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In this paper, we use Schauder and Banach fixed point theorems to study the existence, uniqueness and stability of bounded nonhomogeneous iterative functional differential equations of the form x' (t) = λ1x(t) + λ2x[2](t)+...+λnx[n](t)+f(t). [ABSTRACT FROM AUTHOR]

Abstract: In this paper, a Volterra model with mutual interference and Beddington–DeAngelis functional response is investigated, some sufficient conditions which guarantee the existence and global attractivity of positive periodic solution for the system are obtained. Furthermore, our results improve the main results of paper . [Copyright &y& Elsevier]

Modified direct methods for the computation of Zernike and pseudo-Zernike moments are presented in this paper. The presence of many factorial terms in direct methods for computing Zernike-type moments makes their computation process a very time consuming task. Although the computational power of the modern computers is impressively increasing, the calculation of the factorial of a big number is still an inaccurate numerical procedure. The main concept of this paper is that, using Stirling's approximation for the factorial and applying some suitable mathematical properties, novel factorial-free direct methods can be developed. The resulting moments are not equal to those computed using the original direct methods, but they are a sufficiently accurate approximation of them. In addition, their variability does not affect their ability to uniquely describe and distinguish the objects that they represent. This is verified by appropriate pattern recognition experiments. [ABSTRACT FROM AUTHOR]

In this paper, the following inverse heat conduction problem: ut = uxx, x≥0, t≥0, u(x,0) = 0, x≥0 u(1,t) = g(t), t≥0, u&z.sfnc;x→∞ is bounded, is considered again. This problem is severely ill-posed: its solution (if it exists) does not depend continuously on the data; a small perturbation in the data may cause a dramatically large error in the solution for 0 < x < 1. In this paper, a new wavelet regularization method for this problem is given. Moreover, we can easily find the regularization parameter J such that some sharp stable estimates between the exact solution and the approximate one in Hr(R)-norm meaning is given. [Copyright &y& Elsevier]

In this paper, we present the necessary and sufficient conditions for which the given pair of closed subspaces has a pair of non-trivial principal invariant subspaces. Using this we show that every pairof closed subspaces withorhas a pair of non-trivial principal invariant subspaces. Also we prove that the pairof closed subspaces withhas a pair of non-trivial principal invariant subspaces if and only ifSimilar results are proved for non-degenerate principal invariant subspaces. [ABSTRACT FROM PUBLISHER]

Abstract: In this paper, we study on -analoque of a certain family Szász-beta type operators. We give a Voronovskaja type theorem. [Copyright &y& Elsevier]

For n ⩾ 1, let P(n) = F2 [x1, . . . , x n ] be the polynomial algebra in n variables xi, of degree one, over the field F2 of two elements. The mod-2 Steenrod algebra A acts on P(n) according to well-known rules. Let A+P(n) denote the image of the action of the positively graded part of A. A major problem is that of determining a basis for the quotient vector space Q(n) = P(n)/A+P(n). Both P(n) = ⊕ d⩾0Pd (n) and Q(n) are graded where Pd (n) denotes the set of homogeneous polynomials of degree d. A spike of degree d is a monomial of the form x 12λ1 -1 … x n 2λn -1 where λ i ⩾ 0 for each i. In this paper we show that if n ⩾ 2 and d ⩾ 1 can be expressed in the form d = d(λ) = (n - 1)(2λ - 1) with λ ⩾ 2, then dim(Qd(λ) (n)) ⩾ B(n, d(λ)) + {Σ λ q=2 ( n q ), ifλ < n;2n - (n + 1), ifλ ⩾ n}, where B(n, d(λ)) is the number of spikes of degree d(λ). [ABSTRACT FROM AUTHOR]

