共查询到20条相似文献,搜索用时 15 毫秒
1.
D. Cvijović 《Theoretical and Mathematical Physics》2009,161(3):1663-1668
We find simple explicit closed-form formulas for the Fermi-Dirac function $
\mathcal{F}_{ - n} (z)
$
\mathcal{F}_{ - n} (z)
and Bose-Einstein function $
\mathcal{B}_{ - n} (z)
$
\mathcal{B}_{ - n} (z)
for arbitrary n ε ℕ. The obtained formulas involve the higher tangent numbers defined by Carlitz and Scoville. We present
some examples and direct consequences of applying the main results. 相似文献
2.
In this paper, we introduce the subfamilies H
m
($
\mathcal{R}_{IV}
$
\mathcal{R}_{IV}
(n)) of holomorphic mappings defined on the Lie ball $
\mathcal{R}_{IV}
$
\mathcal{R}_{IV}
(n) which reduce to the family of holomorphic mappings and the family of locally biholomorphic mappings when m = 1 and m → +∞, respectively. Various distortion theorems for holomophic mappings H
m
($
\mathcal{R}_{IV}
$
\mathcal{R}_{IV}
(n)) are established. The distortion theorems coincide with Liu and Minda’s as the special case of the unit disk. When m = 1 and m → +∞, the distortion theorems reduce to the results obtained by Gong for $
\mathcal{R}_{IV}
$
\mathcal{R}_{IV}
(n), respectively. Moreover, our method is different. As an application, the bounds for Bloch constants of H
m
($
\mathcal{R}_{IV}
$
\mathcal{R}_{IV}
(n)) are given. 相似文献
3.
A. Olofsson 《Acta Mathematica Hungarica》2010,128(3):265-286
We develop a Wold decomposition for the shift semigroup on the Hardy space $
\mathcal{H}^2
$
\mathcal{H}^2
of square summable Dirichlet series convergent in the half-plane $
\Re (s) > 1/2
$
\Re (s) > 1/2
. As an application we have that a shift invariant subspace of $
\mathcal{H}^2
$
\mathcal{H}^2
is unitarily equivalent to $
\mathcal{H}^2
$
\mathcal{H}^2
if and only if it has the form $
\phi \mathcal{H}^2
$
\phi \mathcal{H}^2
for some $
\mathcal{H}^2
$
\mathcal{H}^2
-inner function φ. 相似文献
4.
Hongliang Yao 《Proceedings Mathematical Sciences》2010,120(2):199-207
Lin and Su classified A$
\mathcal{T}
$
\mathcal{T}
-algebras of real rank zero. This class includes all A$
\mathbb{T}
$
\mathbb{T}
-algebras of real rank zero as well as many C*-algebras which are not stably finite. An A$
\mathcal{T}
$
\mathcal{T}
-algebra often becomes an extension of an A$
\mathbb{T}
$
\mathbb{T}
-algebra by an AF-algebra. In this paper, we show that there is an essential extension of an A$
\mathbb{T}
$
\mathbb{T}
-algebra by an AF-algebra which is not an A$
\mathcal{T}
$
\mathcal{T}
-algebra. We describe a characterization of an extension E of an A$
\mathbb{T}
$
\mathbb{T}
-algebra by an AF-algebra if E is an A$
\mathcal{T}
$
\mathcal{T}
-algebra. 相似文献
5.
B. Wróbel 《Acta Mathematica Hungarica》2009,124(4):333-351
Imaginary powers associated to the Laguerre differential operator $
L_\alpha = - \Delta + |x|^2 + \sum _{i = 1}^d \frac{1}
{{x_i^2 }}(\alpha _i^2 - 1/4)
$
L_\alpha = - \Delta + |x|^2 + \sum _{i = 1}^d \frac{1}
{{x_i^2 }}(\alpha _i^2 - 1/4)
are investigated. It is proved that for every multi-index α = (α1,...α
d
) such that α
i
≧ −1/2, α
i
∉ (−1/2, 1/2), the imaginary powers $
\mathcal{L}_\alpha ^{ - i\gamma } ,\gamma \in \mathbb{R}
$
\mathcal{L}_\alpha ^{ - i\gamma } ,\gamma \in \mathbb{R}
, of a self-adjoint extension of L
α, are Calderón-Zygmund operators. Consequently, mapping properties of $
\mathcal{L}_\alpha ^{ - i\gamma }
$
\mathcal{L}_\alpha ^{ - i\gamma }
follow by the general theory. 相似文献
6.
