The H-theorem is an extension of the Second Law to a time-sequence of states that need not be equilibrium ones. In this paper we review and we rigorously establish the connection with macroscopic autonomy. If for a Hamiltonian dynamics for many particles, the macrostate evolves autonomously, then its entropy is non-decreasing as a consequence of Liouville’s theorem. That observation, made since...

Egorov's theorem on the classical propagation of quantum observables is related to prominent quasi-classical descriptions of quantum molecular dynamics as the linearized semiclassical initial value representation, the Wigner phase space method, or the statistical quasiclassical method. The error estimates show that different accuracies are achievable for the computation of expectation values an...

We give a new, elementary, purely analytical development of Descartes’ theorem that a smooth connected surface is a perfect focusing lens if and only if it is a connected subset of the ovoid obtained by revolving a cartesian oval around its axis of symmetry.

We develop a version of Afriat’s Theorem that is applicable to a variety of choice environments, beyond the setting of classical consumer theory. This allows us to devise tests for rationalizability in the context of choice data on lotteries, contingent consumption, and intertemporal consumption. We also establish a version of Richter’s Theorem that characterizes the strict rationalizability of...

Abstract. We consider the Cauchy problem We consider the Cauchy problem ut = uxx + f(u), x ∈ R, t > 0, u(x, 0) = u0(x), x ∈ R, where f is a locally Lipschitz function on R with f(0) = 0, and u0 is a nonnegative function in C0(R), the space of continuous functions with limits at ±∞ equal to 0. Assuming that the solution u is bounded, we study its large-time behavior from several points of view. ...

A special case of Wirtinger's theorem asserts that a complex curve (two-dimensional) holomorphically embedded in a Kaehler manifold is a minimal surface. The converse is not necessarily true. Guided by considerations from the theory of moduli of Riemann surfaces, we discover (among other results) sufficient topological and differential-geometric conditions for a minimal (Riemannian) immersion o...

We demonstrate that the main part of the observed nuclear suppression of dilepton and charmonium production, especially the x-dependence of the suppression, can be explained by the absorption of fast initial partons. We assume the absorption to be x 1-dependent and determine the empirical form of this dependence. Several reactions at different energies are described with the same parametrizatio...

We study collective and single-particle intersubband excitations in a system of quantum wires coupled via weak tunneling. For an isolated wire with parabolic confinement, the Kohn's theorem guarantees that the absorption spectrum represents a single sharp peak centered at the frequency given by the bare confining potential. We show that the effect of weak tunneling between two parabolic quantum...

High dimensional statistics deals with the challenge of extracting structured information from complex model settings. Compared with the growing number of frequentist methodologies, there are rather few theoretically optimal Bayes methods that can deal with very general high dimensional models. In contrast, Bayes methods have been extensively studied in various nonparametric settings and rate o...

Abstract−This study intends to predict the harvest period in farming at Regional Technical Implementation Unit of Gabe Hutaraja Various Crops. The method used this is Naive Bayes Classifier. data are time series from 2015 2017. results predictions rice, peanut, and corn crops future.
 Classifier a simple probabilistic classification process based on application Bayes' Theorem (Bayes rule) ...