Abstract: We consider a variational model for image segmentation proposed in Sandberg et al. (2010) [12]. In such a model the image domain is partitioned into a finite collection of subsets denoted as phases. The segmentation is unsupervised, i.e., the model finds automatically an optimal number of phases, which are not required to be connected subsets. Unsupervised segmentation is obtained by minimizing a functional of the Mumford–Shah type (Mumford and Shah, 1989 [1]), but modifying the geometric part of the Mumford–Shah energy with the introduction of a suitable scale term. The results of computer experiments discussed in [12] show that the resulting variational model has several properties which are relevant for applications. In this paper we investigate the theoretical properties of the model. We study the existence of minimizers of the corresponding functional, first looking for a weak solution in a class of phases constituted by sets of finite perimeter. Then we find various regularity properties of such minimizers, particularly we study the structure of triple junctions by determining their optimal angles. [Copyright &y& Elsevier]

Let n > 1 be an integer, φ(e)(n) is a multiplicative function. In this paper, we shall establish a short interval result for the function φ(e)(n). [ABSTRACT FROM AUTHOR]

In this paper, a new lowering operator D u with a linear functional u as a parameter is introduced in the linear space ℙ of all polynomials in one variable with complex coefficients. It is given by The concept of D u -semiclassical polynomial sequence is defined. We show that such a sequence belongs to the family of D-Laguerre–Hahn polynomials. This allows us to provide some characterizations of a D u -semiclassical polynomial sequence in terms of a distributional equation that the linear functional satisfies as well as a structure relation. An illustrative example is considered. [ABSTRACT FROM AUTHOR]

Abstract: Different from involutive negations on [0, 1], the fixed points of an involutive interval-valued negation are uncountable. In this paper, all the fixed points of an involutive interval-valued negation are characterized. Also, it is proved that an involutive interval-valued negation is uniquely determined by its fixed points. Moreover, a constructive representation of involutive interval-valued negations is obtained. [Copyright &y& Elsevier]

Abstract: In the paper, we collect some inequalities and establish a sharp double inequality for bounding the n-th harmonic number. [Copyright &y& Elsevier]

In this paper, we compute the second variational formula for the functional $ \int_M v^{(6)}(g)dv_g$) is a strict local maximum within its conformal class unless the manifold is isometric to a round sphere with the standard metric up to a multiple of a constant. [ABSTRACT FROM AUTHOR]

Abstract: In this paper, we consider the trace theorem for modulation spaces , α-modulation spaces and Besov spaces . For the modulation space, we obtain the sharp results. [ABSTRACT FROM AUTHOR]

In this paper, using the concept of A-statistical convergence for double sequences, we investigate a Korovkin-type approximation theorem for sequences of positive linear operator on the space of all continuous real valued functions defined on any compact subset of the real two-dimensional space. Then we display an application which shows that our new result is stronger than its classical version. We also obtain a Voronovskaya-type theorem and some differential properties for sequences of positive linear operators constructed by means of the Bernstein polynomials of two variables. [ABSTRACT FROM AUTHOR]

This paper deals with a unifying approach to the problems of computing the admissible sets of parametrical multi perturbations in appropriate bounded sets such that some fundamental properties of parameter-varying linear dynamic systems are maintained provided that the so-called (i.e. perturbation-free) nominal system possesses such properties. The sets of parametrical multi perturbations include any combinations of parametrical multi perturbations in the matrix of dynamics as well as in the control, output and input-output interconnection matrices which belong to some prescribed bounded domain in the complex space. The various properties which are investigated are controllability, observability, output controllability, stabilizability and detectability as well as the existence of minimal state-space realizations together with the associate existence or not of associate decoupling, transmission and invariant zeros. All the matrices of parameters including the nominal and the disturbed ones which parameterize the dynamic system may be real or complex. The obtained results are then applied to systems subject to a finite number of discrete internal delays and parametrical multi perturbations by comparing the state- space descriptions of such systems with the general descriptions previously investigated. In particular, the contributions of the delays to the spectral descriptions are assimilated to the contributions of a set of varying parameters in a domain for the general description. [ABSTRACT FROM AUTHOR]

In this paper, we establish generalized Hyres-Ulam-Rassias stability of the mixed type additive and quadratic functional equation f(3x + y) + f(3x - y) = f(x + y) + f(x - y) + 2f(3x) - 2f(x) in non-Archimedean spaces. [ABSTRACT FROM AUTHOR]

