相关论文: Index for Finite Real Factors
We establish formulas for the constant factor in several asymptotic estimates related to the distribution of integer and polynomial divisors. The formulas are then used to approximate these factors numerically.
The coupling complexity index is an information measure introduced within the framework of ordinal symbolic dynamics. This index is used to characterize the complexity of the relationship between dynamical system components. In this work,…
This note aims at obtaining a variational characterization of complex structures by means of a calculus of variations for real vector bundle valued differential forms, and outlines a perspective to study existence questions via functionals…
Factor analysis aims to describe high dimensional random vectors by means of a small number of unknown common factors. In mathematical terms, it is required to decompose the covariance matrix $\Sigma$ of the random vector as the sum of a…
In this article we try to explore the relation between real conjugacy classes and real characters of finite groups at more refined level. This refinement is in terms of properties of groups such as strong reality and total orthogonality. In…
In this paper we examine bases for finite index inclusion of $II_1$ factors and connected inclusion of finite dimensional $C^*$- algebras. These bases behave nicely with respect to basic construction towers. As applications we have studied…
We consider small factor analysis models with one or two factors. Fixing the number of factors, we prove a finiteness result about the covariance matrix parameter space when the size of the covariance matrix increases. According to this…
A complex-analytic structure within the unit disk of the complex plane is presented. It can be used to represent and analyze a large class of real functions. It is shown that any integrable real function can be obtained by means of the…
We count subrings of small index of $\mathbb{Z}^n$, where the addition and multiplication are defined componentwise. Let $f_n(k)$ denote the number of subrings of index $k$. For any $n$, we give a formula for this quantity for all integers…
The roles played by decision factors in making complex subject are decisions are characterized by how these factors affect the overall decision. Evidence that partially matches a factor is evaluated, and then effective computational rules…
This paper offers a solution method that allows one to find exact values for a large class of convergent series of rational terms. Sums of this form arise often in problems dealing with Quantum Field Theory.
The aim of this paper is to show that there exists a deterministic algorithm that can be applied to compute the factors of a polynomial of degree 2, defined over a finite field, given certain conditions.
We provide a complete classification of the singularities of cluster algebras of finite cluster type. This extends our previous work about the case of trivial coefficients. Additionally, we classify the singularities of cluster algebras for…
Some aspects of basic category theory are developed in a finitely complete category $\C$, endowed with two factorization systems which determine the same discrete objects and are linked by a simple reciprocal stability law. Resting on this…
In this paper we examine an inverse problem in the modular theory of von Neumann algebras in the case of finite factors. First we give a characterization of cyclic and separating vectors for finite factors in terms of operators associated…
Some classes of increment martingales, and the corresponding localized classes, are studied. An increment martingale is indexed by the real line and its increment processes are martingales. We focus primarily on the behavior as time goes to…
If the $n-th$ order differential equation is not exact, under certain conditions, an integrating factor exists which transforms the differential equation into an exact one. Hence, its order can be reduced to the lower order. In this paper,…
Factor models are a very efficient way to describe high dimensional vectors of data in terms of a small number of common relevant factors. This problem, which is of fundamental importance in many disciplines, is usually reformulated in…
All components of complements of discriminant varieties of simple real function singularities are explicitly listed. New invariants of such components (for not necessarily simple singularities) are introduced. A combinatorial algorithm…
We determine the subfactors $N\subset R$ of the hyperfinite $II_1$-factor R with finite index for which the $C^*$-tensor category of the associated $(N,N)$-bimodules is equivalent to the $C^*$-tensor category $\C{U}_G$ of all unitary finite…