Search

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 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]

The present paper continues a series of papers of the author (some of them are written in collaboration), in which the Yoneda algebras are calculated for several families of algebras of dihedral and semidihedral type (in K. Erdmann’s classification). In the paper, the Yoneda algebras are described (in terms of quivers with relations) for the algebras of semidihedral type that form the family SD(3 $$\mathcal{K}$$ ). Bibliography: 10 titles. [ABSTRACT FROM AUTHOR]

This paper deals with the numerical solution of optimal control problems for ODEs. The methods considered here rely on some standard optimization code to solve a discretized version of the control problem under consideration. We aim to make available to the optimization software not only the discrete objective functional, but also its gradient. The objective gradient can be computed either from forward (sensitivity) information or backward (adjoint) information. The purpose of this paper is to discuss various ways of adjoint computation. It will be shown both theoretically and numerically that methods based on the continuous adjoint equation require a careful choice of both the integrator and gradient assembly formulas in order to obtain a gradient consistent with the discretized control problem. Particular attention is given to automatic differentiation techniques which generate automatically a suitable integrator. [ABSTRACT FROM AUTHOR]

With the arrival of the nineteenth century, a process of change guided the treatment of three basic elements in the development of mathematics: rigour, the arithmetization and the clarification of the concept of function, categorised as the most important tool in the development of the mathematical analysis. In this paper we will show how several prominent mathematicians contributed greatly to the development of these basic elements that allowed the solid underpinning of mathematics and the consideration of mathematics as an axiomatic way of thinking in which anyone can deduce valid conclusions from certain types of premises. This nineteenth century stage shares, possibly with the Heroic Age of Ancient Greece, the most revolutionary period in all history of mathematics. [ABSTRACT FROM AUTHOR]

Let f∈ L be a real-valued even function with its Fourier series $\frac {a_{0}}{2}+\sum\limits_{n=1}^{\infty}{a_{n}}\cos nx$ , and let S( f, x) be the nth partial sum of the Fourier series, n≧1. The classical result says that if the nonnegative sequence { a} is decreasing and $\lim\limits_{n\to\infty} a_{n} =0$ , then $\lim\limits_{n\to\infty} \|{f-S_{n}(f)}\|_{L}=0$ if and only if $\lim\limits_{n\to\infty} a_{n}\log n=0$ . Later, the monotonicity condition set on { a} is essentially generalized to MVBV (Mean Value Bounded Variation) condition. Very recently, Kórus further generalized the condition in the classical result to the so-called GM condition in real space. In this paper, we give a complete generalization to the complex space. [ABSTRACT FROM AUTHOR]

The main purpose of this paper is to introduce and study generalized hyperconnected spaces. Various characterizations of generalized hyperconnected spaces and preservation theorems are discussed. [ABSTRACT FROM AUTHOR]

Inspired by a theorem of Marcinkiewicz [J. Marcinkiewicz, On a class of functions and their Fourier series, C. R. Soc. Sci. Varsovie, 26:71-77, 1934. Reprinted in: J. Marcinkiewicz, Collected Papers (A. Zygmund (Ed.)), PaństwoweWydawnictwo Naukowe,Warsaw, 1964] stating that the maximum of the absolute values of real Fourier coefficients a and b of a function of bounded p-variation $$ \left( {p \geqslant 1} \right) $$ on an interval [0 , 1] is of order O( n) as n → ∞, we compute the Fourier coefficients of the linear fractional stable motion (LFSM) and of the closely related Riemann-Liouville (RL) process and investigate the rate of their decay. [ABSTRACT FROM AUTHOR]

In this paper we establish two theta function identities with four parameters by the theory of theta functions. Using these identities we introduce common generalizations of Hirschhorn-Garvan-Borwein cubic theta functions, and also re-derive the quintuple product identity, one of Ramanujan’s identities, Winquist’s identity and many other interesting identities. [ABSTRACT FROM AUTHOR]

