Mathematics

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Recently, Kórus [7] studied the Λ 2-strong convergence of numerical sequences. By using the idea of this paper, we introduce [ Λ 2, F, u, p] -strongly convergent sequence spaces defined by a sequence of modulus functions. We also make an effort to study some inclusion relations, topological and geometric properties of these spaces. Some characterizations for strong convergent sequences are given. Finally, we study statistical convergence over these spaces and problems related to Fourier series. © 2016, Akadémiai Kiadó, Budapest, Hungary.

World University root node

(SoNS) School of Natural Sciences

Acta Mathematica Hungarica

Applications of strongly convergent sequences to Fourier series by means of modulus functions

The aim of this paper is twofold. Firstly, to define a solution concept of Pareto-optimality for a multi-objective flexible linear programming (MOFLP) problem (or multi-objective fuzzy linear programming problem) and design a method to extract a Pareto-optimal solution of MOFLP problem from the set of optimal solutions of equivalent optimization problem formulated by Dubey and Mehra (2013). Secondly, to extend this study to multi-objective linear programming problem involving hard and flexible constraints with interval uncertainty. A flexible constraint with interval uncertainty generalizes a flexible constraint by allowing preferences to be expressed in the form of intervals. An optimistic-pessimistic approach is proposed to solve multi-objective flexible linear programming with interval uncertainty (MOFLPIU) using an interval-valued fuzzy set representation and the Hurwicz optimism-pessimism criterion. © 2016 - IOS Press and the authors. All rights reserved.

Journal of Intelligent and Fuzzy Systems

Pareto-optimal solutions for multi-objective flexible linear programming

Physics of Life Reviews

Predicting spatial dynamics of infectious disease: Causes and consequences: Comment on “Pattern transitions in spatial epidemics: Mechanisms and emergent properties” by Gui-Quan Sun et al.

In this paper, we explore various matrix-theoretic aspects of the hidden Z class and demonstrate how the concept of principal pivot transform can be effectively used to extend many existing results. In fact, we revisit various results obtained for hidden Z class by Mangasarian, Cottle and Pang in context of solving linear complementarity problems as linear programs. We identify hidden Z-matrices of special category and discuss the number of solutions of the associated linear complementarity problems. We also present game theoretic interpretation of various results related to hidden Z class and obtain proofs following the game theoretic approach of Raghavan for a subclass of Z-matrices. © 2016 Published by Elsevier Inc.

Linear Algebra and Its Applications

On hidden Z-matrices and the linear complementarity problem

In a recent paper, one of the authors - along with co-authors - extended the famous theorem of Beurling to the context of subspaces that are invariant under the class of subalgebras of H∞ of the form IH∞, where I is the inner function z2. In recent times, several researchers have replaced z2 by an arbitrary inner function I and this has proved important and fruitful in applications such as to interpolation problems of the Pick-Nevanlinna type. Keeping in mind the great deal of interest in such problems, in this paper, we provide analogues of the above mentioned IH∞ related extension of Beurling’s theorem in the setting of the Banach space BM OA, in the context of uniform algebras, on compact abelian groups with ordered duals and the Lebesgue space on the real line. We also provide a significant simplification of the proof of Beurling’s theorem in the setting of uniform algebras and a new proof of Helson’s generalization of Beurling’s theorem in the context of compact abelian groups with ordered duals. © 2016, University at Albany. All rights reserved.

New York Journal of Mathematics

Invariance under bounded analytic functions: Generalizing shifts

Graph theoretic network approach has been used to model the potential connectivity of the natural areas in Darjeeling Himalayas which provide connectivity to the invasive species Maling bamboo (Yushania maling). Centrality indices are a tool for quantifying the intuitive notion of relative importance of the elements of a graph. The probability of connectivity (PC) index which takes into account the impact of functional connectivity among the patches like seed dispersal potential was used to identify the natural patches which can act as stepping stone for the spread of the invasive species. The potential niche map of Maling bamboo modelled using species niche model, MaxEnt have been used as the potential areas of its spread from the regions of its current infestations. An open source software (Confer) has been used to model the various graph indices in the spatial domain. Using areas weighted nodes (forest patches) the extent of connectivity among the various patches in the Darjeeling Himalayas have been computed to identify the critical patches responsible for the spread of Maling bamboo. It has been observed that 3 critical forest patches in the Darjeeling Himalaya Singalilla NP in the west, Senchal WLS in the central region and Neora Valley NP are the key vertices for the spread of Maling bamboo. © 2016 Elsevier B.V.

Ecological Modelling

Modelling critical patches of connectivity for invasive Maling bamboo (Yushania maling) in Darjeeling Himalayas using graph theoretic approach

Suppose M be the projective limit of weak symplectic Banach manifolds {(Mi, øij)}i, j en, where Mi are modeled over reflexive Banach space and Hx is compatible with the projective system (defined in the article). We associate to each point x M, a Fréchet space Hx. We prove that if Hx are locally identical, then with certain smoothness and boundedness condition, there exists a Darboux chart for the weak symplectic structure. © 2015 World Scientific Publishing Company.

International Journal of Geometric Methods in Modern Physics

Darboux chart on projective limit of weak symplectic Banach manifold

We propose a model describing the synergetic feedback between word-of-mouth (WoM) and epidemic dynamics controlled by voluntary vaccination. The key feature consists in combining a game-theoretic model for the spread of WoM and a compartmental model describing VSIR disease dynamics in the presence of a program of voluntary vaccination. We evaluate and compare two scenarios for determinants of behavior, depending on what WoM disseminates: (1) vaccine advertising, which may occur whether or not an epidemic is ongoing and (2) epidemic status, notably disease prevalence. Understanding the synergy between the two strategies could be particularly important for designing voluntary vaccination campaigns. We find that, in the initial phase of an epidemic, vaccination uptake is determined more by vaccine advertising than the epidemic status. As the epidemic progresses, epidemic status becomes increasingly important for vaccination uptake, considerably accelerating vaccination uptake toward a stable vaccination coverage. © 2015 Elsevier Inc.

Fulltext

Mathematical Biosciences

Role of word-of-mouth for programs of voluntary vaccination: A game-theoretic approach

Let F and G be two bounded operators on two Hilbert spaces. Let their numerical radii be no greater than one. This note investigates when there is a Γ-contraction (S, P) such that F is the fundamental operator of (S, P) and G is the fundamental operator of (S*, P*). Theorem 1 puts a necessary condition on F and G for them to be the fundamental operators of (S, P) and (S*, P*) respectively. Theorem 2 shows that this necessary condition is also sufficient provided we restrict our attention to a certain special case. The general case is investigated in Theorem 3. Some of the results obtained for Γ-contractions are then applied to tetrablock contractions to figure out when two pairs (F1, F2) and (G1, G2) acting on two Hilbert spaces can be fundamental operators of a tetrablock contraction (A, B, P) and its adjoint (A*, B*, P*) respectively. This is the content of Theorem 3. © 2015 Elsevier Inc.

Journal of Mathematical Analysis and Applications

Admissible fundamental operators

In this paper, we study the multi-objective flexible linear programming (MOFLP) problems (or fuzzy multi-objective linear programming problems) in the heterogeneous bipolar framework. Bipolarity allows us to distinguish between the negative and the positive preferences. Negative preferences denote what is unacceptable while positive preferences are less restrictive and express what is desirable. This viewpoint enables us to handle fuzzy sets representing constraints and objective functions separately and combine them in distinct ways. In this paper, a solution concept of Pareto-optimality for MOFLP problems is defined and an approach is proposed to single out such a solution for MOFLP with highest possible degree of feasibility. © 2014 Taylor & Francis.