相关论文: Some remarks on the distribution of additive energ…

This paper extends the investigation of energy distribution in finite settings, which is related to the results established in [H]. We analyze the distribution of multiplicative energies using Fourier analytical methods and random…

Differential energy structure of a micro multi-charged-particle system and the beam internal potential energy is derived with consequent property and ecessary inference. Then by combining the energy differential structure with differential…

The electrostatic field energy due to two fixed pointlike charges shows some peculiar features concerning the distribution in space of the field energy density of the system. Here we discuss the evaluation of the field energy and the…

We aim to see the sensitivity of collective transverse in-plane flow to symmetry energy at low as well as high densities and also to see the effect of different density dependencies of symmetry energy on the same.

Partial complementary energy densities are introduced through partial Legendre transforms from the strain energy density of linear elasticity. They have mixed components of the strain and stress tensors. Mixed variational principles based…

In the paper we develop the method of higher energies. New upper bounds for the additive energies of convex sets, sets A with small |AA| and |A(A+1)| are obtained. We prove new structural results, including higher sumsets, and develop the…

We consider the inverse problem of determining the density coefficient appearing in the wave equation from separated point source and point receiver data. Under some assumptions on the coefficients, we prove uniqueness results.

Let $A$ be a set of natural numbers. Recent work has suggested a strong link between the additive energy of $A$ (the number of solutions to $a_1 + a_2 = a_3 + a_4$ with $a_i \in A$) and the metric Poissonian property, which is a fine-scale…

In this note we explore duality in reverse convex optimization with reverse convex inequality constraints. While we are examining the special case of a finite index set of the inequality constraints, we are primarily interested in the…

Dark energy and dark matter are only indirectly measured via their gravitational effects. It is possible that there is an exchange of energy within the dark sector, and this offers an interesting alternative approach to the coincidence…

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…

Density functional theory is usually formulated in terms of the density in configuration space. Functionals of the momentum-space density have also been studied, and yet other densities could be considered. We offer a unified view from a…

We continue to study the relationship between the size of the sum of a set and the common energy of its subsets. We find a rather sharp subexponential dependence between the doubling constant of a set $A$ and the minimal common energy taken…

Observations suggest that nearly seventy per cent of the energy density in the universe is unclustered and exerts negative pressure. Theoretical understanding of this component (`dark energy'), which is driving an accelerated expansion of…

We present a new structure theorem for finite fields of odd order that relates multiplicative and additive structure in an interesting way. This theorem has several applications, including an improved understanding of Dickson and Chebyshev…

This work formulates and gives grounds for general principles and theorems that question the energy function doctrine and its quantum version as a genuine law of nature without borders of adequacy. The emphasis is on the domain where the…

The problem of the `infinite energy' of a point charge is well known in connection with the Lorentz--Abraham--Dirac equation and, more significantly, in quantum electrodynamics. Though it is not stated usually, this is strongly related to…

The additive energy plays a central role in combinatorial number theory. We show an uncertainty inequality which indicates how the additive energy of support of a Boolean function, its degree and subcube partition are related.

In the first section, I will try to convey a sense of the variety of observational inputs that tell us about the existence and the spatial distribution of dark matter in the universe. In the second section, I will briefly review the four…

This short note is concerned with the rotational invariance of the stored energy density in continuum physics as a scalar function of a few vectors. A simple derivation is presented for the determination of the general form of the energy…