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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]

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]

The maximal covering location problem has been shown to be a useful tool in siting emergency services. In this paper we expand the model along two dimensions - workload capacities on facilities and the allocation or multiple levels of backup or prioritized service for all demand points. In emergency service facility location decisions such as ambulance sitting, when all of a facility's resources are needed to meet each call for service and the demand cannot be queued, the need for a backup unit may be required. This need is especially significant in areas of high demand. These areas also will often result in excessive workload for some facilities. Effective siting decisions, therefore, must address both the need for a backup response facility for each demand point and a reasonable limit on each facility's workload. In this paper, we develop a model which captures these concerns as well as present an efficient solution procedure using Lagrangian relaxation. Results of extensive computational experiments are presented to demonstrate the viability of the approach. [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]

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]

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 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]

Let $G$ be a group, let $A$ be an Abelian group, and let $n$ be an integer such that $n\backslash ge\; -1$. In the paper, the sets $\backslash Phi\_n(G,A)$ of functions from $G$ into $A$ of degree not greater than $n$ are studied. In essence, these sets were introduced by Logachev, Sal'nikov, and Yashchenko. We describe all cases in which any function from $G$ into $A$ is of bounded (or not necessarily bounded) finite degree. Moreover, it is shown that if $G$ is finite, then the study of the set $\backslash Phi\_n(G,A)$ is reduced to that of the set $\backslash Phi\_n(G/O^p(G),A\_p)$ for primes $p$ dividing $|G/G\text{'}|$. Here $O^p(G)$ stands for the $p$-coradical of the group $G$, $A\_p$ for the $p$-component of $A$, and $G\text{'}$ for the commutator subgroup of $G$. [ABSTRACT FROM AUTHOR]

The concept of a strict extended partial order (SEPO) has turned out to be very useful in explaining (resp. rationalizing) non-binary choice functions. The present paper provides a general account of the concept of extended binary relations, i.e. relations between subsets and elements of a given universal set of alternatives. In particular, we define the concept of a weak extended partial order (WEPO) and show how it can be used in order to represent rankings of Opportunity sets that display a ‘preference for opportunities’. We also clarify the relationship between SEPOs and WEPOs, which involves a non-trivial condition, called ‘strict properness’. Several characterizations of strict (and weak) properness are provided, based on which we argue for properness as an appropriate condition demarcating ‘choice based’ preference. [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]

In this paper we shall introduce and study subclasses Rλ (α, s, t) and Pλ (α, s, t) of the class of λ - spirallike generalized Sakaguchi type function. Here we shall prove characterization and subordination properties for these subclasses and point out several interesting consequences of our results. [ABSTRACT FROM AUTHOR]

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 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]

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]

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 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]

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]

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]

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]

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]

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 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]

Classes of set functions defined by the positivity or negativity of the higher-order derivatives of their pseudo-Boolean polynomial representations generalize those of monotone, supermodular, and submodular functions. In this paper, these classes are characterized by functional inequalities and are shown to be closed both under algebraic closure conditions and a local closure criterion. It is shown that for every m ≥ 1, in addition to the class of all set functions, there are only three other classes satisfying these algebraic and local closure conditions: those having positive, respectively negative, mth-order derivatives, and those having a polynomial representation of degree less than m. [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]

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 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 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]

The following problem is considered: obtain the asymptotic properties of a function $u$ from the asymptotic properties of the integral $\backslash int\_0^r\{u(t)\}\backslash ,dt$. As is well known, this can be done under additional constraints on the function $u(t)$. In this paper, we obtain a theorem in which these constraints are weaker than in other well-known versions of such theorems. [ABSTRACT FROM AUTHOR]

In this paper, we study the spaces $B\_\{pq\}^s(G)$ and $L\_\{pq\}^s(G)$ of functions with positive exponent of smoothness $s>\; \backslash nomathbreak\; 0$, defined on a domain $G\backslash subset\; \backslash nomathbreak\; \backslash Bbb\; R^n$. For a domain $G$ with specific geometric properties, we establish the embedding $B\_\{pp\}^s(G)=L\_\{pp\}^s(G)\backslash subset\; L\_q(G)$, 1

