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The products of weak values of quantum observables are shown to be of value in deriving quantum uncertainty and complementarity relations, for both weak and strong measurement statistics. First, a 'product representation formula' allows the…
In the paper, we tackle the following questions: Could the difficulty in solving the Schrodinger equation for an arbitrarily large system be a reflection of some nature intrinsic property? And if so, could this difficulty be a resolution to…
In this paper we consider two types of dimension that can be defined for products of one-dimensional topologically totally transcendental (t.t.t) structures. The first is topological and considers the interior of projections of the set onto…
The aim of this paper is to study ultralimits of pointed metric measure spaces (possibly unbounded and having infinite mass). We prove that ultralimits exist under mild assumptions and are consistent with the pointed measured…
In this work we examine two different measures for inhomogeneity and complexity that are derived from nonextensive considerations a' la Tsallis. Their performance is then tested on theoretically generated patterns. All measures are found to…
The Mardia measures of multivariate skewness and kurtosis summarize the respective characteristics of a multivariate distribution with two numbers. However, these measures do not reflect the sub-dimensional features of the distribution.…
We present several applications of matrix-theoretic inequalities to the magnitude of metric spaces. We first resolve an open problem by showing that the magnitude of any finite metric space of negative type is less than or equal to its…
In this article, we discuss the equality of two inner products on a vector space. Particularly, we look at some geometric properties that are given to a vector space by an inner product namely, length and angle, and we ask under what…
In this paper, we study, in a separable metric space, a class of Hausdorff measures $\mathcal{H}_\mu^{q, \xi}$ defined using a measure $\mu$ and a premeasure $\xi$. We discuss a Hausdorff structure of product sets. Weighted Hausdorff…
The paper described a generalized integrated glance to bin packing problems including a brief literature survey and some new problem formulations for the cases of multiset estimates of items. A new systemic viewpoint to bin packing problems…
We propose a definition of magnitude for a length space with a Borel measure, which involves integrals over the set of geodesics. This quantity agrees with the magnitude of finite metric spaces, up to re-scaling the metric to ensure the…
In the article, we study variational eigenvalues on doubling metric measure spaces. We prove existence of minimizers of variational Neumann $(p,q)$-eigenvalues on metric measure spaces and on this base we obtain estimates of Neumann…
We study the Rudin-Blass (and the Rudin-Keisler) ordering on the finite additive measures on $\omega$. We propose a generalization of the notion of Q-point and selective ultrafilter to measures: Q-measures and selective measures. We show…
Motivated by Leinster-Cobbold measures of biodiversity, the notion of the spread of a finite metric space is introduced. This is related to Leinster's magnitude of a metric space. Spread is generalized to infinite metric spaces equipped…
We reorganize, simplify and expand the theory of contractions or interior products of multivectors, and related topics like Hodge star duality. Many results are generalized and new ones are given, like: geometric characterizations of blade…
We consider (not self-similar) Cantor sets defined by a sequence of piecewise linear functions. We prove that the dimension of the harmonic measure on such a set is strictly smaller than its Hausdorff dimension. Some Hausdorff measure…
A unified theory of orthogonal polynomials of a discrete variable is presented through the eigenvalue problem of hermitian matrices of finite or infinite dimensions. It can be considered as a matrix version of exactly solvable Schr\"odinger…
We study Clark measures on the unit polydisc, giving an overview of recent research and investigating the Clark measures of some new examples of multivariate inner functions. In particular, we study the relationship between Clark measures…
A new formalism to express and operate on diversity measures of qualitative variables, built in a Hilbert space, is presented. The abstract character of the Hilbert space naturally incorporates the equivalence between qualitative variables…
We study in details the isoperimetric profile of product probability measures with tails between the exponential and the Gaussian regime. In particular we exhibit many examples where coordinate half-spaces are approximate solutions of the…