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In this paper, we introduce a new class of analytic functions associated with Mittag-Leffler fuction in the open unit disk. Several properties of functions belonging to this class are derived. [ABSTRACT FROM AUTHOR]

In this paper, we study differential equations arising from the generating functions of generalized degenerate tangent polynomials. We give explicit identities for the generalized degenerate tangent polynomials arising from differential equations. [ABSTRACT FROM AUTHOR]

In this paper, we characterize the family of quotients of internally quasicontinuous functions. Moreover, we study cardinal invariants related to quotients in the case of internally quasicontinuous functions and the complement of this family. [ABSTRACT FROM AUTHOR]

This paper discusses the estimation of average treatment effects in observational causal inferences. By employing a working propensity score and two working regression models for treatment and control groups, Robins et al. (1994, 1995) introduced the augmented inverse probability weighting (AIPW) method for estimation of average treatment effects, which extends the inverse probability weighting (IPW) method of Horvitz and Thompson (1952); the AIPW estimators are locally efficient and doubly robust. In this paper, we study a hybrid of the empirical likelihood method and the method of moments by employing three estimating functions, which can generate estimators for average treatment effects that are locally efficient and doubly robust. The proposed estimators of average treatment effects are efficient for the given choice of three estimating functions when the working propensity score is correctly specified, and thus are more efficient than the AIPW estimators. In addition, we consider a regression method for estimation of the average treatment effects when working regression models for both the treatment and control groups are correctly specified; the asymptotic variance of the resulting estimator is no greater than the semiparametric variance bound characterized by the theory of Robins et al. (1994, 1995). Finally, we present a simulation study to compare the finite-sample performance of various methods with respect to bias, efficiency, and robustness to model misspecification. [ABSTRACT FROM AUTHOR]

In this paper we give the definition of [λ ᵘ]-continuity of real-valued functions defined on an open interval, which is an example of path continuity. We give some properties of [λ, ᵘ]-continuous functions. The aim of the paper is to find the maximal additive class and the maximal multiplicative class for the family of [λ, ᵘ]-continuous functions. [ABSTRACT FROM AUTHOR]

The aim of this paper is to introduce two new classes of multifunctions called almost δ-semicontinuous multifunctions and weakly δ-semicontinuous multifunctions which are generalization of δ-semicontinuous multifunctions. In this paper we obtain several properties of such multifunctions. [ABSTRACT FROM AUTHOR]

Abstract: In this paper, we study a nondifferentiable minimax fractional programming problem under the assumptions of -invex function. In this paper we utilize the concept of -invexity [M.A. Noor, On generalized preinvex functions and monotonicities, J. Inequalities Pure Appl. Math. 5 (2004) 1–9] and pseudo--invexity [S.K. Mishra, M.A. Noor, On vector variational-like inequality problems, J. Math. Anal. Appl. 311 (2005) 69–75]. We also introduce the concept of strict pseudo--invex and quasi--invex functions. We derive Karush–Kuhn–Tucker-type sufficient optimality conditions and establish weak, strong and converse duality theorems for the problem and its three different dual problems. The results in this paper extend several known results in the literature. [Copyright &y& Elsevier]

Abstract: In this paper, by means of a series of counterexamples, we study in a systematic way the relationships among (pseudo, quasi) α-preinvexity, (strict, strong, pseudo, quasi) α-invexity and (strict, strong, pseudo, quasi) αη-monotonicity. Results obtained in this paper can be viewed as a refinement and improvement of the results of Noor and Noor [M.A. Noor, K.I. Noor, Some characterizations of strongly preinvex functions, J. Math. Anal. Appl. 316 (2006) 697–706]. [Copyright &y& Elsevier]

We will show in this paper that if λ is very close to 1, then can be attained, where M is a compact–manifold with boundary. This result gives a counter–example to the conjecture of de Figueiredo and Ruf in their paper titled "On an inequality by Trudinger and Moser and related elliptic equations" ( Comm. Pure. Appl. Math., 55, 135–152, 2002). [ABSTRACT FROM AUTHOR]

In the paper of Lee et al. an equivalent condition for a function ƒ to be of the first Baire class has been established. This condition is of an ε -- δ type, similarly as in Cauchy's definition of continuity of a function. In the first part of this paper we examine a problem whether it is possible to obtain other classes of functions by further modifications of the above condition. It turns out that, in some sense, the answer is negative. In the second part we consider a topological version of the condition of Lee et al. [ABSTRACT FROM AUTHOR]

