Analysis of time-varying delay systems via triangular functions

This paper presents a method for finding the analysis of time-varying delay systems using triangular functions. We present the properties of the triangular functions. The operational matrices of integration, delay and product are utilized to reduce the solution of delay systems to the solution of algebraic equations. Illustrative examples is included to demonstrate the validity and applicability of the technique.     

Substitutional doping of Cu in diamond: Mott physics with p orbitals

Discovery of superconductivity in the impurity band formed by heavy doping of boron into diamond (C:B) as well as doping of boron into silicon (Si:B) has provided a rout for the possibility of new families of superconducting materials. Motivated by the special role played by copper atoms in high temperature superconducting materials where essentially Cu d orbitals are responsible for a variety of correlation induced phases, in this paper we investigate the effect of substitutional doping of Cu into diamond. Our extensive first principle calculations based on density functional theory which are averaged over various geometries indicate the formation of a mid-gap band, which mainly arises from the t _{2 g} and 4p states of Cu. For impurity concentrations of more than ~1%, the effect of 2p bands of neighboring carbon atoms can be ignored. Based on our detailed analysis, we suggest a two band model for the mid-gap states consisting of a quarter-filled hole like t _{2 g} band, and a half-filled band of 4p states. Increasing the concentration of the Cu impurity beyond ~5%, completely closes the spectral gap of the host diamond.     

Hybrid functions for nonlinear initial-value problems with applications to Lane-Emden type equations

A numerical method for solving nonlinear initial-value problems is proposed. The Lane-Emden type equations which have many applications in mathematical physics are then considered. The method is based upon hybrid function approximations. The properties of hybrid of block-pulse functions and Lagrange interpolating polynomials are presented and are utilized to reduce the computation of nonlinear initial-value problems to a system of non-algebraic equations. The method is easy to implement and yields very accurate results.     

A thermodynamic study of interaction of Ag+, Mg2+, Ca2+, and K+ cations with 4-hydroxyphenyl-2,5-bis(2-benzofuranyl)pyridine in some binary mixed non-aqueous solvents

In the present work the complexation process between Ag⁺ and Mg²⁺ cations and 4-hydroxyphenyl-2,5-bis(2-benzofuranyl)pyridine (HBFPY) ligand was studied in pure dimethylformamide (DMF), ethanol (EtOH), acetonitrile (AN) and in (DMF-EtOH), (AN-EtOH) and (DMF-AN) binary mixed solvent solutions at different temperatures using the conductometric method. Also in this work the complexation reaction between Ca²⁺, K⁺ cations and HBFPY ligand, was studied in pure dimethylformamide (DMF), propanol (PrOH), 1,4-dioxane (DOX), ethanol (EtOH) and in DMF-PrOH, DMF-DOX and DMF-EtOH binary mixed solvent solutions at different temperatures using the conductometric method. The conductance data show that the stoichiometry of the complexes formed between this ligand and the studied cations is 1 : 1 [ML]. In most cases, addition of HBFPY to solutions of these cations, causes a continuous increase in the molar conductivities which indicates that the mobility of complexed cations is more than the uncomplexed ones. The stability constants of the complexes were obtained from fitting of molar conductivity curves using a computer program, GENPLOT. The stability constant of [Mg(HBFPY)]²⁺ complex in various neat solvents at 15°C decreases in order: EtOH > DMF > AN and the stability constant of [Ag(HBFPY)]⁺ complex in various neat solvents at 35°C decreases in order: DMF > EtOH. The values of standard enthalpy changes (ΔH° _c ) for complexation reactions were obtained from the slope of the Van’t Hoff plots and the changes in standard entropy (ΔS° _c ) were calculated from the relationship ΔH° _c,295.15= ΔH° _c –298.15ΔS° _c .     

A hybrid approximation method for solving Hutchinson’s equation

The hybrid function approximation method for solving Hutchinson’s equation which is a nonlinear delay partial differential equation, is investigated. The properties of hybrid of block-pulse functions and Lagrange interpolating polynomials based on Legendre-Gauss-type points are presented and are utilized to replace the system of nonlinear delay differential equations resulting from the application of Legendre pseudospectral method, by a system of nonlinear algebraic equations. The validity and applicability of the proposed method are demonstrated through two illustrative examples on Hutchinson’s equation.     

Transition-metal-free oxidative amidation of benzyl alcohols with amines catalyzed by NaI: a new method for the synthesis of benzamides

A simple, inexpensive, and efficient method for the synthesis of benzamides via the reaction of benzyl alcohols and amine hydrochloride salts in the presence of NaI as a green catalyst is described. Various derivatives of benzamide were synthesized in moderate to good yields using this method.     

Fluorescence quantum yield of the two novel macrocyclic lactams

Fluorescence quantum yield of two novel compounds—dibenzo[c,k]-1,2-dithia-6,9-diazacyclododecane-5,10-dione (1) and dibenzo[c,k]-1,2-dithia-6,9-diaza-7-methylcyclododecane-5,10-dione (2) was studied by Williams method using anthracene as a reference.     

Observer-based adaptive robust control of nonlinear nonaffine systems with unknown gain sign

In this paper, a direct adaptive robust controller for a class of SISO nonaffine nonlinear systems is presented. The existence of an ideal controller is proved based on the Implicit Function Theorem. Since the Implicit Function Theorem only guarantees the existence of the controller and does not provide a way to construct it, a neural network is employed to approximate the unknown ideal controller. In addition, an observer is designed to estimate the system states because all the states may not be available for measurements. In this method, a priori knowledge about the sign of control gain is not required and, in order to cope with unknown control direction, the Nussbaum-type technique is used. Moreover, only one adaptive parameter is needed to be updated and also a robust term is used in the control signal to reduce the effect of external disturbances and approximation errors. Furthermore, the stability analysis for the closed-loop system is presented based on the Lyapunov stability method. Theoretical results are illustrated through a simulation example. These simulations show the effectiveness of the proposed method.     

Surface effect and non-local elasticity in wave propagation of functionally graded piezoelectric nano-rod excited to applied voltage

A non-local solution for a functionally graded piezoelectric nano-rod is presented by accounting the surface effect. This solution is used to evaluate the characteristics of the wave propagation in the rod structure. The model is loaded under a two-dimensional (2D) electric potential and an initially applied voltage at the top of the rod. The mechanical and electrical properties are assumed to be variable along the thickness direction of the rod according to the power law. The Hamilton principle is used to derive the governing differential equations of the electromechanical system. The effects of some important parameters such as the applied voltage and gradation of the material properties on the wave characteristics of the rod are studied.