共查询到20条相似文献,搜索用时 15 毫秒
1.
Farhad HSSEINOV 《数学学报(英文版)》2013,29(6):1185-1198
The paper studies a relaxation of the basic multidimensional variational problem, when the class of admissible functions is endowed with the Lipschitz convergence introduced by Morrey. It is shown that in this setup, the integral of a variational problem must satisfy a classical growth condition, unlike the case of uniform convergence. The relaxations constructed here imply the existence of a Lipschitz convergent minimizing sequence. Based on this observation, the paper also shows that the Lavrentiev phenomenon does not occur for a class of nonconvex problems. 相似文献
2.
3.
Alexander J. Zaslavski 《Calculus of Variations and Partial Differential Equations》2007,28(3):351-381
In this paper we study nonoccurrence of the Lavrentiev phenomenon for a large class of nonconvex nonautonomous constrained
variational problems. A state variable belongs to a convex subset of a Banach space with nonempty interior. Integrands belong
to a complete metric space of functions
which satisfy a growth condition common in the literature and are Lipschitzian on bounded sets. In our previous work Zaslavski
(Ann. Inst. H. Poincare, Anal. non lineare, 2006) we considered a class of nonconstrained variational problems with integrands
belonging to a subset
and showed that for any such integrand the infimum on the full admissible class is equal to the infimum on a subclass of
Lipschitzian functions with the same Lipschitzian constant. In the present paper we show that if an integrand f belongs to
, then this property also holds for any integrand which is contained in a certain neighborhood of f in
. Using this result we establish nonoccurrence of the Lavrentiev phenomenon for most elements of
in the sense of Baire category.
相似文献
4.
Li Cuiping 《数学学报(英文版)》1996,12(1):89-104
In this paper, we apply the asymptotic methods to the study of the evolution and vanishing of limit cycles of a one parameter family of differential equations. Some sufficient conditions are given to guarantee the existence of duck solutions and duck cycles. The abruptness of this evolution is illustrated by a computer-analysis study. 相似文献
5.
Relaxation problems for a functional of the type
are analyzed, where
is a bounded smooth open subset of
and g is a Carathéodory function. The admissible functions u are forced to satisfy a pointwise gradient constraint of the type
for a.e.
being, for every
, a bounded convex subset of
, in general varying with x not necessarily in a smooth way. The relaxed functionals
and
of G obtained letting u vary respectively in
, the set of the piecewise C
1-functions in
, and in
in the definition of G are considered. For both of them integral representation results are proved, with an explicit representation formula for the density of
. Examples are proposed showing that in general the two densities are different, and that the one of
is not obtained from g simply by convexification arguments. Eventually, the results are discussed in the framework of Lavrentieff phenomenon, showing by means of an example that deep differences occur between
and
. Results in more general settings are also obtained.Received: 18 December 2002, Accepted: 18 November 2003, Published online: 16 July 2004Mathematics Subject Classification (2000):
49J45, 49J10, 49J53This work is part of the European Research Training Network Homogenization and Multiple Scales (HMS 2000), under contract HPRN-2000-00109. It is also part of the 2003-G.N.A.M.P.A. Project Metodi Variazionali per Strutture Sottili, Frontiere Oscillanti ed Energie Vincolate. 相似文献
6.
Gerard G. L. Meyer 《Mathematical Programming》1988,40(1-3):205-212
Adaptive relaxation algorithms use anti-jamming schemes that require either a large amount of computation or a large amount of memory. In this paper we present a non-adaptive approach that possesses substantial cómputational and memory advantages over the adaptive schemes. The approach uses averaging and may be applied whenever the relaxation algorithm's point-to-set maps satisfy appropriate assumptions.This work was supported by the Air Force Office of Scientific Research under Contract AFOSR-85-0097. 相似文献
7.
We study a time relaxation regularization of flow problems proposed and tested extensively by Stolz and Adams. The aim of the relaxation term is to drive the unresolved fluctuations in a computational simulation to zero exponentially fast by an appropriate and often problem dependent choice of its coefficient; this relaxation term is thus intermediate between a tunable numerical stabilization and a continuum modeling term. Our aim herein is to understand how this term, by itself, acts to truncate solution scales and to use this understanding to give insight into parameter selection. 相似文献
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9.
《Advances in Applied Mathematics》1987,8(2):194-207
The multiple digest mapping problem arising in molecular biology can be stated roughly as follows. A linear or circular segment of DNA is cut at all occurrences of a specific short pattern by restriction enzymes. By using restriction enzymes singly and in combination it is required to construct a map showing the location of cleavage sites. In this paper we first consider the efficacy of a simulated annealing algorithm towards the solution to the multiple digest problem. Second, the double digest problem, the simplest version of the multiple digest problem with only two restriction enzymes used, is shown to admit an exponentially increasing number of solutions as a function of the length of the segment under a particular probability model. Next, the double digest problem is shown to lie in the class of NP complete problems which are conjectured to have no polynomial time solution. Last, the construction of circular maps is considered and the problem of measurement error is discussed. 相似文献
10.
We define a kind of spectral series to filter off completely the Gibbs phenomenon without overshooting and distortional approximation near a point of discontinuity. The construction of this series is based on the method of adding the Fourier coefficients of a Heaviside function to the given Fourier partial sums. More precisely, we prove the uniform convergence of the proposed series on the class of piecewise smooth functions. Also, we attach two numerical examples which illustrate the uniform convergence of the suggested series in comparison with the Fourier partial sums. 相似文献
11.
