Search

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 introduce and compare four different syntactic methods for generating sequent calculi for the main systems of modal logic: the multiple sequents method, the higher-arity sequents method, the tree-hypersequents method and the display method. More precisely we show how the first three methods can all be translated in the fourth one. This result sheds new light on these generalisations of the sequent calculus and raises issues that will be examined in the last section. [ABSTRACT FROM AUTHOR]

The paper considers issues related to constructing asymptotic formulas for deviations of Riesz sums. The error estimates in the spaces C and L p in terms of the best approximations are obtained. Bibliography: 9 titles. [ABSTRACT FROM AUTHOR]

The paper studies the region of values of the system { f( z1), f( z2), c2},where z j, j=1, 2, are arbitrary fixed points of the disk | z|<1; f ∈ T, and the class T consists of all functions f( z) = z + c2 z2 + ··· regular in the disk | z| < 1 and satisfying the condition Im f( z)·Im z>0 for Im z > 0 for Im z ≠ 0. The region of values of f( z1) in the subclass of functions f ( z) ∈ T with prescribed values c2 and f( z2) is determined. Bibliography: 8 titles. [ABSTRACT FROM AUTHOR]

The paper considers the capacity of a polycondenser and the module of a family of measures associated with the class of curves connecting the polycondenser’s plates. It is proved that these quantities are equal. Also a relation between the polycondenser’s capacity and the module of a family of vector measures associated with the class of functions admissible for the polycondenser’s capacity is established. The results obtained generalize the earlier results by M. Ohtsuka and H. Aikawa. [ABSTRACT FROM AUTHOR]

The paper presents sharp inequalities for the moduli of rational functions under certain constraints on the modulus of the independent variable. These inequalities supplement some results of Govil, Mohapatra, and Dubinin. Bibliography: 6 titles. [ABSTRACT FROM AUTHOR]

This paper proposes a generalization of column generation, reformulating the master problem with fewer variables at the expense of adding more constraints; the sub-problem structure does not change. It shows both analytically and computationally that the reformulation promotes faster convergence to an optimal solution in application to a linear program and to the relaxation of an integer program at each node in the branch-and-bound tree. Further, it shows that this reformulation subsumes and generalizes prior approaches that have been shown to improve the rate of convergence in special cases. [ABSTRACT FROM AUTHOR]

Classical location models fix an objective function and then attempt to find optimal points to this objective. In the last years a flexible approach, the ordered median problem, has been introduced. It handles a wide class of objectives, such as the median, the center and the centdian function. In this paper we present new properties of the ordered median problem such as solvability for the situation of attractive and repulsive locations. We also develop a new solution method that even yields local optimal points for non-convex objective functions. Furthermore, we discuss separability of ordered median problems without repulsion and derive a sufficient criterion. Finally, we introduce a useful model extension, the facility class model, which allows to deal with a wider range of real world problems in the ordered median setting. [ABSTRACT FROM AUTHOR]

A directed graph has a natural Z-module homomorphism from the underlying graph's cycle space to Z where the image of an oriented cycle is the number of forward edges minus the number of backward edges. Such a homomorphism preserves the parity of the length of a cycle and the image of a cycle is bounded by the length of that cycle. Pretzel and Youngs (SIAM J. Discrete Math. 3(4):544-553, 1990) showed that any Z-module homomorphism of a graph's cycle space to Z that satisfies these two properties for all cycles must be such a map induced from an edge direction on the graph. In this paper we will prove a generalization of this theorem and an analogue as well. [ABSTRACT FROM AUTHOR]

Model checking is a useful method to verify automatically the correctness of a system with respect to a desired behavior, by checking whether a mathematical model of the system satisfies a formal specification of this behavior. Many systems of interest are open, in the sense that their behavior depends on the interaction with their environment. The model checking problem for finite-state open systems (called module checking) has been intensively studied in the literature. In this paper, we focus on open pushdown systems and we study the related model-checking problem ( pushdown module checking, for short) with respect to properties expressed by CTL and CTL* formulas. We show that pushdown module checking against CTL (resp., CTL*) is 2Exptime-complete (resp., 3Exptime-complete). Moreover, we prove that for a fixed CTL or CTL* formula, the problem is Exptime-complete. [ABSTRACT FROM AUTHOR]

