Approximation by an iterative method of a low‐Mach model with temperature dependent viscosity

In this work, we prove the existence and the uniqueness of the strong solution of a low‐Mach model, for which the dynamic viscosity of the fluid is a given function of its temperature. The method is based on the convergence study of a sequence towards the solution, for which the rates are also given. The originality of the approach is to consider the system in terms of the temperature and the velocity, leading to a nonlinear temperature equation and the development of some specific tools and results.     

A fast iterative method to find the matrix geometric mean of two HPD matrices

The purpose of this research is to present a novel scheme based on a quick iterative scheme for calculating the matrix geometric mean of two Hermitian positive definite (HPD) matrices. To do this, an iterative scheme with global convergence is constructed for the sign function using a novel three‐step root‐solver. It is proved that the new scheme is convergent and shown to have global convergence behavior for this target, when square matrices having no pure imaginary eigenvalues. Next, the constructed scheme is used and extended through a well‐known identity for the calculation of the matrix geometric mean of two HPD matrices. Ultimately, several experiments are collected to show its usefulness.     

第二类端点奇异Fredholm积分方程的分数阶退化核方法

本文针对第二类端点奇异Fredholm积分方程构造基于分数阶Taylor展开的退化核方法，设计了两种计算格式，一是在全区间上使用分数阶Taylor展开式近似核函数，二是在包含奇点的小区间上采用分数阶插值，在剩余区间上采用分段二次多项式插值逼近核函数.讨论了两种退化核方法收敛的条件，并给出了混合插值法的收敛阶估计.数值算例表明对于非光滑核函数分数阶退化核方法有着良好的计算效果，且混合二次插值法比全区间上的分数阶退化核方法有着更广泛的适用范围.     

Cooling of Al-Cu-Fe-Cr-Ni high entropy alloy with different size

Cooling rate is critical in synthesizing nanoparticles (NPs), which determines the microstructure and the corresponding mechanical, thermal and electrical properties. This research, as the most initiative one, studies microstructure formation of three different sized high entropy alloy (HEA) NPs under three different cooling rates, employing molecular dynamics (MD). Through analysis of potential energy, “common neighbor analysis”, radial distribution function, and also the mean square displacement, it is found that phase transition temperature is independent of HEA NP size, and as cooling rate decrease, more amorphous atoms transform to fcc and hcp orders, which can alternate the mechanical and thermodynamic properties of the final structure. The Cr atoms are found to aggregate into one cluster inside the NP and also try to migrate to the surface of the HEA NP, due to the large diffusivity. This research provides new insights in the size dependency of the nanoparticles, which may motivate more applications in which the strong size dependency is not desirable.     

How vector feeding preference through an infectious host relates to the seasonal transmission rates in a mathematical vector‐host model

Vector‐borne diseases, such as leishmaniasis, dengue, malaria, and yellow fever, transmitted by microparasites show periodic fluctuations in their prevalence. The novelty of this research is to assess the relationship between the vector feeding preference for an infectious host and the annual seasonal transmission through a vector‐host mathematical model. For the first time, numerical simulations illustrate that by increasing the vector feeding preference value in the transmission dynamics, periodic fluctuations accentuate and the endemic equilibrium average increases in vector and host populations. Moreover, increasing the vector feeding preference value, the amplitude strengthens for the infectious host and vector populations. This periodic behavior shows a similar pattern with the Peruvian incidence data from 2000 to 2016 for Andean cutaneous leishmaniasis provided by the Ministry of Health of Peru (MINSA). In addition, using the Floquet theory, the time average method and the linear operator method provides for the first time that the basic reproduction number for a nonautonomous system depends explicitly on the vector feeding preference for the infectious host. The nonautonomous model system shows that is a threshold parameter for the local stability of the disease‐free periodic solution. Therefore, the vector feeding preference is an important factor that should be considered and attended to for future research. Public and veterinary health in Peru and other countries should consider the vector feeding preference for specific host to vector control.     

Complete Moment Convergence for the Dependent Linear Processes with Random Coefficients

In this paper, we investigate the complete moment convergence for dependent linear processes with random coefficients to form     

Phase segregation of metastable quenched liquid mixtures and the effect of the quenching rate

The effect of the quenching rate on the phase separation of partially miscible liquid mixtures is studied, showing that it may influence the growth rate of single-phase domains. In particular, the phase separation of metastable binary mixtures in the presence of strong emulsifiers appears to be heavily retarded. These effects constitute an important limitation to the phase transition extraction process introduced by the authors in previous works, which is based on the fact that phase separation of unstable mixtures is rapid, even in the presence of surface active compounds.     

Asymptotic analysis for multi-objective sequential stochastic assignment problems

ABSTRACT

We provide an asymptotic analysis of multi-objective sequential stochastic assignment problems (MOSSAP). In MOSSAP, a fixed number of tasks arrive sequentially, with an n-dimensional value vector revealed upon arrival. Each task is assigned to one of a group of known workers immediately upon arrival, with the reward given by an n-dimensional product-form vector. The objective is to maximize each component of the expected reward vector. We provide expressions for the asymptotic expected reward per task for each component of the reward vector and compare the convergence rates for three classes of Pareto optimal policies.