The paper developed the method of multivalent vector guiding functions (MVGF). The notions of full collection of the strict MVGF's, full and sharp collection of the generalized MVGF's, and the regular MVGF were introduced and considered. These methods were extended to the problem of periodic trajectories of the controlled system obeying a differential inclusion. [ABSTRACT FROM AUTHOR]

The purpose of the present paper is to investigate some properties of H-continuous (Almost Hcontinuous) multifunctions defined from a product space to a product space. The relations between the strongly closed graph of a multivalued functions and H-upper semicontinuity of multivalued functions are also investigated. [ABSTRACT FROM AUTHOR]

In this paper, we present, first- and second-order variational conditions for a convex composite function go F, where g is a nonsmooth convex function and F is a vector valued map. The first-order results, which apply to (not, necessarily locally Lipsehitz) continuous maps F, not only recapture the results of the special cases where F is locally Lipschitz or Gâteaux differentiable but also yield sharp necessary variational conditions in these eases. The result, s arc achieved by applying a new strengthened notion of approximate Jacobian, called a Gâteaux (G) approximate Jacobian, without the use of the upper semicontinuity of the approximate Jacobian. These variational results are generally derived by using a chain rule formula or by constructing upper convex approximations to the composite function. These approaches often need the upper semicontinuity requirement of a generalized Jacobian map. Such a requirement not only limits the derivation of sharp optimality conditions, as the "small" approximate Jacobians (or generalized subdifferentials) lack an upper semi-continuity property, but also restricts the treatment of Gâteaux differentiable maps F. This situation is overcome by the use of G-approximate Jacobians. The second order variational conditions are shown to hold, in particular, in the case where F is continuously Gâteaux differentiable. [ABSTRACT FROM AUTHOR]

Numerical representations of choice functions allow the expression of a problem of choice as a problem of finding maxima of real-valued functions, which requires that less information be defined and which is easier to work with. In this paper, the existence of numerical representations of choice functions by imposing assumptions directly on the choice function is obtained. In particular, it is proved that (IIA) is a necessary and sufficient condition for a choice function to be representable, if the set of alternatives is countable, while the conjunction of (IIA) and a ‘continuity condition’ is sufficient to ensure it in separable topological spaces. [ABSTRACT FROM AUTHOR]

An extremely simple proof of the K-K-M-S Theorem is given involving only Brouwer's fixed point theorem and some elementary calculus. A function is explicitly given such that a fixed point of it yields an intersection point of a balanced collection of sets together with balancing weights. Moreover, any intersection point of a balanced collection of sets together with balancing weights corresponds to a fixed point of the function. Furthermore, the proof can be used to show π-balanced versions of the K-K-M-S Theorem, with π-balancedness as introduced in Billera (1970). The proof makes clear that the conditions made with respect to π by Billera can be even weakened. [ABSTRACT FROM AUTHOR]

When u is a von Neumann-Morgenstern utility function on X ⊗ Y. Y is ‘utility independent’ of X if u can be written as u(x, y)=f(x)g(y) + a(x) with f positive. This paper introduces a fundamental extension of utility independence that is base on induced indifference relations over gambles on one factor when the level of the other factor is fixed. It is proved that Y is ‘degree-n utility independent’ of X if and only if u can be written as u(x, y)= f1(x)g1(y)+ … + fn(x)gn(y)+ a(x) and cannot be written in a similar way with fewer than n products of single-factor functions. A similar theorem holds when the roles of Y and X are interchanged. It follows that if Y is degree-n utility independent of X, then X is degree-m utility independent of Y for some m ∈ ¦ n - l . n . n + l ¦; it is then shown that u can be represented in terms of n conditional utility functions on Y . m conditional utility functions on X, and at most (n + l)(m + 1) scaling constants. [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]

Sufficient conditions for the existence of solutions of nonlinear boundary value problems for higher-order functional difference equations with p-Laplacian are established by making of continuation theorems. We allow f to be at most linear, superlinear, or sublinear in obtained results. [ABSTRACT FROM AUTHOR]

In this article, we investigate the chaotic behaviours in the fractional-order Lorenz system. By utilizing the fractional calculus techniques, we found that chaos exists in the fractional-order Lorenz system of order less than 3. The lowest order we found to have chaos in this system is 2.97. [ABSTRACT FROM AUTHOR]