Related papers: New Proofs for Several Properties of Capacities
An unexpected and somewhat surprising observation is that two counter-cascaded systems, given the right conditions, can exhibit multivaluedness from one of the outputs to the other. The main result presented here is a necessary and…
An approximate analytical expression for "capacitance" of MWPC configurations circulates in the literature since decades and is copied over and over again. In this paper we will try to show that this formula corresponds to a physical…
We perform certain alternating binomial summations with parameters that occur in the analysis of algorithms. A combination of integral and special function and special number representations is used. The results are sufficiently general to…
In this note, we present two new identities for derangements. As a corollary, we have a combinatorial proof of the irreducibility of the standard representation of symmetric groups.
We introduce a new method in the attempt to prove the Jacobian conjecture. In the complex dimension 2 case, we apply this method to prove some new results related the Jacobian conjecture.
This paper introduces a novel approach to multi-parameter persistence using 2-categorical structures. We develop a framework that captures hierarchical interactions between filter parameters, overcoming fundamental limitations of…
Recently, Drema and Saikia (2023) proved several congruences modulo powers of 2 and 3 for overpartition triples with odd parts. We extend their list substantially. We prove several congruences modulo powers of 2 for overpartition k-tuples…
The concept of partnership of potentials is studied in detail and in particular the non-uniqueness due to the ambiguity in the election of the factorization energy and in the choice of the solution of certain Riccati equation. We generate…
We present another proof for the well-known {\em small model property} of two-variable logic. As far as we know, existing proofs of this property rely heavily on model theoretic concepts. In contrast, ours is purely combinatorial and uses…
We prove isoperimetric inequalities for quotients of $n$-dimensional Affine buildings. We use these inequalities to prove topological overlapping for the 2-dimensional skeletons of these buildings.
We offer new proofs, refinements as well as new results related to classical means of two variables, including the identric and logarithmic means.
This object of this paper to give several properties and applications of multiple p-adic q-L-function of two variables.
It is shown that the famous paradox of two charged capacitors is successfully resolved if all the energy changes in the system are properly considered when some of the charges are transferred from one capacitor to the other. It happens so…
In this paper, we reveal an internal structure within Dedekind numbers, demonstrating that they can be expressed as polynomials of powers of 2. This discovery is based on innovative concepts and methods, offering a new perspective on the…
We consider an overdetermined problem arising in potential theory for the capacitary potential and we prove a radial symmetry result.
This was significantly extended from the previous article quant-ph/9705043,especially in an information theoretic aspect, by adding new results.
A summary is presented of the properties of the coefficient matrices formed by expanding the two-body reduced density matrix in a complete set of two-electron wave functions. Calculating the relationship between the many electron wave…
Wave-particle duality, intertwining two inherently contradictory properties of quantum systems, remains one of the most conceptually profound aspects of quantum mechanics. By using the concept of energy capacity, the ability of a quantum…
An technically interesting proof of a known theorem.
We consider the capability of $p$ groups of class two and odd prime exponent. We use linear algebra and counting arguments to establish a number of new results. In particular, we settle the 4-generator case, and prove a sufficient condition…