Frederick F. Ling Edward Saibel 《Zeitschrift für Angewandte Mathematik und Physik (ZAMP)》1958,9(4):315-322
Zusammenfassung Das Problem des Bremsschwindens wird für einen linear mit der Temperatur abnehmenden Reibungskoeffizienten untersucht. Die verwendete Methode lässt sich auch auf kompliziertere Zusammenhänge zwischen der Temperatur und dem Reibungskoeffizienten anwenden.
This work was sponsored by the Office of Ordnance Research, US. Army. 相似文献
This work was sponsored by the Office of Ordnance Research, US. Army. 相似文献
12.
Bernhard Beckermann Ana C. Matos Franck Wielonsky 《Journal of Computational and Applied Mathematics》2008,219(2):329
Recently, Brezinski has proposed to use Wynn's ε-algorithm in order to reduce the Gibbs phenomenon for partial Fourier sums of smooth functions with jumps, by displaying very convincing numerical experiments. In the present paper we derive analytic estimates for the error corresponding to a particular class of hypergeometric functions, and obtain the rate of column convergence for such functions, possibly perturbed by another sufficiently differentiable function. We also analyze the connection to Padé–Fourier and Padé–Chebyshev approximants, including those recently studied by Kaber and Maday. 相似文献
13.
Yu. A. Anikin 《Computational Mathematics and Mathematical Physics》2011,51(11):1923-1932
The two-dimensional rarefied gas flow around a rotating Crookes radiometer and the arising radiometric forces are studied by numerically solving the Boltzmann kinetic equation. The computations are performed in a noninertial frame of reference rotating together with the radiometer. The collision integral is directly evaluated using a projection method, while second- and third-order accurate TVD schemes are used to solve the advection equation and the equation for inertia-induced transport in the velocity space, respectively. The radiometric forces are found as functions of the rotation frequency. 相似文献
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15.
Alfio Borzì Georg Propst 《Zeitschrift für Angewandte Mathematik und Physik (ZAMP)》2003,4(2):1050-1072
The Liebau phenomenon is the occurrence of valveless
pumping through the application of a periodic force at a place
which lies asymmetric with respect to system configuration. This
paper is concerned with two different physical configurations and
respective models. Comparison and derivation among the models is
discussed. Accurate numerical schemes which solve these models are
presented. By means of numerical simulations it is investigated
under which conditions valveless pumping takes place. 相似文献
16.
The Liebau phenomenon is the occurrence of valveless
pumping through the application of a periodic force at a place
which lies asymmetric with respect to system configuration. This
paper is concerned with two different physical configurations and
respective models. Comparison and derivation among the models is
discussed. Accurate numerical schemes which solve these models are
presented. By means of numerical simulations it is investigated
under which conditions valveless pumping takes place. 相似文献
17.
《European Journal of Operational Research》1996,89(3):496-515
The bowl phenomenon provides a way of increasing the throughput of some production line systems with variable processing times by purposely unbalancing the line in a certain manner. However, achieving this increase in throughput depends on correctly identifying the values of the system parameters to estimate the optimal amount of unbalance and then actually being able to assign work to stations according to the optimal bowl allocation. In this paper we study the robustness of the bowl phenomenon by examining the effect of inaccurately estimating the optimal amount of unbalance and the effect of deviating from the optimal bowl allocation. Our results show that the bowl phenomenon is relatively robust in the sense that fairly large errors (even 50%) in the amount of unbalance still provide most of the potential improvement in throughput over a perfectly balanced line. Moreover, the throughput still exceeds that of a perfectly balanced line in most cases even when the work allocation to each station deviates from the optimal bowl allocation by as much as 10%. We also address the question of whether the optimal bowl allocation or the balanced line provides a more robust ‘target’ when assigning work to stations. When the deviations from these two targets are of the same magnitude, we found that the optimal bowl allocation target yields the larger throughput in most cases, where the average difference between their throughputs is roughly the same as the difference between the optimal throughput and the throughput of a balanced line. Furthermore, for the same magnitude of deviation, the throughput depends more heavily on the direction of the deviation from the balanced line than that from the optimal bowl allocation, so that the risk of a substantially reduced throughput is much larger when using the balanced line as the target. Therefore, the optimal bowl allocation provides a much more robust target than the balanced line. 相似文献
18.
Robert Plato 《BIT Numerical Mathematics》1997,37(2):404-423
In this paper, for the numerical solution of linear accretive Volterra integral equations of the first kind in Hilbert spaces
we consider the Galerkin scheme for Lavrentiev’sm-times iterated method, i.e., for each parameter choice for Lavrentiev’sm-times iterated method the arisingm stabilized equations are discretized by the Galerkin scheme. An associated discrepancy principle as parameter choice strategy
for this finite-dimensional version of Lavrentiev’sm-times iterated method is proposed, and corresponding convergence results are provided. 相似文献
19.
Takeshi Morita 《The Ramanujan Journal》2014,34(3):329-346
We show connection formulae between the origin and infinity for local solutions of the q-difference equation satisfied by the Ramanujan entire function. These solutions are given by the Ramanujan entire function, the q-Airy function, and the divergent basic hypergeometric series 2 φ 0(0,0;?;q,x). We use two different q-Borel–Laplace resummation methods to obtain our connection formulae. 相似文献
20.
We consider Lavrentiev regularization for a class of semilinear parabolic optimal control problems with control constraints and pointwise state constraints and review convergence results for local solutions under Slater type assumptions as well as quadratic growth conditions. Moreover, we state a local uniqueness result for local optima under the assumptions of strict separability of the active sets as well as a second order sufficient condition for the regularized solution. (© 2008 WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim) 相似文献