相关论文: On VC-density in VC-minimal theories

Results from spectral geometry such as Weyl's formula can be used to relate the thermodynamic properties of a free massless field to the spatial manifold on which it is defined. We begin by calculating the free energy in two cases:…

A reliable model of viscosity in liquids using a dual liquid model framework is developed. The analytical expression arrived at exhibits the correct T-dependence Arrhenius-like. It is compared with the values of viscosity for water with…

By using a formulation of motion equations for a viscous (compressible) fluid flow in terms of the vorticity and the rate of expansion as the main fluid dynamical variables, an approximation model is established for compressible flows with…

In this paper we suggest new effective criteria for the density property. This enables us to give a trivial proof of the original Anders\'en-Lempert result and to establish (almost free of charge) the algebraic density property for all…

We present a detailed study on the properties of the free energy density at the high temperature by applying the principle of maximum conformality (PMC) scale-setting method within the effective field theory. The PMC utilizes the…

We introduce a density model for random quotients of a free product of finitely generated groups. We prove that a random quotient in this model has the following properties with overwhelming probability: if the density is below $1/2$, the…

The Contextuality-by-Default approach to determining and measuring the (non)contextuality of a system of random variables requires that every random variable in the system be represented by an equivalent set of dichotomous random variables.…

String theoretical arguments led to the hypothesis that the ratio of viscosity to entropy of any physical system has a lower bound. Strongly coupled systems usually have a small viscosity compared to weakly coupled plasmas in which the…

The multivariable theory of nucleation [N. V. Alekseechkin, J. Chem. Phys. 124, 124512 (2006)] is applied to the droplet nucleation in a supersaturated single-component vapor; the droplet volume V, temperature T, and volume change rate…

The Hohenberg-Kohn theorem of the density functional theory is extended by modifying the Levy constrained-search formulation. The new theorem allows us to choose arbitrary physical quantities as the basic variables which determine the…

We discuss variational formulas for the limits of certain models of motion in a random medium: namely, the limiting time constant for last-passage percolation and the limiting free energy for directed polymers. The results are valid for…

We study liquid crystal models with bulk free energy from the point of view of the second law of thermodynamics. We formulate these models as objective internal variable models. Examples of application are given for the de Gennes free…

We incorporate the role of free volume in the density function of the amorphous structure and study its effects on the stability of such structures. The Density Functional Theory is used to explore this ``Free Volume Model'' of the…

We ask some questions and make some observations about the (complete) theory T (infinity, V) of free algebras in V on infinitely many generators, where V is a variety in the sense of universal algebra. We focus on the case T(infinity, R)…

Cavitation is a general phenomenon of the fluid flows with obstacles. It appears in the cooling conduits of the fast nuclear engines. A model of this phenomenon using the theory of Laplace and a common non-convex energy for the liquid and…

Set systems of finite VC dimension are frequently used in applications relating to machine learning theory and statistics. Two simple types of VC classes which have been widely studied are the maximum classes (those which are extremal with…

We propose an improved viscosity model accounting for experiments of emulsions of two immiscible liquids at arbitrary volume fractions and low shear rates. The model is based on a recursive-differential method formulated in terms of the…

We examine the dependence structure of finite block-maxima of multivariate distributions. We provide a closed form expression for the copula density of the vector of the block-maxima. Further, we show how partial derivatives of…

It is shown that the dynamics of a two-dimensional crystal with a finite concentration of dislocations, as well as vacancy and interstitial defects, is governed by the hydrodynamic equations of a viscoelastic medium. At the longest length…

The selection of basic variables in current-density functional theory and formal properties of the resulting formulations are critically examined. Focus is placed on the extent to which the Hohenberg--Kohn theorem, constrained-search…