The paper characterizes the boundedness of the composition operator Cφf(z) = f(φ(z)) from the Hardy space Hp(X), p > 0, where X is the upper half-plane Π+ = {z ∈ ℂ : Im z > 0} or the unit disk D = {z ∈ ℂ : ∣z∣ < 1} in the complex plane ℂ, to Zygmund-type spaces, where φ is an analytic selfmap of X. [ABSTRACT FROM AUTHOR]

In this paper, new results concerning shape preserving weighted uniform approximation on the real line are presented. [ABSTRACT FROM AUTHOR]

This paper presents an efficient approximate method to obtain a numerical solution, which is bounded at the end point x = -1, for Cauchy type singular integral equations of the first kind on the interval [-1,1]. The solution is derived by approximating the unknown density function using the weighted Chebyshev polynomials of the third kind, and then computing the Cauchy singular integral which is obtained analytically. The known force function is interpolated using the Chebyshev polynomials of the fourth kind. The exactness of this approximate method is shown for characteristic equation when the force function is a cubic. Particular result is also given to show the exactness of this method. [ABSTRACT FROM AUTHOR]

In this paper, we study the nonlocal ∞-Laplacian type diffusion equation obtained as the limit as p → ∞ to the nonlocal analogous to the p-Laplacian evolution, We prove exist ence and uniqueness of a limit solution that verifies an equation governed by the subdifferential of a convex energy functional associated to the indicator function of the set $${K = \{ u \in L^2(\mathbb{R}^N) \, : \, | u(x) - u(y)| \le 1, \mbox{ when } x-y \in {\rm supp} (J)\}}$$ . We also find some explicit examples of solutions to the limit equation. If the kernel J is rescaled in an appropriate way, we show that the solutions to the corresponding nonlocal problems converge strongly in L∞(0, T; L2 ( Ω)) to the limit solution of the local evolutions of the p-Laplacian, v t = Δ p v. This last limit problem has been proposed as a model to describe the formation of a sandpile. Moreover, we also analyze the collapse of the initial condition when it does not belong to K by means of a suitable rescale of the solution that describes the initial layer that appears for p large. Finally, we give an interpretation of the limit problem in terms of Monge–Kantorovich mass transport theory. [ABSTRACT FROM AUTHOR]

In this paper, we deal with the problem of uniqueness of meromorphic functions that share two small functions with their derivatives, and obtain the following result which improves a result of Yao and Li: Let f(z) be a nonconstant meromorphic function, k > 5 be an integer. If f(z) and g(z) = α1(z)f(z) + α2(z)f(k)(z) share the value 0 CM, and share b(z) IM, N E(r, f = 0 = f(k)) = S(r), then f ≡ g, where α1(z), α2(z) and b(z) are small functions of f(z). [ABSTRACT FROM AUTHOR]

This paper is an attempt to stress the usefulness of multi-variable special functions. We derive generating relations involving multi-variable Hermite-Tricomi functions by using the Lie-algebraic method. Further, we derive certain new and known generating relations involving other forms of Hermite-Tricomi functions as applications. [ABSTRACT FROM AUTHOR]

The paper presents an error bound of the Ritz method for the problem of minimizing the functional in the space $$ {\mathop W\limits^{\text{o}} }^{1}_{2} {\left( {0,1} \right)} $$ in the case where the standard assumption on the continuity of q(t) is replaced by the condition q2(t)t(1-t) ∈ L(0,1). In the case where q(t) is continuous, the new bound is sharper than the known one. Bibliography: 5 titles. [ABSTRACT FROM AUTHOR]

We consider in this paper the question of when the finite sum of products of two Toeplitz operators is a finite-rank perturbation of a single Toeplitz operator on the Hardy space over the unit disk. A necessary condition is found. As a consequence we obtain a necessary and sufficient condition for the product of three Toeplitz operators to be a finite-rank perturbation of a single Toeplitz operator. [ABSTRACT FROM AUTHOR]

