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1.
Beloslav Riečan 《Mathematica Slovaca》2010,60(5):655-664
The classical Poincaré strong recurrence theorem states that for any probability space (Ω, ℒ, P), any P-measure preserving transformation T, and any A ∈ ℒ, almost all points of A return to A infinitely many times. In the present paper the Poincaré theorem is proved when the σ-algebra ℒ is substituted by an MV-algebra of a special type. Another approach is used in [RIEČAN, B.: Poincaré recurrence theorem in MV-algebras. In: Proc. IFSA-EUSFLAT 2009 (To appear)], where the weak variant of the theorem is proved, of course, for arbitrary MV-algebras.
Such generalizations were already done in the literature, e.g. for quantum logic, see [DVUREČENSKIJ, A.: On some properties of transformations of a logic, Math. Slovaca 26 (1976), 131–137. 相似文献
2.
Wataru Takahashi 《Journal of Fixed Point Theory and Applications》2007,1(1):135-147
In this paper, we first prove a strong convergence theorem for resolvents of accretive operators in a Banach space by the
viscosity approximation method, which is a generalization of the results of Reich [J. Math. Anal. Appl. 75 (1980), 287–292],
and Takahashi and Ueda [J. Math. Anal. Appl. 104 (1984), 546–553]. Further using this result, we consider the proximal point
algorithm in a Banach space by the viscosity approximation method, and obtain a strong convergence theorem which is a generalization
of the result of Kamimura and Takahashi [Set-Valued Anal. 8 (2000), 361–374].
Dedicated to the memory of Jean Leray 相似文献
3.
Maria Karmanova 《Geometric And Functional Analysis》2011,21(6):1358-1374
We develop a new approach to studying the geometry of Carnot–Carathéodory spaces under minimal assumptions on the smoothness
of basis vector fields. We obtain quantitative comparison estimates for the local geometries of two different local Carnot
groups, as well as of a local Carnot group and the original space. As corollaries, we deduce some results that are well-known
and basic for the “smooth” case: the generalized triangle inequality for d
∞, the local approximation theorem for the quasimetric d
∞, the Rashevskiǐ–Chow theorem, the ball-box theorem, and so on. 相似文献
4.
K. Mahler introduced the concept of perfect systems in the general theory he developed for the simultaneous Hermite–Padé approximation
of analytic functions. We prove that Nikishin systems are perfect, providing by far the largest class of systems of functions
for which this important property holds. As consequences, in the context of Nikishin systems, we obtain: an extension of Markov’s
theorem to simultaneous Hermite–Padé approximation, a general result on the convergence of simultaneous quadrature rules of
Gauss–Jacobi type, the logarithmic asymptotics of general sequences of multiple orthogonal polynomials, and an extension of
the Denisov–Rakhmanov theorem for the ratio asymptotics of mixed type multiple orthogonal polynomials. 相似文献
5.
Ibrahim A. Ahmad 《Annals of the Institute of Statistical Mathematics》1981,33(1):375-383
Summary The conditioned central limit theorem for the vector of maximum partial sums based on independent identically distributed
random vectors is investigated and the rate of convergence is discussed. The conditioning is that of Rényi (1958,Acta Math. Acad. Sci. Hungar.,9, 215–228). Analogous results for the vector of partial sums are obtained.
University of Petroleum and Minerals 相似文献
6.
William J. McGraw 《Mathematische Annalen》2003,326(1):105-122
In a recent paper [Duke Math. J., 97, 219–233], Borcherds asks whether or not the spaces of vector valued modular forms associated to the Weil representation
have bases of modular forms whose Fourier expansions have only integer coefficients. We give an affirmative answer to Borcherds'
question. This strengthens and simplifies Borcherds' main theorem which is a generalization of a theorem of Gross, Kohnen,
and Zagier [Math. Ann., 278, 497–562].
Received: 27 September 2001 / Revised version: 22 July 2002 /
Published online: 28 March 2003
Mathematics Subject Classification (1991): 11F30; 11F27 相似文献
7.
As a development of the theory of linear error bounds for lower semicontinuous functions defined on complete metric spaces,
introduced in Azé et al. (Nonlinear Anal 49, 643–670, 2002) and refined in Azé and Corvellec (ESAIM Control Optim Calc Var 10, 409–425, 2004), we propose a similar approach to nonlinear error bounds, based on the notion of strong slope, the variational
principle, and the change-of-metric principle, the latter allowing to obtain sharp estimates for such error bounds through
a reduction to the linear case. 相似文献
8.
