Limit cycles and invariant cylinders for a class of continuous and discontinuous vector field in dimention 2n

The subject of this paper concerns with the bifurcation of limit cycles and invariant cylinders from a global center of a linear differential system in dimension 2n perturbed inside a class of continuous and discontinuous piecewise linear differential systems. Our main results show that at most one limit cycle and at most one invariant cylinder can bifurcate using the expansion of the displacement function up to first order with respect to a small parameter. This upper bound is reached. For proving these results we use the averaging theory in a form where the differentiability of the system is not needed.     

Preservation of stability properties near fixed points of linear Hamiltonian systems by symplectic integrators

Based on reasonable testing model problems, we study the preservation by symplectic Runge-Kutta method (SRK) and symplectic partitioned Runge-Kutta method (SPRK) of structures for fixed points of linear Hamiltonian systems. The structure-preservation region provides a practical criterion for choosing step-size in symplectic computation. Examples are given to justify the investigation.     

Mathematical modeling on the effect of equivalence ratio in emission characteristics of compression ignition engine with hydrogen substitution

The investigation presented in this paper concerns on the computational simulation of emissions characteristics in compression ignition engine with hydrogen substitution. Combustion process has been modeled based on Equilibrium Constants Method (ECM) with MATLAB program to calculate the mole fractions of 18 combustion products when hydrogen is burnt along with diesel fuel at variable equivalence ratios. It can be observed that hydrogen substitution causes significant increase in NH₃, H₂, atom H emissions during rich combustion and OH, NO₂, HNO₃ emissions during lean combustion. As the equivalence ratio increases during rich combustion, mole fractions of HCN, CH₄, CO and atom C decreases with increment of hydrogen substitution. N₂, atom N and CO₂ emissions decrease whereas no significant changes in O₂, NO, O₃ and atom O emissions throughout all equivalence ratios as hydrogen is added to the combustion.     

Convergence analysis for finite family of relatively quasi nonexpansive mappings and systems of equilibrium problems

In this paper, a new iterative scheme by hybrid method is constructed. Strong convergence of the scheme to a common element of the set of common fixed points of finite family of relatively quasi-nonexpansive mappings and set of common solutions of a system of equilibrium problems in a uniformly convex and uniformly smooth real Banach space is proved using the properties of generalized f-projection operator. Our results extend important recent results.     

Global Existence of the Equilibrium Diffusion Model in Radiative Hydrodynamics

This paper is devoted to the analysis of the Cauchy problem for a system of PDEs arising in radiative hydrodynamics. This system, which comes from the so-called equilibrium diffusion regime, is a variant of the usual Euler equations, where the energy and pressure functionals are modified to take into account the effect of radiation and the energy balance containing a nonlinear diffusion term acting on the temperature. The problem is studied in the multi-dimensional framework. The authors identify the existence of a strictly convex entropy and a stability property of the system, and check that the Kawashima-Shizuta condition holds. Then, based on these structure properties, the well-posedness close to a constant state can be proved by using fine energy estimates. The asymptotic decay of the solutions are also investigated.     

Equilibrium solubility of carbon dioxide in 2(methylamino)ethanol

In this paper the equilibrium solubility of carbon dioxide in 1.0 M, 2.0 M and 4.0 M 2(methylamino)ethanol (MAE) is measured at 303, 313 and 333 K, and at CO₂ partial pressures ranging from 1 to 100 kPa using stirred cell reactor. The Kent-Eisenberg model was used to predict the solubility of carbon dioxide in MAE solutions. The equilibrium constant representing hydrolysis of carbamate ion is correlated with temperature, CO₂ partial pressure and amine concentration by non-linear regression, using experimental results of carbamate ion concentrations. The model predicted results showed good agreement with the experimental solubility results. The solubility profile of CO₂ in MAE showed better performance when compared with other commercial amines.     

Competition of methyltrioxorhenium (MTO) with osmium tetroxide (OsO4) for pyridines binding: Ligand binding assay

Competition of methyltrioxorhenium (MTO) with osmium tetroxide (OsO₄) toward L = pyridine and its derivatives, based on the equilibrium constant for the reaction OsO₄·L + MTO = MTO·L + OsO₄, has been measured. A successful correlation of log K_eq with the Hammett σ constants of the substituents on the ligands was realized. A negative reaction constant, obtained for the reactions, shows that a more positive charge expands on the pyridine nitrogen in the complex MTO·L as compared with the complex OsO₄·L. So, the rhenium center acts as a better electron acceptor than osmium center. The thermodynamic parameters have been obtained and an excellent linear relationship was observed between the enthalpy and entropy of the reactions.     

Universal scaling for the dilemma strength in evolutionary games

Why would natural selection favor the prevalence of cooperation within the groups of selfish individuals? A fruitful framework to address this question is evolutionary game theory, the essence of which is captured in the so-called social dilemmas. Such dilemmas have sparked the development of a variety of mathematical approaches to assess the conditions under which cooperation evolves. Furthermore, borrowing from statistical physics and network science, the research of the evolutionary game dynamics has been enriched with phenomena such as pattern formation, equilibrium selection, and self-organization. Numerous advances in understanding the evolution of cooperative behavior over the last few decades have recently been distilled into five reciprocity mechanisms: direct reciprocity, indirect reciprocity, kin selection, group selection, and network reciprocity. However, when social viscosity is introduced into a population via any of the reciprocity mechanisms, the existing scaling parameters for the dilemma strength do not yield a unique answer as to how the evolutionary dynamics should unfold. Motivated by this problem, we review the developments that led to the present state of affairs, highlight the accompanying pitfalls, and propose new universal scaling parameters for the dilemma strength. We prove universality by showing that the conditions for an ESS and the expressions for the internal equilibriums in an infinite, well-mixed population subjected to any of the five reciprocity mechanisms depend only on the new scaling parameters. A similar result is shown to hold for the fixation probability of the different strategies in a finite, well-mixed population. Furthermore, by means of numerical simulations, the same scaling parameters are shown to be effective even if the evolution of cooperation is considered on the spatial networks (with the exception of highly heterogeneous setups). We close the discussion by suggesting promising directions for future research including (i) how to handle the dilemma strength in the context of co-evolution and (ii) where to seek opportunities for applying the game theoretical approach with meaningful impact.     

Adsorption and Equilibrium Isotherm Study of Removal of Copper (II) Ions from Aqueous Solution by Chemically Modified Abelmoschus esculentus Fibers

The present study explores surface modification of Abelmoschus esculentus by graft copolymerization reaction using acrylonitrile as a monomer and ascorbic acid/H₂O₂ as a redox initiator. Further, polyacrylonitrile grafted fibers were treated with hydroxylamine to convert the nitrile group of the grafted fiber into the amidoxime group to enhance adsorption of copper ions from wastewater. The graft copolymers and amidoximated fibers were characterized by FT-IR and FE-SEM. The effects of physicochemical parameters such as pH of the solution, initial metal ion concentration, and time on Cu(II) adsorption were studied to optimize condition for maximum adsorption. In addition, Langmuir, Freundlich, and Tempkin models were applied to describe the adsorption isotherm of Cu²⁺ ions.     

Existence of solutions in variational relation problems without convexity

Two main existence conditions for solutions of variational relation problems are established without convexity. The first one is based on a finite solvability property and the second one on generalized KKM mappings. These conditions unify and strengthen several existing results in the literature on the topic. A model of satisficing process by rejection is considered which gives an economic interpretation of the introduced concepts.