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1.
Yilmaz Simsek 《Nonlinear Analysis: Theory, Methods & Applications》2009,71(12):e377
The aim of this paper is to define new generating functions. By applying a derivative operator and the Mellin transformation to these generating functions, we define q-analogue of the Genocchi zeta function, q-analogue Hurwitz type Genocchi zeta function, and q-Genocchi type l-function. We define partial zeta function. By using this function, we construct p-adic interpolation functions which interpolate generalized q-Genocchi numbers at negative integers. We also define p-adic meromorphic functions on Cp. Furthermore, we construct new generating functions of q-Hardy-Berndt type sums and q-Hardy-Berndt type sums attached to Dirichlet character. We also give some new relations, related to these sums. 相似文献
2.
The Sz.-Nagy-FoiaŞ functional model for completely non-unitary contractions is extended to completely non-coisometric sequences
of bounded operatorsT = (T1,...,T
d) (d finite or infinite) on a Hilbert space, with bounded characteristic functions. For this class of sequences, it is shown
that the characteristic function θT is a complete unitary invariant.
We obtain, as the main result, necessary and sufficient conditions for a bounded multi-analytic operator on Fock spaces to
coincide with the characteristic function associated with a completely non-coisometric sequence of bounded operators on a
Hilbert space.
Research supported in part by a COBASE grant from the National Research Council.
The first author was partially supported by a grant from Ministerul Educaţiei Şi Cercetarii.
The second author was partially supported by a National Science Foundation grant. 相似文献
3.
A permutation group on a countably infinite domain is called oligomorphic if it has finitely many orbits of finitary tuples. We define a clone on a countable domain to be oligomorphic if its set of permutations forms an oligomorphic permutation group. There is a close relationship to ω-categorical structures, i.e., countably infinite structures with a first-order theory that has only one countable model, up to isomorphism. Every
locally closed oligomorphic permutation group is the automorphism group of an ω-categorical structure, and conversely, the canonical structure of an oligomorphic permutation group is an ω-categorical structure that contains all first-order definable relations. There is a similar Galois connection between locally
closed oligomorphic clones and ω-categorical structures containing all primitive positive definable relations.
In this article we generalise some fundamental theorems of universal algebra from clones over a finite domain to oligomorphic
clones. First, we define minimal oligomorphic clones, and present equivalent characterisations of minimality, and then generalise Rosenberg’s five types classification
to minimal oligomorphic clones. We also present a generalisation of the theorem of Baker and Pixley to oligomorphic clones.
Presented by A. Szendrei.
Received July 12, 2005; accepted in final form August 29, 2006. 相似文献
4.
Recently a new basis for the Hopf algebra of quasisymmetric functions QSym, called quasisymmetric Schur functions, has been introduced by Haglund, Luoto, Mason, van Willigenburg. In this paper we extend the definition of quasisymmetric Schur functions to introduce skew quasisymmetric Schur functions. These functions include both classical skew Schur functions and quasisymmetric Schur functions as examples, and give rise to a new poset LC that is analogous to Young's lattice. We also introduce a new basis for the Hopf algebra of noncommutative symmetric functions NSym. This basis of NSym is dual to the basis of quasisymmetric Schur functions and its elements are the pre-image of the Schur functions under the forgetful map χ:NSym→Sym. We prove that the multiplicative structure constants of the noncommutative Schur functions, equivalently the coefficients of the skew quasisymmetric Schur functions when expanded in the quasisymmetric Schur basis, are nonnegative integers, satisfying a Littlewood–Richardson rule analogue that reduces to the classical Littlewood–Richardson rule under χ.As an application we show that the morphism of algebras from the algebra of Poirier–Reutenauer to Sym factors through NSym. We also extend the definition of Schur functions in noncommuting variables of Rosas–Sagan in the algebra NCSym to define quasisymmetric Schur functions in the algebra NCQSym. We prove these latter functions refine the former and their properties, and project onto quasisymmetric Schur functions under the forgetful map. Lastly, we show that by suitably labeling LC, skew quasisymmetric Schur functions arise in the theory of Pieri operators on posets. 相似文献
5.
Albert Visser 《Archive for Mathematical Logic》2008,47(4):299-326
In this paper we study the idea of theories with containers, like sets, pairs, sequences. We provide a modest framework to
study such theories. We prove two concrete results. First, we show that first-order theories of finite signature that have
functional non-surjective ordered pairing are definitionally equivalent to extensions in the same language of the basic theory
of non-surjective ordered pairing. Second, we show that a first-order theory of finite signature is sequential (is a theory
of sequences) iff it is definitionally equivalent to an extension in the same language of a system of weak set theory called
WS.
相似文献
6.
