Search results for "Group Theory"

READING WORDS, NUMB3R5 and $YMßOL$

2007

Words in alphabetic languages are processed via their constituents [1]. To recognize a printed word, we need to process the identity and position of its letters, hence distinguishing between cat and fat, or dog and god, but not between tABLe and TabLE, or and . Dehaene and colleagues [2] proposed a neuronal model with feed-forward connections only, according to which the brain decodes words through a hierarchy of local combination detectors in the occipito–infero–temporal pathway sensitive to increasingly larger fragments of words.

Bounds for the relative n-th nilpotency degree in compact groups

2009

The line of investigation of the present paper goes back to a classical work of W. H. Gustafson of the 1973, in which it is described the probability that two randomly chosen group elements commute. In the same work, he gave some bounds for this kind of probability, providing information on the group structure. We have recently obtained some generalizations of his results for finite groups. Here we improve them in the context of the compact groups.

Solving fully randomized higher-order linear control differential equations: Application to study the dynamics of an oscillator

2021

[EN] In this work, we consider control problems represented by a linear differential equation assuming that all the coefficients are random variables and with an additive control that is a stochastic process. Specifically, we will work with controllable problems in which the initial condition and the final target are random variables. The probability density function of the solution and the control has been calculated. The theoretical results have been applied to study, from a probabilistic standpoint, a damped oscillator.

Landau theory applied to phase transitions in calcium orthotungstate and isostructural compounds

2007

The pressure-driven tetragonal-to-monoclinic phase transition in CaWO4 and related scheelite-structured orthotungstates is analysed in terms of spontaneous strains. Based upon our previous high-pressure x-ray diffraction results and the Landau theory, it is suggested that the scheelite-to-fergusonite transition is of second order in nature.

About the reliability of the Maximum Entropy Method in reconstructing electron density: the case of MgO

2006

Abstract The reliability of the Maximum Entropy Method (MEM) to reconstruct finite temperature electron density (ED) is here discussed, investigating the case of periclase (MgO). A theoretical electron density has been generated by quantum mechanic calculations and folded with a function simulating atomic thermal motion, in order to produce a reference errorless ED [ρ(r)REF]. The Fourier coefficients of ρ(r)REF have been calculated, and used as “observed” diffraction intensities to reconstruct via MEM the original ED. The electron density attained by MEM [ρ(r)MEM] and ρ(r)REF have been compared with each other (pixel-by-pixel and critical points) to assess the ability of MEM to retrieve EDs…

Mechanisms at structural phase transitions

2007

Abstract Structural phase transitions in crystalline solids are accompanied with the change of symmetry. After EHRENFEST [Ehrenfest, P., Phasenumwandlungen im ublichen und erweiterten Sinn, klassifiziert nach den entsprechenden Singularitaten des thermodynamischen Potentials. Proc. Kon., Amsterdam Acad., 1933, 36(Suppl 75b), 153–157] they can be distinguished between first and second order transitions. Two examples for first and second order transitions will be discussed in order two elaborate the characteristic features. The statements are verified by diffraction experiments; the second order transitions will be discussed on the basis of the LANDAU [Landau, L. and Lifshitz, E.M., Lehrbuch …

Charge transfer states of C2 in Kr clusters

2004

Abstract Ab initio and diatomics-in-ionic-systems (DIIS) calculations are carried out for the C 2 –Kr pair and C 2 –Kr n clusters, respectively. Energetics and transition dipole moments between the ground and excited states are obtained from the calculations. This data is then used to predict the UV charge transfer absorption spectrum of C 2 embedded in Kr n clusters with n  = 1, 12, and 224. The results reveal discrete structure in the computed UV spectrum, which is mainly related to the spin–orbit splitting of Kr + .

Dipolar NLO-phores with large off-diagonal components of the second-order polarizability tensor

1997

Branches of index-preserving solutions to systems of second order ODEs

2009

We investigate the existence of a continuum of index-preserving solutions to a Dirichlet problem associated with a parameter-dependent system of second order ordinary differential equations, developing a detailed analysis on the behaviour of the branches of nontrivial solutions. Our approach is based on the Rabinowitz global bifurcation Theorem combined with the notion of index and nullity of suitable linear boundary value problems. An application of the result to the study of branches of odd, periodic solutions for suitable systems of two linearly coupled pendulums of lenghts variables is also analyzed.

Longest Motifs with a Functionally Equivalent Central Block

2004

International audience; This paper presents a generalization of the notion of longest repeats with a block of k don't care symbols introduced by [Crochemore et al., LATIN 2004] (for k fixed) to longest motifs composed of three parts: a first and last that parameterize match (that is, match via some symbol renaming, initially unknown), and a functionally equivalent central block. Such three-part motifs are called longest block motifs. Different types of functional equivalence, and thus of matching criteria for the central block are considered, which include as a subcase the one treated in [Crochemore et al., LATIN 2004] and extend to the case of regular expressions with no Kleene closure or …