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1.
The auxiliary problem principle has been proposed by the first author as a framework to describe and analyze iterative algorithms such as gradient as well as decomposition/coordination algorithms for optimization problems (Refs. 1–3) and variational inequalities (Ref. 4). The key assumption to prove the global and strong convergence of such algorithms, as well as of most of the other algorithms proposed in the literature, is the strong monotony of the operator involved in the variational inequalities. In this paper, we consider variational inequalities defined over a product of spaces and we introduce a new property of strong nested monotony, which is weaker than the ordinary overall strong monotony generally assumed. In some sense, this new concept seems to be a minimal requirement to insure convergence of the algorithms alluded to above. A convergence theorem based on this weaker assumption is given. Application of this result to the computation of Nash equilibria can be found in another paper (Ref. 5).This research has been supported by the Centre National de la Recherche Scientifique (ATP Complex Technological Systems) and by the Centre National d'Etudes des Télécommunications (Contract 83.5B.034.PAA).  相似文献   

2.
Centre de Physique Théorique CNRS, France. Translated from Funktsional'nyi Analiz i Ego Prilozheniya, Vol. 28, No. 3, pp. 47–60, July–September, 1994.  相似文献   

3.
A partially integrable extension of the Eckhaus equation is first converted to one real fourth-order equation. The only integrable case is isolated by simply solving a diophantine equation, and its linearizing transformation, not obvious at first glance, is shown to be the singular part transformation of Painlevé analysis. In the partially integrable case, three exact solutions are found by the truncation procedure. The third oneis a six-parameter solution, whose dependence on x is elliptic and dependence ont involves the equation of Chazy.Service de physique de l'état condensé, Centre d'études de Saclay, F-91190 Gif-sur-Yvette Cedex, France. Dienst Theoretische Natuurkunde, Vrije Universiteit Brussel, B-1050 Brussels, Belgium. Translated from Teoreticheskaya i Matematicheskaya Fizika, Vol. 99, No. 2, pp. 226–233, May, 1994.  相似文献   

4.
We define a class of summation operators with applications to the self-improving nature of Poincaré–Sobolev estimates, in fairly general quasimetric spaces of homogeneous type. We show that these sum operators play the familiar role of integral operators of potential type (e.g., Riesz fractional integrals) in deriving Poincaré–Sobolev estimates in cases when representations of functions by such integral operators are not readily available. In particular, we derive norm estimates for sum operators and use these estimates to obtain improved Poincaré–Sobolev results.  相似文献   

5.
In a previous paper, the author introduced a new class of multivariate rational interpolants, which are called Optimal Padé-type Approximants (OPTA). There, for this class of rational interpolants, which extends classical univariate Padé Approximants, a direct extension of the “de Montessus de Ballore's Theorem” for meromorphic functions in several variables is established. In the univariate case, this theorem ensures uniform convergence of a row of Pade Approximants when the denominator degree equals the number of poles (counting multiplicities) in a certain disc. When one overshoots the number of poles when fixing the denominator degree, convergence in measure or capacity has been proved and, under certain additional restrictions, the uniform convergence of a subsequence of the row. The author tackles the latter case and studies its generalization to functions in several variables by using OPTA.  相似文献   

6.
Résumé On discute un procédé radial de purification et on décrit son application; un appareil pour la production de monocristaux de glace. Les cristaux purs (50 mm, de diamètre et 300 mm de longueur) possèdent un cur de 25 mm de diamètre ayant une conductivité moyenne de 1,5·10–7 ohm–1 à–10°C. On peut également produire des monocristaux transparents dotés d'acide fluorhydrique qui ne présentent qu'une faible inhomogénéité (20%) si la concentration dans la glace est inférieure à 3·10–5HF/H2O.  相似文献   

7.
Finding the Bäcklund transformation from the singularity structure is only impossible with the method of Weiss if the PDE has two families of singularities with opposite principal parts, such as the modified KdV and sine-Gordon equations. For such PDEs, we first consider the truncation with one manifold, derive the Darboux transformation (DT), and show that it involves the two entire functions associated with each family. Their ratio is then assumed to satisfy the most general Riccati system. This hypothesis, combined with the DT, generates a very small number of determining equations, admitting a unique solution, equivalent to the matricial Lax pair by the usual linearization of the Riccati system.Dienst Theoretische Natuurkunde, Vrije Universiteit Brussel B-1050 Brussels, Belgium. Service de physique de l'état condensé, Centre d'études de Saclay, F-91190 Gif-sur-Yvette Cedex, France. Translated from Teoreticheskaya i Matematicheskaya Fizika, Vol. 99, No. 3, pp 478–486, June, 1994.  相似文献   

8.
Summary In this paper we characterize the, what we call, visible projection of a point process on an arbitrary space as a Radon-Nikodym-derivative in the same manner the dual previsible projection of a process on + is defined by Dellacherie and Meyer [1]; this visible projection turns out to coïncide with the conditional intensity as defined by Papangelou [3]; a neat behaviour is imposed to the point process by only one intuïtively clear condition, which is proved to be equivalent to the classical smoothnessconditions () and (*).

Ces recherches ont été subventionées par l'Organisation Néerlandaise pour le Développement de la Recherche Scientifique (Z.W.O.; n de bourse 62–138) et partiellement par le Centre National de la Recherche Scientifique  相似文献   

9.
In this paper we give two derivative-free computational algorithms for nonlinear least squares approximation. The algorithms are finite difference analogues of the Levenberg-Marquardt and Gauss methods. Local convergence theorems for the algorithms are proven. In the special case when the residuals are zero at the minimum, we show that certain computationally simple choices of the parameters lead to quadratic convergence. Numerical examples are included.On leave 1970–71 at Yale UniversityThe work of this author was supported in part by the National Science Foundation under Grant GJ-844.  相似文献   

10.
A system of second-order partial differential equations for the Feynman amplitude of a single-loop graph with four vertices is obtained. It is proved that the symbol of differential operators of this system is singular (in the sense of I. N. Bernshtein) on the Landau manifold of the Feynman amplitude under consideration. The derived system of differential equations is a multidimensional generalization of the system of differential equations for the hypergeometric function of two variables of Appell and Kampé de Fériet.Translated from Matematicheskie Zametki, Vol. 23, No. 1, pp. 113–119, January, 1978.  相似文献   

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