A fractional order HIV-TB coinfection model with nonsingular Mittag-Leffler Law

The biological models for the study of human immunodeficiency virus (HIV) and its advanced stage acquired immune deficiency syndrome (AIDS) have been widely studied in last two decades. HIV virus can be transmitted by different means including blood, semen, preseminal fluid, rectal fluid, breast milk, and many more. Therefore, initiating HIV treatment with the TB treatment development has some advantages including less HIV-related losses and an inferior risk of HIV spread also having difficulties including incidence of immune reconstitution inflammatory syndrome (IRIS) because of a large pill encumbrance. It has been analyzed that patients with HIV have more weaker immune system and are susceptible to infections, for example, tuberculosis (TB). Keeping the importance of the HIV models, we are interested to consider an analysis of HIV-TB coinfected model in the Atangana-Baleanu fractional differential form. The model is studied for the existence, uniqueness of solution, Hyers-Ulam (HU) stability and numerical simulations with assumption of specific parameters.     

On a resolvent approach for perturbed semigroups and application to $$L^1$$-neutron transport theory

We give new sufficient and practical conditions in terms of the generators ensuring the stability of the critical or the essential type of a perturbed \(C_0\)-semigroup in general Banach spaces. We apply our theoretical results in order to investigate the control and in particular the time asymptotic behavior of solutions to a broad class of transport equations in \(L^1\)-spaces and higher dimension. Our results improve, complete and enrich several earlier works.     

Decomposition of group rings and the converse of Schur’s lemma

In this work, we give necessary and su?cient conditions for a group ring (of finite group) to satisfy the converse of Schur’s lemma for group rings of finite groups. Rings considered here are commutative or noncommutative perfect. Some cases of twisted group rings are studied. Also we introduce the notion of semi-CSL ring.     

Computationally efficient modular nonlinear filter stabilization for high Reynolds number flows

The nonlinear filter based stabilization proposed in Layton et al. (J. Math. Fluid Mech. 14(2), 325–354 2012) allows to incorporate an eddy viscosity model into an existing laminar flow codes in a modular way. However, the proposed nonlinear filtering step requires the assembly of the associated matrix at each time step and solving a linear system with an indefinte matrix. We propose computationally efficient version of the filtering step that only requires the assembly once, and the solution of two symmetric, positive definite systems at each time step. We also test a new indicator function based on the entropy viscosity model of Guermond (Int. J. Numer. Meth. Fluids. 57(9), 1153–1170 2008); Guermond et al. (J. Sci. Comput. 49(1), 35–50 2011).     

Existence theorems and Hyers-Ulam stability for a class of Hybrid fractional differential equations with $p$-Laplacian operator

In this paper, we prove necessary conditions for existence and uniqueness of solution (EUS) as well Hyers-Ulam stability for a class of hybrid fractional differential equations (HFDEs) with $p$-Laplacian operator. For these aims, we take help from topological degree theory and Leray Schauder-type fixed point theorem. An example is provided to illustrate the results.     

An optimization-based heuristic for the robotic cell problem

This study investigates an optimization-based heuristic for the robotic cell problem. This problem arises in automated cells and is a complex flow shop problem with a single transportation robot and a blocking constraint. We propose an approximate decomposition algorithm. The proposed approach breaks the problem into two scheduling problems that are solved sequentially: a flow shop problem with additional constraints (blocking and transportation times) and a single machine problem with precedence constraints, time lags, and setup times. For each of these problems, we propose an exact branch-and-bound algorithm. Also, we describe a genetic algorithm that includes, as a mutation operator, a local search procedure. We report the results of a computational study that provides evidence that the proposed optimization-based approach delivers high-quality solutions and consistently outperforms the genetic algorithm. However, the genetic algorithm delivers reasonably good solutions while requiring significantly shorter CPU times.     

Synthesis and Photophysical Properties of Alkoxysilyl Derivatives of Dibenzoylmethanatoboron Difluoride

Alkoxysilyl derivatives of dibenzoylmethanatoboron difluoride (DBMBF₂) are synthesized by the hydrosilylation reaction of the corresponding O‐allyl derivatives of DBMBF₂ with triethoxysilane. The photophysical properties of the synthesized O‐allyl and alkoxysilyl derivatives are investigated. It is found that the absorption and fluorescence spectra of the DBMBF₂ derivatives essentially depend on the position of the O‐allyl or O‐propyl alkoxysilyl substituent. The highest fluorescence quantum yield is obtained for the para‐position, whereas the substitution at the meta‐position gives the largest bathochromic shift in the fluorescence spectrum. Density functional theory calculations of the structures and time‐dependent density functional theory calculations of the gas‐phase excitation and emission energies of alkoxysilyl derivatives are performed at the PBE0/SVP level of theory. Some spectral features of para‐, ortho‐, and meta‐substituted derivatives can be adequately explained by the overlapping of two absorption bands.     

Assessment of health risk associated with natural gamma dose rate levels and isodose mapping of Jordan

ABSTRACT

As a pioneering study in Jordan, an extensive measurement for external gamma dose rate (GDR) was conducted. A portable gamma radiation detector was used to perform these measurements at 1?m above the soil surface. A geographical positioning system Garmin was used to record a total of 823 measured points. The GDRs’ measurement ranged from 35 to 470?nGy?h^?1 giving a mean value of 90?nGy?h^?1, which was found to be one and half times higher than the world average of 59?nGy?h^?1. The lowest mean GDR 72?nGy?h^?1 was found in the Albalqa governate, while the highest mean GDR 131?nGy?h^?1 was found to be for the Alkarak governate. The mean annual effective dose was found to be 0.551?mSv, which is higher than the world average value of 0.48?mSv. This is a pivotal study evaluating the risks associated with GDR levels in Jordan that were the relative excess lifetime cancer risk, the mean collective effective dose, the mean weighted GDR and the mean lifetime dose that are 2.24?×?10^?3, 5538manSv?y^?1, 0.531?mSv and 39?mSv, respectively. The cosmic rays mean GDR was determined to be 20?nGy?h^?1. This study focuses on constructing GDRs’ baseline data in Jordan, which will be used to determine the possible change in the natural radiation due to other human activities in the future. ArcGIS software was employed to generate an isodose map to characterise exposure rates caused by GDR in Jordan.     

Computation of the random arrival rule for bankruptcy problems

Bankruptcy problems are a fundamental class of fair division problems in microeconomics. Among the various solution concepts proposed for the problem, the random arrival rule is one of the most prominent. In this paper, we conduct a computational analysis of the rule. It is shown that the allocation returned by the rule is #P-complete to compute. The general complexity result is complemented by a pseudo-polynomial-time dynamic programming algorithm for the random arrival rule.