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1.
The Belavkin equation, describing the continuous measurement of the position of a quantum particle, is studied. A rigorous
representation of its solution by means of an infinite dimensional oscillatory integral (Feynman path integral) defined on
the complex Cameron-Martin space is given.
Received: 7 January 2002 / Revised version: 20 June 2002 / Published online: 19 December 2002
Mathematics Subject Classification (2000): 81, 81S40, 60H15
Key words or phrases: Belavkin equation – Continuous measurement – Quantum theory – Oscillatory integrals – Feynman path integrals 相似文献
2.
On polynomial collocation for second kind integral equations with fixed singularities of Mellin type
Summary. We consider a polynomial collocation for the numerical solution of a second kind integral equation with an integral kernel
of Mellin convolution type. Using a stability result by Junghanns and one of the authors, we prove that the error of the approximate
solution is less than a logarithmic factor times the best approximation and, using the asymptotics of the solution, we derive
the rates of convergence. Finally, we describe an algorithm to compute the stiffness matrix based on simple Gau? quadratures
and an alternative algorithm based on a recursion in the spirit of Monegato and Palamara Orsi. All together an almost best
approximation to the solution of the integral equation can be computed with 𝒪(n
2[log n]2) resp. 𝒪(n
2) operations, where n is the dimension of the polynomial trial space.
Received February 18, 2002 / Revised version received May 15, 2002 / Published online October 29, 2002
RID="⋆"
ID="⋆" Correspondence to: A. Rathsfeld
Mathematics Subject Classification (1991): 65R20 相似文献
3.
This paper presents a renormalization and homogenization theory for fractional-in-space or in-time diffusion equations with
singular random initial conditions. The spectral representations for the solutions of these equations are provided. Gaussian
and non-Gaussian limiting distributions of the renormalized solutions of these equations are then described in terms of multiple
stochastic integral representations.
Received: 30 May 2000 / Revised version: 9 November 2001 / Published online: 10 September 2002
Mathematics Subject Classification (2000): Primary 62M40, 62M15; Secondary 60H05, 60G60
Key words or phrases: Fractional diffusion equation – Scaling laws – Renormalised solution – Long-range dependence – Non-Gaussian scenario – Mittag-Leffler
function – Stable distributions – Bessel potential – Riesz potential 相似文献
4.
Tadahisa Funaki 《Probability Theory and Related Fields》2003,126(2):155-183
We consider random evolution of an interface on a hard wall under periodic boundary conditions. The dynamics are governed
by a system of stochastic differential equations of Skorohod type, which is Langevin equation associated with massless Hamiltonian
added a strong repelling force for the interface to stay over the wall. We study its macroscopic behavior under a suitable
large scale space-time limit and derive a nonlinear partial differential equation, which describes the mean curvature motion
except for some anisotropy effects, with reflection at the wall. Such equation is characterized by an evolutionary variational
inequality.
Received: 10 January 2002 / Revised version: 18 August 2002 /
Published online: 15 April 2003
Mathematics Subject Classification (2000): 60K35, 82C24, 35K55, 35K85
Key words or phrases: Hydrodynamic limit – Effective interfaces – Hard wall – Skorohod's stochastic differential equation – Evolutionary variational
inequality 相似文献
5.
Andrzej Rozkosz 《Probability Theory and Related Fields》2003,125(3):393-407
We extend the definition of solutions of backward stochastic differential equations to the case where the driving process
is a diffusion corresponding to symmetric uniformly elliptic divergence form operator. We show existence and uniqueness of
solutions of such equations under natural assumptions on the data and show its connections with solutions of semilinear parabolic
partial differential equations in Sobolev spaces.
Received: 22 January 2002 / Revised version: 10 September 2002 / Published online: 19 December 2002
Research supported by KBN Grant 0253 P03 2000 19.
Mathematics Subject Classification (2002): Primary 60H30; Secondary 35K55
Key words or phrases: Backward stochastic differential equation – Semilinear partial differential equation – Divergence form operator – Weak solution 相似文献
6.
Byeong-Kweon Oh 《Mathematische Zeitschrift》2003,244(2):399-413
In this article, we prove that there are only finitely many positive definite integral quadratic forms of rank n+3(n≥2) that represent all positive definite integral quadratic forms of rank n but finitely many exceptions. Furthermore we determine all diagonal quadratic forms having such property and its exceptions
remaining four as candidates.
Received: 29 November 2000 ; in final form: 8 August 2002 /
Published online: 1 April 2003
Mathematics Subject Classification (2000): 11E12, 11E20. 相似文献
7.
Summary. We construct and analyze combinations of rational implicit and explicit multistep methods for nonlinear evolution equations
and extend thus recent results concerning the discretization of nonlinear parabolic equations. The resulting schemes are linearly
implicit and include as particular cases implicit–explicit multistep schemes as well as the combination of implicit Runge–Kutta
schemes and extrapolation. We establish optimal order error estimates. The abstract results are applied to a third–order evolution
equation arising in the modelling of flow in a fluidized bed. We discretize this equation in space by a Petrov–Galerkin method.