For a locally compact group G, the measure convolution algebra M( G) carries a natural coproduct. In previous work, we showed that the canonical predual C0( G) of M( G) is the unique predual which makes both the product and the coproduct on M( G) weak*-continuous. Given a discrete semigroup S, the convolution algebra ℓ1( S) also carries a coproduct. In this paper we examine preduals for ℓ1( S) making both the product and the coproduct weak*-continuous. Under certain conditions on S, we show that ℓ1( S) has a unique such predual. Such S include the free semigroup on finitely many generators. In general, however, this need not be the case even for quite simple semigroups and we construct uncountably many such preduals on ℓ1( S) when S is either ℤ+×ℤ or (ℕ,⋅). [ABSTRACT FROM AUTHOR]

We discuss several features of coherent choice functions—where the admissible options in a decision problem are exactly those that maximize expected utility for some probability/utility pair in fixed set S of probability/utility pairs. In this paper we consider, primarily, normal form decision problems under uncertainty—where only the probability component of S is indeterminate and utility for two privileged outcomes is determinate. Coherent choice distinguishes between each pair of sets of probabilities regardless the “shape” or “connectedness” of the sets of probabilities. We axiomatize the theory of choice functions and show these axioms are necessary for coherence. The axioms are sufficient for coherence using a set of probability/almost-state-independent utility pairs. We give sufficient conditions when a choice function satisfying our axioms is represented by a set of probability/state-independent utility pairs with a common utility. [ABSTRACT FROM AUTHOR]

This paper investigates the structure of the quasi-spectrum of divided powers and its behavior under the Taylor homomorphism. General as well as stronger particular results are obtained. In particular, the answer for the Hurwitz series is stated. [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]

In this paper we show for every pair language L ⊆ {0, 1}* x {0, 1}* in NTIME(T) for some non-decreasing function T : ℤ+ → ℤ+ there is a PCPP-verifier such that the following holds. In time poly(|x|, log |y|, log T(|x| + |y|)) it decides the membership of a purported word (x, y) by reading the explicit input x entirely and querying the implicit input y and the auxiliary proof of length T(|x| + |y|) ⋅ poly log T(|x| + |y|) in a constant number of positions. [ABSTRACT FROM AUTHOR]

In this paper the notions of (α, β) - (mX , mY )-continuous and (α, β) - (mX , mY )-semi continuous functions are introduced and some properties of such functions are given. [ABSTRACT FROM AUTHOR]

This paper focuses on a part of the presentation given by the third author at the Shanghai Forum on Industrial and Applied Mathematics (Shanghai 2006). It is related to the existence of a periodic solution of evolution variational inequalities. The approach is based on the method of guiding functions. [ABSTRACT FROM AUTHOR]

It is known that optimal mappings in optimal transportation problems are uniquely determined by corresponding potential functions. In this paper we prove various local properties of potential functions. In particular we obtain the C1, α regularity of potential functions with optimal exponent α, which improves previous regularity results of Loeper. [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]

The aim of this paper is to prove that for an arbitrary set of measure zero there exists a bounded function for which the Fejér means of the Walsh-Fourier series of the function diverge. [ABSTRACT FROM AUTHOR]

An estimate for the Riemann localization principle for trigonometric series is established. At the same time, there is an error in treating this problem in the paper [3] which is now being corrected. [ABSTRACT FROM AUTHOR]

The relationships among the central path in the context of semidefinite programming, generalized proximal-point method and Cauchy trajectory in a Riemannian manifolds is studied in this paper. First, it is proved that the central path associated to a general function is well defined. The convergence and characterization of its limit point is established for functions satisfying a certain continuity property. Also, the generalized proximal-point method is considered and it is proved that the correspondingly generated sequence is contained in the central path. As a consequence, both converge to the same point. Finally, it is proved that the central path coincides with the Cauchy trajectory in a Riemannian manifold. [ABSTRACT FROM AUTHOR]

