On the generating function e xt+yϕ(t) and its fractional calculus

In this article, we derive the coefficient set {H _m (x,y)} _m=1 ^∞ using the generating function e ^xt+y?(t). When the complex function ?(t) is entire, using the inverse Mellin transform, and when ?(t) has singular points, using the inverse Laplace transform, the coefficient set is obtained. Also, bi-orthogonality of this set with its associated functions and its applications in the explicit solutions of partial fractional differential equations is discussed.     

Spontaneous nano pattern formation under pulsed exposure: relaxation kinetics study

Formation of spontaneous surface relief grating under pulsed exposure on the surface of an azo polymer film has been investigated. We did experiments in different repetition rates and pulse widths by use an electro mechanical chopper and a diode-pumped solid-state laser with wavelength of 532?nm as pump beam. Incidence of pump beam, has been set normal to the surface of azo-polymer film. Spontaneous surface relief grating with grating pitch of ~1,250?nm was formed. For low repetition rate, relaxation due to cis-trans isomerization becomes dominant and growth rate becomes slower. A threshold for spontaneous pattern formation was found. In addition to an increase in the diffraction intensity during illumination, anomalous variation of diffraction intensity by switching on and off the laser was observed. By switching off the recording beam sharp enhancement occurred. By switching on the recording beam, after a sharp decrease in the intensity of diffracted beam, it increased further under illumination. Anomalous variations, strongly depends on polarization of the probe beam and the irradiation time for the formation of spontaneous SRG. Sharp enhancement has been attributed to cis-trans thermal isomerization and sharp decrease has been attributed to isomeration in whole surface under illumination.     

Optimal sliding mode control of single degree-of-freedom hysteretic structural system

This paper addresses the controller design problem of a nonlinear single degree-of-freedom structural system excited by the earthquake. Bouc–Wen model, as an efficient hysteresis modeling method, is used to model the system nonlinearity. Sliding mode control (SMC), due to its robustness in dealing with uncertainty, is utilized as the main control strategy. An optimal sliding surface is presented which minimizes the displacement and control force in terms of a quadratic cost function. Two numerical examples are given to illustrate the effectiveness of the proposed strategy subject to three earthquakes of El-Centro, Rinaldi and Kobe. Simulation results show a significant and considerable reduction in structural response and indicate that the performance of suggested optimal SMC strategy is remarkable.     

Backstepping-based Lyapunov redesign control of hysteretic single degree-of-freedom structural systems

This paper considers the problem of active control design for a hysteretic single-degree-of-freedom (SDOF) structural system which is exposed to an earthquake excitation. First, backstepping-based control is used to design a controller for the structural system neglecting the effect of the earthquake disturbance. Then, Lyapunov redesign is utilized to design a robust controller for the system in the presence of the earthquake excitation. The hysteretic part of the structural system is modeled by the well-known Bouc–Wen equation, and this equation is directly utilized in the controller design. The controller is proposed for two cases: (a) when the parameters of the structure and the Bouc–Wen model are known, and (b) when these parameters are uncertain. A Lyapunov function is introduced for the closed-loop system, which guarantees the stability of the system equilibrium point. Since the controllers use the nominal and/or minimum and maximum values of the system parameters, the proposed methods are model based. Numerical evaluations are conducted to show the effectiveness of the proposed method. Seven different earthquakes are considered as the external excitations. Simulation results show that the displacement, velocity, and acceleration responses of the controlled structure are reduced significantly compared to the uncontrolled structure.     

Kinetic Study of the Electro-Catalytic Oxidation of Hydrazine on Cobalt Hydroxide Modified Glassy Carbon Electrode

Electrocatalytic oxidation of hydrazine was investigated on a cobalt hydroxide modified glassy carbon (CHM-GC) electrode in alkaline solution. The process of oxidation involved and its kinetics were established by using cyclic voltammetry, chronoamperometry techniques as well as steady state polarization measurements. In cyclic voltammetry (CV) studies, in the presence of hydrazine the peak current increase of the oxidation of cobalt hydroxide is followed by a decrease in the corresponding cathodic current. This indicates that hydrazine is oxidized on the redox mediator that is immobilized on the electrode surface via an electrocatalytic mechanism. A mechanism based on the electrochemical generation of Co(IV) active sites and their subsequent consumption by the hydrazine in question was also investigated.     

Phase Transition in Modified Newtonian Dynamics (MONDian) Self-Gravitating Systems

We study the statistical mechanics of binary systems under the gravitational interaction of the Modified Newtonian Dynamics (MOND) in three-dimensional space. Considering the binary systems in the microcanonical and canonical ensembles, we show that in the microcanonical systems, unlike the Newtonian gravity, there is a sharp phase transition, with a high-temperature homogeneous phase and a low-temperature clumped binary one. Defining an order parameter in the canonical systems, we find a smoother phase transition and identify the corresponding critical temperature in terms of the physical parameters of the binary system.     

Numerical solution of nonlinear integral equations using alternative Legendre polynomials

In this paper, the operational matrices of integration and the product for the alternative Legendre polynomials (ALPs) are first derived. Then, using these operational matrices and the collocation method, the nonlinear Volterra–Fredholm–Hammerstein integral equations are reduced to a set of nonlinear algebraic equations with unknown ALP coefficients. Some error estimations are provided and the efficiency and accuracy is verified by applying the method to some examples chosen from other literature.     

An unusual (10,3)-a racemic twofold interpenetrating network assembled from isolable tris(cyclopentadienyl)manganate and cesocene building blocks

The syntheses and X-ray crystal structures of [([18]crown-6)2Cs](+)-[Cp3Mn]- (1), [([18]crown-6)2Cs](+)-[Cp'3Mn]- (2), [CsCp'] (3), [(CsCp')2-([18]crown-6)] (4), and Cs[MnCp3] (5), and the synthesis of Cs[MnCp'3] (6) are reported (Cp' = C5H4Me). The anions [Cp3Mn]- (1-) and [Cp'3Mn]- (2-) are characterized by eta 2 coordination of all three Cp or Cp' rings. Measurements of the magnetic susceptibilities chi M resulted in values of mu eff = 6.20 microB (300 K), mu eff = 6.33 microB (301 K), and mu eff = 5.83 microB (300 K) for 1, 2, and 5, respectively, which are indicative of high-spin d5-Mn2+ centers. Density functional calculations illustrate that the coordination mode of 1- is characteristic for its sextet electronic ground state. Compound 3 forms infinite chains of cesocene-type sandwiches in the solid state, which are broken up into small subunits by the addition of crown ether to form 4. Compound 5 is a rare example of a (10,3)-a racemic interpenetrating network that crystallizes in the orthorhombic space group Pbca.     

Synthesis of benzoxazinone derivatives: a new route to 2 (N phthaloylmethyl)-4H-3,1-benzoxazin-4-one

A new method has been designed to prepare the known benzoxazinone derivative 2-(N-phthaloylmethyl)-4H-3,1-benzoxazin-4-one (4). The acyl chloride derivative N-phthaloylglycine reacts with anthranilic acid in chloroform, in the presence of triethylamine, to give an intermediate that is then reacted with cyanuric chloride, used as a cyclization agent, to produce the benzoxazinone derivative.