Search results for "Computational Mathematic"
showing 10 items of 987 documents
Structure, magnetizability, and nuclear magnetic shielding tensors of bis-heteropentalenes. IV. Dihydrophospholophosphole isomers
2005
The geometry of the heteropentalenes formed by two phosphole units has been determined at the DFT level. The magnetic susceptibility and the nuclear magnetic shielding at the nuclei of these systems have also been calculated using gauge-including atomic orbitals and a large Gaussian basis set to achieve near Hartree-Fock estimates. A comparative study of the various isomers, of their flattened analogs, and of the parent phosphole molecule, shows that the [3,4-c] isomer is the most aromatic system in the set considered, assuming diatropicity and degree of planarity as indicators, even if it is the less stable in terms of total molecular energy. Plots of magnetic field-induced current densiti…
Semiempirical PM5 molecular orbital study on chlorophylls and bacteriochlorophylls: Comparison of semiempirical,ab initio, and density functional res…
2003
The semiempirical PM5 method has been used to calculate fully optimized structures of magnesium-bacteriochlorin, magnesium-chlorin, magnesium-porphin, mesochlorophyll a, chlorophylls a, b, c(1), c(2), c(3), and d, and bacteriochlorophylls a, b, c, d, e, f, g, and h with all homologous structures. Hartree-Fock/6-31G* ab initio and density functional B3LYP/6-31G* methods were used to optimize structures of methyl chlorophyllide a, chlorophyll c(1), and methyl bacteriochlorophyllides a and c for comparison. Spectroscopic transition energies of the chromophores and their 1:1 or 1:2 solvent complexes were calculated with the Zindo/S CIS method. The self-consistent reaction field model was used t…
Musical pitch quantization as an eigenvalue problem
2020
How can discrete pitches and chords emerge from the continuum of sound? Using a quantum cognition model of tonal music, we prove that the associated Schrödinger equation in Fourier space is invariant under continuous pitch transpositions. However, this symmetry is broken in the case of transpositions of chords, entailing a discrete cyclic group as transposition symmetry. Our research relates quantum mechanics with music and is consistent with music theory and seminal insights by Hermann von Helmholtz.
Functional Type Error Control for Stabilised Space-Time IgA Approximations to Parabolic Problems
2018
The paper is concerned with reliable space-time IgA schemes for parabolic initial-boundary value problems. We deduce a posteriori error estimates and investigate their applicability to space-time IgA approximations. Since the derivation is based on purely functional arguments, the estimates do not contain mesh dependent constants and are valid for any approximation from the admissible (energy) class. In particular, they imply estimates for discrete norms associated with stabilised space-time IgA approximations. Finally, we illustrate the reliability and efficiency of presented error estimates for the approximate solutions recovered with IgA techniques on a model example.
Duality theory for multi-marginal optimal transport with repulsive costs in metric spaces
2018
In this paper we extend the duality theory of the multi-marginal optimal transport problem for cost functions depending on a decreasing function of the distance (not necessarily bounded). This class of cost functions appears in the context of SCE Density Functional Theory introduced in "Strong-interaction limit of density-functional theory" by M. Seidl.
Local minimizers and gamma-convergence for nonlocal perimeters in Carnot groups
2020
We prove the local minimality of halfspaces in Carnot groups for a class of nonlocal functionals usually addressed as nonlocal perimeters. Moreover, in a class of Carnot groups in which the De Giorgi's rectifiability Theorem holds, we provide a lower bound for the $\Gamma$-liminf of the rescaled energy in terms of the horizontal perimeter.
Guaranteed error bounds and local indicators for adaptive solvers using stabilised space–time IgA approximations to parabolic problems
2019
Abstract The paper is concerned with space–time IgA approximations to parabolic initial–boundary value problems. We deduce guaranteed and fully computable error bounds adapted to special features of such type of approximations and investigate their efficiency. The derivation of error estimates is based on the analysis of the corresponding integral identity and exploits purely functional arguments in the maximal parabolic regularity setting. The estimates are valid for any approximation from the admissible (energy) class and do not contain mesh-dependent constants. They provide computable and fully guaranteed error bounds for the norms arising in stabilised space–time approximations. Further…
A musical reading of a contemporary installation and back: mathematical investigations of patterns in Qwalala
2021
Mathematical music theory helps us investigate musical compositions in mathematical terms. Some hints can be extended towards the visual arts. Mathematical approaches can also help formalize a "translation" from the visual domain to the auditory one and vice versa. Thus, a visual artwork can be mathematically investigated, then translated into music. The final, refined musical rendition can be compared to the initial visual idea. Can an artistic idea be preserved through these changes of media? Can a non-trivial pattern be envisaged in an artwork, and then still be identified after the change of medium? Here, we consider a contemporary installation and an ensemble musical piece derived from…
Blow-up collocation solutions of nonlinear homogeneous Volterra integral equations
2011
In this paper, collocation methods are used for detecting blow-up solutions of nonlinear homogeneous Volterra-Hammerstein integral equations. To do this, we introduce the concept of "blow-up collocation solution" and analyze numerically some blow-up time estimates using collocation methods in particular examples where previous results about existence and uniqueness can be applied. Finally, we discuss the relationships between necessary conditions for blow-up of collocation solutions and exact solutions.
Collocation Method for Linear BVPs via B-spline Based Fuzzy Transform
2018
The paper is devoted to an application of a modified F-transform technique based on B-splines in solving linear boundary value problems via the collocation method. An approximate solution is sought as a composite F-transform of a discrete function (which allows the solution to be compactly stored as the values of this discrete function). We demonstrate the effectiveness of the described technique with numerical examples, compare it with other methods and propose theoretical results on the order of approximation when the fuzzy partition is based on cubic B-splines.