The resulting fully discrete schemes require solving some linear systems to advance in time with coefficient matrices the
same for all time levels.
Received October 22, 2001 / Revised version received April 22, 2002 /
Published online December 13, 2002
Mathematics Subject Classification (1991): Primary 65M60, 65M12; Secondary 65L06
Correspondence to: G. Akrivis 相似文献
8.
Let be a parametric variational double integral and γ ⊂ ℝ
n
be a system of several distinct Jordan curves. We prove the existence of multiply connected, conformally parametrized minimizers
of spanned in γ by solving the Douglas problem for parametric functionals on multiply connected schlicht domains. As a by-product
we obtain a simple isoperimetric inequality for multiply connected -minimizers, and we discuss regularity results up to the boundary which follow from corresponding results for the Plateau
problem.
Received: 19 April 2002
Mathematics Subject Classification (2000): 49J45, 49Q10, 53A07, 53A10 相似文献
9.
Andreas Fischer 《Mathematical Programming》2002,94(1):91-124
An iterative framework for solving generalized equations with nonisolated solutions is presented. For generalized equations
with the structure , where is a multifunction and F is single-valued, the framework covers methods that, at each step, solve subproblems of the type . The multifunction approximates F around s. Besides a condition on the quality of this approximation, two other basic assumptions are employed to show Q-superlinear
or Q-quadratic convergence of the iterates to a solution. A key assumption is the upper Lipschitz-continuity of the solution
set map of the perturbed generalized equation . Moreover, the solvability of the subproblems is required. Conditions that ensure these assumptions are discussed in general
and by means of several applications. They include monotone mixed complementarity problems, Karush-Kuhn-Tucker systems arising
from nonlinear programs, and nonlinear equations. Particular results deal with error bounds and upper Lipschitz-continuity
properties for these problems.
Received: November 2001 / Accepted: November 2002 Published online: December 9, 2002
Key Words. generalized equation – nonisolated solutions – Newton's method – superlinear convergence – upper Lipschitz-continuity – mixed
complementarity problem – error bounds
Mathematics Subject Classification (1991): 90C30, 65K05, 90C31, 90C33 相似文献
10.
Starting from the definition of `amorphous set' in set theory without the axiom of choice, we propose a notion of rank (which
will only make sense for, at most, the class of Dedekind finite sets), which is intended to be an analogue in this situation
of Morley rank in model theory.
Received: 22 September 2000 / Revised version: 14 May 2002 Published online: 19 December 2002
The research of the first author was supported by the SERC.
Mathematics Subject Classification (2000): 03E25
Key words or phrases: Rank – Degree – Amorphous 相似文献
11.
Kenji Nishihara 《Mathematische Zeitschrift》2003,244(3):631-649
It has been asserted that the damped wave equation has the diffusive structure as t→∞. In this paper we consider the Cauchy problem in 3-dimensional space for the linear damped wave equation and the corresponding
parabolic equation, and obtain the L
p
−L
q
estimates of the difference of each solution, which represent the assertion precisely. Explicit formulas of the solutions
are analyzed for the proof. The second aim is to apply the L
p
−L
q
estimates to the semilinear damped wave equation with power nonlinearity. If the power is larger than the Fujita exponent,
then the time global existence of small weak solution is proved and its optimal decay order is obtained.
Received: 8 June 2001; in final form: 12 August 2002 /
Published online: 1 April 2003
Mathematical Subject Classification (2000): 35L15. 相似文献
12.
Loïc Grenié 《manuscripta mathematica》2003,110(3):283-311
We compute, up to an element of a fixed number field, the critical values of the L-function of a pair of automorphic, cuspidal,
cohomological representations of any GL(r). The result is expressed as a product of cohomological periods divided by an archimedean integral. The main tool used is
the rationality of the cohomology of the three representations involved in the Rankin–Selberg integral. As an intermediate
step, we also obtained the rationality of the Eisenstein cohomology.
Received: 14 February 2002 / Revised version: 17 September 2002 Published online: 14 February 2003 相似文献
13.
Wensheng Wang 《Probability Theory and Related Fields》2003,126(2):203-220
Kesten and Spitzer have shown that certain random walks in random sceneries converge to stable processes in random sceneries.
In this paper, we consider certain random walks in sceneries defined using stationary Gaussian sequence, and show their convergence
towards a certain self-similar process that we call fractional Brownian motion in Brownian scenery.
Received: 17 April 2002 / Revised version: 11 October 2002 /
Published online: 15 April 2003
Research supported by NSFC (10131040).
Mathematics Subject Classification (2002): 60J55, 60J15, 60J65
Key words or phrases: Weak convergence – Random walk in random scenery – Local time – Fractional Brownian motion in Brownian scenery 相似文献
14.