In this paper we introduce the notion of decomposability in the space of Henstock-Kurzweil-Pettis integrable (for short HKP-integrable) functions. We show representations theorems for decomposable sets of HKP-integrable or Henstock integrable functions, in terms of the family of selections of suitable multifunctions. [ABSTRACT FROM AUTHOR]

Abstract: In this paper we consider non-linear differential equations which are closely related to the generating functions of Frobenius–Euler polynomials. From our non-linear differential equations, we derive some new identities between the sums of products of Frobenius–Euler polynomials and Frobenius–Euler polynomials of higher order. [Copyright &y& Elsevier]

In this paper we prove existence theorems for integro - differential equations xΔ(t) = f(t, x(t), ∫ 0 t k(t, s, x(s))Δs), x(0) = x0 t ∊ Ia = [0, a] ∩ T, a ∊ R+, where T denotes a time scale (nonempty closed subset of real numbers R), Ia is a time scale interval. Functions f, k are Carathéodory functions with values in a Banach space E and the integral is taken in the sense of Henstock-Kurzweil delta integral, which generalizes the Henstock-Kurzweil integral. Additionally, functions f and k satisfy some boundary conditions and conditions expressed in terms of measures of noncompactness. Moreover, we prove an Ambrosetti type lemma on a time scale. [ABSTRACT FROM AUTHOR]

The aim of this paper is to prove the complete monotonicity of a class of functions arising from Kazarinoff's inequality [Edinburgh Math. Notes 40 (1956) 19-21]. As applications, new sharp inequalities for the gamma and digamma functions are established. [ABSTRACT FROM AUTHOR]

Abstract. In this paper, we obtain some applications of first order differential subordination and superordination results for some analytic functions defined by convolution. [ABSTRACT FROM AUTHOR]

We establish new oscillation criteria for second-order delay differential equations with mixed nonlinearities of the form Due to image rights restrictions, multiple line equation(s) cannot be graphically displayed. are continuous functions defined on [0, ∞), and p(t) > 0, p'(t) ≥ 0, and a1 >…> αm > α m+1 >…> α n > 0. No restriction is imposed on the potentials pi(t), qi(t), and e(t) to be nonnegative. These oscillation criteria extend and improve the results given in the recent papers. An interesting example illustrating the sharpness of our results is also provided. [ABSTRACT FROM AUTHOR]

In this paper, we establish some inequalities of Fejér type for g-convex dominated functions. [ABSTRACT FROM AUTHOR]

In this paper, we consider a perturbation of a Laguerre-Hahn functional by adding a derivative of a Dirac delta. This transformation leaves invariant the family of Laguerre-Hahn linear functionals. We shall also analyse the class of the perturbed linear functional. Finally, we illustrate these perturbations by adding the derivative of a Dirac delta to the first kind associated functional of the classical Laguerre functional. The expression of the new orthogonal polynomials is obtained. [ABSTRACT FROM AUTHOR]

We consider a problem of finding optimal contracts in continuous time, when the agent’s actions are unobservable by the principal, who pays the agent with a one-time payoff at the end of the contract. We fully solve the case of quadratic cost and separable utility, for general utility functions. The optimal contract is, in general, a nonlinear function of the final outcome only, while in the previously solved cases, for exponential and linear utility functions, the optimal contract is linear in the final output value. In a specific example we compute, the first-best principal’s utility is infinite, while it becomes finite with hidden action, which is increasing in value of the output. In the second part of the paper we formulate a general mathematical theory for the problem. We apply the stochastic maximum principle to give necessary conditions for optimal contracts. Sufficient conditions are hard to establish, but we suggest a way to check sufficiency using non-convex optimization. [ABSTRACT FROM AUTHOR]

Abstract: The paper presents a new method introducing an anchored discrete convolution for calculating the length of a digital curve. The method is based on discrete convolution by using convolution masks and point anchoring in the pixel. The use of ordinary convolution distorts the curve shape and gives large errors in length calculation. The advantage of anchoring is that it limits the point shifting into the pixel during the calculation of the curve length. The method is applied to an analytical arc and various calculations are performed. In addition different methods from the literature were compared and a real sample was tested. [Copyright &y& Elsevier]

Abstract: In this paper, a further improved extended Fan sub-equation method is used to construct exact solutions of the (2+1)-dimensional breaking soliton equations. As a result, many new and more general non-travelling wave and coefficient function solutions are obtained including soliton-like solutions, triangular-like solutions, single and combined non-degenerate Jacobi elliptic wave function-like solutions, Weierstrass elliptic doubly-like periodic solutions, each of which contains an arbitrary function of two variables. The results show the proposed method give new and more general exact solutions. More importantly, the method with the aid of symbolic computation provides a very effective and powerful mathematical tool for solving a great many non-linear partial differential equations in mathematical physics. [Copyright &y& Elsevier]