《Quaestiones Mathematicae》2013,36(2):185-214
Abstract We study Dieudonné-Köthe spaces of Lusin-measurable functions with values in a locally convex space. Let Λ be a solid locally convex lattice of scalar-valued measurable functions defined on a measure space Ω. If E is a locally convex space, define Λ {E} as the space of all Lusinmeasurable functions f: Ω → E such that q(f(·)) is a function in Λ for every continuous seminorm q on E. The space Λ {E} is topologized in a natural way and we study some aspects of the locally convex structure of A {E}; namely, bounded sets, completeness, duality and barrelledness. In particular, we focus on the important case when Λ and E are both either metrizable or (DF)-spaces and derive good permanence results for reflexivity when the density condition holds. 相似文献
7.
Janusz Matkowski 《Aequationes Mathematicae》1992,43(1):106-112
Summary Leta (0, 1/2] be fixed. A functionf satisfying the inequalityf(ax + (1 – a)y) + f((1 – a)x + ay) f(x) + f(y), called herea-Wright convexity, appears in connection with the converse of Minkowski's inequality. We prove that every lower semicontinuousa-Wright convex function is Jensen convex and we pose an open problem. Moreover, using the fact that 1/2-Wright convexity coincides with Jensen convexity, we prove a converse of Minkowski's inequality without any regularity conditions. 相似文献
8.
We consider nested sequences of linear or convex closed sets of the form arising in estimation and other inverse problems. We show that such sequences may fail to converge in any of the recently studied set convergences other than Mosco convergence. We also provide a positive result concerning the epislice convergence of related sequences of functions.Research partially supported by NSERC operating grants. 相似文献
9.
Regenerative simulation has become a familiar and established tool for simulation-based estimation. However, many applications (e.g., traffic in high-speed communications networks) call for autocorrelated stochastic models to which traditional regenerative theory is not directly applicable. Consequently, extensions of regenerative simulation to dependent time series is increasingly gaining in theoretical and practical interest, with Markov chains constituting an important case. Fortunately, a regenerative structure can be identified in Harris-recurrent Markov chains with minor modification, and this structure can be exploited for standard regenerative estimation. In this paper we focus on a versatile class of Harris-recurrent Markov chains, called TES (Transform-Expand-Sample). TES processes can generate a variety of sample paths with arbitrary marginal distributions, and autocorrelation functions with a variety of functional forms (monotone, oscillating and alternating). A practical advantage of TES processes is that they can simultaneously capture the first and second order statistics of empirical sample paths (raw field measurements). Specifically, the TES modeling methodology can simultaneously match the empirical marginal distribution (histogram), as well as approximate the empirical autocorrelation function. We explicitly identify regenerative structures in TES processes and proceed to address efficiency and accuracy issues of prospective simulations. To show the efficacy of our approach, we report on a TES/M/1 case study. In this study, we used the likelihood ratio method to calculate the mean waiting time performance as a function of the regenerative structure and the intrinsic TES parameter controlling burstiness (degree of autocorrelation) in the arrival process. The score function method was used to estimate the corresponding sensitivity (gradient) with respect to the service rate. Finally, we demonstrated the importance of the particular regenerative structure selected in regard to the estimation efficiency and accuracy induced by the regeneration cycle length. 相似文献
10.
We study timelike surfaces in Anti de Sitter 3-space as an application of singularity theory. We define two mappings associated
to a timelike surface which are called Anti de Sitter nullcone Gauss image and Anti de Sitter torus Gauss map. We also define a family of functions named Anti de Sitter null height function on the timelike surface. We use this family of functions as a basic tool to investigate the geometric meanings of singularities
of the Anti de Sitter nullcone Gauss image and the Anti de Sitter torus Gauss map. 相似文献
11.
We show that no finite set of first-order axioms can define the class of representable semilattice-ordered monoids.
Received July 2, 2004; accepted in final form February 22, 2007. 相似文献
12.
Alberto Seeger 《Aequationes Mathematicae》1991,42(1):47-71
Summary The Schur complement relative to the linear mappingA of a functionf is denotedAf and defined as the image off underA. In this paper we give some estimates for the second-order differential ofAf whenf is either a partially quadratic convex function or aC
2 convex function with a nonsingular second-order differential. We then consider an arbitrary convex functionf and study the second-order differentiability ofAf in a more general sense. 相似文献
13.
《Optimization》2012,61(6):673-692
In this article we examine various kinds of convergence of sequences of increasing positively homogeneous (IPH) functions and nonnegative decreasing functions defined on the interior of a pointed closed solid convex cone K. We show that five different types of convergency (including pointwise and epi-convergence) coincide for IPH functions. If the space under consideration is finite dimensional then the sixth type can be added: uniform convergence on bounded subsets of itn K. Using IPH functions, we study epi-convergence of sequences of lower semi-continuous (lsc) nonnegative decreasing functions. 相似文献
14.
