Search results for "ComputingMethodologies_SYMBOLICANDALGEBRAICMANIPULATION"
showing 10 items of 140 documents
Modification of Nanocrystalline WO3 with a Dicationic Perylene Bisimide: Applications to Molecular Level Solar Water Splitting
2015
[(N,N?-Bis(2-(trimethylammonium)ethylene) perylene 3,4,9,10-tetracarboxylic acid bisimide)(PF6)2] (1) was observed to spontaneously adsorb on nanocrystalline WO3 surfaces via aggregation/hydrophobic forces. Under visible irradiation (? > 435 nm), the excited state of 1 underwent oxidative quenching by electron injection (kinj > 108 s-1) to WO3, leaving a strongly positive hole (Eox ? 1.7 V vs SCE), which allows to drive demanding photo-oxidation reactions in photoelectrochemical cells (PECs). The casting of IrO2 nanoparticles (NPs), acting as water oxidation catalysts (WOCs) on the sensitized electrodes, led to a 4-fold enhancement in photoanodic current, consistent with hole transfer from …
Protein knot server: detection of knots in protein structures
2007
KNOTS (http://knots.mit.edu) is a web server that detects knots in protein structures. Several protein structures have been reported to contain intricate knots. The physiological role of knots and their effect on folding and evolution is an area of active research. The user submits a PDB id or uploads a 3D protein structure in PDB or mmCIF format. The current implementation of the server uses the Alexander polynomial to detect knots. The results of the analysis that are presented to the user are the location of the knot in the structure, the type of the knot and an interactive visualization of the knot. The results can also be downloaded and viewed offline. The server also maintains a regul…
Algebraic Curves and Riemann Surfaces in Matlab
2010
In the previous chapter, a detailed description of the algorithms for the ‘algcurves’ package in Maple was presented. As discussed there, the package is able to handle general algebraic curves with coefficients given as exact arithmetic expressions, a restriction due to the use of exact integer arithmetic. Coefficients in terms of floating point numbers, i.e., the representation of decimal numbers of finite length on a computer, can in principle be handled, but the floating point numbers have to be converted to rational numbers. This can lead to technical difficulties in practice. One also faces limitations if one wants to study families of Riemann surfaces, where the coefficients in the al…
Bases for induced characters
1996
AbstractIf G is a finite solvable group, we show that Isaacs' theory on partial characters on Hall π-subgroups can be developed for the nilpotent injectors of G. Therefore, the irreducible characters of G are partitioned into blocks associated to some nilpotent subgroups of G.
A code to calculate (high order) Bessel functions based on the continued fractions method
1993
Abstract We have developed a fast code to calculate Bessel functions of integer and fractional order based on the continued fractions method. This algorithm is specially useful in the case of Bessel functions of high order because it does not require any recalculation using normalization relations.
Hermite interpolation: The barycentric approach
1991
The barycentric formulas for polynomial and rational Hermite interpolation are derived; an efficient algorithm for the computation of these interpolants is developed. Some new interpolation principles based on rational interpolation are discussed.
Numerical Study of Two Sparse AMG-methods
2003
A sparse algebraic multigrid method is studied as a cheap and accurate way to compute approximations of Schur complements of matrices arising from the discretization of some symmetric and positive definite partial differential operators. The construction of such a multigrid is discussed and numerical experiments are used to verify the properties of the method.
Mellin transform approach for the solution of coupled systems of fractional differential equations
2015
In this paper, the solution of a multi-order, multi-degree-of-freedom fractional differential equation is addressed by using the Mellin integral transform. By taking advantage of a technique that relates the transformed function, in points of the complex plane differing in the value of their real part, the solution is found in the Mellin domain by solving a linear set of algebraic equations. The approximate solution of the differential (or integral) equation is restored, in the time domain, by using the inverse Mellin transform in its discretized form.
Walsh function analysis of 2-D generalized continuous systems
1990
The importance of the generalized or singular 2D continuous systems are demonstrated by showing their use in the solution of partial differential equations in two variables. A technique is presented for solving these systems in terms of Walsh functions. The method replaces the solution of a two-variable partial differential equation with the solution of a linear algebraic generalized 2D Sylvester equation. An efficient technique for the recursive solution of the latter equation is offered. All the results apply also in the usual Roesser 2D state-space case. >
Singular distributed parameter systems
1993
The paper deals with the distributed parameter systems described by coupled partial differential equations with singular matrix coefficients. Initial-boundary-value problems are considered in the light of both singular 1d systems theory and the Fourier approach to distributed parameter systems. The method presented in this paper gives the possibility of determining acceptable initial-boundary conditions. An illustrative example is given.