This paper considers the problems of determining center or focus and isochronous centers for the planar quasi-analytic systems. Two recursive formulas to determine the focal values and period constants are given. The convergence of first integral near the center is proved. Using the general results to quasi-quadratic systems, the problem of the isochronous center of the origin is completely solved. [ABSTRACT FROM AUTHOR]

Logic of proofs $\mathsf{LP}$ , introduced by S. Artemov, originally designed for describing properties of formal proofs, now became a basis for the theory of knowledge with justification (cf. S. Artemov, Evidence-based common knowledge, Technical report TR–2004018, CUNY Ph.D. Program in Computer Science, 2005). So far, in epistemic systems with justification the corresponding “evidence part”, even for multi-agent systems, consisted of a single explicit evidence logic. In this paper we introduce logics describing two interacting explicit evidence systems. We find an appropriate formalization of the intended semantics and prove the completeness of these logics with respect to both symbolic and arithmetical models. Also, we find the forgetful projections for the two-agent justification logics which are extensions of the bimodal logic $\mathsf{S4}^{2}$ . [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]

In this paper, we study Levitin–Polyak type well-posedness for generalized vector variational inequality problems with abstract and functional constraints. Various criteria and characterizations for these types of well-posednesses are given. [ABSTRACT FROM AUTHOR]

This paper presents a set of complete solutions and optimality conditions for a nonconvex quadratic-exponential optimization problem. By using the canonical duality theory developed by the first author, the nonconvex primal problem in n-dimensional space can be converted into an one-dimensional canonical dual problem with zero duality gap, which can be solved easily to obtain all dual solutions. Each dual solution leads to a primal solution. Both global and local extremality conditions of these primal solutions can be identified by the triality theory associated with the canonical duality theory. Several examples are illustrated. [ABSTRACT FROM AUTHOR]

In this paper, we introduce and study a relaxed extragradient method for finding solutions of a general system of variational inequalities with inverse-strongly monotone mappings in a real Hilbert space. First, this system of variational inequalities is proven to be equivalent to a fixed point problem of nonexpansive mapping. Second, by using the demi-closedness principle for nonexpansive mappings, we prove that under quite mild conditions the iterative sequence defined by the relaxed extragradient method converges strongly to a solution of this system of variational inequalities. In addition, utilizing this result, we provide some applications of the considered problem not just giving a pure extension of existing mathematical problems. [ABSTRACT FROM AUTHOR]

In this paper we analyze cooperative games whose characteristic function takes values in a partially ordered linear space. Thus, the classical solution concepts in cooperative game theory have to be revisited and redefined: the core concept, Shapley–Bondareva theorem and the Shapley value are extended for this class of games. The classes of standard, vector-valued and stochastic cooperative games among others are particular cases of this general theory. [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]

Abstract  While integrating components into systems, we will be confronted with problems concerned with the interoperability of components due to the interaction mismatches at multiple levels, such as interaction behaviors between components and features imposed by architectural styles. In this paper, we studied the interoperability of components and explored the approach to supporting high interoperability of components involved in mismatching interactions. First, we formalized components involved in different architectural styles in the pi-calculus. Next, we studied the formal foundation of the interoperability of components for reasoning about the conditions under which two heterogeneous components are possible to interoperate and interconnect together properly. Then, we described a wrapper-based solution for integrating components into systems that impose mismatching assumptions about usage of the components. In the end, we presented an agent-based implementation for the solution, in which agents are used to wrap components and can automatically resolve multiple levels of interaction mismatches between components. We also gave a simple example to illustrate our approach. [ABSTRACT FROM AUTHOR]

The paper studies the structure of k-vertex cutsets in a k-connected graph. As an illustration of the method proposed, the well-known case of a biconnected graph is considered. Bibliography: 8 titles. [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]