We characterize functions satisfying a dissipative inequality associated with a control problem. Such a characterization
is provided in terms of an epicontingent solution, or a viscosity supersolution to a partial differential equation called
Isaacs' equation. Links between supersolutions and epicontingent solutions to Isaacs' equation are studied. Finally, we derive
(possibly discontinuous) disturbance attenuation feedback of the H
∞
problem from contingent formulation of Isaacs' equation.
Accepted 20 January 1998 相似文献
15.
This paper deals with the boundary behavior of functions in the de Branges–Rovnyak spaces. First, we give a criterion for
the existence of radial limits for the derivatives of functions in the de Branges–Rovnyak spaces. This criterion generalizes
a result of Ahern–Clark. Then we prove that the continuity of all functions in a de Branges–Rovnyak space on an open arc I of the boundary is enough to ensure the analyticity of these functions on I. We use this property in a question related to Bernstein’s inequality.
Received: May 10, 2007. Revised: August 8, 2007. Accepted: August 8, 2007. 相似文献
16.
L. M. García. Raffi E. A. Sánchez. Pérez J. V. Sánchez. Pérez 《Integral Equations and Operator Theory》2006,54(4):495-510
Let λ be a countably additive vector measure with values in a separable real Hilbert space H. We define and study a pseudo metric on a Banach lattice of integrable functions related to λ that we call a λ-weighted distance.
We compute the best approximation with respect to this distance to elements of the function space by the use of sequences
with special geometric properties. The requirements on the sequence of functions are given in terms of a commutation relation
between these functions that involves integration with respect to λ. We also compare the approximation that is obtained in
this way with the corresponding projection on a particular Hilbert space. 相似文献
17.
Jean-Daniel Boissonnat Frank Nielsen Richard Nock 《Discrete and Computational Geometry》2010,44(2):281-307
The Voronoi diagram of a finite set of objects is a fundamental geometric structure that subdivides the embedding space into
regions, each region consisting of the points that are closer to a given object than to the others. We may define various
variants of Voronoi diagrams depending on the class of objects, the distance function and the embedding space. In this paper,
we investigate a framework for defining and building Voronoi diagrams for a broad class of distance functions called Bregman
divergences. Bregman divergences include not only the traditional (squared) Euclidean distance but also various divergence
measures based on entropic functions. Accordingly, Bregman Voronoi diagrams allow one to define information-theoretic Voronoi
diagrams in statistical parametric spaces based on the relative entropy of distributions. We define several types of Bregman
diagrams, establish correspondences between those diagrams (using the Legendre transformation), and show how to compute them
efficiently. We also introduce extensions of these diagrams, e.g., k-order and k-bag Bregman Voronoi diagrams, and introduce Bregman triangulations of a set of points and their connection with Bregman Voronoi
diagrams. We show that these triangulations capture many of the properties of the celebrated Delaunay triangulation. 相似文献
18.
Yoshinori Yamasaki 《Journal of Number Theory》2009,129(10):2369-2386
We explicitly evaluate a special type of multiple Dirichlet L-values at positive integers in two different ways: One approach involves using of symmetric functions, while the other involves using of a generating function of the values. Equating these two expressions, we derive several summation formulae involving the Bernoulli and Euler numbers. Moreover, values at non-positive integers, called central limit values, are also studied. 相似文献
19.
This paper originates from the investigation of support measures of convex bodies (sets of positive reach), which form a
central subject in convex geometry and also represent an important tool in related fields. We show that these measures are
absolutely continuous with respect to Hausdorff measures of appropriate dimensions, and we determine the Radon-Nikodym derivatives
explicitly on sets of σ-finite Hausdorff measure. The results which we obtain in the setting of the theory of convex bodies
(sets of positive reach) are achieved as applications of various new results on Hessian measures of convex (semi-convex) functions.
Among these are a Crofton formula, results on the absolute continuity of Hessian measures, and a duality theorem which relates
the Hessian measures of a convex function to those of the conjugate function. In particular, it turns out that curvature and
surface area measures of a convex body K are the Hessian measures of special functions, namely the distance function and the support function of K.
Received: 15 July 1999 相似文献
20.
Andrzej Kryczka 《Integral Equations and Operator Theory》2008,61(4):559-572
We introduce the arithmetic separation of a sequence—a geometric characteristic for bounded sequences in a Banach space which
describes the Banach-Saks property. We define an operator seminorm vanishing for operators with the Banach-Saks property.
We prove quantitative stability of the seminorm for a class of operators acting between l
p
-sums of Banach spaces. We show logarithmically convex-type estimates of the seminorm for operators interpolated by the real
method of Lions and Peetre.
相似文献