In this paper, we consider an initial value problem related to a class of hyperbolic equation in a bounded domain is studied. We prove local existence and uniqueness of the solution by using the Faedo-Galerkin method and that the local solution is global in time. We also prove that the solutions with some conditions exponentially decay. The key tool in the proof is an idea of Haraux and Zuazua with is based on the construction of a suitable Lyapunov function.

The inverse degree of a graph was defined as the sum of the inverses of the degrees of the vertices. In this paper, we focus on finding sufficient conditions in terms of the inverse degree for a graph to be \(k\)-path-coverable, \(k\)-edge-hamiltonian, Hamilton-connected and traceable, respectively. The results obtained are not dropped.

Quantum mechanical mathematical methods are utilized for theoretical engineering and testing of hydrocellular engineering for quantum computation criteria and quantum power engineering.

This paper introduces the concept of homomorphism in intuitionistic fuzzy multigroups context. It also investigates Some homomorphic properties of intuitionistic fuzzy multigroups. It is shown that the homomorphic image and homomorphic preimage of intuitionistic fuzzy multigroups are also intuitionistic fuzzy multigroups. Finally, it presents some homomorphic properties of normalizer of intuitionistic fuzzy multigroups.

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.

This paper concerns with the global solutions and general decay to an initial-boundary value problem of the dispersive wave equation with memory and source terms.

This work concerns the study of the controllability for some impulsive partial functional integrodifferential equation with infinite delay in Banach spaces. We give sufficient conditions that ensure the controllability of the system by supposing that its undelayed part admits a resolvent operator in the sense of Grimmer, and by making use of the measure of noncompactness and the Mönch fixed-point Theorem. As a result, we obtain a generalization of the work of K. Balachandran and R. Sakthivel (Journal of Mathematical Analysis and Applications, 255, 447-457, (2001)) and a host of important results in the literature, without assuming the compactness of the resolvent operator. An example is given for illustration.