Sándor Jenei 《Archive for Mathematical Logic》2003,42(5):489-514
We generalize the notions of Girard algebras and MV-algebras by introducing rotation-invariant semigroups. Based on a geometrical
characterization, we present five construction methods which result in rotation-invariant semigroups and in particular, Girard
algebras and MV-algebras. We characterize divisibility of MV-algebras, and point out that integrality of Girard algebras follows
from their other axioms.
Received: 7 January 2002 / Revised version: 4 April 2002 /
Published online: 19 December 2002
RID="*"
ID="*" Supported by the National Scientific Research Fund Hungary (OTKA F/032782).
Mathematics Subject Classification (2000): 20M14, 06F05
Key words or phrases: Residuated lattice – Conjunction for non-classical logics 相似文献
15.
Hans Schoutens 《manuscripta mathematica》2003,111(3):379-412
In this paper, non-standard tight closure is proposed as an alternative for classical tight closure on finitely generated
algebras over ℂ. It has the advantage that it admits a functional definition, similar to the characteristic p definition of tight closure, where instead of the characteristic p Frobenius, its ultraproduct, the non-standard Frobenius, is used. This new closure operation cl(⋅) has the same properties as classical tight closure, to wit, (1) if A is regular, then 𝔞=cl(𝔞); (2) if A⊂B is an integral extension of domains, then cl(𝔞 B)∩A⊂cl(𝔞); (3) if A is local and is a system of parameters, then (Colon-Capturing); (4) if 𝔞 is generated by m elements, then cl𝔞 contains the integral closure of 𝔞
m
and is contained in the integral closure of 𝔞 (Brian?on-Skoda).
Received: 25 June 2002 / Revised version: 14 February 2003
Published online: 19 May 2003
Partially supported by a grant from the National Science Foundation. 相似文献
16.
Mirjana Borisavljević 《Archive for Mathematical Logic》2003,42(4):371-387
This paper presents a cut-elimination procedure for classical and intuitionistic logic, in which cut is eliminated directly,
without introducing the mix rule. The well-known problem of cut eliminations, when in the derivation the contractions of the
cut-formulae are above the premisses of the cut, will be solved by new transformations of the derivation.
Received: 1 June 2001 /
Published online: 5 November 2002
Mathematics Subject Classification (2000): 03F05
Key words or phrases: Systems of sequents – Cut-elimination theorem 相似文献
17.
Let X be the solution of the stochastic differential equation where B
H
is a fractional Brownian motion with Hurst parameter H. In this paper we compute the Onsager-Machlup functional of X for the supremum norm and H?lder norms of order β with in the case and for H?lder norms of order β with when .
Received: 16 July 2001 / Revised version: 12 March 2002 / Published online: 10 September 2002 相似文献
18.
Ikuo Yoneda 《Archive for Mathematical Logic》2003,42(5):423-433
We show that any relational generic structure whose theory has finite closure and amalgamation over closed sets is stable
CM-trivial with weak elimination of imaginaries.
Received: 21 December 2001 /
Published online: 5 November 2002
Mathematics Subject Classification (2000): 03C45
Key words or phrases: CM-triviality – Generic structures – Stability 相似文献
19.
The purpose of this work is the study of the partition function of a -dimensional lattice directed polymer in a Gaussian random environment being the inverse of temperature). In the low-dimensional cases , we prove that for all , the renormalized partition function converges to 0 and the correlation of two independent configurations does not converge to 0. In the high dimensional case (), a lower tail of has been obtained for small . Furthermore, we express some thermodynamic quantities in terms of the path measure alone.
Received: 8 June 2001 / Revised version: 8 February 2002 / Published online: 22 August 2002
Mathematics Subject Classification (2000): 60K37, 82D30
Key words or phrases: Directed polymer in random environment – Gaussian environment – partition function 相似文献
20.
Theodoros Vlachos 《manuscripta mathematica》2003,110(1):77-91
We show that minimal surfaces in space forms are determined, up to ambient isometries, by the induced metric and certain
invariants which are defined in terms of the higher fundamental forms and the complex structure.
Received: 6 May 2002 / Revised version: 5 July 2002
Current address: Institut für Mathematik, Universit?t Augsburg, Universit?tsstrasse 12, D-86135 Augsburg, Germany. e-mail: Theodoros.Vlachos@Math.Uni-Augsburg.De
The author was supported by the Alexander von Humboldt Foundation
Mathematics Subject Classification (2000): 53A10, 53C42
Acknowledgements. This work was written during the author's stay at the University of Augsburg as a research fellow of the Alexander von Humboldt
Foundation. I wish to express my gratitude to the Alexander von Humboldt Foundation for its generous support. Moreover, I
wish to thank Professor J.H. Eschenburg for many fruitful and stimulating conversations. 相似文献