In this paper, we prove an L2-concentration result of Zakharov system in space dimension two, with radial initial data $(u_0,n_0,n_1) \in H^s \times L^2 \times H^{-1} (\frac{16}{17} < s < 1)$, when blow up of the solution happens by I-method. In addition to that, we find a blow up character of this system. Furthermore, we improve the global existence result of Bourgain's to the above-mentioned spaces. [ABSTRACT FROM AUTHOR]

In this paper we characterize the boundedness and compactness of weighted composition operators of H∞ into α-Bloch spaces on the unit ball in ℂ n. [ABSTRACT FROM AUTHOR]

Temlyakov considered the optimal recovery on the classes of functions with bounded mixed derivative in the L p metrics and gave the upper estimates of the optimal recovery errors. In this paper, we determine the asymptotic orders of the optimal recovery in Sobolev spaces by standard information, i.e., function values, and give the nearly optimal algorithms which attain the asymptotic orders of the optimal recovery. [ABSTRACT FROM AUTHOR]

In this paper, we establish existence, multiplicity and nonexistence of periodic solutions for a class of first-order n-dimensional neutral functional differential equations. Our results improve the previous ones established by Wang and O'Regan. Our approach is based on the fixed point theorem in cones as well as some analysis techniques. [ABSTRACT FROM AUTHOR]

Abstract: This paper extends the Hille–Phillips functional calculus and rational approximations results due to R. Hersh, T. Kato, P. Brenner, and V. Thomée to generators of bi-continuous semigroups. The method yields error estimates for rational time-discretization schemes for such semigroups, in particular for dual semigroups, Feller semigroups such as the Ornstein–Uhlenbeck semigroup, the heat semigroup, semigroups induced by nonlinear flows, implemented semigroups, and evolution semigroups. Furthermore, the results provide error estimates for a new class of inversion formulas for the Laplace transform. [Copyright &y& Elsevier]

In this paper we consider a second order mock theta function, recently given by Hikami. We define a generalized function and show it is a Fq - function and give its integral representation and multibasic expansion. We also show that this mock theta function can be obtained by performing a left half-shift transformation on a certain theta series. [ABSTRACT FROM AUTHOR]

For variational inequalities, various merit functions, such as the gap function, the regularized gap function, the D-gap function and so on, have been proposed. These functions lead to equivalent optimization formulations and are used to optimization-based methods for solving variational inequalities. In this paper, we extend the regularized gap function and the D-gap functions for a quasi-variational inequality, which is a generalization of the variational inequality and is used to formulate generalized equilibrium problems. These extensions are shown to formulate equivalent optimization problems for quasi-variational inequalities and are shown to be continuous and directionally differentiable. [ABSTRACT FROM AUTHOR]

The purpose of the present paper is to investigate some inclusion properties of certain subclasses of analytic functions associated with a family of linear operators, which are defined by means of the Hadamard product (or convolution). Some integral preserving properties are also considered. [ABSTRACT FROM AUTHOR]

We first define upper sign continuity for a set-valued mapping and then we consider two type of generalized vector equilibrium problems in topological vector spaces and provide sufficient conditions under which the solution sets are nonempty and compact. Finally, we give an application of our main results. The paper generalizes and improves results obtained by Fang and Huang in (2005). [ABSTRACT FROM AUTHOR]

This paper finds some lower and upper bounds for the essential norm of the weighted composition operator from α-Bloch spaces to the weighted-type space Hμ∞ on the unit ball for the case α ≥ 1. [ABSTRACT FROM AUTHOR]

The functional inequality ∥f (x) + 2f(y) + 2f(z)∥ ≤ ∥ 2f(x)/2 + y + z)∥ + ϕ (x, y, z ϵ G) is investigated, where G is a group divisible by 2, f : G → X and ϕ : G³→ [0,∞) are mappings, and X is a Banach space. The main result of the paper states that the assumptions above together with (1) ϕ(2x, -x, 0) = 0 = ϕ(0,x,-x) (x ϵ G) and (2) limn→∞ (1/2n+1 ϕ (2n+1x, 2nz) = 0, or limn→∞2nϕ(x/2n-1, y/2n, z/2n = 0 (x, y, z ϵ G), imply that f is additive. In addition, some stability theorems are proved. [ABSTRACT FROM AUTHOR]

