Sovarani Memorial College, established in 1971, is an undergraduate college in Goalpota, Jagatballavpur, Howrah, West Bengal, India. The college is affiliated with the University of Calcutta.
In this paper, novel control techniques are presented for stabilization and synchronization of Hopfield neural networks by the fast terminal sliding mode controller in the first case and projective synchronization in the second case. To summarize the main contributions and innovations presented in this research paper, the following issues are considered as part of the innovations. First, a novel chaotic Hopfield network is discovered. Second, the projective stabilization and synchronization by terminal sliding mode control is provided. This study begins with the dynamic analysis of the chaotic neural networks. This consists of the stability and bifurcation of a single neuron or node of the network and in the case of the stability analysis, the respective Lyapunov stability of the whole chaotic neural networks. Then, the stabilization of the neural network is performed by a terminal sliding mode controller FTSMC which is designed by the implementation of a Lyapunov functional. The closed-loop stability and fast convergence to the sliding phase is achieved by means of the FTSMC, improving other results found in the literature. Then, a projective synchronization controller is designed in order to achieve an accurate synchronization between the drive and response chaotic system. Finally, a numerical example is provided to ensure and validate the theoretical results obtained in this research study. Conclusions and discussions are provided in the end of this paper.
In this paper, we introduce two new φ-fixed point problems in the setting of complete metric spaces using α-admissible mappings. The motivation of the work is derived from the efforts for combining several trends of research in fixed point theory to create new results. Existence and uniqueness results are established under appropriate conditions. The main results are supported by two separate illustrative examples. The well-posedness property of the proposed problems are investigated. One of the theorems is effectively applied to study the solvability of a problem involving functional equations.
Researchers and health authorities in several countries are trying to formulate new medicines and action plans to solve the antimicrobial resistance (AMR) problem. Due to non-toxicity, chemical stability, low cost, photocatalytic properties, and GRAS (Generally Recognized as Safe) status, TiO2 (titanium dioxide) in particular, has been regarded as an appealing antibacterial molecule. Additionally, TiO2 nanoparticles promote the inactivation of microbes due to their potent oxidizing capability by producing free radicals, including hydroxyl and superoxide anion radicals, which exhibit reduced growth against a variety of microbes like E.coli and S. aureus. In this review, several synthesis and characterization processes of TiO2 nanoparticles have been discussed in detail which can help in the development of the simplest route of synthesis with the most cost-effectiveness. The mechanism of action of TiO2 nanoparticles to inhibit the growth of microorganisms and its application in targeted drug delivery are the second most important purpose of this paper. Finally, a path through which future research on these nanoparticles can be developed has also been indicated. This review may help the researcher to find a new route for the facile, simple, and cost-effective development of a new antimicrobial agent with TiO2 as the base material.
The present paper is on fixed point theory in set valued analysis. Here putting several concepts together, we define a set valued contraction and establish that such contractions have fixed points in a complete metric space. We have two main theorems in one of which we use α -regularity condition of the space as a substitute of the continuity requirement on the multivalued contraction. There are some illustrative examples and corollaries. We also perform stability analysis of fixed point sets. We establish that the fixed point sets associated with the mappings we consider in our theorems are stable. In the last section we discuss some consequences of the main results of this paper.
In this paper, we establish existence of the coupled fixed point for set-valued Feng–Liu-type contractions in complete metric spaces under two different sets of conditions. Some consequences are obtained and an application to a nonlinear integral equation is included.
