Open Journal of mathematical Sciences (OMS)

The objective of this paper is to study the stability of the weak solutions of stochastic 2D Navier-Stokes equations with memory and Poisson jumps. The asymptotic stability of the stochastic Navier-Stoke equation as a semilinear stochastic evolution equation in Hilbert spaces is obtained in both mean square and almost sure senses. Our results can extend and improve some existing ones.

In this paper, we concerned to prove the existence of a random attractor for the stochastic dynamical system generated by the extensible beam equation with localized non-linear damping and linear memory defined on bounded domain. First we investigate the existence and uniqueness of solutions, bounded absorbing set, then the asymptotic compactness. Longtime behavior of solutions is analyzed. In particular, in the non-autonomous case, the existence of a random attractor attractors for solutions is achieved.

In this article, authors discussed the existence of solution of non-linear diophantine equation \({379}^x+{397}^y=z^2,\) where \(x,y,z\) are non-negative integers. Results show that the considered non-linear diophantine equation has no non-negative integer solution.

This paper provides a procedure for estimating Stochastic Volatility (SV) in financial time series via latent autoregressive in a Bayesian setting. A Gaussian distributional combined prior and posterior of all hyper-parameters (autoregressive coefficients) were specified such that the Markov Chain Monte Carlo (MCMC) iterative procedure via the Gibbs and Metropolis-Hasting sampling method was used in estimating the resulting exponentiated forms (quadratic forms) from the posterior kernel density. A case study of Naira to eleven (11) exchangeable currencies’ rates by Central Bank of Nigeria (CBN) was subjected to the estimated solutions of the autoregressive stochastic volatility. The posterior volatility estimates at 5%, 50%, and 95% quantiles of \({e^{\frac{\mu }{2}}}\) = (0.130041, 0.1502 and 0.1795) respectively unveiled that the Naira-US Dollar exchange rates has the highest rates bartered by fluctuations.

The theory of multigroups is a generalized group’s theoretic notions in multiset framework. Although myriad of researches have been done in multigroup theory, but some group’s analogue concepts have not been investigated in multigroup setting. In this paper we propose the notions of divisible and pure multigroups and characterize some of their properties. It is established that the image and preimage of homomorphism of divisible and pure multigroups are divisible and pure multigroups. The nexus between divisible and pure multigroups and that of divisible and pure groups are instituted using the concept of cuts of multigroups.

In this paper, we have established a theorem involving a pair of mappings satisfying a weakly contraction type condition in the context of quasi \(\alpha\)b-metric space and proved the existence and uniqueness of coupled coincidence and coupled common fixed points. The concept of weakly compatibility of the pair of maps is applied to show the uniqueness of coupled common fixed point. This work offers an extension to the published work of Nurwahyu and Aris [1].

In this paper we are interested in the existence of solutions for Navier problem associated with the degenerate nonlinear elliptic equations in the setting of the weighted Sobolev spaces.

The critical analysis of the foundations of vector calculus and classical electrodynamics is proposed. Methodological basis of the analysis is the unity of formal logic and rational dialectics. The main results are the following statements: (1) a vector is a property of the motion and of the interaction of material objects, i.e., the concept of a vector is the concept of a physical property. Therefore, the concept of a vector is a general and abstract concept; (2) a vector is depicted in the form of an arrow (i.e., “straight-line segment with arrowhead”) in a real (material) coordinate system. A vector drawn (depicted) in a coordinate system does not have the measure “meter”. Therefore, a vector is a pseudo-geometric figure in a coordinate system. A vector is an imaginary (fictitious) geometric figure; (3) geometrical constructions containing vectors (as pseudo-geometric figures) and vector operations in a coordinate system are fictitious actions; (4) the scalar and vector products of vectors represent absurd because vectors (as abstract concepts, as fictional geometric figures that have different measures) cannot intersect at the material point of the coordinate system; (5) the concepts of gradient, divergence, and rotor as the basic concepts of vector analysis are a consequence of the main mathematical error in the foundations of differential and integral calculus. This error is that the definition of the derivative function contains the inadmissible operation: the division by zero; (6) Maxwell’s equations the main content of classical electrodynamics are based on vector calculus. This is the first blunder in the foundations of electrodynamics. The second blunder is the methodological errors because Maxwell’s equations contradict to the following points: (a) the dialectical definition of the concept of measure; (b) the formal-logical law of identity and the law of lack of contradiction. The logical contradiction is that the left and right sides of the equations do not have identical measures (i.e., the sides do not have identical qualitative determinacy). Thus, vector calculus and classical electrodynamics represent false theories.

In this paper, we study some properties of induced topology by a uniform space generated by a family of ideals of a BCC-algebra. Also, by using Cauchy nets we construct a uniform space which is completion of this space.

In this paper, the boundedness of Calderón-Zygmund operators is obtained on Morrey-Herz spaces with variable exponents \(MK_{q(\cdot),p(\cdot)}^{\alpha(\cdot),\lambda}(\mathbb{R}^{n})\) and several norm inequalities for the commutator generated by Calderó-Zygmund operators, BMO function and Lipschitz function are given.