相关论文: Product measures without utilizing integrals

With a view to quantum foundations, we define the concepts of an empirical model (a probabilistic model describing measurements and outcomes), a hidden-variable model (an empirical model augmented by unobserved variables), and various…

This article studies a structural aspect of measure-preserving actions of products of countable discrete groups, involving a so-called 'synergodic decomposition' in terms of the ergodic components of the actions of the two factor groups. We…

The sum-product phenomena over a finite extension K of $\mathbb{Q}_p$ is explored. The main feature of the results is the fact that the implied constants are independent of $p$.

An efficient coordinate-free notation is elucidated for differentiating matrix expressions and other functions between higher-dimensional vector spaces. This method of differentiation is known, but not explained well, in the literature.…

We construct an entanglement measure that coincides with the generalized concurrence for a general pure bipartite state based on wedge product. Moreover, we construct an entanglement measure for pure multi-qubit states, which are…

This paper introduces product relation correlation, a measure of product relatedness that assesses the extent to which products may function as substitutes or complements through analysis of shared purchasing patterns. Product relation…

Nonlocal measurement, or instantaneous measurement of nonlocal observables, is a considerably difficult task even for a simple form of product observable since relativistic causality prohibits interaction between spacelike separate…

Proof that under simple assumptions, such as constraints of Put-Call Parity, the probability measure for the valuation of a European option has the mean derived from the forward price which can, but does not have to be the risk-neutral one,…

The relation between the requirement of efficient implementability and the product state representation of numbers is examined. Numbers are defined to be any model of the axioms of number theory or arithmetic. Efficient implementability…

An alternative proof for existence of ``quantum nonlocality without entanglement'', i.e. existence of variables with product-state eigenstates which cannot be measured locally, is presented. A simple``nonlocal'' variable for the case of…

In the context of locally constant skew-products over the shift with circle fiber maps we introduce the notion of measures with periodic repetitive pattern, inspired by \cite{GorIlyKleNal:05} and which includes the non-hyperbolic measures…

We present methods that provide all zeroes and extrema of a function that do not require differentiation. Using point process theory, we are able to describe the locations of zeroes or maxima, their number, as well as their distribution…

We compute the divisors of Borcherds products on integral models of orthogonal Shimura varieties. As an application, we obtain an integral version of a theorem of Borcherds on the modularity of a generating series of special divisors.

The progress in artificial intelligence and machine learning algorithms over the past decade has enabled the development of new methods for the objective measurement of eating, including both the measurement of eating episodes as well as…

This is a survey on the geometry of warped products, without, or essentially with only soft, calculation. Somewhere in the paper, the goal was to give a synthetic account since existing approaches are rather analytic. Somewhere else, we…

We prove a new general multiplicity estimate applicable to sets of functions without any assumption on algebraic independence. The multiplicity estimates are commonly used in determining measures of algebraic independence of values of…

In this paper, we study the formulae for a product of two product Euler polynomials. From this study, we derive some formulae for the integral of the product of two or more Ruler polynomials.

Following our previous work on copula-based nonsymmetric dependence measures, we introduce similar measures for discrete random variables. The measures cover the range between two extremes: independence and complete dependence, which take…

We consider crossed product von Neumann algebras arising from free Bogoljubov actions of the integers. We describe several presentations of them as amalgamated free products and cocycle crossed products and give a criterion for…

We present ir-measures, a new tool that makes it convenient to calculate a diverse set of evaluation measures used in information retrieval. Rather than implementing its own measure calculations, ir-measures provides a common interface to a…