Abstract: This paper deals with a nonlinear parabolic equation with a more complicated source term, which is a product of localized source u q (0, t), local source u p (x, t), and weight function a(x). We investigate how the three factors influence the asymptotic behavior of solutions. It is shown that the blow-up set consists of single point {x =0} if p >1. When 0⩽ p ⩽1 with p + q >1, the blow-up take place everywhere in B. Moreover, the blow-up rate estimate is established with more precise coefficients determined. [Copyright &y& Elsevier]

Abstract: In this paper, characterizations of the existence of the directional derivative and second-order parabolic directional derivative of a locally Lipschitzian function are established. These characterizations involve the adjacent cone and second-order adjacent set of the graph of the function. [Copyright &y& Elsevier]

Abstract: Let and be analytic in the unit disk. The Hadamard product of f and g is defined by . This paper gives some characterizations of functions in spaces in terms of the Hadamard products. [Copyright &y& Elsevier]

Abstract: In an earlier paper [D. Richards, Q. Zheng, Determinant formulas for multidimensional hypergeometric period matrices, Adv. in Appl. Math. 29 (2002) 137–151] on the determinants of certain period matrices, we formulated a conjecture about the determinant of a certain hypergeometric matrix. In this article, we establish this conjecture by constructing a system of linear equations in which that determinant is one of the variables. As a consequence, we obtain the value of an integral which generalizes the well-known multidimensional beta integral of A. Selberg [A. Selberg, Bemerkninger om et multipelt integral, Norsk. Mat. Tidsskr. 26 (1944) 71–78] and some hypergeometric determinant formulas of A. Varchenko [A. Varchenko, The Euler beta-function, the Vandermonde determinant, the Legendre equation, and critical values of linear functions on a configuration of hyperplanes. I, Izv. Akad. Nauk SSSR Ser. Mat. 53 (1989) 1206–1235, English translation, Math. USSR-Izv. 35 (1990) 543–571; A. Varchenko, The Euler beta-function, the Vandermonde determinant, the Legendre equation, and critical values of linear functions on a configuration of hyperplanes. II, Izv. Akad. Nauk SSSR Ser. Mat. 54 (1990) 146–158, English translation, Math. USSR-Izv. 36 (1991) 155–167]. [Copyright &y& Elsevier]

Abstract: In this paper, we study the normality of a family of meromorphic functions and obtain some normality results for meromorphic functions, which improve and generalize the related results of Gu, Bergweiler and Lin. [Copyright &y& Elsevier]

Abstract: The persistence of some stage structured predator–prey model with finite and infinite delay was studied in this paper. By analyzing right-hand functions and using the comparison theorem, some sufficient conditions for the persistence of populations with finite and infinite delay were derived. [Copyright &y& Elsevier]

In this paper, it is proved that with at most $$ O{\left( {N^{{\frac{{65}} {{66}}}} } \right)} $$ exceptions, all even positive integers up to N are expressible in the form $$ p^{2}_{2} + p^{3}_{3} + p^{4}_{4} + p^{5}_{5} $$ . This improves a recent result $$ O{\left( {N^{{\frac{{19193}} {{19200}} + \varepsilon }} } \right)} $$ due to C. Bauer. [ABSTRACT FROM AUTHOR]

Abstract: This paper discusses a kind of bent functions that have some symmetric properties about some variables. Section 2 mainly discusses the bent functions symmetric about some two variables and gives the necessary and sufficient condition for these functions. Section 3 gives algebraic expressions of some bent functions. [Copyright &y& Elsevier]

Abstract: This paper investigates the decentralized control of LTI continuous-time plants using generalized sampled-data hold functions (GSHF). GSHFs can be used to modify the structure of the digraph of the resultant discrete plant, by removing certain interconnections in the discrete-time equivalent model to form a hierarchical system model of the plant. This is a new application of discretization and has, as its motivation, the design of decentralized controllers using centralized methods. [Copyright &y& Elsevier]