Huffman, Park and Skoug established several results involving Fourier-Feynman transform and convolution for functionals in
a Banach algebra S on the classical Wiener space. Chang, Kim and Yoo extended these results to abstract Wiener space for a more generalized
Fresnel class $
\mathcal{F}_{\mathcal{A}_1 ,\mathcal{A}_2 }
$
\mathcal{F}_{\mathcal{A}_1 ,\mathcal{A}_2 }
A1,A2 than the Fresnel class $
\mathcal{F}
$
\mathcal{F}
(B)which corresponds to the Banach algebra S. In this paper we study Fourier-Feynman transform, convolution and first variation of unbounded functionals on abstract Wiener
space having the form
$
F\left( x \right) = G\left( x \right)\psi \left( {\left( {\vec e,x} \right)^ \sim } \right)
$
F\left( x \right) = G\left( x \right)\psi \left( {\left( {\vec e,x} \right)^ \sim } \right)
相似文献
7.
8.
The paper presents the analysis, approximation and numerical realization of 3D contact problems for an elastic body unilaterally
supported by a rigid half space taking into account friction on the common surface. Friction obeys the simplest Tresca model
(a slip bound is given a priori) but with a coefficient of friction $
\mathcal{F}
$
\mathcal{F}
which depends on a solution. It is shown that a solution exists for a large class of $
\mathcal{F}
$
\mathcal{F}
and is unique provided that $
\mathcal{F}
$
\mathcal{F}
is Lipschitz continuous with a sufficiently small modulus of the Lipschitz continuity. The problem is discretized by finite
elements, and convergence of discrete solutions is established. Finally, methods for numerical realization are described and
several model examples illustrate the efficiency of the proposed approach. 相似文献
9.
A. V. Parfenenkov 《Proceedings of the Steklov Institute of Mathematics》2009,266(Z1):194-204
We study the class $
\mathfrak{P}_n
$
\mathfrak{P}_n
of algebraic polynomials P
n
(x, y) in two variables of total degree n whose uniform norm on the unit circle Γ1 centered at the origin is at most 1: $
\left\| {P_n } \right\|_{C(\Gamma _1 )}
$
\left\| {P_n } \right\|_{C(\Gamma _1 )}
≤ 1. The extension of polynomials from the class $
\mathfrak{P}_n
$
\mathfrak{P}_n
to the plane with the least uniform norm on the concentric circle Γ
r
of radius r is investigated. It is proved that the values θ
n
(r) of the best extension of the class $
\mathfrak{P}_n
$
\mathfrak{P}_n
satisfy the equalities θ
n
(r) = r
n
for r > 1 and θ
n
(r) = r
n−1 for 0 < r < 1. 相似文献
10.
Yu. V. Brezhnev 《Theoretical and Mathematical Physics》2009,161(3):1616-1633
We represent and analyze the general solution of the sixth Painlevé transcendent $
\mathcal{P}_6
$
\mathcal{P}_6
in the Picard-Hitchin-Okamoto class in the Painlevé form as the logarithmic derivative of the ratio of τ-functions. We express
these functions explicitly in terms of the elliptic Legendre integrals and Jacobi theta functions, for which we write the
general differentiation rules. We also establish a relation between the $
\mathcal{P}_6
$
\mathcal{P}_6
equation and the uniformization of algebraic curves and present examples. 相似文献
11.
F. Chebana 《Mathematical Methods of Statistics》2009,18(3):231-240
Consider a class of M-estimators indexed by a criterion function ψ. When the function ψ is taken to be in a class of functions $
\mathcal{F}
$
\mathcal{F}
, a family of processes indexed by the class $
\mathcal{F}
$
\mathcal{F}
is obtained and called M-processes. Pooling the M-estimators in such class may be used to define new kind of estimators. In order to get the asymptotic properties of these
pooled estimators, the convergence in probability of the corresponding M-process is studied uniformly on $
\mathcal{F}
$
\mathcal{F}
together with their weak convergence towards a Gaussian process. An application to location estimation is presented and discussed. 相似文献
12.
