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In this paper, we investigate a non-linear Langevin equation with periodic, multi-point and non-local fractional integral boundary conditions. The contraction mapping theorem is employed to determine sufficient conditions for the uniqueness of the solution. Also, different results in the existence of solution are demonstrated by using Krasnoselskii and Leray-Schauder theorems. Finally, some examples are provided as applications of the theorems in order to support the main outcomes of this paper. [ABSTRACT FROM AUTHOR]

In this paper, we study an excision theorem of the dihedral and reflexive (co)homology theory of associative algebras. That is, for such an extension, we obtain a six-term exact sequence in the dihedral cohomology. Also, we present and prove the relation between cyclic and dihedral cohomology of algebras and some examples. [ABSTRACT FROM AUTHOR]

This paper deals with the numerical solution of singularly perturbed parabolic convection-diffusion problems with two small positive parameters multiplying the convection and diffusion terms. A parameter-uniform computational method is developed to solve these problems. The stability and consistency of the method are well established. Numerical experimentation is done and it is observed that the formulated method is stable, consistent and gives more accurate results than some methods exist in the literature. [ABSTRACT FROM AUTHOR]

In this paper, it has been proved that if a 3-dimensional cosymplectic manifold M 3 admits a Yamabe soliton, then either M 3 is locally flat or the potential field is a contact vector field. Some special potential vector fields of Yamabe solitons on 3-dimensional cosymplectic manifolds have been considered and some other results have been obtained. Also, for general (2 n + 1) -dimensional case, it will be shown that if an f − cosymplectic manifold M 2 n + 1 admits a contact Yamabe soliton structure, then M 2 n + 1 is a cosymplectic manifold. Finally, an example of Yamabe soliton on a 3-dimensional cosymplectic manifold is provided. [ABSTRACT FROM AUTHOR]

In this paper, by applying the behavior of measure of noncompactness in L∞( R n), we study the existence of solutions of an infinite system of integral equations in the space L∞( R n). Finally, an example is included to show the usefulness of the outcome. [ABSTRACT FROM AUTHOR]

Substance/drug abuse poses a significant threat to the health and socio-economic fabric of individuals and nations. The combined abuse of alcohol and the highly addictive methamphetamine has worsened the drug epidemic in South Africa, especially in the Western Cape province. In this paper, a mathematical model is formulated to model the dynamics of alcohol and methamphetamine co-abuse. We prove that the equilibria of the submodels are locally and globally asymptotically stable when the sub-model threshold parameters are less than unity. The basic reproduction number due to co-abuse is shown to be the maximum of the two sub-model reproduction numbers. Sensitivity analysis reveals that the most sensitive parameters in the co-abuse epidemic are the alcohol and methamphetamine recruitment rates β1 and β2 respectively. The prevalence curve is indicative of a persistent drug problem in the region. Hence, the need to promote social programs that raise awareness of the dangers posed by multiple substance abuse, through educational campaigns in learning institutions, social media and health institutions. Transmission control must focus on enhancing the quitting process while promoting support services to drug users during and after treatment to minimize cases of relapse. [ABSTRACT FROM AUTHOR]