The paper details a comprehensive system for the treatment of the topic of limits—conceptually, computationally, and formally. The system addresses fundamental linguistic flaws in the standard presentation of limits, which attempts to force limit discussion into the language of individual real numbers and equality. The system of near-numbers properly fits the context of limits, allowing precise and unambiguous notation in limit computation. More importantly, the near-numbers are a set of concrete mathematical objects that provide a scaffold both for building an accurate intuitive understanding of the limit concept and for connecting that understanding to the formal definition of the limit. [ABSTRACT FROM AUTHOR]

Abstract: In this paper we study the problem where are positive radial functions, and . We give existence and nonexistence results, depending on the parameters p and λ. It turns out that is a critical value for the existence of solutions. [Copyright &y& Elsevier]

In this paper, we introduce an iterative process for finding the common element of the set of fixed points of a nonexpansive mapping and the set of solutions of the variational inequality problem for a monotone, Lipschitz-continuous mapping. The iterative process is based on the so-called extragradient method. We obtain a weak convergence theorem for two sequences generated by this process. [ABSTRACT FROM AUTHOR]

Abstract: In this paper, harmonic wavelets, which are analytically defined and band limited, are studied, together with their differentiable properties. Harmonic wavelets were recently applied to the solution of evolution problems and, more generally, to describe evolution operators. In order to consider the evolution of a solitary profile (and to focus on the localization property of wavelets), it seems to be more expedient to make use of functions with limited compact support (either in space or in frequency). The connection coefficients of harmonic wavelets are explicitly computed (in the following) at any order, and characterized by some recursive formulas. In particular, they are functionally and finitely defined by a simple formula for any order of the basis derivatives. [Copyright &y& Elsevier]

The paper determines the region of values of the system occurring in the title on the class T of functions f(z) = z + ⋯ regular in the unit disk and satisfying the condition Bibliography: 7 titles. [ABSTRACT FROM AUTHOR]

For a fixed positive number γ, a real-valued function f defined on a convex subset D of a normed space X is said to be γ-convex if it satisfies the inequality f(x′0) + f (x′1) ⩽ f(x0) + f(x1), for x′i ∊ [x0, x1], for x′i ∊[x0, x1], ∥x′i - xi∥ = γ, i = 0, 1, whenever x0, x1 ∊ D and ∥x0 - x1∥ ➮ γ. This paper presents some results on the boundedness and continuity of γ-convex functions. For instance, (a) if there is some x* ∊ D such that f is bounded below on D ∩ B (x*, γ), then so it is on each bounded subset of D; (b) if f is bounded on some closed ball B(x*, γ/2) ⊂ D and D′ is a closed bounded subset of D, then f is bounded on D′ if it is bounded above on the boundary of D′; (c) if dim X > 1 and the interior of D contains a closed ball of radius γ, then f is either locally bounded or nowhere locally bounded in the interior of D; (d) if D contains some open ball B(x*, γ/2) in which f has at most countably many discontinuities, then the set of all points at which f is continuous is dense in D. [ABSTRACT FROM AUTHOR]

In this paper, we deal with the determination of the entire set of Pareto solutions of location problems involving Q general criteria. These criteria include median, center, or centdian objective functions as particular instances. We characterize the set of Pareto solutions of all these multicriteria problems for any polyhedral gauge. An efficient algorithm is developed for the planar case and its complexity is established. Extensions to the nonconvex case are also considered. The proposed approach is more general than previously published approaches to multicriteria location problems. [ABSTRACT FROM AUTHOR]

In this paper, we analyze different schemes for obtaining gradient estimates when the underlying functions are noisy. Good gradient estimation is important e.g. for nonlinear programming solvers. As error criterion, we take the norm of the difference between the real and estimated gradients. The total error can be split into a deterministic error and a stochastic error. For three finite-difference schemes and two design of experiments (DoE) schemes, we analyze both the deterministic errors and stochastic errors. We derive also optimal stepsizes for each scheme, such that the total error is minimized. Some of the schemes have the nice property that this stepsize minimizes also the variance of the error. Based on these results, we show that, to obtain good gradient estimates for noisy functions, it is worthwhile to use DoE schemes. We recommend to implement such schemes in NLP solvers. [ABSTRACT FROM AUTHOR]

The present paper is a continuation of [1]; therefore, we preserve the notation and continue the numbering of sections, formulas, and theorems. [ABSTRACT FROM AUTHOR]

Noiri in 1984, Dontchev, Ganster and Reilly in recent years and Reilly and Vamanamurthy in 1983 introduced the notion of perfectly continuous, regular set-connected and clopen functions, respectively. The aim of this paper is to introduce the notion of a new class of functions which is called almost clopen functions including the classes of perfectly continuous, regular set-connected and clopen functions. Furthermore, properties of almost clopen functions are obtained and relationships among almost clopenness, perfect continuity, regular set-connectedness, clopenness and almost continuity are investigated. [ABSTRACT FROM AUTHOR]

