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

We show that the theory of the free group -- and more generally the theory of any torsion-free hyperbolic group -- is $n$-ample for any $n\geq 1$. We give also an explicit description of the imaginary algebraic closure in free groups.

This paper is concerned with the free boundary value problem for multi-dimensional Navier-Stokes equations with density-dependent viscosity where the flow density vanishes continuously across the free boundary. A local (in time) existence…

In this paper we study the quasi-static problem for a viscoelastic fluid by means of the concept of minimal state. This implies the use of a different free energy defined in a wider space of data. The existence and uniqueness is proved in…

The paper presents an elaboration of some results on Lin's conditions. A new proof of the fact that if densities of independent random variables $\xi_1$ and $\xi_2$ satisfy Lin's condition, the same is true for their product is presented.…

By combining methods of kinetic and density functional theory, we present a description of molecular fluids which accounts for their microscopic structure and thermodynamic properties as well as for the hydrodynamic behavior. We focus on…

We present a general discussion of the properties of three dimensional CFT duals to the AdS string theory vacua coming from type IIB Calabi-Yau flux compactifications. Both KKLT and Large Volume Scenario (LVS) minima are considered. In both…

We prove an expansion for densities in the free CLT and apply this result to an expansion in the entropic free central limit theorem assuming a moment condition of order 8 for the free summands.

We introduce the concepts of max-closedness and numeraires of convex subsets in the nonnegative orthant of the topological vector space of all random variables built over a probability space, equipped with a topology consistent with…

In a companion paper, equations for partially molten media were derived using two-scale homogenization theory. One advantage of homogenization is that material properties, such as permeability and viscosity, readily emerge. A caveat is that…

A hydrodynamic theory is formulated for buoyancy-driven ("thermal") granular convection, recently predicted in molecular dynamic simulations and observed in experiment. The limit of a dilute flow is considered. The problem is fully…

We present the virial equation of state of low-density nuclear matter composed of neutrons, protons and alpha particles. The virial equation of state is model-independent, and therefore sets a benchmark for all nuclear equations of state at…

3+1-dimensional free inviscid fluid dynamics is shown to satisfy the criteria for exact integrability, i.e. having an infinite set of independent, conserved quantities in involution, with the Hamiltonian being one of them. With (density…

In this paper, we introduce a concept of non-dependence of variables in formulas. A formula in first-order logic is non-dependent of a variable if the truth value of this formula does not depend on the value of that variable. This variable…

We investigate experimentally the statistics of the free volume inside bidimensional granular packings, for two different kinds of grains and two levels of compaction. With the aim to gain new insight into the statistical description of…

The theory of vapor bubbles nucleation in single-component liquids developed in [J. Phys. Chem. B 116, 9445 (2012)] for the case of high viscosity (the (V,/rho,T)- theory) is extended to the case of arbitrary viscosity. For this purpose,…

Computer simulations of hard spheres and disks are used to estimate the most probable cavity size, $\xi_{\rm cavity}$, and a ``rattle'' size, $\xi_{\rm rattle}$, over which a particle can translate holding all other particles fixed. Both of…

In this work, the molar volume thermal expansion coefficient of 60 room temperature ionic liquids is compared with their van der Waals volume Vw. Regular correlation can be discerned between the two quantities. An average free volume model,…

Critical coagulation concentration (CCC) is a key parameter of particle dispersions, since it provides the threshold limit of electrolyte concentrations, above which the dispersions are destabilized due to rapid particle aggregation. A…

We study the combination of orbital-optimized density cumulant theory and a new parameterization of the reduced density matrices in which the variables are the particle-hole cumulant elements. We call this combination O$\lambda$DCT. We find…

We prove that the abundance conjecture holds on a variety $X$ with mild singularities if $X$ has many reflexive differential forms with coefficients in pluricanonical bundles, assuming the Minimal Model Program in lower dimensions. This…