Korovkin-type theorem and application

Let (L_n) be a sequence of positive linear operators on C[0,1], satisfying that (L_n(e_i)) converge in C[0,1] (not necessarily to e_i) for i=0,1,2, where e_i(x)=xⁱ. We prove that the conditions that (L_n) is monotonicity-preserving, convexity-preserving and variation diminishing do not suffice to insure the convergence of (L_n(f)) for all fC[0,1]. We obtain the Korovkin-type theorem and give quantitative results for the approximation properties of the q-Bernstein operators B_n,q as an application.     

Modifying the generalized singular value decomposition with application with application in direction-of-arrival finding

We consider updating and downdating problems for the generalized singular value decomposition (GSVD) of matrix pairs when new rows are added to one of the matrices or old rows are deleted. Two classes of algorithms are developed, one based on the CS decomposition formulation of the GSVD and the other based on the generalized eigenvalue decomposition formulation. In both cases we show that the updating and downdating problems can be reduced to a rank-one SVD updating problem. We also provide perturbation analysis for the cases when the added or deleted rows are subject to errors. Numerical experiments on direction-of-arrival (DOA) finding with colored noises are carried out to demonstrate the tracking ability of the algorithms. The work of the first author was supported in part by NSF grants CCR-9308399 and CCR-9619452. The work of the second author was supported in part by China State Major Key Project for Basic Researches.     

An application of Sylvester matrices

In a Banach lattice, the convergence of a series of absolute values $ \sum\limits_{{k\geq 1}} {\left| {{x_k}} \right|} $ implies the unconditional convergence of the series $ \sum\limits_{{k\geq 1}} {{x_k}} $ . The converse assertion is valid only in Banach lattices order-isomorphic to M-spaces. In this paper a new proof of this fact using Sylvester series is given.     

The application oft-measures of fuzziness

By introducing thet-measures of fuzziness we give a method for determination the degree of interference between the elements with different properties of a universe. Finally, we apply this method in geography of population.     

An application of Bernstein-Durrmeyer operators

In the present paper, we find that the Bemstein-Durrmeyer operators, besides their better applications in approximation theory and some other fields, are good tools in constructing translation network. With the help of the de la Vallee properties of the Bernstein-Durrmeyer operators a sequence of translation network operators is constructed and its degree of approximation is dealt.     

An application of parabolic H-measures

A new, parabolic variant of H-measures, as well as its application to the advection-diffusion equation is presented. By the means of localisation property, the strong compactness for gradients of solutions is obtained in the case of variable coefficients. (© 2008 WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim)     

Two inequalities with an application

Summary An inequality used in Brown and Cohen (1974,Ann. Statist., 2(5), 963–976) and Bhattacharya (1978,Ann. Inst. Statist. Math., A,30, 407–414) is generalized and another useful inequality derived from it. An application of the latter which provides a more elegant approach to and an improvement over a result in Shinozaki (1978,Commun. Statist. Theor. Meth., A,7, 1421–1432), is also presented.     

An application of dominating families

In this paper, we prove that_χ(Seq_ξ)=d, when ξ is Frechet filter orP-point in ω^* withx(ξ,ω^*)≤d.     

An application of Jack-Fukui-Sakaguchi Lemma

We present some applications of Jack-Fukui-Sakaguchi Lemma which become sufficient criteria for a function to be in the class of strongly starlike, strongly close-to-convex or in the other classes.     

Static duality and a stationary-action application

Conservative dynamical systems propagate as stationary points of the action functional. Using this representation, it has previously been demonstrated that one may obtain fundamental solutions for two-point boundary value problems for some classes of conservative systems via solution of an associated dynamic program. Further, such a fundamental solution may be represented as a set of solutions of differential Riccati equations (DREs), where the solutions may need to be propagated past escape times. Notions of “static duality” and “stat-quad duality” are developed, where the relationship between the two is loosely analogous to that between convex and semiconvex duality. Static duality is useful for smooth functionals where one may not be guaranteed of convexity or concavity. Some simple properties of this duality are examined, particularly commutativity. Application to stationary action is considered, which leads to propagation of DREs past escape times via propagation of stat-quad dual DREs.     

An application of the Difference-Patterson method

Proceedings - Mathematical Sciences - The Difference-Patterson (D-P) technique is applied to a complicated example, namely, the isomorphous crystals, di-p-tolyl telluride and di-p-tolyl selenide,...     

An application of quasi-f-power increasing sequences

In Bor (C. R. Acad. Sci. Paris, Ser. I 346:391–394, 2008), we have proved a result dealing with $\mid {\bar{N}, p_n, \theta _{n}} \mid _{k}$ summability factors by using a quasi- $\beta $ -power increasing sequence . In this paper, that result has been generalized by using a new class of power increasing sequences , which is a wider calss of sequences, instead of a quasi- $\beta $ -power increasing sequence. Some new results have also been obtained.     

A new application of non-increasing sequences

In Bor (J Class Anal 1:31–34, 2012), we proved a main theorem dealing with an application of convex sequences. In this paper, we prove that theorem under weaker conditions by using a non-increasing sequence instead of a convex sequence. Some new results have also been obtained.     

Une application de Corps des Normes

Let k be a perfect field of characteristic p > 0, K₀ = Frac(W(k)), a uniformizer in K₀ and _n K ₀ (n N) such that ₀ = and _n+1 ^p = _n. We write K = _nN K₀ (_n), H = Gal (K₀/ K and G = Gal(K₀/ K₀). The main result of this paper is that the functor restriction of the Galois action from the category of crystalline representations of G with Hodge–Tate weights in an interval of length p - 2 to the category of p-adic representations of H is fully faithful and its essential image is stable by sub-object and quotient. The proof uses the comparison between two ways of building mod. p representations of H: one thanks to the norm field of K, the other thanks to some categories of filtered modules with divided powers previously introduced by the author.     

Conditional Lagrange derivative and its application

Our paper aims to show what to do in material modeling for an inelastic body. The method we use is based on the virtual work σ ′δε and on the variation of some function W with respect to the strain tensor. (© 2008 WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim)     

A fractional differential inequality with application

We establish a fractional differential inequality using desingularization techniques combined with some generalizations of algebraic Bihari-type inequalities. We use this inequality to prove global existence and determine the asymptotic behavior of solutions for a family of fractional differential equations.