B R Wong

On the overlap integral of associated Legendre polynomials.

A simple compact closed-form expression is derived from the definite integral using a convenient analytical formula for the associated Legendre function . This result is easily generalized for integrands involving products of an arbitrary number of associated Legendre polynomials.

Generalized inequalities on warped product submanifolds in nearly trans-Sasakian manifolds

In this paper, we study warped product submanifolds of nearly trans-Sasakian manifolds. The non-existence of warped product semi-slant submanifolds of type Nθ×fNT is shown, whereas some characterization and new geometric obstructions are obtained for the warped products of type NT×fNθ. We establish two general inequalities for the squared norm of the second fundamental form. The first inequality generalizes derived inequalities for some contact metric manifolds (Kadri et al. in J.xa0Korean Math. Soc. 42:1101-1110, 2005; Munteanu in Publ. Math. (Debr.) 66:75-120, 2005; Mustafa et al. in Taiwan. J. Math. 17:1473-1486, 2013; Uddin and Khan in J.xa0Inequal. Appl. 2012:304, 2012), while by a new technique, the second inequality is constructed to express the relation between extrinsic invariant (second fundamental form) and intrinsic invariant (scalar curvatures). The equality cases are also discussed.MSC:53C40, 53C42, 53C15.

Warped Product Pseudo-Slant Submanifolds of a Nearly Cosymplectic Manifold

We study warped product pseudo-slant submanifolds of a nearly cosymplectic manifold. We obtain some characterization results on the existence or nonexistence of warped product pseudo-slant submanifolds of a nearly cosymplectic manifold in terms of the canonical structures 𝑃 and 𝐹.

An analytical solution of the time-independent Schrödinger equation for the Woods-Saxon potential for arbitrary angular momentum l states

The Woods-Saxon potential is probably the most studied and widely used short range potential in all of nuclear physics. For the angular momentum l= 0 case, Flugge had devised a method to obtain an analytical expression for the bound state energies of the radial time-independent Schrӧdinger equation for a neutron confined in a Woods-Saxon potential well. In this study, we extend Flugges method to solve the radial Schrӧdinger equation for a neutron within the Woods-Saxon potential and the centrifugal potential for arbitrary values of l. Here, the Pekeris method is used to deal with the centrifugal term. We obtain an analytical expression for the bound states, valid for arbitrary angular momentum, and show that our expression reduces to that of Flugge, which applies to the l= 0 case. The numerical computations performed also show very good agreement with our analytical expression.

Optimal control for fuzzy linear partial differential algebraic equations using Simulink

In this paper, optimal control for fuzzy linear partial differential algebraic equations (FPDAE) with quadratic performance is obtained using Simulink. By using the method of lines, the FPDAE is transformed into a fuzzy differential algebraic equations (FDAE). Hence, the optimal control of FPDAE can be found out by finding the optimal control of the corresponding FDAE. The goal is to provide optimal control with reduced calculus effort by the solutions of the matrix Riccati differential equation (MRDE) obtained from Simulink. Accuracy of the solution of the Simulink approach to the problem is qualitatively better. The advantage of the proposed approach is that, once the Simulink model is constructed, it allows to evaluate the solution at any desired number of points spending negligible computing time and memory and the solution curves can be obtained from the model without writing any code. An illustrative numerical example is presented for the proposed method.

Excitation of the 3p states in electron-sodium scattering at intermediate energies

A coupled-channel-optical method (CCOM), to investigate the excitation of the 3p states for e−-Na scattering at intermediate energies, is reported. Nine atomic states( Na(3s), Na(3p), Na(4s), Na(3d), Na(4p), Na(5s), Na(4d), Na(5p), Na(5d) ) together with three optical potentials are used in this work. The inelastic differential cross sections (DCS) as well as the reduced Stokes parameters are compared with latest theoretical data and experimental measurements.

Modeling of fast capillary-discharge for soft x-ray lasers

In this work we present the results of the numerical investigations of the one- dimensional single-fluid magneto-hydrodynamics (MHD) model, with separate electron and ion temperatures, of a capillary-discharge collisional soft x-ray laser. The MHD equations are solved by the Lagrangian cylindrical geometry approach. The effects of the gas filling pressure on the plasma densities and temperatures, and implosion-pinch phase for soft x-ray lasing conditions have been analyzed. The results are compared with experimental measurements of the operating pressure ranges.

Analytical Proton Transfer Amplitude for Heavy Ion Induced Nuclear Reactions

Direct reactions between heavy ions have been studied widely using semi‐classical theories. The Distorted Wave Born Approximation or DWBA has been extensively applied to analyse transfer reaction processes. Initial attempts to gain insights into the simple semi‐classical parametrisation starting from the DWBA had focused mainly on neutron transfer reactions. An analytical formula for the semi‐classical amplitude for the transfer of a single neutron between bound classical orbits states in heavy ion collisions that agrees well with the DWBA calculations has been successfully derived. In this paper, we have successfully derived the corresponding analytical expression for the proton transfer amplitude by using a technique analogous to the transfer of a single neutron between bound states. Our result reduces to the well known expression for the neutron transfer amplitude in the limit that the nuclear charge tends to zero.

Optimal control for Navier-Stokes Takagi-Sugeno Fuzzy Equations Using Simulink

In this paper, the unsteady Navier-Stokes Takagi-Sugeno (T-S) fuzzy equations (UNSTSFEs) are represented as a differential algebraic system of strangeness index one by applying any spatial discretization. Since such differential algebraic systems have a difficulty to solve in their original form, most approaches use some kind of index reduction. While processing this index reduction, it is important to take care of the manifolds contained in the differential algebraic equation (DAE) /singular system (SS) for each fuzzy rule. The Navier-Stokes equations are investigated along the lines of the theoretically best index reduction by using several discretization schemes. Applying this technique, the UNSTSFEs can be reduced into DAE. Optimal control for Navier-Stokes T-S fuzzy system with quadratic performance is obtained by finding the optimal control of singular T-S fuzzy system using Simulink. To obtain the optimal control, the solution of matrix Riccati differential equation (MRDE) is found by solving differential algebraic equation (DAE) using Simulink approach. The solution of Simulink approach is equivalent or very close to the exact solution of the problem. An illustrative numerical example is presented for the proposed method.

Analytical formalism for heavy-ion-induced direct nuclear reactions: elastic and inelastic scattering

An analytical formalism for heavy-ion-induced elastic and inelastic scattering is developed within the framework of direct reaction theories. This formalism is based on a generalised semiclassical method which has been shown to be in excellent quantitative agreement with a fully quantum mechanical approach over a wide range of Q-values. Analytical expressions for the elastic phase shift, the inelastic amplitudes due to the Coulomb and nuclear excitation are derived and the magnetic substate dependence is explicitly shown. In particular, the Coulomb inelastic amplitude is found to be exact provided the heavy ions do not overlap. It is shown that the analytical formalism developed in this paper is in excellent agreement with the numerical calculations.