Herein, we developed the first report on the chemical retrial queue and hybrid vacation process for the significant Ullmann coupling for enhanced high-throughput reaction discovery. The problem of controlling the waiting time for chemical retrials is addressed here. We incorporated the supplementary variables method (SVT) and generated the steady-state probability generating function (PGF) for system size and orbit size. Important cases are outlined, and a few key metrics are utilized to evaluate system performance. Additionally, the impact of changing certain system parameters has also been analyzed via numerical examples. One particularly interesting aspect of this research is the comparison of neuro-fuzzy technique results with validation results utilizing the "adaptive neuro-fuzzy inference system" (ANFIS).

In this paper, a non-steady-state amperometric biosensor with the mixed enzyme kinetics and diffusion limitations under the inhibitions of substrate and product is modeled mathematically. The non-steady-state reaction-diffusion equations of the system consist non-linear terms related to an enzymatic reaction of non-Michaelis-Menten kinetics. We have presented the approximate analytical solutions for the concentrations of substrate and product in non-steady and steady-state models using the new approach of Homotopy perturbation method (HPM). The provided expression is presented for all potential diffusion and kinetic parameter values. Analytical expressions of the biosensor current and sensitivity are also presented and discussed. In addition, we also provided numerical solutions for the proposed model by utilizing the pdepe tool in MATLAB software. When comparing the analytical solution with the numerical solution, a satisfactory result is noted for all the possible values of the parameters. Furthermore, the influence of diffusion and kinetic parameters on both the current and the sensitivity are discussed. Analytical expressions for the limiting cases of biosensor enzyme kinetics are presented in this research article. Additionally, an analytical expression for determining the effective thickness of the membrane is derived and presented.

The notion of hyperstructures first introduced by Marty in 1934 as a generalization of algebraic structures. Next, by associating fuzzy sets, Corsini introduced new notion in hyperstructures, that is fuzzy hyperstructures. After fuzzy hyperstructures introduced by Corsini, Cristea introduced the notion of intuitionistic fuzzy hyperstructures as a generalization of fuzzy hyperstructures. In 2023, Violeta-Fotea related the notion of fuzzy hyperstructures with genetic inheritance. Inspired by this research, this paper aims to find relation between fuzzy and intuitionistic fuzzy hyperstructures with chemical hyperstructures, that is to finding the fuzzy degree and intuitionistic fuzzy degree on chemical hyperstructures such as redox reactions, electrochemical cells, equilibrium reactions, and acid rain reactions.

Wederive upper and lower bounds to first-order properties in the H¨uckel model: π charge, bond order, bond number, and matrices of higher spectral moments. Bounds that depend on the electronic configuration, and on the molecular graph alone are derived. A ladder of relations between higher and lower spectral moments leads to bounds via the Cauchy-Schwarz theorem. The old square-root degree bound on bond number implicit in the work of Coulson, Moffitt and Longuet-Higgins is sharpened. Key to this development is the distinction between core and core-forbidden vertices of a graph.

Benzenoid chains, also known as hexagonal chains, are a class of organic compounds that consist of an arrangement of hexagonal rings fused together. In this article, we first present reduction formulas to compute the matching polynomial and independence polynomial of any benzenoid chain by utilizing the transfer matrix technique. Subsequently, computational formulas for the Hosoya index and Merrifield-Simmons index of benzenoid chains are derived. Furthermore, the expected values of the Hosoya index and Merrifield-Simmons index for random benzenoid chains are also obtained.

Delayed differential equation plays a vital role in revealing the dynamics of chemical reaction law. In this work, we propose a novel fractional-order Lengyel-Epstein model owing time delay. By regarding the delay as parameter and investigating the distribution of roots of the associated characteristic equation of the formulated fractional-order delayed Lengyel-Epstein model, we set up a new delay-dependent criterion on stability and bifurcation of the involved fractional-order delayed Lengyel-Epstein model. Making use of nonlinear delayed feedback controller, we can effectually control the stability domain and the time of bifurcation phenomenon of the formulated fractional-order delayed Lengyel-Epstein model. Taking advantage of hybrid controller, we are able to adjust the stability domain and the time of bifurcation phenomenon of the established fractional-order delayed Lengyel-Epstein model. The study shows that delay is a vital factor which affects the stability and bifurcation behavior of the addressed fractional-order delayed Lengyel-Epstein model. In order to illustrate the rationality of the acquired theoretical outcomes, we execute Matlab simulations to check this fact. The gained outcomes in this work are absolutely innovative and possess enormous theoretical significance in adjusting concentrations of different chemical substance.