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Ever since the appearance of the seminal work of Einstein, Podolsky and Rosen (The EPR-paradox), the phenomenon of entanglement, which features the essential difference between classical and quantum physics, has received wide theoretical…

We are able to rederive in a very simple way the standard generalized Wick's theorem for overlaps of mean field wave functions by using the extension of the statistical Wick's theorem (Gaudin's theorem) in the appropriate limits.

We extend the Dirichlet principle to non-reversible Markov processes on countable state spaces. We present two variational formulas for the solution of the Poisson equation or, equivalently, for the capacity between two disjoint sets. As an…

By Zeckendorf's theorem, an equivalent definition of the Fibonacci sequence (appropriately normalized) is that it is the unique sequence of increasing integers such that every positive number can be written uniquely as a sum of non-adjacent…

Empirical science needs to be based on facts and claims that can be reproduced. This calls for replicating the studies that proclaim the claims, but practice in most fields still fails to implement this idea. When such studies emerged in…

There are several extensions of the classical Banach Fixed Point Theorem in technical literature. A branch of generalizations replaces usual contractivity by weaker but still effective assumptions. Our note follows this stream, presenting…

We give recurrence relations for any family of generalized Appell polynomials unifying so some known recurrences of many classical sequences of polynomials. Our main tool to get our goal is the Riordan group. We use the product of Riordan…

A new $q$-analogue of Appell polynomial sequences and their generalizations are introduced and their main characterizations are proved. As consequences new $q$-analogue of Bernoulli and Euler polynomials and numbers is introduced, their…

Let $(X,T,\mu,d)$ be a metric measure-preserving system for which $3$-fold correlations decay exponentially for Lipschitz continuous observables. Suppose that $(M_k)$ is a sequence satisfying some weak decay conditions and suppose there…

In this note, we present a refinement of the well-known AM-GM inequality. We use this improved inequalty to establish corresponding inequalities on Hilbert space. We also give some refinements of the Kantorovich inequality.

New iterative methods for solving linear equations are presented that are easy to use, generalize good existing methods, and appear to be faster. The new algorithms mix two kinds of linear recurrence formulas. Older methods have either high…

The theory of ``Markov-up'' processes is being developed. This is a new class of stochastic processes with ``partial'' markovian features; it could also be called ``one-sided Markov''. Such a behavior may be found in the real world and in…

We introduce a series of numbers which serve as a generalization of Bernoulli, Euler numbers and binomial coefficients. Their properties are applied to solve a probability problem and suggest a statistical test for independence and…

We state and prove a Lemma in 1 variable Calculus, that justifies some arguments previously used to ilustrate non-uniqueness of some generalized physical quantities.

An approach to build Probabilistic Arithmetic in which initial values of all correlated random variables are known, but with varying degrees of accuracy. As a result of the proposed Probabilistic Arithmetic operations, variable values,…

We prove a generalization of Lopes's theorem, that is, of the converse of Brolin's theorem.

We prove a simple inequality for a sum of squares of norms of two vectors in an inner product space. Next, using this inequality we derive the so--called "reverse uncertainty relation" and analyze its properties.

Recently we discovered (cond-mat/0212043) that the majority of scientific citations are copied from the lists of references used in other papers. Here we show that a model, in which a scientist picks three random papers, cites them,and also…

For an arbitrary homogeneous linear recurrence sequence of order d with constant coefficients, we derive recurrence relations for all subsequences with indices in arithmetic progression. The coefficients of these recurrences are given…

We explore and generalize a Cauchy-Schwarz-type inequality originally proved in [Electronic Journal of Linear Algebra 35, 156-180 (2019)]: $\|\mathbf{v}^2\|\|\mathbf{w}^2\| - \langle\mathbf{v}^2,\mathbf{w}^2\rangle \leq…