Search results for "Computational Mathematic"
showing 10 items of 987 documents
Hilbert modularity of some double octic Calabi--Yau threefolds
2018
We exhibit three double octic Calabi--Yau threefolds over the certain quadratic fields and prove their modularity. The non-rigid threefold has two conjugate Hilbert modular forms of weight [4,2] and [2,4] attached while the two rigid threefolds correspond to a Hilbert modular form of weight [4,4] and to the twist of the restriction of a classical modular form of weight 4.
Self-organized modularization in evolutionary algorithms.
2005
The principle of modularization has proven to be extremely successful in the field of technical applications and particularly for Software Engineering purposes. The question to be answered within the present article is whether mechanisms can also be identified within the framework of Evolutionary Computation that cause a modularization of solutions. We will concentrate on processes, where modularization results only from the typical evolutionary operators, i.e. selection and variation by recombination and mutation (and not, e.g., from special modularization operators). This is what we call Self-Organized Modularization. Based on a combination of two formalizations by Radcliffe and Altenber…
Diatropicity of tetraazanaphthalenes
2006
Tetraazanaphthalenes are diatropic molecules, whose magnetic response to a magnetic field perpendicular to the molecular plane closely resembles that of naphthalene. The out-of-plane component of the magnetic susceptibility tensor and its strong anisotropy can be used as quantifiers of magnetic aromaticity. Maps showing streamlines and modulus of the current density field provide clear evidence for diatropicity of these systems. They also explain the strong anisotropy of carbon and nitrogen magnetic shielding, which is determined by the big out-of-plane component of the nuclear shielding tensor. The electronic ring currents observed in the map deshield the nuclei of ring hydrogens by enforc…
VIBPACK: A package to treat multidimensional electron-vibrational molecular problems with application to magnetic and optical properties
2018
We present a FORTRAN code based on a new powerful and efficient computational approach to solve multidimensional dynamic Jahn-Teller and pseudo Jahn-Teller problems. This symmetry-assisted approach constituting a theoretical core of the program is based on the full exploration of the point symmetry of the electronic and vibrational states. We also report some selected examples of increasing complexity aimed to display the theoretical background as well as the advantages and capabilities of the program to evaluate of the energy pattern, magnetic and optical properties of large multimode vibronic systems. © 2018 Wiley Periodicals, Inc.
Efficient High-Order Iterative Methods for Solving Nonlinear Systems and Their Application on Heat Conduction Problems
2017
[EN] For solving nonlinear systems of big size, such as those obtained by applying finite differences for approximating the solution of diffusion problem and heat conduction equations, three-step iterative methods with eighth-order local convergence are presented. The computational efficiency of the new methods is compared with those of some known ones, obtaining good conclusions, due to the particular structure of the iterative expression of the proposed methods. Numerical comparisons are made with the same existing methods, on standard nonlinear systems and a nonlinear one-dimensional heat conduction equation by transforming it in a nonlinear system by using finite differences. From these…
Traced tensor norms and multiple summing multilinear operators
2016
[EN] Using a general tensor norm approach, our aim is to show that some distinguished classes of summing operators can be characterized by means of an 'order reduction' procedure for multiple summing multilinear operators, which becomes the keystone of our arguments and can be considered our main result. We work in a tensor product framework involving traced tensor norms and the representation theorem for maximal operator ideals. Several applications are given not only to multi-ideals, but also to linear operator ideals. In particular, we get applications to multiple p-summing bilinear operators, (p, q)-factorable linear operators, tau(p)-summing linear operators and absolutely p-summing li…
QuBiLS-MIDAS: A parallel free-software for molecular descriptors computation based on multilinear algebraic maps
2014
The present report introduces the QuBiLS-MIDAS software belonging to the ToMoCoMD-CARDD suite for the calculation of three-dimensional molecular descriptors (MDs) based on the two-linear (bilinear), three-linear, and four-linear (multilinear or N-linear) algebraic forms. Thus, it is unique software that computes these tensor-based indices. These descriptors, establish relations for two, three, and four atoms by using several (dis-)similarity metrics or multimetrics, matrix transformations, cutoffs, local calculations and aggregation operators. The theoretical background of these N-linear indices is also presented. The QuBiLS-MIDAS software was developed in the Java programming language and …
Transition state theory thermal rate constants and RRKM-based branching ratios for the N((2)D) + CH(4) reaction based on multi-state and multi-refere…
2012
International audience; Multireference single and double configuration interaction (MRCI) calculations including Davidson (+Q) or Pople (+P) corrections have been conducted in this work for the reactants, products, and extrema of the doublet ground state potential energy surface involved in the N(2D) + CH4 reaction. Such highly correlated ab initio calculations are then compared with previous PMP4, CCSD(T), W1, and DFT/B3LYP studies. Large relative differences are observed in particular for the transition state in the entrance channel resolving the disagreement between previous ab initio calculations. We confirm the existence of a small but positive potential barrier (3.86 +/- 0.84 kJ mol-1…
Molecular polarizability of Si/Ge/GaAs semiconductors clusters
2004
The interacting induced dipole polarization model implemented in our program for the calculation of molecular polarizabilities (POLAR) is used for the calculation of the molecular dipole-dipole polarizability ${\overline{\overline{α}}}$. POLAR is tested with Si$_{n}$, Ge$_{n}$ and Ga$_{n}$As$_{m}$ small clusters. The polarizability is an important quantity for the identification of clusters with different numbers of atoms and even for the separation of isomers. The results for the polarizability are in agreement with reference calculations performed with our version of the program PAPID (polarisabilites atomiques par interactions dipolaires) and with reference computations from Dr. J.R. Che…
A Smoothed Particle Image Reconstruction method
2010
Many image processing techniques work with scattered data distribution usually employing grid based methods leading to numerical problems. To address this issue, a numerical method avoiding mesh generation can be used. Such a method performs an integral representation by means of a smoothing kernel function and, in the discrete formulation, involves domain particles. In this paper the meshless Smoothed Particle Hydrodynamics method is proposed in the Image Reconstruction context and a new computational strategy called Smoothed Particle Image Reconstruction is presented; the new method is based on a scatter approach and several innovative ideas are introduced in order to improve the computat…