Multifunctional material Bi4Ge3O12: thermodynamic properties

Thermodynamic characteristics of a single crystal of bismuth orthogermanate (Bi₄Ge₃O₁₂), which are necessary to improve device portfolio, have been studied. It has been shown that bismuth orthogermanate is thermodynamically stable against decomposition into binary oxides at 50 °C, which gives us grounds to consider this compound promising for various applications.     

Hermite‐Hadamard‐type inequalities for interval‐valued coordinated convex functions involving generalized fractional integrals

In this paper, we define interval‐valued left‐sided and right‐sided generalized fractional double integrals. We establish inequalities of Hermite‐Hadamard like for coordinated interval‐valued convex functions by applying our newly defined integrals.     

Addendum to “On the Riesz potential operator of variable order from variable exponent Morrey space to variable exponent Campanato space”, Math Meth Appl Sci. 2020; 1–8

In the paper mentioned in the title, it is proved the boundedness of the Riesz potential operator of variable order α(x) from variable exponent Morrey space to variable exponent Campanato space, under certain assumptions on the variable exponents p(x) and λ(x) of the Morrey space. Assumptions on the exponents were different depending on whether $\frac{\alpha (x)p(x)?n+\lambda (x)}{p(x)}$ takes or not the critical values 0 or 1. In this note, we improve those results by unifying all the cases and covering the whole range $0?\frac{\alpha (x)p(x)?n+\lambda (x)}{p(x)}?1$. We also provide a correction to some minor technicality in the proof of Theorem 2 in the aforementioned paper.     

Generalized Jacobi spectral Galerkin method for fractional pantograph differential equation

This work is concerned with the extension of the Jacobi spectral Galerkin method to a class of nonlinear fractional pantograph differential equations. First, the fractional differential equation is converted to a nonlinear Volterra integral equation with weakly singular kernel. Second, we analyze the existence and uniqueness of solutions for the obtained integral equation. Then, the Galerkin method is used for solving the equivalent integral equation. The error estimates for the proposed method are also investigated. Finally, illustrative examples are presented to confirm our theoretical analysis.     

Construction of long MDS self-dual codes from short codes

In this paper, we propose a mechanism on how to construct long MDS self-dual codes from short ones. These codes are special types of generalized Reed-Solomon (GRS) codes or extended generalized Reed-Solomon codes. The main tool is utilizing additive structure or multiplicative structure on finite fields. By applying this method, more MDS self-dual codes can be constructed.     

Thermoelastic solutions for thermal distributions moving over thin slim rod under memory-dependent three-phase lag magneto-thermoelasticity

Abstract

Enlightened by the Caputo fractional derivative, the present study deals with a novel mathematical model of generalized thermoelasticity to investigate the transient phenomena due to the influence of magnetic field and moving heat source in a rod in the context of three-phase lag (TPL) theory of thermoelasticity. Both ends of the rod are fixed and heat insulated. Employing Laplace transform as a tool, the problem has been transformed into the space-domain and solved analytically. Finally, solutions in the real-time domain are obtained by applying the inverse Laplace transform. Numerical calculation for stress, displacement, and temperature within the rod is carried out and displayed graphically. The effect of moving heat source speed on temperature, stress, and temperature is studied. It is found from the distributions that the temperature, thermally induced displacement and stress of the rod are found to decrease at large source speed. For the better understanding of the effect of moving heat source on all the distributions, three animations are added.