In this paper, we present upper and lower linear bounds for the Shannon function for length of checking tests for repetition-free functions in the basis {0, 1, &, ∨, ¬}. The research was supported by Russian Foundation for Basic Research, grants 04-01-00359 and 05-01-01000. [ABSTRACT FROM AUTHOR]

In this paper, we study triples of the form (E, θ, ϕ) over a compact Riemann surface, where (E, θ) is a Higgs bundle and ϕ is a global holomorphic section of the Higgs bundle. Our main result is an description of a birational equivalence which relates geometrically the moduli space of Higgs bundles of rank r and degree d to the moduli space of Higgs bundles of rank r-1 and degree d. [ABSTRACT FROM AUTHOR]

In this paper, a class of global optimization problems is considered. Corresponding to each local minimizer obtained, we introduced a new modified function and construct a corresponding optimization subproblem with one constraint. Then, by applying a local search method to the one-constraint optimization subproblem and using the local minimizer as the starting point, we obtain a better local optimal solution. This process is continued iteratively. A termination rule is obtained which can serve as stopping criterion for the iterating process. To demonstrate the efficiency of the proposed approach, numerical examples are solved. [ABSTRACT FROM AUTHOR]

Abstract: In this paper, the author investigates two-species nonautonomous delay diffusive preypredator models with Michaelis-Menten functional response. Sufficient conditions are derived for permanence of the species. Further, the author also establishs the sufficient conditions that guarantee the arbitrary positive periodic solution of the systems is global attractive. [Copyright &y& Elsevier]

Abstract: In this paper, nutrient-phytoplankton-zooplankton interaction with general uptake functions in which nutrient recycling is either instantaneous or delayed is considered. To account for higher predation, zooplankton''s death rate is modeled by a quadratic term instead of the usual linear function. Persistence conditions for each of the delayed and nondelayed models are derived. Numerical simulations with data from the existing literature are explored to compare the two models. It is demonstrated numerically that increasing zooplankton death rate can eliminate periodic solutions of the system in both the instantaneous and the delayed nutrient recycling models. However, the delayed nutrient recycling can actually stabilize the nutrient-plankton interaction. [Copyright &y& Elsevier]

In this paper, in the setting of sequential spaces, we consider the value functions vS and vI defined by vS(x)=supy∈K(x)f(x,y) and vI(x)=infy∈K(x)f(x,y), and we introduce sufficient conditions on the value functions and on the data, weaker than upper semicontinuity, which guarantee the existence of maximum for such functions. Various examples illustrate the results and the connections with previous results. [Copyright &y& Elsevier]

In this paper, we prove, under natural assumptions, that the semilinear elliptic system -Δu+u=g(x,v), x ∈ RN, -Δv+v=f(x,u), x∈RN (0.1) possesses at least one positive solution pair (u, v) ∈ H¹(RN) × H¹(RN), where f(x, t) and g(x, t) are continuous functions on RN × R and asymptotically linear as t → + ∞. [ABSTRACT FROM AUTHOR]

In this paper, the lower bounds of Bloch constants Bn, for functions with multiplicity at least n, are improved by showing [Copyright &y& Elsevier]

Let Σ(p, k)(p, k ∈ N) be the class of functions f(z) = z-p+ak-p²k-p+... analytic in 0 < |z| < 1. A subclass M(p, k, α, λ) of Σ(p, k) is introduced. The object of the present paper is to investigate convolution properties for the class M(p, k, α, λ). Also a property of the partial sums of certain functions in this class is given. [ABSTRACT FROM AUTHOR]

In previous work we introduced and studied a function R(a+, a_, c; v, &vcaron;) that generalizes the hypergeometric function. In this paper we focus on a similarity-transformed function ε (a+, a_, γ; v, &vcaron;), with parameters γ ∈ C4 related to the couplings c ∈ C4 by a shift depending on a+, a_. We show that the ε-function is invariant under all maps γ → w(γ), with w in the Weyl group of type D4. Choosing a+, a_ positive and y, &vcaron; real, we obtain detailed information on the ¦Re v¦ → ∞ asymptotics of the ε-function. In particular, we explicitly determine the leading asymptotics in terms of plane waves and the c-function that implements the similarity R → &epsilon. [ABSTRACT FROM AUTHOR]