Florian Méhats 《Monatshefte für Mathematik》2006,147(1):43-73
This paper is devoted to the analysis of a quantum subband model, which is presented as an alternative to the standard 3D
Schr?dinger-Poisson system for modeling the transport of electrons strongly confined along one direction. This subband model
is composed of quasistatic 1D Schr?dinger equations in the direction of the confinement, coupled to 2D time-dependent Schr?dinger
equations describing the transport in the non-confined directions. Selfconsistent electrostatic interactions are also taken
into account via the Poisson equation. This system is studied in the framework of the strong partial confinement asymptotics
introduced in the article “Adiabatic approximation of the Schr?dinger-Poisson system with a partial confinement”, by Ben Abdallah,
Méhats and Pinaud (SIAM J. Math. Anal. 36 (2005), 986–1013). 相似文献
9.
Florian Méhats 《Monatshefte für Mathematik》2006,292(3):43-73
This paper is devoted to the analysis of a quantum subband model, which is presented as an alternative to the standard 3D
Schr?dinger-Poisson system for modeling the transport of electrons strongly confined along one direction. This subband model
is composed of quasistatic 1D Schr?dinger equations in the direction of the confinement, coupled to 2D time-dependent Schr?dinger
equations describing the transport in the non-confined directions. Selfconsistent electrostatic interactions are also taken
into account via the Poisson equation. This system is studied in the framework of the strong partial confinement asymptotics
introduced in the article “Adiabatic approximation of the Schr?dinger-Poisson system with a partial confinement”, by Ben Abdallah,
Méhats and Pinaud (SIAM J. Math. Anal. 36 (2005), 986–1013). 相似文献
10.
Bogdan Szal 《Proceedings Mathematical Sciences》2010,120(5):563-582
We consider the embedding relation between the class W
q
H
β
ω
, including only odd functions and a set of functions defined via the strong means of Fourier series of odd continuous functions.
We establish an improvement of a recent theorem of Le and Zhou [Math. Inequal. Appl.
11(4) (2008) 749–756] which is a generalization of Tikhonov’s results [Anal. Math.
31 (2005) 183–194]. We also extend the Leindler theorem [Anal. Math.
31 (2005) 175–182] concerning sequences of Fourier coefficients. 相似文献
11.
We generalise the famous Helly–Lovász theorem leading to a generalisation of the Bárány–Carathéodory theorem for oriented
matroids in dimension ≤3. We also provide a non-metric proof of the latter colourful theorem for arbitrary dimensions and
explore some generalisations in dimension 2. 相似文献
12.
K. Kubilius 《Acta Appl Math》2007,97(1-3):1-13
We obtain conditions under which a Stratonovich integral equation driven by a continuous p-semimartingale has a weak solution and a unique strong solution-measure. Generalization of the Wong–Zakai theorem and the
convergence rate of the corresponding approximation are given. 相似文献
13.
J. Sunklodas 《Lithuanian Mathematical Journal》1995,35(2):185-196
The estimate of the remainder term is obtained in the global central limit theorem for π-mixing r.v.s. As a consequence of
Theorem 1 the convergence rate of absolute moments for sums of π-mixing r.v.s. to corresponding absolute moments of the normal
r.v. is found.
Published in Lietuvos Matematikos Rinkinys, Vol. 35, No. 2, pp. 233–247, April–June, 1995. 相似文献
14.
A. V. Greshnov 《Siberian Advances in Mathematics》2010,20(3):164-179
We consider some metric spaces with quasimetric (quasispaces) comprising uniformly regular (equiregular) Carnot — Carathéodory
quasispaces whose quasimetric is induced by C
ϒ−1-smooth vector fields of formal degree not higher than ϒ. For these spaces, some analogues of the Campbell — Hausdorff formula
are derived, which allows us to prove a theorem on a nilpotent tangent cone, a theorem on isomorphism of various nilpotent
tangent cones defined at a common point, and a local approximation theorem. 相似文献
15.
