Search results for "Model theory"
showing 10 items of 681 documents
The Binggeli effect
2016
We found the alignement of elongated clusters of BM type I and III (the excess of small values of the \Delta\theta angles is observed), having range till about 60Mpc/h. The first one is probably connected with the origin of supergiant galaxy, while the second one with environmental effects in clusters, originated on the long filament or plane.
Plane foliations with a saddle singularity
2012
Abstract We study the set of planar vector fields with a unique singularity of hyperbolic saddle type. We found conditions to assure that a such vector field is topologically equivalent to a linear saddle. Furthermore, we describe the plane foliations associated to these vector fields. Such a foliation can be split in two subfoliations. One without restriction and another one that is topologically characterized by means of trees.
Homomorphisms on spaces of weakly continuous holomorphic functions
1999
Let X be a Banach space and let $X^{\ast }$ be its topological dual space. We study the algebra ${\cal H}_{w^\ast}(X^{\ast})$ of entire functions on $X^{\ast }$ that are weak-star continuous on bounded sets. We prove that every m-homogeneous polynomial of finite type P on $X^*$ that is weak-star continuous on bounded sets can be written in the form $P=\textstyle\sum\limits _{j=1}^q x_{1j}\cdots x_{mj}$ where $x_{ij} \in X$ , for all i,j. As an application, we characterize convolution homomorphisms on ${\cal H}_{w^\ast}(X^{\ast})$ and on the space ${\cal H}_{wu}(X)$ of entire functions on X which are weakly uniformly continuous on bounded subsets of X, assuming that X * has the approximation…
Chiral corrections to the SU(2) x SU(2) Gell-Mann-Oakes-Renner relation
2010
The next to leading order chiral corrections to the SU(2) x SU(2) Gell-Mann-Oakes- Renner (GMOR) relation are obtained using the pseudoscalar correlator to five-loop order in perturbative QCD, together with new finite energy sum rules (FESR) incorporating polynomial, Legendre type, integration kernels. The purpose of these kernels is to suppress hadronic contributions in the region where they are least known. This reduces considerably the systematic uncertainties arising from the lack of direct experimental information on the hadronic resonance spectral function. Three different methods are used to compute the FESR contour integral in the complex energy (squared) s-plane, i.e. Fixed Order P…
Matrix algebras with degenerate traces and trace identities
2022
In this paper we study matrix algebras with a degenerate trace in the framework of the theory of polynomial identities. The first part is devoted to the study of the algebra $D_n$ of $n \times n$ diagonal matrices. We prove that, in case of a degenerate trace, all its trace identities follow by the commutativity law and by pure trace identities. Moreover we relate the trace identities of $D_{n+1}$ endowed with a degenerate trace, to those of $D_n$ with the corresponding trace. This allows us to determine the generators of the trace T-ideal of $D_3$. In the second part we study commutative subalgebras of $M_k(F)$, denoted by $C_k$ of the type $F + J$ that can be endowed with the so-called st…
A computational approximation for the solution of retarded functional differential equations and their applications to science and engineering
2021
<p style='text-indent:20px;'>Delay differential equations are of great importance in science, engineering, medicine and biological models. These type of models include time delay phenomena which is helpful for characterising the real-world applications in machine learning, mechanics, economics, electrodynamics and so on. Besides, special classes of functional differential equations have been investigated in many researches. In this study, a numerical investigation of retarded type of these models together with initial conditions are introduced. The technique is based on a polynomial approach along with collocation points which maintains an approximated solutions to the problem. Beside…
Non Linear Fitting Methods for Machine Learning
2017
This manuscript presents an analysis of numerical fitting methods used for solving classification problems as discriminant functions in machine learning. Non linear polynomial, exponential, and trigonometric models are mathematically deduced and discussed. Analysis about their pros and cons, and their mathematical modelling are made on what method to chose for what type of highly non linear multi-dimension problems are more suitable to be solved. In this study only deterministic models with analytic solutions are involved, or parameters calculation by numeric methods, which the complete model can subsequently be treated as a theoretical model. Models deduction are summarised and presented a…
AN HYPERBOLIC-PARABOLIC PREDATOR-PREY MODEL INVOLVING A VOLE POPULATION STRUCTURED IN AGE
2020
Abstract We prove existence and stability of entropy solutions for a predator-prey system consisting of an hyperbolic equation for predators and a parabolic-hyperbolic equation for preys. The preys' equation, which represents the evolution of a population of voles as in [2] , depends on time, t, age, a, and on a 2-dimensional space variable x, and it is supplemented by a nonlocal boundary condition at a = 0 . The drift term in the predators' equation depends nonlocally on the density of preys and the two equations are also coupled via classical source terms of Lotka-Volterra type, as in [4] . We establish existence of solutions by applying the vanishing viscosity method, and we prove stabil…
Full Sliding “Adhesive-Like” Contact of V-Belts
2002
Abstract Analysis of power transmission in a belt drive consisting of e. g. two pulleys might be treated as a boundary value problem. Tight side tension FT, slack side tension FS and the wrap angle α are the three natural boundary conditions. In the literature, theories are developed where seating and unseating as well as the power transmitting part of the contact are considered. The solutions presented so far don’t fulfil the boundary conditions properly, since a certain tension ratio FT/FS is associated with a certain contact angle and not an a priori specified one. It appears that a new type of full sliding solution must be introduced to handle the boundary condition problem. During part…
$V$-filtrations in positive characteristic and test modules
2013
Let $R$ be a ring essentially of finite type over an $F$-finite field. Given an ideal $\mathfrak{a}$ and a principal Cartier module $M$ we introduce the notion of a $V$-filtration of $M$ along $\mathfrak{a}$. If $M$ is $F$-regular then this coincides with the test module filtration. We also show that the associated graded induces a functor $Gr^{[0,1]}$ from Cartier crystals to Cartier crystals supported on $V(\mathfrak{a})$. This functor commutes with finite pushforwards for principal ideals and with pullbacks along essentially \'etale morphisms. We also derive corresponding transformation rules for test modules generalizing previous results by Schwede and Tucker in the \'etale case (cf. ar…