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1.
We obtain estimates for L p -norms of simple partial fractions in terms of their L r -norms on bounded and unbounded segments of the real axis for various p > 1 and r > 1 (S. M. Nikolskii type inequalities). We adduce examples and remarks concerning sharpness of the inequalities and area of their application.  相似文献   

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We consider a multiple interpolation by Padé simple partial fractions and propose a method for calculating the values of rational functions and polynomials on the basis of approximation by special rational functions (their numerator and denominator are represented as the differences between two simple partial fractions). We obtain an extrapolation formula for an analytic function h(z) in a neighborhood of the origin. For an extrapolation tool we use the expressions Σ k λ k h(λ k z), where λ k are calculated by a certain algorithm and are independent of the choice of h. Bibliography: 17 titles.  相似文献   

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We study a generalized interpolation of a rational function at n nodes by a simple partial fraction of degree n and reduce the consideration to the solvability question for a special difference equation. We construct explicit interpolation formulas in the case where the equation order is equal to 1. We show that for functions A(x − a) m , m ? \mathbbN m \in \mathbb{N} , it is possible to reduce the consideration to a system of m + 1 independent first order equations and construct explicit interpolation formulas. Bibliography: 6 titles.  相似文献   

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The problem of the best uniform approximation of a real constant c by real-valued simple partial fractions R n on a closed interval of the real axis is considered. For sufficiently small (in absolute value) c, |c| ≤ c n , it is proved that R n is a fraction of best approximation if, for the difference R n ? c, there exists a Chebyshev alternance of n + 1 points on a closed interval. A criterion for best approximation in terms of alternance is stated.  相似文献   

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Under simple interpolation by simple partial fractions, the poles of the interpolation fraction may arise at some nodes irrespective of the values of the interpolated function at these nodes. Such nodes are said to be singular. In the presence of singular nodes, the interpolation problem is unsolvable. We establish two criteria for the appearance of singular nodes under an extension of interpolation tables and obtain an algebraic equation for calculating such nodes.  相似文献   

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A partial \((k-1)\)-spread in \({\text {PG}}(n-1,q)\) is a collection of \((k-1)\)-dimensional subspaces with trivial intersection. So far, the maximum size of a partial \((k-1)\)-spread in \({\text {PG}}(n-1,q)\) was known for the cases \(n\equiv 0\pmod k\), \(n\equiv 1\pmod k\), and \(n\equiv 2\pmod k\) with the additional requirements \(q=2\) and \(k=3\). We completely resolve the case \(n\equiv 2\pmod k\) for the binary case \(q=2\).  相似文献   

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Differential inequality techniques are used to obtain upper bounds for theL 1 norm of solutions of nonlinear reaction-diffusion equations. Essential use is made of Sobolev type integral inequalities. An extension to third order pseudo-parabolic equations is included.
Résumé On utilise des techniques d'inégalités differentielles afin d'obtenir des bornes supérieures pour les normes de typeL 1 des solutions des équations des réaction et diffusion non linéaires. On utilise de façon essentielle des inégalités intégrales du type de Sobolev. On inclut une extension aux équations pseudo-paraboliques du troisième ordre.
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Using reduction to polynomial interpolation, we study the multiple interpolation problem by simple partial fractions. Algebraic conditions are obtained for the solvability and the unique solvability of the problem. We introduce the notion of generalized multiple interpolation by simple partial fractions of order ≤ n. The incomplete interpolation problems (i.e., the interpolation problems with the total multiplicity of nodes strictly less than n) are considered; the unimprovable value of the total multiplicity of nodes is found for which the incomplete problem is surely solvable. We obtain an order n differential equation whose solution set coincides with the set of all simple partial fractions of order ≤ n.  相似文献   

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We consider solutions in the whole of the space of a partial differential equation driven by the anisotropic Laplacian. We prove a pointwise energy bound and we derive from that some rigidity results.  相似文献   

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Although it is difficult to differentiate analytic functions defined by continued fractions, it is relatively easy in some cases to determine uniform bounds on such derivatives by perceiving the continued fraction as an infinite composition of linear fractional transformations and applying an infinite chain rule for differentiation.  相似文献   

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Following Li and Yau (Acta Math 156:153?C201 1986) and similar to Perelman (The entropy formula for the Ricci flow and its geometric applications), we define an energy functional ${\mathcal{J}}$ associated to a smooth function ${\phi}$ on a complete Riemannian manifold. As an application, we deduce integral Ricci curvature upper bounds along modified geodesics for complete steady and shrinking gradient Ricci solitons.  相似文献   

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This paper discusses a general approach to obtain optimum performance bounds for (N+1)-person deterministic decision problems,N+1>2, with several levels of hierarchy and under partial dynamic information. Both cooperative and noncooperative modes of decision making are considered at the lower levels of hierarchy; in each case, it is shown that the optimum performance of the decision maker at the top of the hierarchy can be obtained by solving a sequence of open-loop (static) optimization problems. A numerical example included in the paper illustrates the general approach.  相似文献   

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An unusual form of the maximum entropy problem is considered, that includes simple bound constraints on the Fourier coefficients of the required image, as well as nonnegativity conditions on the image intensities. The algorithm avoids mixing these constraints by introducing a parameter into the objective function that is adjusted by an outer iteration. For each parameter value an inner iteration solves a large optimization calculation, whose constraints are just the simple bounds, by a combination of the conjugate gradient procedure and an active set method. An important feature is the ability to make many changes to the active set at once. The outer iteration includes a test for inconsistency of all the given constraints. The algorithm is described, a proof of convergence is given, and there are some second-hand remarks on numerical results.  相似文献   

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We focus on the numerical solution of medium scale bound-constrained systems of nonlinear equations. In this context, we consider an affine-scaling trust region approach that allows a great flexibility in choosing the scaling matrix used to handle the bounds. The method is based on a dogleg procedure tailored for constrained problems and so, it is named Constrained Dogleg method. It generates only strictly feasible iterates. Global and locally fast convergence is ensured under standard assumptions. The method has been implemented in the Matlab solver CoDoSol that supports several diagonal scalings in both spherical and elliptical trust region frameworks. We give a brief account of CoDoSol and report on the computational experience performed on a number of representative test problems.  相似文献   

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