U. Fidalgo Prieto J. R. Illán González G. López Lagomasino 《Numerische Mathematik》2007,106(1):99-128
We discuss the convergence and numerical evaluation of simultaneous quadrature formulas which are exact for rational functions.
The problem consists in integrating a single function with respect to different measures using a common set of quadrature
nodes. Given a multi-index n, the nodes of the integration rule are the zeros of the multi-orthogonal Hermite–Padé polynomial with respect to (S, α, n), where S is a collection of measures, and α is a polynomial which modifies the measures in S. The theory is based on the connection between Gauss-type simultaneous quadrature formulas of rational type and multipoint
Hermite–Padé approximation. The numerical treatment relies on the technique of modifying the integrand by means of a change
of variable when it has real poles close to the integration interval. The output of some tests show the power of this approach
in comparison with other ones in use. 相似文献
16.
Alexandre Masquelein Anne Quéguiner-Mathieu Jean-Pierre Tignol 《Archiv der Mathematik》2009,93(2):129-138
Izhboldin and Karpenko proved in Math. Z. (234 (2000), 647–695, Theorem 16.10) that any quadratic form of dimension 8 with trivial discriminant and Clifford algebra of
index 4 is isometric to the transfer, with respect to some quadratic étale extension, of a quadratic form similar to a two-fold
Pfister form. We give a new proof of this result, based on a theorem of decomposability for degree 8 and index 4 algebras
with orthogonal involution. 相似文献
17.
Salomon Sambou 《Annali di Matematica Pura ed Applicata》2006,185(3):381-394
We give an Andreotti–Vesentini separation theorem on q-concave at infinity CR submanifolds.
Mathematics Subject Classification (2000) 32V20, 32F10
Mots-clés: q-concave· variété CR·théorème de séparation·q-concave à l’infini 相似文献
18.
Hitomi Terajima 《Annali di Matematica Pura ed Applicata》2007,186(1):99-144
In [as reported by Saito et al. (J. Algebraic Geom. 11:311–362, 2002)], generalized Okamoto–Painlevé pairs are introduced
as a generalization of Okamoto’s space of initial conditions of Painlevé equations (cf. [Okamoto (Jpn. J. Math. 5:1–79, 1979)])
and we established a way to derive differential equations from generalized rational Okamoto–Painlevé pairs through deformation
theory of nonsingular pairs. In this article, we apply the method to concrete families of generalized rational Okamoto–Painlevé
pairs with given affine coordinate systems and for all eight types of such Okamoto–Painlvé pairs we write down Painlevé equations
in the coordinate systems explicitly. Moreover, except for a few cases, Hamitonians associated to these Painlevé equations
are also given in all coordinate charts.
Mathematics Subject Classification (2000) 34M55, 32G05, 14J26 相似文献
19.
Michael Greenblatt 《Mathematische Annalen》2010,346(4):857-895
Extending some resolution of singularities methods (Greenblatt in J Funct Anal 255(8):1957–1994, 2008) of the author, a generalization
of a well-known theorem of Varchenko (Funct Anal Appl 18(3):175–196, 1976) relating decay of oscillatory integrals to the
Newton polyhedron is proven. They are derived from analogous results for sublevel integrals, proven here. Varchenko’s theorem
requires a certain nondegeneracy condition on the faces of the Newton polyhedron on the phase. In this paper, it is shown
that the estimates of Varchenko’s theorem also hold for a significant class of phase functions for which this nondegeneracy
condition does not hold. Thus in problems where one wants to switch coordinates to a coordinate system where Varchenko’s estimates
are valid, one has greater flexibility. Some additional estimates are also proven for more degenerate situations, including
some too degenerate for the Newton polyhedron to give the optimal decay in the sense of Varchenko. 相似文献
20.
Conditioned, in the sense of Rényi (Acta Math. Acad. Sci. Hungar. 9, 215–228 1958), limit theorem in the Lp-norm of the maximum of absolute sums of independent identically distributed random variables is established and its exact
rate of convergence is given. The results are equivalent to establishing analogous results for the supremum of random functions
of partial sums defined on C[0,1], i.e., the invariance principle. New methodologies are used to prove the results that are profoundly different from
those used in Rényi (Acta Math. Acad. Sci. Hungar. 9, 215–228, 1958) and subsequent authors in proving the conditioned central
limit theorem for partial sums. 相似文献