Császár introduced the notions of ascending operation, ascending hull of operation and ascending generalized neighborhood system in [2]. In this paper, we introduce the notions of interior and closure operators and ( ϕ,ϕ′)-continuity on ascending generalized neighborhood systems. We characterize some properties of such notions in terms of convergence of p-stacks. [ABSTRACT FROM AUTHOR]

In this paper, we solve the problem proposed by Lan Wen for the case of dim M = 3. Roughly speaking, we prove that for fixed i, f has C1 persistently no small angles of index i if and only if f has a dominated splitting of index i on the C1 i-preperiodic set P( f). [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]

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]

In [1], the strong ratio limit theorems associated with Markov chains were first proved for some “test” functions with specific properties and were then generalized to a wider family of functions. In the present paper, this family is significantly extended by functions that can be majorized in a sense by the potentials of the original functions. The verification of whether a function belongs of the new family can be simplified by using small functions and their analogs. Here the traditional recurrency-or irreducibility-type requirements for the corresponding Markov chains are replaced by more flexible requirements. [ABSTRACT FROM AUTHOR]

The main purpose of this paper is to establish the second-order nonsmooth sufficient unconstrained optimality condition for so called ℓ-stable at some point functions and in this way to generalize some previous results in this direction. We provide the comparisons with other results by examples. [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.

The main purpose of this paper is to introduce the concepts of $$ \mathcal{C} $$ *-sets, $$ \mathcal{C} $$ *-continuous functions and to obtain new decompositions of continuous and ηζ-continuous functions. Moreover, properties of $$ \mathcal{C} $$ *-sets and some properties of $$ \mathcal{C} $$ -sets are discussed. [ABSTRACT FROM AUTHOR]

In this paper, we study conditions for the existence of a function satisfying constraints on its value at each point and on its derivative. [ABSTRACT FROM AUTHOR]

In this paper, we prove several results concerning meromorphic functions f and g of hyperorder less than one such that f ( j) and g ( j) have the same zeros and poles for j = 0, 1, 2. We provide some examples to show that our results are sharp. [ABSTRACT FROM AUTHOR]

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]

In this paper, we prove some properties of the Seneta sequences and functions, and in particular we prove a representation theorem in the Karamata sense for the sequences from the Seneta class SOc. [ABSTRACT FROM AUTHOR]

Let X be an irreducible algebraic variety over ℂ, endowed with an algebraic foliation $$ {\user1{\mathcal{F}}} $$ . In this paper, we introduce the notion of minimal invariant variety V( $$ {\user1{\mathcal{F}}} $$ , Y) with respect to ( $$ {\user1{\mathcal{F}}} $$ , Y), where Y is a subvariety of X. If Y = { x} is a smooth point where the foliation is regular, its minimal invariant variety is simply the Zariski closure of the leaf passing through x. First we prove that for very generic x, the varieties V( $$ {\user1{\mathcal{F}}} $$ , x) have the same dimension p. Second we generalize a result due to X. Gomez- Mont (see [G-M]). More precisely, we prove the existence of a dominant rational map F : X → Z, where Z has dimension ( n − p), such that for very generic x, the Zariski closure of F −1( F( x)) is one and only one minimal invariant variety of a point. We end up with an example illustrating both results. [ABSTRACT FROM AUTHOR]

In this paper, we apply the dual approach developed by A. Chambolle for the Rudin-Osher-Fatemi model to regularization functionals with higher order derivatives. We emphasize the linear algebra point of view by consequently using matrix-vector notation. Numerical examples demonstrate the differences between various second order regularization approaches. [ABSTRACT FROM AUTHOR]

In this paper, we discuss here-and-now type stochastic programs with equilibrium constraints. We give a general formulation of such problems and study their basic properties such as measurability and continuity of the corresponding integrand functions. We discuss also the consistency and rate of convergence of sample average approximations of such stochastic problems. [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 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]

The paper is devoted to nonstationary Stokes equations in a half-space. The existence and uniqueness of a solution are proved in spaces of bounded or continuous functions. Estimates of solutions are given in the uniform norm and in the norms of Hölder spaces. Bibliography:17titles. [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, 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]

