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Mathematics, Volume 6, Issue 9

September 2018 - 31 articles

Cover Story: In this article, we study the asymptotic stability of the nontrivial endemic equilibrium of an age-structured susceptible-infective-recovered epidemic model by reducing the model into a system of ordinary differential equations. We show that the endemic equilibrium uniquely exists if the basic reproduction number is greater than the unity. Furthermore, we numerically show that the Routh-Hurwitz criterion is satisfied and, thus, the endemic equilibrium is asymptotically stable for some epidemiologically realistic parameters. View this paper.
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Articles (31)

  • Article
  • Open Access
6 Citations
5,217 Views
14 Pages

9 September 2018

It is well-documented that individuals care about how others around them are doing. This paper studies a production economy in which consumers provide labor supply to a representative firm to earn income for consumption, and their utility depends on...

  • Article
  • Open Access
1 Citations
3,128 Views
17 Pages

Resolving Decompositions for Polynomial Modules

  • Mario Albert and
  • Werner M. Seiler

7 September 2018

We introduce the novel concept of a resolving decomposition of a polynomial module as a combinatorial structure that allows for the effective construction of free resolutions. It provides a unifying framework for recent results of the authors for dif...

  • Article
  • Open Access
9 Citations
4,395 Views
14 Pages

6 September 2018

Allocation of the power losses to distributed generators and consumers has been a challenging concern for decades in restructured power systems. This paper proposes a promising approach for loss allocation in power distribution systems based on a coo...

  • Article
  • Open Access
21 Citations
4,414 Views
26 Pages

Fractional Queues with Catastrophes and Their Transient Behaviour

  • Giacomo Ascione,
  • Nikolai Leonenko and
  • Enrica Pirozzi

6 September 2018

Starting from the definition of fractional M/M/1 queue given in the reference by Cahoy et al. in 2015 and M/M/1 queue with catastrophes given in the reference by Di Crescenzo et al. in 2003, we define and study a fractional M/M/1 queue with catastrop...

  • Article
  • Open Access
7 Citations
3,268 Views
7 Pages

On Magnifying Elements in E-Preserving Partial Transformation Semigroups

  • Thananya Kaewnoi,
  • Montakarn Petapirak and
  • Ronnason Chinram

6 September 2018

Let S be a semigroup. An element a of S is called a right [left] magnifying element if there exists a proper subset M of S satisfying S = M a [ S = a M ] . Let E be an equivalence relation on a nonempty set X. In this paper, we conside...

  • Article
  • Open Access
8 Citations
3,889 Views
18 Pages

4 September 2018

Short-term animal movements play an integral role in the transmission and control of zoonotic infections such as brucellosis, in communal farming zones where animal movements are highly uncontrolled. Such movements need to be incorporated in models t...

  • Article
  • Open Access
16 Citations
4,810 Views
14 Pages

4 September 2018

In relativistic quantum field theory with local interactions, charge is locally conserved. This implies local conservation of probability for the Dirac and Klein–Gordon wavefunctions, as special cases; and in turn for non-relativistic quantum f...

  • Article
  • Open Access
1 Citations
6,738 Views
9 Pages

31 August 2018

The aim of this paper is to show the mathematical basis for a precise treatment of double-entry bookkeeping, which was first developed in the nineteenth century by Sir William Rowan Hamilton. This is done by using basic notions of matrix algebra foun...

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Mathematics - ISSN 2227-7390