Journal of Mathematics

We consider a regularized periodic three-dimensional Boussinesq system. For a mean free initial temperature, we use the coupling between the velocity and temperature to close the energy estimates independently of time. This allows proving the existence of a global in time unique weak solution. Also, we establish that this solution depends continuously on the initial data. Moreover, we prove that this solution converges to a Leray-Hopf weak solution of the three-dimensional Boussinesq system as the regularizing parameter vanishes.

This article introduces a new probability model based on reflected parameter called the reflected Pareto (RP) distribution. The key properties of the RP model are investigated. A simulation study of the RP model is conducted to evaluate the performances of its estimators. A real-life application is considered to examine the performance of proposed model. The different criteria are discussed numerically as well as graphically to show the flexibility of the RP model. The exponential weighted moving average control charts based on the maximum likelihood and modified maximum likelihood estimators for the shape parameter of the RP distribution are obtained. Detailed simulation results of proposed charts are performed to examine and analyze the performance of these charts with three in-control average run length values and two sample sizes. Finally, the application of the proposed control charts is shown by considering a real-life data set.

The focus of this study is to classify flag-transitive 2-designs. We have come to the conclusion that if is a nontrivial 2-design having block size 5 and is a two-dimensional projective special linear group which acts flag-transitively on with (mod 4), then is a 2-(11, 5, 2) design, a 2-(11, 5, 12) design, a 2- design with (mod 4) or a 2- design with (where is an even).

In this paper, we delve into the intricate connections between the numerical ranges of specific operators and their transformations using a convex function. Furthermore, we derive inequalities related to the numerical radius. These relationships and inequalities are built upon well-established principles of convexity, which are applicable to non-negative real numbers and operator inequalities. To be more precise, our investigation yields the following outcome: consider the operators and , both of which are positive and have spectra within the interval , denoted as and . In addition, let us introduce two monotone continuous functions, namely, and , defined on the interval . Let be a positive, increasing, convex function possessing a supermultiplicative property, which means that for all real numbers and , we have . Under these specified conditions, we establish the following inequality: for all , this outcome highlights the intricate relationship between the numerical range of the expression when transformed by the convex function and the norm of . Importantly, this inequality holds true for a broad range of values of . Furthermore, we provide supportive examples to validate these results.

Let be a graph with vertices and is an -clique of . A vertex is said to resolve a pair of cliques in if where is the distance function of . For a pair of cliques , the resolving neighbourhood of and , denoted by , is the collection of all vertices which resolve the pair . A subset of is called an -clique metric generator for if for each pair of distinct -cliques and of . The -clique metric dimension of , denoted by , is defined as is an -clique metric generator of . In this paper, the -clique metric dimension of corona and edge corona of two graphs are computed. In addition, an integer linear programming model is presented for the -clique metric basis for a given graph and its -cliques.

We consider an ordered vector space . We define the net to be unbounded order convergent to (denoted as ). This means that for every , there exists a net (potentially over a different index set) such that , and for every , there exists such that whenever . The emergence of a broader convergence, stemming from the recognition of more ordered vector spaces compared to lattice vector spaces, has prompted an expansion and broadening of discussions surrounding lattices to encompass additional spaces. We delve into studying the properties of this convergence and explore its relationships with other established order convergence. In every ordered vector space, we demonstrate that under certain conditions, every -convergent net implies -Cauchy, and vice versa. Let be an order dense subspace of the directed ordered vector space . If is a -band in , then we establish that is a -band in .