Many important concepts of the calculus are difficult to grasp, and they may appear epistemologically unjustified. For example, how does a real function appear in “small” neighborhoods of its points? How does it appear at infinity? Diagrams allow us to overcome the difficulty in constructing representations of mathematical critical situations and objects. For example, they actually reveal the behavior of a real function not “close to” a point (as in the standard limit theory) but “in” the point. We are interested in our research in the diagrams which play an optical role –microscopes and “microscopes within microscopes”, telescopes, windows, a mirror role (to externalize rough mental models), and an unveiling role (to help create new and interesting mathematical concepts, theories, and structures). In this paper we describe some examples of optical diagrams as a particular kind of epistemic mediator able to perform the explanatory abductive task of providing a better understanding of the calculus, through a non-standard model of analysis. We also maintain they can be used in many other different epistemological and cognitive situations. [ABSTRACT FROM AUTHOR]

In an important recent paper, [2], S. Franz and M. Leone prove rigorous lower bounds for the free energy of the dilutedp-spin model and theK-sat model at any temperature. We show that the results for these two models are consequences of a single general principle. Our calculations are significantly simpler than those of [2], even in the replica-symmetric case. [ABSTRACT FROM AUTHOR]

In this paper, a model of a linear multilevel programming problem with dominated objective functions (LMPPD(l)) is proposed, where multiple reactions of the lower levels do not lead to any uncertainty in the upper-level decision making. Under the assumption that the constrained set is nonempty and bounded, a necessary optimality condition is obtained. Two types of geometric properties of the solution sets are studied. It is demonstrated that the feasible set of LMPPD(l) is neither necessarily composed of faces of the constrained set nor necessarily connected. These properties are different from the existing theoretical results for linear multilevel programming problems. [ABSTRACT FROM AUTHOR]

In this paper, we characterize the nonemptiness and compactness of the set of weakly efficient solutions of a convex vector optimization problem with cone constraints in terms of the level-boundedness of the component functions of the objective on the perturbed sets of the original constraint set. This characterization is then applied to carry out the asymptotic analysis of a class of penalization methods. More specifically, under the assumption of nonemptiness and compactness of the weakly efficient solution set, we prove the existence of a path of weakly efficient solutions to the penalty problem and its convergence to a weakly efficient solution of the original problem. Furthermore, for any efficient point of the original problem, there exists a path of efficient solutions to the penalty problem whose function values (with respect to the objective function of the original problem) converge to this efficient point. [ABSTRACT FROM AUTHOR]

In this paper, we show that Goodwillie calculus, as applied to functors from stable homotopy to itself, interacts in striking ways with chromatic aspects of the stable category. Localized at a fixed prime p, let T(n) be the telescope of a vn self map of a finite S-module of type n. The Periodicity Theorem of Hopkins and Smith implies that the Bousfield localization functor associated to T(n)* is independent of choices. Goodwillie's general theory says that to any homotopy functor F from S-modules to S-modules, there is an associated tower under F, {PdF}, such that F → PdF is the universal arrow to a d-excisive functor. Our first main theorem says that PdF → Pd-1F always admits a homotopy section after localization with respect to T(n)* (and so also after localization with respect to Morava K-theory K(n)*). Thus, after periodic localization, polynomial functors split as the product of their homogeneous factors. This theorem follows from our second main theorem which is equivalent to the following: for any finite group G, the Tate spectrum TG (T(n)) is weakly contractible. This strengthens and extends previous theorems of Greenlees-Sadofsky, Hovey-Sadofsky, and Mahowald-Shick. The Periodicity Theorem is used in an essential way in our proof The connection between the two theorems is via a reformulation of a result of McCarthy on dual calculus. [ABSTRACT FROM AUTHOR]