Abstract  The χ calculus is a model of concurrent and mobile systems. It emphasizes that communications are information exchanges. In the paper, two constructions are incorporated into the framework of the chi calculus, which are asymmetric communication and mismatch condition widely used in applications. Since the barbed bisimilarity has proved its generality and gained its popularity as an effective approach to generating a reasonable observational equivalence, we study both the operational and algebraic properties of the barbed bisimilarity in this enriched calculus. The investigation supports an improved understanding of the bisimulation behaviors of the model. It also gives a general picture of how the two constructions affect the observational theory. [ABSTRACT FROM AUTHOR]

In the present paper, a problem of Ioana Mihaila is negatively answered on the invertibility of composition operators on Riemann surfaces, and it is proved that the composition operator C p is Fredholm if and only if it is invertible if and only if p is invertible for some special cases. In addition, the Toeplitz operators on $$ \Lambda _{2,a}^1 (M) $$ for Riemann surface M are defined and some properties of these operators are discussed. [ABSTRACT FROM AUTHOR]

In this paper, we investigate the relation between the rate of convergence for the derivatives of the combinations of Baskakov operators and the smoothness for the derivatives of the functions approximated. We give some direct and inverse results on pointwise simultaneous approximation by the combinations of Baskakov operators. We also give a new equivalent result on pointwise approximation by these operators. [ABSTRACT FROM AUTHOR]

In this paper, a cryptogroup is constructed by a band and a family of groups and homomorphisms satisfying some conditions. [ABSTRACT FROM AUTHOR]

The paper produces new versions of the minimax theorem based on original conditions. Moreover, we investigate not only the sufficiency, but also the necessity of such conditions. The proofs are very simple and preclude any topological technique. [ABSTRACT FROM AUTHOR]

In this paper, we introduce the concept of feasible set for an equilibrium problem with a convex cone and generalize the notion of a Z-function for bifunctions. Under suitable assumptions, we derive some equivalence results of equilibrium problems, least element problems, and nonlinear programming problems. The results presented extend some results of [Riddell, R.C.: Equivalence of nonlinear complementarity problems and least element problems in Banach lattices. Math. Oper. Res. 6, 462—474 (1981)] to equilibrium problems. [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 give a structure theorem for cryptogroups by means of bands and homomorphisms between completely simple semigroups. [ABSTRACT FROM AUTHOR]

To verify the universal validity of the “two-sided” monotonicity condition introduced in [4], we will apply it to include more classical examples. The present paper selects the L p convergence case for this purpose. Furthermore, Theorem 3 shows that our improvements are not trivial. [ABSTRACT FROM AUTHOR]

In the paper the ϕ-homogeneity equation almost everywhere is studied. Let and H be groups with zero. Assume that (X,G) is a G-space and (Y,H) is an H-space. We prove, under some assumption on (Y,H), that if the functions ϕ : G → H and F : X → Y satisfy the equation of ϕ-homogeneity F(αx) = ϕ (α)F(x) almost everywhere in G× X then either F is a zero function or there exists a homomorphism ... : G → H such that ϕ almost ... everywhere in G and there exists a function F : → Y such that ... (αx) = ...(α)... (x) for α η G\{0}, x ϵ X, and F = ... almost everywhere in X. [ABSTRACT FROM AUTHOR]

The article highlights various publications related to mathematical analysis. In a paper titled "Making the Epsilons Matter," by Stephen Abbott, the author discusses the use of an introductory real analysis to challenge and sharpen intuition. The exposition of the notion and the basic properties of convex functions are described in an article in a 1999 issue of "Nastava Matematike."

This paper presents a variational inequality (VI) approach to the problem of minimizing a sum of p-norms. First the original problem is reformulated as an equivalent linear VI. Then an improved extra-gradient method is presented to solve the linear VI. Applications to the problem of p-norm Steiner Minimum Trees (SMT) shows that the proposed method is effective. Comparison with the general extra-gradient method is also provided to show the improvements of the new method. [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]