On weak (measure-valued)-strong uniqueness for compressible MHD system with non-monotone pressure law

<p style='text-indent:20px;'>In this paper, we define a renormalized dissipative measure-valued (rDMV) solution of the compressible magnetohydrodynamics (MHD) equations with non-monotone pressure law. We prove the existence of the rDMV solutions and establish a suitable relative energy inequality. And we obtain the weak (measure-valued)-strong uniqueness property of this rDMV solution with the help of the relative energy inequality.</p>

On a generalized fractional boundary value problem based on the thermostat model and its numerical solutions via Bernstein polynomials

In this paper, we introduce a new structure of the generalized multi-point thermostat control model motivated by its standard model. By presenting integral solution of this boundary problem, the existence property along with the uniqueness property are investigated by means of a special version of contractions named μ-φ-contractions and the Banach contraction principle. Then, on the given nonlinear generalized BVP of thermostat, the Bernstein polynomials are introduced and numerical solutions obtained by them are presented. At the end, three different structures of nonlinear thermostat models are designed and the results are examined.

Weak-Strong Uniqueness for Compressible Magnetohydrodynamic Equations with Coulomb Force

In this paper, we consider the two-dimensional compressible magnetohydrodynamic system with Coulomb force. We apply the method of relative entropy to establish the weak-strong uniqueness property of this system.

Stability of stochastic differential equations driven by multifractional Brownian motion

Our aim in this paper is to establish some strong stability results for solutions of stochastic differential equations driven by a Riemann–Liouville multifractional Brownian motion. The latter is defined as a Gaussian non-stationary process with a Hurst parameter as a function of time. The results are obtained assuming that the pathwise uniqueness property holds and using Skorokhod’s selection theorem.

Existence of the Essential Features of the Function Concept in Public Secondary Students’ Definitions

This paper aims to explore the existence of the essential features of the function concept in public secondary students’ definitions of it across grade-level of the scientific and humanities tracks. A sample of 465 secondary students was chosen from 5 public secondary schools located in Beirut. The findings of the study showed that secondary students in the different grade levels lack a thorough conceptualization of what is a function. For instance, the majority of them failed to give definitions that reflect the essential features of the concept. The relation feature was the most one noticed in students’ definitions. Compartmentalization phenomenon was observed where even the students who succeeded to state the uniqueness property, were not truly aware of it and seemed not to consult this property when presented with non-examples of function.