Mathematics

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Shiv Nadar University

Quadratic programming problems involving distance matrix (D) that arises in trees are considered in the literature by Dankelmann (Discrete Math 312:12–20, 2012), Bapat and Neogy (Ann Oper Res 243:365–373, 2016). In this paper, we consider the question of solving the quadratic programming problem of finding maximum of xTRx subject to x being a nonnegative vector with sum 1 and show that for the class of simple graphs with resistance distance matrix (R) which are not necessarily a tree, this problem can be reformulated as a strictly convex quadratic programming problem. An application to symmetric bimatrix game is also presented. © 2018, Springer Science+Business Media, LLC, part of Springer Nature.

(SoNS) School of Natural Sciences

World University root node

Annals of Operations Research

On solving a non-convex quadratic programming problem involving resistance distances in graphs

Antibiotic drug resistance is a global crisis today. The deleterious impact of this crisis is acting relatively in higher degrees in poor nations compared to developed countries in the world. Low economy and irrational perspective on medical practice are accelerating the development of drug resistance, leading the population in more economically challenged situations. This article discusses current situations, expresses opinions and views on the self-reinforcement process in the emergence and development of drug resistance. © Indian Academy of Sciences.

Current Science

Emergence and burden of antibiotic drug resistance: An endogenous cycle

Public perceptions and sentiments play a crucial role in the success of vaccine uptake in the community. While vaccines have proven to be the best preventive method to combat the flu, the attitude and knowledge about vaccines are a major hindrance to higher uptake in most of the countries. The yearly coverage, especially in the vulnerable groups in the population, often remains below the herd immunity level despite the Flu Awareness Campaign organized by WHO every year worldwide. This brings immense challenges to the nation’s public health protection agency for strategic decision-making in controlling the flu outbreak every year. To understand the impact of public perceptions and vaccination decisions while designing optimal immunization policy, we model the individual decision-making as a two-strategy pairwise contest game, where pay-off is considered as a function of public health effort for the campaign. We use Pontryagin’s maximum principle to identify the best possible strategy for public health to implement vaccination and reduce infection at a minimum cost. Our optimal analysis shows that the cost of public health initiatives is qualitatively and quantitatively different under different public perceptions and attitudes towards vaccinations. When individual risk perception evolves with vaccine uptake or disease induced death, our model demonstrates a feed-forward mechanism in the dynamics of vaccination and exhibits an increase in vaccine uptake. Using numerical simulation, we also observe that the optimal cost can be minimized by putting the effort in the beginning and later part of the outbreak rather than during the peak. It confers that public health efforts towards disseminating disease severity or actual vaccination risk might accelerate the vaccination coverage and mitigate the infection faster. © 2020, Society for Mathematical Biology.

Fulltext

Bulletin of Mathematical Biology

Optimal Management of Public Perceptions During A Flu Outbreak: A Game-Theoretic Perspective

The objective of this paper is to introduce and study some sequence spaces over the geometric complex numbers by means of Museilak–Orlicz function. We make an effort to study some topological properties and inclusion relations between these sequence spaces. Moreover, by using the concept of non-Newtonian calculus we prove the completeness of the spaces. © 2018, African Mathematical Union and Springer-Verlag GmbH Deutschland, ein Teil von Springer Nature.

Afrika Matematika

Applications of non-Newtonian calculus for classical spaces and Orlicz functions

In the present paper we study the applications of generalized difference matrices and Orlicz function to generate some spaces of almost convergent sequences. We make an effort to study some algebraic and topological properties of these sequence spaces. Some inclusion relations between these spaces are establish. Furthermore, we study matrix transformations and compute β-, γ-duals of these spaces. © 2019 Kudilp Raj and Charu Sharma.

Proyecciones

A relation of banach limit and difference matrix to generate some orlicz sequence spaces

The aim of this paper is to study some lacunary sequence spaces originated with infinite matrices and a sequence of Orlicz functions. We make an effort to study some algebraic and topological properties of these sequence spaces. Some inclusion relations are also establish between these spaces. Furthermore, we compute the beta-, gamma-duals and matrix transformations of these spaces. © 2019 University of Houston

Houston Journal of Mathematics

Matrix transformations on lacunary orlicz sequence spaces and their toeplitz duals

A nonnegative matrix A is primitive if for some positive integer m all entries in Am are positive. The smallest such m is called the exponent of A and written exp(A). For the class of primitive companion matrices X, we find exp(A) for certain A ∈ X. We find certain values of m for which there is an n×n primitive companion matrix (for given n) with exponent m. We also propose open problems for further research. © 2019 Rocky Mountain Mathematics Consortium.

Rocky Mountain Journal of Mathematics

Exponents of primitive companion matrices

A cyclotomic polynomial φk(x) is an essential cyclotomic factor of f (x) ∈ Z[x] if φk(x) ∥ f (x) and every prime divisor of k is less than or equal to the number of terms of f: We show that if a monic polynomial with coefficients from {-1, 0, 1} has a cyclotomic factor, then it has an essential cyclotomic factor. We use this result to prove a conjecture posed by Mercer ['Newman polynomials, reducibility, and roots on the unit circle', Integers 12(4) (2012), 503-519]. © 2019 Australian Mathematical Publishing Association Inc.

Bulletin of the Australian Mathematical Society

Cyclotomic factors of borwein polynomials

Communicable diseases are leading cause of child mortality in developing and under-developed countries. Public health ministries in states and country allocate a considerable amount of budget every year for vaccination campaigns to control infections. Even third-party agencies such as Gates Foundation, UNDP, GAVI, World Bank, WHO also allocate huge funds to under-developed and developing countries for vaccination programs and disease eliminations. However, economic constraints and current disease prevalence are not enough driving factors for optimal decisions in budget allocations for vaccinations and controlling the disease. In a population under voluntary vaccination campaign, high vaccine coverage cannot be taken for granted, as individuals’ free-riding behaviour plays a significant role in achieving the herd immunity level coverage. Individual-level vaccine exemptions and ignoring this important component by the policymakers are key determinants for failure of disease elimination program these days in many under-developed and developing countries. We integrate evolutionary game theory and compartmental model of disease transmission to analyze how individual vaccination choice influence the budget allocations and vice-versa. Our model illustrates that individuals’ perceived risk plays an important role in optimal budget allocations to minimize infections. Analyses of our model indicate that the optimal distribution of third-party funds may be very different than usual, especially in multiple populations with contrasting demographic and economic profiles. These findings are certainly useful to public health policymakers and may help to quantify certain parameters in budget allocations to control vaccine-preventable diseases. © 2019 Elsevier Ltd

Journal of Theoretical Biology

Game dynamic model of optimal budget allocation under individual vaccination choice

In this article, we compile the work done by various mathematicians on the topic of the fixed divisor of a polynomial. This article explains most of the results concisely and is intended to be an exhaustive survey. We present the results on fixed divisors in various algebraic settings as well as the applications of fixed divisors to various algebraic and number theoretic problems. The work is presented in an orderly fashion so as to start from the simplest case of Z, progressively leading up to the case of Dedekind domains. We also ask a few open questions according to their context, which may give impetus to the reader to work further in this direction. We describe various bounds for fixed divisors as well as the connection of fixed divisors with different notions in the ring of integervalued polynomials. Finally, we suggest how the generalization of the ring of integer-valued polynomials in the case of the ring of n × n matrices over Z (or a Dedekind domain) could lead to the generalization of fixed divisors in that setting. © 2019, Institut Camille Jordan. All rights reserved.