Malaya Journal of Matematik

Approximation of time separating stochastic processes by neural networks revisited

George A. Anastassiou — 2024-07-01

Here we study the univariate quantitative approximation of time separating stochastic process over the whole real line by the normalized bell and squashing type neural network operators. Activation functions here are of compact support. These approximations are derived by establishing Jackson type inequalities involving the modulus of continuity of the engaged stochastic function or its high order derivative. The approximations are pointwise and with respect to the Lp norm. The feed-forward neural networks are with one hidden layer. We finish with a great variety of special applications.

On existence of extremal integrable solutions and integral inequalities for nonlinear Volterra type integral equations

Bapurao Dhage — 2024-07-01

We prove the existence of maximal and minimal integrable solutions of nonlinear Volterra type integral equations. Two basic integral inequalities are obtained in the form of extremal integrable solutions which are further exploited for proving the boundedness and uniqueness of the integrable solutions of the considered integral equation.

Study of the inverse continuous Bernoulli distribution

Festus Opone — 2024-07-01

The continuous Bernoulli distribution, a one-parameter probability distribution defined over the interval [0, 1], has recently garnered increased attention in the realm of applied statistics. Numerous studies have underscored both its merits and limitations, alongside proposing extended variants. In this article, we introduce an innovative modification of the continuous Bernoulli distribution through an inverse transformation, thereby introducing the inverse continuous Bernoulli distribution. The main characteristic of this distribution lies in its transposition of the continuous distribution’s properties onto the interval \( [1, +\infty)\), without necessitating any additional parameters. The initial section of this article elucidates the mathematical properties of this novel inverse distribution, encompassing essential probability functions and quantiles. Inference for the associated model is carried out via the widely employed maximum likelihood estimation method. To evaluate the efficacy of the estimated model, a comprehensive simulation study is conducted. Subsequently, the model’s performance is assessed in a practical context, using data sets from a diverse array of sources. Notably, our findings demonstrate its superior performance in comparison to a broad spectrum of analogous models defined over the support interval \( [1, +\infty)\), even surpassing the established Pareto model.

On \(\beta-\gamma\)-connectedness and \( \beta_{(\gamma,\delta)}\)-continuous functions

Sanjay Tahiliani — 2024-07-01

The aim of the paper is to introduce the notion of \(\beta-\gamma\)-separated sets and study their properties in topological spaces,then we introduce the notation of \(\beta-\gamma\)-connected and \(\beta-\gamma\)-disconnectedness. Also, \(\beta-\gamma\)-disconnected spaces are defined through \(\beta-\gamma\)-separated sets and their topological properties are studied. The characterizations of \(\beta-\gamma\)-connected spaces and their behaviour under \( \beta_{(\gamma,\delta)}\)-continuous functions are analysed. The notions of \(\beta-\gamma\)-components in a space \(X\) and \(\beta-\gamma\)-locally connected spaces are also introduced.

Approximate and exact solution of Korteweg de Vries problem using Aboodh Adomian polynomial method

OLUDAPO OLUBANWO — 2024-07-01

This study introduce Aboodh Adomian polynomial Method (AAPM) to solve nonlinear third order KdV problems providing it approximate and exact solution. To get the approximate analytical answers to the issues, the Aboodh transform approach was used. Given that the Aboodh transform cannot handle the nonlinear elements in the equation, the Adomian polynomial was thought to be a crucial tool for linearizing the associated nonlinearities. All of the issues examined demonstrated the strength and effectiveness of the Adomian polynomial and Aboodh transforms in solving various nonlinear equations when compared to other well-known methods. To show how this strategy may be applied and is beneficial, three cases were examined.

On preserved properties for slant ruled surfaces under homothety in \(E^{3}\)

Emel Karaca — 2024-07-01

In mathematics, it is known that if \(E^{3} \rightarrow E^{3}\) is a homothety and \(N\) is a surface in \(E^{3}\), then \(f(N)=\bar{N}\) is a surface in \(E^{3}\). In this study, especially, the surface \(N\) is considered a slant ruled surface. Then, it is proved that the image surface \(f(N)=\bar{N}\) is a slant ruled surface, too. Moreover, some significant properties are shown to be preserved under homothety in \(E^{3}\).

Uncertainty principles for the continuous wavelet transform associated with a Bessel type operator on the half line

Cyrine Baccar — 2024-07-01

This paper presents uncertainty principles pertaining to generalized wavelet transforms associated with a second-order differential operator on the half line, extending the concept of the Bessel operator. Specifically, we derive a Heisenberg-Pauli-Weyl type uncertainty principle, as well as other uncertainty relations involving sets of finite measure

Formal derivation and existence of global weak solutions of an energetically consistent viscous sedimentation model

Yacouba ZONGO — 2024-07-01

The purpose of this paper is to derive a viscous sedimentation model from the Navier-Stokes system for incompressible flows

with a free moving boundary. The derivation is based on the different properties of the fluids; thus, we perform a multiscale analysis in space and

time, and a different asymptotic analysis to derive a system coupling two different models: the sediment transport equation for the lower layer and the shallow water model for the

upper one. We finally prove the existence of global weak solutions in time for model containing some additional terms.