The article examines a perturbed Ostrowski-type inequality on time scales for k points for functions whose second derivatives are bounded. Authors of this paper have also point out some particular perturbed integral inequalities on time scales for functions whose second derivatives are bounded as special cases. These include perturbed rectangle inequality on time scales, perturbed trapezoid inequality on time scales, and perturbed mid-point inequality on time scales. The theory of time scales is considered as a theory capable to contain both difference and differential calculus in a consistent way.

Any Boolean function can be defined by a Boolean circuit, provided we may use sufficiently strong functions in its gates. On the other hand, what Boolean functions can be defined depends on these gate functions: Each set B of gate functions defines the class of Boolean functions that can be defined by circuits over B. Although these classes have been known since the 1920s, their computational complexity was never investigated. In this paper we will study how difficult it is to decide for a Boolean function f and a class B, whether f is in B. Moreover, we will provide such a decision algorithm with additional information: How difficult is it to decide whether or not f is in B, provided we already know a circuit for f, but with gates from another class A? Given such a circuit, we know that f is in A. Is the problem harder if we do not have a concrete representation for f, but still know that it is from A? For nearly all possible combinations, we show that this is not the case, and that the problem is either in P or coNP-complete. [ABSTRACT FROM AUTHOR]

We introduce new data structures for compressed suffix trees whose size are linear in the text size. The size is measured in bits; thus they occupy only O(n log|A|) bits for a text of length n on an alphabet A. This is a remarkable improvement on current suffix trees which require O(n log n) bits. Though some components of suffix trees have been compressed, there is no linear-size data structure for suffix trees with full functionality such as computing suffix links, string-depths and lowest common ancestors. The data structure proposed in this paper is the first one that has linear size and supports all operations efficiently. Any algorithm running on a suffix tree can also be executed on our compressed suffix trees with a slight slowdown of a factor of polylog(n). [ABSTRACT FROM AUTHOR]

Abstract: In this paper we study the hyponormality and subnormality of 2-variable weighted shifts using the Schur product techniques in matrices. As applications, we generalize the result in [R. Curto, J. Yoon, Jointly hyponormal pairs of subnormal operators need not be jointly subnormal, Trans. Amer. Math. Soc. 358 (2006) 5135–5159, Theorem 5.2] and give a non-trivial, large class satisfying the Curto–Muhly–Xia conjecture [R. Curto, P. Muhly, J. Xia, Hyponormal pairs of commuting operators, Oper. Theory Adv. Appl. 35 (1988) 1–22] for 2-variable weighted shifts. Further, we give a complete characterization of hyponormality and subnormality in the class of flat, contractive, 2-variable weighted shifts with the condition that the norm of the 0th horizontal 1-variable weighted shift of T is a given constant. [Copyright &y& Elsevier]

The article analyzes the development of the variational Tikhonov regularization method for ill-posed problems. A. N. Tikhonov published papers on the development of efficient solution methods for a broad class of ill-posed problems in 1963. He was also credited for coming up with the generalization of the notion of approximate solution. Definitions of the regularizing algorithm and regularized solution are provided.

In this paper, we study the regularity of solutions for two–dimensional Cahn–Hilliard equation with non–constant mobility. Basing on the L p type estimates and Schauder type estimates, we prove the global existence of classical solutions. [ABSTRACT FROM AUTHOR]

This paper considers the problem of approximating an integrable function by piecewise linear functions that keep the integral and positivity of the original function. [ABSTRACT FROM AUTHOR]

Abstract: In this paper, we study the existence of nontrivial nonnegative periodic solutions for the quasilinear parabolic equation with nonlocal terms based on the theory of Leray-Schauder''s degree. [Copyright &y& Elsevier]

