Vector Arithmetic in the Triangular Grid

Vector arithmetic is a base of (coordinate) geometry, physics and various other disciplines. The usual method is based on Cartesian coordinate-system which fits both to continuous plane/space and digital rectangular-grids. The triangular grid is also regular, but it is not a point lattice: it is not closed under vector-addition, which gives a challenge. The points of the triangular grid are represented by zero-sum and one-sum coordinate-triplets keeping the symmetry of the grid and reflecting the orientations of the triangles. This system is expanded to the plane using restrictions like, at least one of the coordinates is an integer and the sum of the three coordinates is in the interval [−1,1]. However, the vector arithmetic is still not straightforward; by purely adding two such vectors the result may not fulfill the above conditions. On the other hand, for various applications of digital grids, e.g., in image processing, cartography and physical simulations, one needs to do vector arithmetic. In this paper, we provide formulae that give the sum, difference and scalar product of vectors of the continuous coordinate system. Our work is essential for applications, e.g., to compute discrete rotations or interpolations of images on the triangular grid.     

Optical detection of single-electron spin resonance in a quantum dot

We demonstrate optically detected spin resonance of a single electron confined to a self-assembled quantum dot. The dot is rendered dark by resonant optical pumping of the spin with a laser. Contrast is restored by applying a radio frequency (rf) magnetic field at the spin resonance. The scheme is sensitive even to rf fields of just a few microT. In one case, the spin resonance behaves as a driven 3-level lambda system with weak damping; in another one, the dot exhibits remarkably strong (67% signal recovery) and narrow (0.34 MHz) spin resonances with fluctuating resonant positions, evidence of unusual dynamic processes.     

Exact solutions for nonlinear partial fractional differential equations

In this article,we use the fractional complex transformation to convert nonlinear partial fractional differential equations to nonlinear ordinary differential equations.We use the improved(G’/G)-expansion function method to calculate the exact solutions to the time-and space-fractional derivative foam drainage equation and the time-and space-fractional derivative nonlinear KdV equation.This method is efficient and powerful for solving wide classes of nonlinear evolution fractional order equations.     

Asymptotic Behavior of Solutions for a Class of Fractional Integro-differential Equations

In this paper, we study the asymptotic behavior of solutions for a general class of fractional integro-differential equations. We consider the Caputo fractional derivative. Reasonable sufficient conditions under which the solutions behave like power functions at infinity are established. For this purpose, we use and generalize some well-known integral inequalities. It was found that the solutions behave like the solutions of the associated linear differential equation with zero right hand side. Our findings are supported by examples.     

Simulation of planar ionization wave front propagation on an unstructured adaptive grid

The paper deals with the numerical solution of a basic 2D model of the propagation of an ionization wave. The system of equations describing this propagation consists of a coupled set of reaction–diffusion-convection equations and a Poissons equation. The transport equations are solved by a finite volume method on an unstructured triangular adaptive grid. The upwind scheme and the diamond scheme are used for the discretization of the convection and diffusion fluxes, respectively. The Poisson equation is also discretized by the diamond scheme. Numerical results are presented. We deal in more detail with numerical tests of the grid adaptation technique and its influence on the numerical results. An original behavior is observed. The grid refinement is not sufficient to obtain accurate results for this particular phenomenon. Using a second order scheme for convection is necessary.     

Solvability of some quadratic BSDEs without exponential moments

We establish the existence and uniqueness of square integrable solutions for a class of one-dimensional quadratic backward stochastic differential equations (QBSDEs). This is done with a merely square integrable terminal condition, and in some cases with a measurable generator. This shows, in particular, that neither the existence of exponential moments for the terminal condition nor the continuity of the generator are needed for the existence and/or uniqueness of solutions for quadratic BSDEs. These conditions are used in the previous papers on QBSDEs. To do this, we show that Itô?s formula remains valid for functions having a merely locally integrable second (generalized) derivative. A comparison theorem is also established.     

Extreme value modeling under power normalization

In this paper the mathematical modeling of extremes under power normalization is developed. An estimate of the shape parameter within the generalized extreme value distribution under power normalization is suggested. The statistical inference about the upper tail of a distribution function by using the power normalization is studied. Two models for generalized Pareto distribution under power normalization (GPDP) are given. Estimates for the shape and scale parameters within these GPDP’s are obtained. Finally, a simulation study illustrates and corroborates theoretical results.     

Micellar catalysis on the redox reaction of glycolic acid with chromium(VI)

Chromium(VI) oxidation of glycolic acid in the absence and presence of cetyltrimethylammonium bromide (CTAB) and cetylpyridinium bromide (CPB) followed the same mechanism as shown by kinetic study. The reaction followed second‐order kinetics, first‐order in each reactant. The oxidation is strongly catalyzed by manganese(II) and cationic micelles of CTAB or CPB. The catalytic effect of micelles can be fitted to a model in which the reaction rate depends upon the concentration of both reactants in the micellar pseudophase. Some added inorganic salts (NaCl, NaBr, NaNO₃, and Na₂SO₄) reduce the micellar catalysis by excluding glycolic acid from the reaction site. The reactivity of glycolic acid towards chromium(VI) has been discussed and also compared with those obtained previously for the reaction between chromium(VI) and the reductants oxalic and lactic acids. On the basis of the observed results, probable mechanisms have been proposed. © 2001 John Wiley & Sons, Inc. Int J Chem Kinet 33: 377–386, 2001     

An analytical solution of the dynamics of a symmetrically operated parallel flow heat exchanger

An investigation of an analytical solution of the dynamics of a symmetrically operated parallel flow heat exchanger in the form of transfer matrix was performed. Perturbation method was used to linearize the usual non-linear model of such systems. A non-interactive controller to decouple the outputs and a controller to offset any expected disturbances in the boundary temperature was considered. A discrete model was established and found to predict the heat exchanger dynamics adequately. The results are acceptable and encouraging and the model has been found to be sufficient enough to achieve the objective of countering uncontrolled disturbance without requiring precise knowledge of process dynamics. The validity of the proposed control design is examined by comparing it with other models in the literature.