Ab initio calculation of chain structures in chalcohalide glasses

Local structure of Te₃X₂ (X = Cl, Br) chalcohalide glasses were studied using ab initio molecular orbital (MO) theory. The calculation results were compared with Mössbauer spectroscopic parameters in terms of electric-field gradient and electron density at each Te site. In addition, the existence of terminal bond –Te–X was examined. The MO analysis of Te-chain and Te-chain with Cl atoms within a picture of the frontier orbital theory elucidated that the localized orbital at –TeCl₂– site is important to form tellurium halide glass.     

Optimization and Validation of an In Vitro Standardized Glycogen Phosphorylase Activity Assay

Glycogen phosphorylase (GP) is a key enzyme in the glycogenolysis pathway and a potential therapeutic target in the management of type 2 diabetes. It catalyzes a reversible reaction: the release of the terminal glucosyl residue from glycogen as glucose 1-phosphate; or the transfer of glucose from glucose 1-phosphate to glycogen. A colorimetric method to follow in vitro the activity of GP with usefulness in structure-activity relationship studies and high-throughput screening capability is herein described. The obtained results allowed the choice of the optimal concentration of enzyme of 0.38 U/mL, 0.25 mM glucose 1-phosphate, 0.25 mg/mL glycogen, and temperature of 37 °C. Three known GP inhibitors, CP-91149, a synthetic inhibitor, caffeine, an alkaloid, and ellagic acid, a polyphenol, were used to validate the method, CP-91149 being the most active inhibitor. The effect of glucose on the IC₅₀ value of CP-91149 was also investigated, which decreased when the concentration of glucose increased. The assay parameters for a high-throughput screening method for discovery of new potential GP inhibitors were optimized and standardized, which is desirable for the reproducibility and comparison of results in the literature. The optimized method can be applied to the study of a panel of synthetic and/or natural compounds, such as polyphenols.     

A numerical method for European Option Pricing with transaction costs nonlinear equation

This paper deals with the construction of a finite difference scheme and the numerical analysis of its solution for a nonlinear Black–Scholes partial differential equation modelling stock option pricing in the realistic case when transaction costs arising in the hedging of portfolios are taken into account. The analysed model is the Barles–Soner one for which an appropriate fully nonlinear numerical method has not still applied. After construction of the numerical solution, consistency and stability are studied and some illustrative examples are included.     

Piecewise finite series solution of nonlinear initial value differential problem

In this paper, we apply a piecewise finite series as a hybrid analytical-numerical technique for solving some nonlinear systems of ordinary differential equations. The finite series is generated by using the Adomian decomposition method, which is an analytical method that gives the solution based on a power series and has been successfully used in a wide range of problems in applied mathematics. We study the influence of the step size and the truncation order of the piecewise finite series Adomian (PFSA) method on the accuracy of the solutions when applied to nonlinear ODEs. Numerical comparisons between the PFSA method with different time steps and truncation orders against Runge-Kutta type methods are presented. Based on the numerical results we propose a low value truncation order approach with small time step size. The numerical results show that the PFSA method is accurate and easy to implement with the proposed approach.     

On the roots of Wiener polynomials of graphs

The Wiener polynomial of a connected graph $G$ is defined as $W(G;x)=\sum x^{d(u,v)}$, where $d(u,v)$ denotes the distance between $u$ and $v$, and the sum is taken over all unordered pairs of distinct vertices of $G$. We examine the nature and location of the roots of Wiener polynomials of graphs, and in particular trees. We show that while the maximum modulus among all roots of Wiener polynomials of graphs of order $n$ is $\left(\genfrac{}{}{0ex}{}{n}{2}\right)?1$, the maximum modulus among all roots of Wiener polynomials of trees of order $n$ grows linearly in $n$. We prove that the closure of the collection of real roots of Wiener polynomials of all graphs is precisely $(?\infty ,0]$, while in the case of trees, it contains $(?\infty ,?1]$. Finally, we demonstrate that the imaginary parts and (positive) real parts of roots of Wiener polynomials can be arbitrarily large.     

The semi-analytical method for time-dependent wave problems with uncertainties

This paper provides a constructive procedure for the computation of approximate solutions of random time-dependent hyperbolic mean square partial differential problems. Based on the theoretical representation of the solution as an infinite random improper integral, obtained via the random Fourier transform method, a double approximation process is implemented. Firstly, a random Gauss-Hermite quadrature is applied, and then, the evaluations at the nodes of the integrand are approximated by using a random Störmer numerical method. Numerical results are illustrated with examples.     

Transmission eigenvalues with artificial background for explicit material index identification

We are interested in the problem of retrieving information on the refractive index n of a penetrable inclusion embedded in a reference medium from farfield data associated with incident plane waves. Our approach relies on the use of transmission eigenvalues (TEs) that carry information on n and that can be determined from the knowledge of the farfield operator F. In this note, we explain how to modify F into a farfield operator $F^{\mathrm{art}}=F?\stackrel{?}{F}$, where $\stackrel{?}{F}$ is computed numerically, corresponding to well-chosen artificial background and for which the associated TEs provide more accessible information on n.     

Efficiency of a DC magnetic field used for braking the flow within a continuous casting mould

The continuous casting technology provides about 90 percent of the world steel production. The application of DC magnetic fields in form of so-called electromagnetic brakes is considered for an effective flow control with substantial capabilities to improve the product quality or to enhance the productivity of the process. The main effect of the DC magnetic field is supposed to result in a uniform reduction of the maximum velocities in the discharging jet from the submerged entry nozzle and to damp violent turbulent fluctuations. However, the electromagnetic braking of such highly turbulent and complex flows is complicated phenomenon and has not been understood fully until now. We present numerical and experimental investigations focusing on the fluid flow in the continuous casting mould under the influence of a transverse magnetic field. Numerical calculations were performed using the software package CFX with an implemented RANS-SST turbulence model. the non-isotropic nature of the MHD turbulence was taken into account by specific modifications of the turbulence model. Corresponding experimental investigations were carried out at the mock-up LIMMCAST at HZDR. The comparison between our numerical calculations and the experimental results display a very well agreement. An important outcome of this study is the feature that the magnetic field does not provide a continuous reduction of the velocity fluctuations at the nozzle port. (© 2011 Wiley-VCH Verlag GmbH & Co. KGaA, Weinheim)