相关论文: Index for Finite Real Factors

The main object of this paper is to find closed form expressions for finite and infinite sums that are weighted by $\omega(n)$, where $\omega(n)$ is the number of distinct prime factors of $n$. We then derive general convergence criteria…

In this study, a recursive solution technique in conjunction with generalized integrating factors is presented and applied to address first and second order linear differential equations. This approach demonstrates practical utility in…

We introduce a \textit{quantum index} for oriented real curves inside toric varieties. This quantum index is related to the computation of the area of the amoeba of the curve for some chosen 2-form. We then make a refined signed count of…

Two doubly indexed families of polynomials in several indeterminates are considered. They are related to the falling and rising factorials in a similar way as the potential polynomials (introduced by L. Comtet) are related to the ordinary…

We study the complexity of deterministic and probabilistic inversions of partial computable functions on the reals.

An inclusion of II$_1$ factors $N \subset M$ with finite Jones index gives rise to a powerful set of invariants that can be approached successfully in a number of different ways. We describe Jones' pictorial description of the standard…

This paper generalizes the results obtained in an earlier paper (math.OA/0003087) for finite factors to infinite but still semifinite factors. First we give a characterization of cyclic and separating vectors for infinite semifinite factors…

We introduce three classes of analytic functions with fixed second coefficient which are defined using the class $\mathcal{P}$ of analytic functions with positive real part. The objective is to determine radii such that the three classes…

In this paper, we have studied first the idea of rough continuity of real valued functions of real variables and then we have discussed some important properties of rough continuity. Then we study the idea of rough $I$-continuity of real…

In calculus, an indefinite integral of a function $f$ is a differentiable function $F$ whose derivative is equal to $f$. In present paper, we generalize this notion of the indefinite integral from the ring of real functions to any ring. The…

Given any finite index quadrilateral $(N, P, Q, M)$ of $II_1$-factors, the notions of interior and exterior angles between $P$ and $Q$ were introduced in \cite{BDLR2017}. We determine the possible values of these angles when the…

Consider a regression or some regression-type model for a certain response variable where the linear predictor includes an ordered factor among the explanatory variables. The inclusion of a factor of this type can take place is a few…

We study II_1 factors M and N associated with good generalized Bernoulli actions of groups having an infinite almost normal subgroup with the relative property (T). We prove the following rigidity result: every finite index M-N-bimodule (in…

We study the number of real rational degree n functions (considered up to linear fractional transformations of the independent variable) with a given set of 2n-2 distinct real critical values. We present a combinatorial reformulation of…

Graded rings provide a natural algebraic framework for encoding symmetry via decompositions into homogeneous components indexed by a group, together with multiplication rules reflecting the group operation. Among graded rings, strongly…

Correction terms generated in the correlator analysis due to multiplicity-dependent observable mean are investigated. A procedure for subtraction of such terms from calculated correlator estimates is suggested and the obtained results are…

We construct approximately inner actions of discrete amenable groups on strongly amenable subfactors of type II_1 with given invariants, and obtain classification results under some conditions. We also study the lifting of the relative \chi…

The present report extends the method of fixed point clustering (Phys.Rev. E 61,5, R4691-4693, 2000) by introducing an indirect criterion for the number of clusters. The derived probability function allows an objective distinction of…

We recall two approaches to recent improvements of the classical Sobolev inequality. The first one follows the point of view of Real Analysis, while the second one relies on tools from Convex Geometry. In this paper we prove a (sharp)…

This is a conspectus of definite integrals, products and series. These formulae involve special functions in the integrand and summand functions and closed form solutions. Some of the special cases are stated in terms of fundamental…