相关论文: New Proofs for Several Properties of Capacities

This note is devotes to some remarks regarding the use of variational methods, of minimax type, to establish continuity type results

Quantum batteries, consisting of quantum cells, are anticipated to surpass their classical counterparts in performance because of the presence of quantum correlations. Recent theoretical study introduces the quantum battery capacity that is…

In this paper we study the two disks capacitor, for equal and different radii. The new results obtained allow a complete characterization of capacity coefficients and forces at short distances. An extensive numerical calculation confirms…

The generalized divided differences are introduced. They are applied to investigate some properties characterizing generalized higher-order convexity. Among others some support-type property is proved.

The capacitance between two adjacent nodes on an infinite square grid of identical capacitors can easily be found by superposition, and the solution is found by explotting the symmetry of the grid. The mathematical problem presented in this…

We use capacity theory to analyze Coppersmith's method for finding small solutions of linear two variable polynomial congruences. We show that the method will succeed in a positive proportion of cases and fail in a different positive…

The incompressibility method is an elementary yet powerful proof technique. It has been used successfully in many areas. To further demonstrate its power and elegance we exhibit new simple proofs using the incompressibility method.

Quantum capacities are fundamental quantities that are notoriously hard to compute and can exhibit surprising properties such as superadditivity. Thus, a vast amount of literature is devoted to finding tight and computable bounds on these…

We survey various origins and expressions for the quantum potential with some new observations.

This article offers different proofs of ten inequalities from those already published. So that the readers can see for themselves, the tasks specified in the condition of the source and classical inequalities which used in previously…

Recently there has been quite a bit of study carried out related to arithmetic properties of overpartitions into non-multiples of two co-prime integers. The paper [19] by Nadji et al. looked into congruences modulo $3$ and powers of $2$ for…

Several new estimates for the 2-adic valuations of Stirling numbers of the second kind are proved. These estimates, together with criteria for when they are sharp, lead to improvements in several known theorems and their proofs, as well as…

In this paper, we gave some properties of binomial coefficient.

We present a new topological proof of the infinitude of prime numbers with a new topology. Furthermore, in this topology, we characterize the infinitude of any non-empty subset of prime numbers.

We derive two complementarity relations that constrain the individual and bipartite properties that may simultaneously exist in a multi-qubit system. The first expression, valid for an arbitrary pure state of n qubits, demonstrates that the…

In this paper, we introduce a new two-parameter deformation of the Gamma function that generalizes some existing Gamma-type functions in the literature. We study properties of this function that depend on the parameters. We also prove some…

A multiparameter class of integrable systems is introduced.

In this note, we give an alternate proof of the multinomial theorem using a probabilistic approach. Although the multinomial theorem is basically a combinatorial result, our proof may be simpler for a student familiar with only basic…

We introduce a new capacity associated to a non negative function V. We apply this notion to the study of a necessary and sufficient condition to ensure the existence and uniqueness of a Schrodinger type equation with measure data and with…

A multidimensional generalization of the Bernstein class of functions and the properties of functions of the introduced class are examined. In particular, a new proof of the integral representation of Bernstein functions of many variables…