Using the Jordan algebras methods, specially the properties of Peirce decomposition and the Frobenius transformation, we compute the coefficients of the zeta functional equation, in the case of Jordan algebras of type II. As particular cases of our result, we can cite the case of V=M(n,R) studied by Gelbart [Mem. Amer. Math. Soc. 108 (1971)] and Godement and Jacquet [Zeta functions of simple algebras, Lecture Notes in Math., vol. 260, Springer-Verlag, Berlin, 1972], and the case of V=Herm(3,Os) studied by Muro [Adv. Stud. Pure Math. 15 (1989) 429]. Let us also mention, that recently, Bopp and Rubenthaler have obtained a more general result on the zeta functional equation by using methods based on the algebraic properties of regular graded algebras which are in one-to-one correspondence with simple Jordan algebras [Local Zeta Functions Attached to the Minimal Spherical Series for a Class of Symmetric Spaces, IRMA, Strasbourg, 2003]. The method used in this paper is a direct application of specific properties of Jordan algebras of type II. [Copyright &y& Elsevier]

This paper is concerned with a computational method for recovering induced magnetic fields due to the existence of surface or subsurface cracks. The inversion formula can be simply represented by an integral equation of the first kind. The problem is transformed into a well-posed difference equation using output least squares approach with a Tikhonov regularization. A fast computational algorithm is also proposed using discrete Fourier convolution techniques. [ABSTRACT FROM AUTHOR]

This paper is devoted to investigating certain aspects of Fredholm multipliers on topological algebras. Precisely, we establish that if T is a multiplier defined on a semisimple commutative Fréchet locally m-convex algebra A having dense socle, then it is a Fredholm multiplier if and only if it is invertible in M(A) modulo the compact multipliers, where M(A) denotes the multiplier algebra of A. In particular, the same characterization is valid for every Fréchet locally m-convex algebra possessing an orthogonal basis. We also illustrate by giving an example that the hypothesis of dense socle can not be relaxed. Finally, we present some applications of these results. [ABSTRACT FROM AUTHOR]

In this paper we present duality theory for compact groups in the case when the C&ast;-algebra A, the fixed point algebra of the corresponding Hilbert C&ast;-system (F; G), has a nontrivial center Z ⊃ C1 and the relative commutant satisfies the minimality condition A′ ∩ F = Z, as well as a technical condition called regularity. The abstract characterization of the mentioned Hilbert C&ast;-system is expressed by means of an inclusion of C&ast;-categories TC < T , where TC is a suitable DR-category and T a full subcategory of the category of endomorphisms of A. Both categories have the same objects and the arrows of T can be generated from the arrows of TC and the center Z. A crucial new element that appears in the present analysis is an abelian group C(G), which we call the chain group of G, and that can be constructed from certain equivalence relation defined on Ĝ, the dual object of G. The chain group, which is isomorphic to the character group of the center of G, determines the action of irreducible endomorphisms of A when restricted to Z. Moreover, C(G) encodes the possibility of defining a symmetry ∈ also for the larger category T of the previous inclusion. [ABSTRACT FROM AUTHOR]

A solution concept for fuzzy multiobjective programming problems based on ordering cones (convex cones) is proposed in this paper. The notions of ordering cones and partial orderings on a vector space are essentially equivalent. Therefore, the optimality notions in a real vector space can be elicited naturally by invoking a concept similar to that of the Pareto-optimal solution in vector optimization problems. We introduce a corresponding multiobjective programming problem and a weighting problem of the original fuzzy multiobjective programming problem using linear functionals so that the optimal solution of its corresponding weighting problem is also the Pareto-optimal solution of the original fuzzy multiobjective programming problem. [ABSTRACT FROM AUTHOR]

The aim of this paper is to study the Laguerre-Hahn affine functionals on the unit circle, and to establish the relation with the semiclassical ones. We prove that both classes are different and we characterize those functionals which are Laguerre-Hahn affine and which are not semiclassical. Some examples are given. Finally, we present several modifications of the functional that preserve the Laguerre-Hahn affine character. [ABSTRACT FROM AUTHOR]