Some new classes of nonconvex inverse variational inequalities are considered and studied. Using the projection technique, we establish the equivalence between the nonconvex inverse variational inequalities and the fixed point problems. This alternative equivalent formulation is used to study the existence of a solution of the nonconvex inverse variational inequalities. Several techniques including the projection, auxiliary principle, dynamical systems and nonexpansive mappings are explored for computing the approximate solution of nonconvex inverse variational inequalities. Convergence criteria of the proposed hybrid multi-step methods is investigated under suitable conditions. Our method of proofs is very simple as compared with other techniques. Some special cases are pointed are pointed as applications of the results. It is an open problem to explore the applications of the nonconvex inverse variational inequalities in various fields of mathematical and engineering sciences.

The purpose of this paper is to abstractly describe the notion of a generative mechanism that implements a code and to provide a number of examples including the DNA-RNA machinery that implements the genetic code, Chomsky’s Principles & Parameters model of a child acquiring a specific grammar given `chunks’ of linguistic experience (which play the role of the received code), and embryonic development where positional information in the developing embryo plays the role of the received code. A generative mechanism is distinguished from a selectionist mechanism that has heretofore played an important role in biological modeling (e.g., Darwinian evolution and the immune system).

Let \((X,d)\) be a metric space, \(D\subset (X,d)\) and \(f:D \longrightarrow \mathbb{R}\) a continuous function (with respect to the metric \(d\) and the Euclidean metric on \(\mathbb{R}\)) . Under suitable conditions on the function \(f\) and the set \(D\), we prove the existence of zeros of the function \(f\) on \(D\) by using the so-called \(\alpha\)-dense curves. To be more precise, we prove that if \(f(x_{1})f(x_{2})<0\) for some \(x_{1},x_{2}\in D\) and \(D\) is densifiable then \(f\) has some zero in \(D\). Moreover, from this result we derive a numerical method to approximate, with arbitrarily small error, at least one of these zeros. In particular, as a compact interval \([a,b]\) is densifiable, our method generalizes the well known bisection method. The feasibility and reliability of the proposed method is illustrated by several numerical examples.

The Hardy-Hilbert integral inequality is a classic result in mathematical analysis that has inspired numerous generalizations and modifications. In this article, we present two comprehensive frameworks that unify many of these developments. Our approach introduces kernel functions that take into account both the maximum and the product of the variables, controlled by three independent, adjustable parameters. Although the kernels are primarily inhomogeneous and somewhat complicated, they offer much greater generality. We provide detailed proofs, together with thorough discussions and context within the wider mathematical literature. In addition, several intermediate integral results emerge naturally from our framework and may serve as useful tools for further exploration.

In this paper we introduce an approach to increase density of field-effect heterotransistors in the framework of the three-stage differential amplifier. In the framework of the approach we consider manufacturing the amplifier in heterostructure with specific configuration. Several required areas of the heterostructure should be doped by diffusion or ion implantation. After that dopant and radiation defects should by annealed framework optimized scheme. We also consider an approach to decrease value of mismatch-induced stress in the considered heterostructure. We introduce an analytical approach to analyze mass and heat transport in heterostructures during manufacturing of integrated circuits with account mismatch-induced stress.

Muga silk is the most important composite material used in textile manufacturing in India. Muga silk is derived from the Muga silkworms, namely Antheraea assamensis Helfer. The golden yellow silk yarn is the fanciest because it has strange properties like being able to handle different textures well, being bright, and lasting a long time. Fibrin (a fibrous protein) and sericin (a globular protein) are the two most important protein units that make up silk. To make silk usable in the textile business, sericin, a gum, has to be cleaned off the surface of the silk. Generally, surface active agents are used in the extraction of sericin from silk material. The present research describes a comparison between the degumming activity of a natural surfactant saponin isolated from Sapindus laurifolia and Sapindus laurifolia-\(Na_{2}CO_{3}\) mixed system. The effect of the salt \(Na_{2}CO_{3}\) on the degumming ability of Sapindus laurifolia is systematically studied and reported. The surface morphology of the raw and degummed silk fibers is compared using scanning electron microscope.

Gas Tungsten Arc welding (GTAW) widely uses for many welding applications, especially for good quality welds in fabrication, manufacturing, and construction industries. Perfection level exhibits by the weld are associated with the entire volume of the weld, its profile, surface appearance, and microstructure and show the quality of that weld. Several controllable process parameters may affect the quality of weld in terms of weld shape, bead, imperfections, and desire mechanical/chemical properties. Therefore effect of some important parameters like current, travel speed, and gas flow rate on the final weld structure and its quality for SS TP304L material are studied through different experiments and analyses by using a design of experiment-based advanced statistical tools. Joints weld by using several levels of these parameters and then weld quality of these joints analyze in terms of ultimate tensile strength, and hardness. The optimization results of different statistical techniques compare to find the accuracy of this study. Moreover, the microstructure of final weldment welded based on optimal results is also analyzed. Therefore this study finds out the best welding conditions for the quality weld after optimizing these process parameters.

The optimal selection of a site for cement plant development is a multifaceted decision-making process that demands careful consideration of environmental, economic, and social dimensions. This research delves into the utilization of Circular Intuitionistic Fuzzy Soft Sets (CIFSS) as an advanced mathematical framework to enhance the precision and reliability of sustainable decision-making in cement plant site selection. The CIFSS approach adeptly manages the inherent uncertainties and ambiguities associated with evaluating potential locations, offering a comprehensive methodology for assessing various criteria. By embedding CIFSS within the context of sustainable development, this technique provides decision-makers with a robust and adaptable tool for identifying the most appropriate site, thereby ensuring long-term viability and minimizing environmental impacts. The results underscore the effectiveness of CIFSS in facilitating complex, multi-criteria decision-making in industrial site selection, underscoring its broader applicability in sustainable infrastructure planning.

This paper introduces the concept of the extended \(H\)-cover of a graph \(G\), denoted as \(G^*_H\) , as a generalization inspired by the extended double cover graphs discussed in Chen [1]. We explore the spectral properties and energy characteristics of \(G^*_H\), deriving formulae for the number of spanning trees in cases where both \(G\) and \(H\) are regular. Our investigation identifies several infinite families of equienergetic graphs and highlights instances of cospectral graphs within \(G^*_H\) . Additionally, we analyze various graph parameters related to the Indu-Bala product of graphs and the partial complement of the subdivision graph (PCSD) of \(G\).

A dominator coloring of a graph \(\mathscr{G}\) is a proper coloring where each vertex of \(\mathscr{G}\) is within the closed neighborhood of at least one vertex from each color class. The minimum number of color classes required for a dominator coloring of \(\mathscr{G}\) is termed the dominator chromatic number. Additionally, a total dominator coloring of a graph \(\mathscr{G}\) is a proper coloring in which every vertex dominates at least one color class other than its own. The minimum number of color classes needed for a total dominator coloring of \(\mathscr{G}\) is known as the total dominator chromatic number. In this paper, our objective is to derive findings concerning dominator and total dominator coloring of the duplication corresponding corona of specific graphs.