Search results for " Tensor"
showing 10 items of 210 documents
Noetherian type in topological products
2010
The cardinal invariant "Noetherian type" of a topological space $X$ (Nt(X)) was introduced by Peregudov in 1997 to deal with base properties that were studied by the Russian School as early as 1976. We study its behavior in products and box-products of topological spaces. We prove in Section 2: 1) There are spaces $X$ and $Y$ such that $Nt(X \times Y) < \min\{Nt(X), Nt(Y)\}$. 2) In several classes of compact spaces, the Noetherian type is preserved by the operations of forming a square and of passing to a dense subspace. The Noetherian type of the Cantor Cube of weight $\aleph_\omega$ with the countable box topology, $(2^{\aleph_\omega})_\delta$, is shown in Section 3 to be closely related …
Localification of variable-basis topological systems
2011
The paper provides another approach to the notion of variable-basis topological system generalizing the fixed-basis concept of S. Vickers, considers functorial relationships between the categories of modified variable-basis topological systems and variable-basis fuzzy topological spaces in the sense of S.E. Rodabaugh and shows that the procedure of localification is possible in the new setting. Quaestiones Mathematicae 33(2010), 11–33
The relationship between genetic risk variants with brain structure and function in bipolar disorder: A systematic review of genetic-neuroimaging stu…
2017
Genetic-neuroimaging paradigms could provide insights regarding the pathophysiology of bipolar disorder (BD). Nevertheless, findings have been inconsistent across studies. A systematic review of gene-imaging studies involving individuals with BD was conducted across electronic major databases from inception until January 9th, 2017. Forty-four studies met eligibility criteria (N = 2122 BD participants). Twenty-six gene variants were investigated across candidate gene studies and 4 studies used a genome-wide association approach. Replicated evidence (i.e. in >2 studies) suggests that individuals with BD carrying the BDNF Val66Met risk allele could have reduced hippocampal volumes compared …
Approximation problems in linear and non-linear analysis
2023
En esta tesis estudiamos problemas relacionados con aplicaciones de varios tipos que alcanzan su norma u operadores que alcanzan su radio numérico. Tras un capítulo introductorio donde se comentan las notaciones, los principales conceptos, y un resumen histórico del estado del arte, hay 4 capítulos de contenido matemático donde se estudian diversos tipos de problemas. En el capítulo 2, se estudian clases de operadores entre espacios de Banach tales que cuando casi alcanzan su norma (respectivamente, su radio numérico) en un punto (respectivamente, un estado), necesariamente la alcanzan en un punto cercano (respectivamente, en un estado cercano). Se obtienen resultados positivos para dominio…
Multi-domain Feature of Event-Related Potential Extracted by Nonnegative Tensor Factorization: 5 vs. 14 Electrodes EEG Data
2012
As nonnegative tensor factorization (NTF) is particularly useful for the problem of underdetermined linear transform model, we performed NTF on the EEG data recorded from 14 electrodes to extract the multi-domain feature of N170 which is a visual event-related potential (ERP), as well as 5 typical electrodes in occipital-temporal sites for N170 and in frontal-central sites for vertex positive potential (VPP) which is the counterpart of N170, respectively. We found that the multi-domain feature of N170 from 5 electrodes was very similar to that from 14 electrodes and more discriminative for different groups of participants than that of VPP from 5 electrodes. Hence, we conclude that when the …
Testing of a constitutive equation with free volume dependent relaxation spectrum
1979
A model of non-linear viscoelasticity with relaxation times dependent upon free volume is here proposed. The free volume is related to the isotropic part of the stress tensor by means of a simple differential equation. The model predictions are compared with a large amount of experimental results taken on polymeric melts or concentrated solutions and reported in the literature. The single parameter of the model is determined, within each set of data, by fitting of the viscosity curve. A satisfactory agreement is obtained with data taken under both elongation and shear for which also the relaxation behavior after single and double strain steps is considered.
The dynamical equation of the effective gluon mass
2011
In this article we derive the integral equation that controls the momentum dependence of the effective gluon mass in the Landau gauge. This is accomplished by means of a well-defined separation of the corresponding "one-loop dressed" Schwinger-Dyson equation into two distinct contributions, one associated with the mass and one with the standard kinetic part of the gluon. The entire construction relies on the existence of a longitudinally coupled vertex of nonperturbative origin, which enforces gauge invariance in the presence of a dynamical mass. The specific structure of the resulting mass equation, supplemented by the additional requirement of a positive-definite gluon mass, imposes a rat…
Fast relaxation phenomena and slow mode in extended thermodynamics of superfluids
2003
A macroscopic monofluid model of liquid helium II which is based on extended thermodynamics was formulated in previous works, both in the presence and in the absence of dissipative phenomena. In all these studies, the time evolution of the nonequilibrium stress tensor was neglected, putting the relaxation times @t"0 and @t"2 of the nonequilibrium pressure and of the stress deviator equal to zero. In this work, the time evolution of these fields is not neglected and the complete model with 14 fields is studied, in the linear approximation. The propagation of waves is studied and a dispersion relation of degree 14 is obtained. The solutions of this equation are carried out, perturbing the sol…
Relation between quasirigidity andL-rigidity in space-times of constant curvature and weak fields
1997
The relation between quasirigidity andL-rigidity in space-times of constant nonzero curvature and in space-times with small curvature (weak fields) is studied. The covariant expansion of bitensors about a point is considered. We obtain an increase in the order of magnitude, underL-rigidity conditions, of the rate of change with respect to a comoving orthonormal frame of the linear momentum, angular momentum, and reduced multipole moments of the energy-momentum tensor. Thus,L-rigidity leads to quasirigidity in such space-times.
Vacuum type I spacetimes and aligned Papapetrou fields: symmetries
2003
We analyze type I vacuum solutions admitting an isometry whose Killing 2--form is aligned with a principal bivector of the Weyl tensor, and we show that these solutions belong to a family of type I metrics which admit a group $G_3$ of isometries. We give a classification of this family and we study the Bianchi type for each class. The classes compatible with an aligned Killing 2--form are also determined. The Szekeres-Brans theorem is extended to non vacuum spacetimes with vanishing Cotton tensor.