A. The notion of divisibility is introduced in an Almost Distributive Lattice(ADL) with respect to a filter and it is proved that the set of all multipliers of an element is a filter.A congruence is defined on an ADL with respect to these multiplier filters and established a set of equivalent conditions for the corresponding quotient lattice to become a Boolean algebra.The concepts of D-prime elements and D-irreducible elements are introduced and characterized in terms of corresponding multiplier filters.

A. In this paper, we use the discrete case methodology to the continuous situation in order to identify closed-form of fractional order continuous and discrete integration.We have derived several theorems and formula using Riemann Liouville fractional integral with gamma function.Also, we develop the discrete analog of the continuous version for ν th fractional order integration.The novelty of this article is the introduction of fractional order exponential functions and obtaining its related theorems.

A. Nowadays cryptographical protocols are developed by the use of tropical linear and non linear systems.To attack such cryptographical protocols solutions of tropical linear and non linear systems are essential.In this paper, we present the final general maximal solution of linear systems with some special matrices over the tropical semiring.These matrices include natural arithmetic matrices, γ-diagonal matrices, J-matrices, and circulant matrices.We provide proofs for several theorems based on the general maximal solution of max linear systems, which can be utilized to solve cryptographic algorithms employing the discrepancy method.We also compare the discrepancy method with the normalization method and present results regarding the relationship between these two methods.

A. The COVID-19 pandemic has had a significant impact on the global population, with millions of cases and deaths reported worldwide.In this study, we use mathematical models to analyze the spread of the disease, with a focus on careless infective models.We develop and analyze mathematical models to understand the transmission dynamics of COVID-19 , taking into account the impact of human behavior, such as the spread of the disease by individuals who are unaware that they are infected.Our results provide insights into the role of careless infective individuals in the spread of the disease and suggest the need for targeted interventions to reduce the impact of COVID-19 The results of this study contribute to a better understanding of the spread of COVID-19 and inform public health measures to control its transmission.

A. This article deals with the concepts of p(, p)-open functions and p(, p)-closed functions.Moreover, several characterizations of p(, p)-open functions and p(, p)-closed functions are considered.2020 Mathematics

. In this paper, we give the existence and uniqueness of solutions for an abstract Caputotype fractional evolution problem with generalized real numbers in the initial conditions. The mild solutions of our proposed model is constructed by using Laplace transform and a density function. By applying some fixed point theorems on Colombeau algebra, we prove our main results. As application, an illustrative example is given to show the applicability of our theoretical results.

. This study presents a non-linear mathematical model to analyze the impact of corruption on a society where honest individuals are exposed to corrupt practices. The model considers key factors such as the level of corruption, the behavior of honest individuals, and the dynamics of corruption. We estimate the basic reproduction number of the model, accounting for constant recruitment and death-based demographic factors. The equilibria of the model have been analyzed in depth, and their stability has been comprehensively investigated and discussed. We carried out a sensitivity analysis on the proposed model in order to determine the primary parameters that are responsible for the model's basic reproduction number and conducted the bifurcation analysis. We present numerical simulations in order to highlight the outcomes of our analytical work. Our findings suggest that , and 2 have a significant impact on the corrupted and honest compartments.

A. In this study, the polar moments of inertia for the trajectories drawn by the non linear points are obtained during the one parameter planar homothetic motions in the generalized complex plane C p .Then, we express the polar moment of inertia with respect to the Cauchy length formula.Moreover, for non linear three points we give new version of Holditch type theorem during the homothetic motions C p .Consequently, we obtain some conclusions.

. In this paper, we present the Fractional Orlicz-Sobolev spaces and we deal with the existence to a result for the following elliptic system:

. In this paper, we introduce the concept of weighted Stepanov-like square-mean pseudo almost periodic process and study the existence and uniqueness of square-mean almost periodic mild solution for several neutral partial stochastic differential equations with weighted