This paper deals with three classes of function of great importance in analysis and its applications. we construct a family of Hölder functions in the closed unit interval having two continuous parameters. Those functions are not a bounded variation for any pair of values of the Hölder constant and exponent. The construction depends on a change of variables given by a Lipschitz function with constant equal to 1. Several questions related to the concepts of genericity, surjectivity and deformability are posed at the end. [ABSTRACT FROM AUTHOR]

In this paper, we investigate the properties of the optimal solutions obtained when we translate the concepts of perfect, proper, and weakly proper solutions from the context of linear complementarity to the framework of linear programming. [ABSTRACT FROM AUTHOR]

Rockafellar has shown that the subdifferentials of convex functions are always cyclically monotone operators. Moreover, maximal cyclically monotone operators are necessarily operators of this type, since one can construct explicitly a convex function, which turns out to be unique up to a constant, whose subdifferential gives back the operator. This result is a cornerstone in convex analysis and relates tightly convexity and monotonicity. In this paper, we establish analogous robust results that relate weak convexity notions to cor- responding notions of weak monotonicity, provided one deals with locally Lipschitz functions and locally bounded operators. In particular, the subdifferentials of locally Lipschitz functions that are directionally hypomonotone [respectively, directionally submonotone] enjoy also an additional cyclic strengthening of this notion and in fact are maximal under this new property. Moreover, every maximal cyclically hypomonotone [respectively, maximal cyclically submonotone] opera- tor is always the Clarke subdifferential of some directionally weakly convex [respectively, directionally approximately convex] locally Lipschitz function, unique up to a constant, which in finite dimentions is a lower C² function [respectively, a lower C¹ function]. [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]

For the problem of minimizing the sum of Euclidean norms (MSN), most existing quadratically convergent algorithms require a strict complementarity assumption. However, this assumption is not satisfied for a number of MSN problems. In this paper, we present a globally and quadratically convergent algorithm for the MSN problem. In particular, the quadratic convergence result is obtained without assuming strict complementarity. Examples without strictly complementary solutions are given to show that our algorithm can indeed achieve quadratic convergence. Preliminary numerical results are reported. [ABSTRACT FROM AUTHOR]

The aim of this paper is to investigate homomorphisms which reserve square-free languages or primitive languages. A characterization of square-free-preserving homomorphisms is presented. We show that every square-free-preserving homomorphism is primitive-preserving. Strongly cube-free-preserving homomorphisms are also studied. [ABSTRACT FROM AUTHOR]

In [2, Theorem 3], Bell and Kappe proved that if d is a derivation of a prime ring R which acts as a homomorphism or an anti-homomorphism on a nonzero right ideal I of R, then d = 0 on R. In the present paper our objective is to extend this result to Lie ideals. The following result is proved: Let R be a 2-torsion free prime ring and U a nonzero Lie ideal of R such that u2 ε U, for all u ε U. If d is a derivation of R which acts as a homomorphism or an anti-homomorphism on U, then either d=0 or U ⫅ Z(R). [ABSTRACT FROM AUTHOR]

This paper gives some characterizations of strongly θ-precontinuous functions. [ABSTRACT FROM AUTHOR]

This paper is concerned with a noncoercive unilateral problem in nonlinear elasticity with stored energy function having fast or slow growth. We prove an existence result for the associated minimization problem by using a recession approach in Orlicz-Sobolev space. Key Words. Nonlinear elasticity; Orlicz-Sobolev space; recession function, property (P). [ABSTRACT FROM AUTHOR]

In a famous and controversial paper, B. H. Slater has argued against the possibility of paraconsistent logics. Our reply is centred on the distinction between two aspects of the meaning of a logical constant *c* in a given logic: its operational meaning, given by the operational rules for *c* in a cut-free sequent calculus for the logic at issue, and its global meaning, specified by the sequents containing *c* which can be proved in the same calculus. Subsequently, we use the same strategy to counter Quine's meaning variance argument against deviant logics. In a nutshell, we claim that genuine rivalry between (similar) logics *L* and *L′* is possible whenever each constant in *L* has the same operational meaning as its counterpart in *L′* although differences in global meaning arise in at least one case. [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 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]