相关论文: On common energies and sumsets II

In this paper, we study additional aspects of the capacity distribution on the set $\mathcal{B}_n$ of compositions of $n$ consisting of $1$'s and $2$'s. Among our results are further recurrences for this distribution as well as formulas for…

We consider the effect of a local perturbation on the energy levels of a system described by random matrix theory. An analytic expression for the joint distribution function of initial and final energy levels is obtained. In the case of…

Fix a positive real number $\theta$. The natural numbers $m$ with largest square-free divisor not exceeding $m^\theta$ form a set $\mathscr{A}$, say. It is shown that whenever $\theta>1/2$ then all large natural numbers $n$ are the sum of…

Statistical mechanics descriptions of the second law of thermodynamics generally imply point-like particles driven by a dissipative overall mechanism for their simultaneous time-evolution. As the number of involved particles grows larger,…

In this paper, we investigate two methods to express the natural powers of $2$ as sums over integer partitions. First we consider a formula by N. J. Fine that allows us to express a binomial coefficient in terms of multinomial coefficients…

Let $A$ be a subset of a finite abelian group such that $A$ has a small difference set $A-A$ and the density of $A$ is small. We prove that, counter--intuitively, the smallness (in terms of $|A-A|$) of the Fourier coefficients of $A$…

The superposition law (SL) sums the components of electromagnetic (EM) waves at each spatial point when these waves meet in space. In contrast, the energy conservation law requires energy to be summed in the quadratic form of the EM fields.…

The low-energy scattering of two charged particles is analyzed using a renormalization group approach based on dimensional regularization with power-divergence subtraction. A nontrivial solution with a marginally unstable direction is…

We study the asymptotic equidistribution of points with discrete energy close to Robin's constant of a compact set in the plane. Our main tools are the energy estimates from potential theory. We also consider the quantitative aspects of…

Energy has an ambiguous status in general relativity. For systems embedded in asymptotically flat space-times it is possible to construct an integral invariant that corresponds to total energy, however there is no local differential…

We search for approximate, but analytic solutions of the pairing problem for one pair of nucleons in many levels of a potential well. For the collective energy a general formula, independent of the details of the single particle spectrum,…

We consider strictly increasing sequences $\left(a_{n}\right)_{n \geq 1}$ of integers and sequences of fractional parts $\left(\left\{a_{n} \alpha\right\}\right)_{n \geq 1}$ where $\alpha \in \mathbb{R}$. We show that a small additive…

This study is grounded in the concept of spatial symmetry, which allows two co-phase RF sources to jointly radiate harmonic electromagnetic (EM) waves, even in presence of electromagnetic couplings between them. The superposition law is…

We consider a set of density matrices. All of which are written in the same orbital basis, but the orbital basis size is less than the total Hilbert space size. We ask how each density matrix is related to each of the others by establishing…

The experimental emission probabilities of complex fragments by low energy compound nuclei and their dependence upon energy and atomic number are compared to the transition state rates. Intermediate-mass-fragment multiplicity distributions…

It is a classical fact that every $n$-element set of positive reals has at least $\binom{n+1}{2}+1$ distinct subset sums, with equality exactly for homogeneous arithmetic progressions (when $n\geq 4$). We establish stability versions of…

Efforts to extract information on magnitude and density dependence of the nuclear symmetry energy are discussed. The utilized data include those on mass dependence of the excitation energies to the isobaric analog states of ground states,…

We investigate subsets with small sumset in arbitrary abelian groups. For an abelian group $G$ and an $n$-element subset $Y \subseteq G$ we show that if $m \ll s^2/(\log n)^2$, then the number of subsets $A \subseteq Y$ with $|A| = s$ and…

Recently, Bauke and Mertens conjectured that the local statistics of energies in random spin systems with discrete spin space should in most circumstances be the same as in the random energy model. Here we give necessary conditions for this…

We present an intuitive and general analytical approximation estimating the energy of covalent single and double bonds between participating atoms in terms of their respective nuclear charges with just three parameters, $[{E_\text{AB}…