Search results for "dimensions"
showing 10 items of 240 documents
New Accurate Fit of an Extended Set of Saturation Data for the ν3 Band of SF6: Comparison of Hamiltonians in the Spherical and Cubic Tensor Formalisms
2000
An extended set of 321 frequencies of vibration-rotation lines of the nu(3) band of SF(6) has been measured by saturation spectroscopy using various isotopic species of CO(2). A least-squares fit of these data has been performed using an effective Hamiltonian written either with a spherical tensor or with a cubic tensor formalism. We have derived correspondence formulas between the parameters in the two approaches and checked that both formalisms give the same results up to the seventh order. Corrected parameters are given for the fit with a fifth-order Hamiltonian. An accurate representation of the band is obtained at the tenth order (standard deviation approximately 12 kHz) with a remarka…
On Codimensions of Algebras with Involution
2020
Let A be an associative algebra with involution ∗ over a field F of characteristic zero. One associates to A, in a natural way, a numerical sequence \(c^{\ast }_n(A),\)n = 1, 2, …, called the sequence of ∗-codimensions of A which is the main tool for the quantitative investigation of the polynomial identities satisfied by A. In this paper we focus our attention on \(c^{\ast }_n(A),\)n = 1, 2, …, by presenting some recent results about it.
Trace identities and almost polynomial growth
2021
In this paper we study algebras with trace and their trace polynomial identities over a field of characteristic 0. We consider two commutative matrix algebras: $D_2$, the algebra of $2\times 2$ diagonal matrices and $C_2$, the algebra of $2 \times 2$ matrices generated by $e_{11}+e_{22}$ and $e_{12}$. We describe all possible traces on these algebras and we study the corresponding trace codimensions. Moreover we characterize the varieties with trace of polynomial growth generated by a finite dimensional algebra. As a consequence, we see that the growth of a variety with trace is either polynomial or exponential.
The relationship of symptom dimensions with premorbid adjustment and cognitive characteristics at first episode psychosis: Findings from the EU-GEI s…
2021
Premorbid functioning and cognitive measures may reflect gradients of developmental impairment across diagnostic categories in psychosis. In this study, we sought to examine the associations of current cognition and premorbid adjustment with symptom dimensions in a large first episode psychosis (FEP) sample. We used data from the international EU-GEI study. Bifactor modelling of the Operational Criteria in Studies of Psychotic Illness (OPCRIT) ratings provided general and specific symptom dimension scores. Premorbid Adjustment Scale estimated premorbid social (PSF) and academic adjustment (PAF), and WAIS-brief version measured IQ. A MANCOVA model examined the relationship between symptom di…
Quantum Entanglement and the Issue of Selective Influences in Psychology: An Overview
2012
Similar formalisms have been independently developed in psychology, to deal with the issue of selective influences (deciding which of several experimental manipulations selectively influences each of several, generally non-independent, response variables), and in quantum mechanics (QM), to deal with the EPR entanglement phenomena (deciding whether an EPR experiment allows for a "classical" account). The parallels between these problems are established by observing that any two noncommuting measurements in QM are mutually exclusive and can therefore be treated as analogs of different values of one and the same input. Both problems reduce to that of the existence of a jointly distributed syst…
Hardy inequalities and Assouad dimensions
2017
We establish both sufficient and necessary conditions for weighted Hardy inequalities in metric spaces in terms of Assouad (co)dimensions. Our sufficient conditions in the case where the complement is thin are new even in Euclidean spaces, while in the case of a thick complement we give new formulations for previously known sufficient conditions which reveal a natural duality between these two cases. Our necessary conditions are rather straight-forward generalizations from the unweighted case, but together with some examples they indicate the essential sharpness of our results. In addition, we consider the mixed case where the complement may contain both thick and thin parts.
Graded polynomial identities and exponential growth
2009
Let $A$ be a finite dimensional algebra over a field of characteristic zero graded by a finite abelian group $G$. Here we study a growth function related to the graded polynomial identities satisfied by $A$ by computing the exponential rate of growth of the sequence of graded codimensions of $A$. We prove that the $G$-exponent of $A$ exists and is an integer related in an explicit way to the dimension of a suitable semisimple subalgebra of $A$.
Trace Identities on Diagonal Matrix Algebras
2020
Let Dn be the algebra of n × n diagonal matrices. On such an algebra it is possible to define very many trace functions. The purpose of this paper is to present several results concerning trace identities satisfied by this kind of algebras.
Measurement of Dijet Angular Distributions ats=1.96 TeVand Searches for Quark Compositeness and Extra Spatial Dimensions
2009
We present the first measurement of dijet angular distributions in ppbar collisions at sqrt{s}=1.96TeV at the Fermilab Tevatron Collider. The measurement is based on a dataset corresponding to an integrated luminosity of up to 0.7fb-1 collected with the D0 detector. Dijet angular distributions have been measured over a range of dijet masses, from 0.25TeV to above 1.1TeV. The data are in good agreement with the predictions of perturbative QCD and are used to constrain new physics models including quark compositeness, large extra dimensions, and TeV-1 scale extra dimensions. For all models we set the most stringent direct limits to date.
Flavor physics in the quark sector
2010
218 páginas, 106 figuras, 89 tablas.-- arXiv:0907.5386v2.-- Report of the CKM workshop, Rome 9-13th Sep. 2008.-- et al.