Characterizations and properties of $
\mathcal{I}_g
$
\mathcal{I}_g
-closed sets and $
\mathcal{I}_g
$
\mathcal{I}_g
-open sets are given. A characterization of normal spaces is given in terms of $
\mathcal{I}_g
$
\mathcal{I}_g
-open sets. Also, it is established that an $
\mathcal{I}_g
$
\mathcal{I}_g
-closed subset of an $
\mathcal{I}
$
\mathcal{I}
-compact space is $
\mathcal{I}
$
\mathcal{I}
-compact. 相似文献
13.
E. V. Mishchenko 《Siberian Mathematical Journal》2010,51(4):660-666
The problem of determining the upper and lower Riesz bounds for the mth order B-spline basis is reduced to analyzing the series
$
\sum\nolimits_{j = - \infty }^\infty {\frac{1}
{{(x - j)^{2m} }}}
$
\sum\nolimits_{j = - \infty }^\infty {\frac{1}
{{(x - j)^{2m} }}}
. The sum of the series is shown to be a ratio of trigonometric polynomials of a particular shape. Some properties of these
polynomials that help to determine the Riesz bounds are established. The results are applied in the theory of series to find
the sums of some power series. 相似文献
14.
Wenhua Zhao 《Central European Journal of Mathematics》2010,8(6):1132-1155
We first propose a generalization of the notion of Mathieu subspaces of associative algebras $
\mathcal{A}
$
\mathcal{A}
, which was introduced recently in [Zhao W., Generalizations of the image conjecture and the Mathieu conjecture, J. Pure Appl.
Algebra, 2010, 214(7), 1200–1216] and [Zhao W., Mathieu subspaces of associative algebras], to $
\mathcal{A}
$
\mathcal{A}
-modules $
\mathcal{M}
$
\mathcal{M}
. The newly introduced notion in a certain sense also generalizes the notion of submodules. Related with this new notion,
we also introduce the sets σ(N) and τ(N) of stable elements and quasi-stable elements, respectively, for all R-subspaces N of $
\mathcal{A}
$
\mathcal{A}
-modules $
\mathcal{M}
$
\mathcal{M}
, where R is the base ring of $
\mathcal{A}
$
\mathcal{A}
. We then prove some general properties of the sets σ(N) and τ(N). Furthermore, examples from certain modules of the quasi-stable algebras [Zhao W., Mathieu subspaces of associative algebras], matrix algebras over fields and polynomial algebras are also studied. 相似文献
15.
The main purpose of this paper is to study the hybrid mean value of $
\frac{{L'}}
{L}(1,\chi )
$
\frac{{L'}}
{L}(1,\chi )
and Gauss sums by using the estimates for trigonometric sums as well as the analytic method. An asymptotic formula for the
hybrid mean value $
\sum\limits_{\chi \ne \chi _0 } {|\tau (\chi )||\frac{{L'}}
{L}(1,\chi )|^{2k} }
$
\sum\limits_{\chi \ne \chi _0 } {|\tau (\chi )||\frac{{L'}}
{L}(1,\chi )|^{2k} }
of $
\frac{{L'}}
{L}
$
\frac{{L'}}
{L}
and Gauss sums will be proved using analytic methods and estimates for trigonometric sums. 相似文献
16.
Suppose that X is a complex Banach space with the norm ‖·‖ and n is a positive integer with dim X ⩾ n ⩾ 2. In this paper, we consider the generalized Roper-Suffridge extension operator $
\Phi _{n,\beta _2 ,\gamma _2 , \ldots ,\beta _{n + 1} ,\gamma _{n + 1} } (f)
$
\Phi _{n,\beta _2 ,\gamma _2 , \ldots ,\beta _{n + 1} ,\gamma _{n + 1} } (f)
on the domain $
\Omega _{p_1 ,p_2 , \ldots ,p_{n + 1} }
$
\Omega _{p_1 ,p_2 , \ldots ,p_{n + 1} }
defined by
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