with
= 2 are classified, where
is the curve genus of
. This allows us to improve some previous results.
Received: 13 June 2006 相似文献
9.
V. V. Makeev 《Journal of Mathematical Sciences》2005,131(1):5395-5400
Let ABCDE be a pentagon inscribed in a circle. It is proved that if
is a C4-generic smooth convex planar oval with four vertices (stationary points of curvature), then there are two similarities φ
such that the quadrangle φ(ABCD) is inscribed in
and the point φ(E)lies inside
, as well as two similarities ψ such that the quadrangle ψ(ABCD) is inscribed in
and ψ(E)lies outside
. Itisalsoprovedthatif n is odd, then any smoothly embedded circle γ ↪ ℝn contains the vertices of an equilateral (n + 1)-link polygonal line lying in a hyperplane of ℝn. Bibliography: 7 titles.
__________
Translated from Zapiski Nauchnykh Seminarov POMI, Vol. 299, 2003, pp. 241–251. 相似文献
10.
Given a unital C*-algebra
and a right C*-module
over
, we consider the problem of finding short smooth curves in the sphere
= {x ∈
: 〈x, x〉 = 1}. Curves in
are measured considering the Finsler metric which consists of the norm of
at each tangent space of
. The initial value problem is solved, for the case when
is a von Neumann algebra and
is selfdual: for any element x
0 ∈
and any tangent vector ν at x
0, there exists a curve γ(t) = e
tZ
(x
0), Z ∈
, Z* = −Z and ∥Z∥ ≤ π, such that γ(0) = x
0 and
(0) = ν, which is minimizing along its path for t ∈ [0, 1]. The existence of such Z is linked to the extension problem of selfadjoint operators. Such minimal curves need not be unique. Also we consider the
boundary value problem: given x
0, x
1 ∈
, find a curve of minimal length which joins them. We give several partial answers to this question. For instance, let us
denote by f
0 the selfadjoint projection I − x
0 ⊗ x
0, if the algebra f
0
f
0 is finite dimensional, then there exists a curve γ joining x
0 and x
1, which is minimizing along its path.
相似文献
11.
L. I. Danilov 《Mathematical Notes》1997,61(1):48-57
We consider Stepanov almost periodic functions μ ∈
ranging in the metric space
of Borel probability measures on a complete separable metric space
is equipped with the Prokhorov metric). The main result is as follows: a function
, belongs to
if and only if for each bounded continuous function
, the function
is Stepanov almost periodic (of order 1) and
Translated fromMatematicheskie Zametki, Vol. 61, No. 1, pp. 57–68, January, 1997.
Translated by I. P. Zvyagin 相似文献
12.
N. V. Smorodina 《Journal of Mathematical Sciences》2007,147(4):6950-6957
Let ξ(t), t ∈ [0, 1], be a jump Lévy process. We denote by
the law of ξ in the Skorokhod space
[0, 1]. Under some nondegeneracy condition on the Lévy measure Λ of the process, we construct a group of
-preserving transformations of the space
[0, 1]. Bibliography: 11 titles.
__________
Translated from Zapiski Nauchnykh Seminarov POMI, Vol. 341, 2007, pp. 175–188. 相似文献
13.
S. Norvidas 《Lithuanian Mathematical Journal》2006,46(4):446-458
Let, for σ > 0,
be the set of complex functions f ∈ L
1 (ℝ) with the Fourier transforms
vanishing outside the interval [−σ; σ]. In this paper, we study the problem of the best approximation of the Dirac function δ (which has the Fourier transform with widest support supp
) by functions
. More precisely, we consider the quantity inf
and its extremal functions
.
__________
Translated from Lietuvos Matematikos Rinkinys, Vol. 46, No. 4, pp. 548–564, October–December, 2006. 相似文献
14.
Milan Jasem 《Mathematica Slovaca》2007,57(2):107-118
In the paper isometries in pseudo MV-algebras are investigated. It is shown that for every isometry f in a pseudo MV-algebra
= (A, ⊕, −, ∼, 0, 1) there exists an internal direct decomposition
of
with
commutative such that
and
for each x ∈ A.
On the other hand, if
is an internal direct decomposition of a pseudo MV-algebra
= (A, ⊕, −, ∼, 0, 1) with
commutative, then the mapping g: A → A defined by
is an isometry in
and
.
相似文献
15.
T. Kühn 《Proceedings of the Steklov Institute of Mathematics》2006,255(1):159-168
The exact asymptotic behavior of the entropy numbers of compact embeddings of weighted Besov spaces is known in many cases,
in particular for power-type weights and logarithmic weights. Here we consider intermediate weights that are strictly between
these two scales; a typical example is
. For such weights we prove almost optimal estimates of the entropy numbers e
k
(id:
).
Dedicated to Sergeĭ Mikhaĭlovich Nikol’skiĭ on the occasion of his 100th birthday 相似文献
16.
Juraj Činčura 《Applied Categorical Structures》1998,6(4):527-530
Let
be an epireflective subcategory of the category Top of topological spaces which is not contained in the category of indiscrete spaces (e.g. Top, the category of Hausdorff spaces, the category of Tychonoff spaces) and
be a coreflective subcategory of
. In this paper we prove that the coreflector
preserves regular epimorphisms if and only if
or
is contained in the category of discrete spaces. 相似文献
17.
Let
be a group of affine transformations of the plane that contains a strict contraction and all translations. It is shown that
any two topological discs
are congruent dissection with respect to
such that only three topological discs are used as pieces of dissection. Two pieces of dissection do not suffice in general
even if
consists of all affine transformations.
This revised version was published online in August 2006 with corrections to the Cover Date. 相似文献
18.
In this paper, we introduce Property ∏σ of operator algebras and prove that nest subalgebras and the finite-width CSL subalgebras of arbitrary von Neumann algebras have Property ∏σ.Finally, we show that the tensor product formula alg ML1-(×)algNL2 = algM-(×)N(L1 (×) L2) holds for any two finite-width CSLs L1 and L2 in arbitrary von Neumann algebras M and N, respectively. 相似文献
19.
M. B. Zvyagina 《Journal of Mathematical Sciences》1998,89(2):1122-1126
Let Λ be an associative ring with identity and let
be the category of left unitary Λ-modules. A subcateqory
of the category
is said to be small if the pairwise nonisomorphic objects of
form a set. The main result of this paper consists of the fact that for every small full subcategory
, there exists a ring Γ such that
is dual to a small full subcategory of the category
. Some applications of this result are indicated. Bibliography: 3 titles.
Translated fromZapiski Nauchnykh Seminarov POMI, Vol. 227, 1995, pp. 66–73. 相似文献
20.
A. I. Budkin 《Algebra and Logic》2000,39(6):363-369
Let
be a class of all groups G for which the normal closure (x)
G
of every element x belongs to a class
.
is a Levi class generated by
. Let
and
0 be classes of finitely generated nilpotent groups and of torsion-free, finitely generated, nilpotent groups, respectively. We prove that
and
, and so
and
. It is shown that quasivarieties
and
are closed under free products, and that each contains at most one maximal proper subquasivariety. It is also proved that
is closed under free products if so is
. 相似文献