We present a parameter-free theory of the collective excitations in simple liquids such as liquid metals or rare gases. The theory is based on the mode-coupling theory (MCT), which has been previously applied successfully for explaining the liquid-to glass transition. The only input is the liquid structure factor. We achieve good agreement both for the liquid dispersion (maximum of the longitud...

Every irrational number x ∈ R\Q has a unique representation of the form x = a 0 + 1 a 1 + 1 a 2 + 1 a 3 +...

Thermally induced conductance jumps of metal nanowires are modeled using stochastic Ginzburg-Landau field theories. Changes in radius are predicted to occur via the nucleation of surface kinks at the wire ends, consistent with recent electron microscopy studies. The activation rate displays nontrivial dependence on nanowire length, and undergoes first- or second-order-like transitions as a func...

1.1 Deciding between two simple hypotheses: the Neyman-Pearson Lemma. Probability theory is reviewed in Appendix D. Suppose an experiment has a set X of possible outcomes. The outcome has some probability distribution µ defined on X. In statistics, we typically don't know what µ is, but we have hypotheses about what it may be. After making observations we'll try to make a decision between or am...

We report experiments designed to test the theoretical possibility, first discovered by Shapley (1964), that in some games learning fails to converge to any equilibrium, either in terms of marginal frequencies or of average play. Subjects played repeatedly in fixed pairings one of two 3× 3 games, each having a unique Nash equilibrium in mixed strategies. The equilibrium of one game is predicted...

Simple type theory is suited as framework for combining classical and non-classical logics. This claim is based on the observation that various prominent logics, including (quantified) multimodal logics and intuitionistic logics, can be elegantly embedded in simple type theory. Furthermore, simple type theory is sufficiently expressive to model combinations of embedded logics and it has a well ...

Scattering theory between the fractional power H0 = κ−1(−∆)κ/2 (κ ≥ 1) of negative Laplacian and the Hamiltonian H = H0 + V perturbed by shortand longrange potentials considered in [10] is revisited and a new proof of the existence and asymptotic completeness of wave operators is given with utilizing the smooth operator technique. AMS Subject Classification: Primary 35P25, 81U05 ; Secondary 47A...

The paper presents a theory of the industrial transformation amongst sectors along the balanced growth path equilibrium, using endogenous growth theory. Allowing only a slight upward trend in the productivity of the human capital sector, combined with ascending degrees of human capital shares of sectoral output, in say, agriculture, manufacturing and services, output gradually shifts relatively...

This paper shows how we might successfully introduce students in principles and intermediate microeconomic theory classes to the topic of bundling, i.e., the selling of two or more goods as a package, rather than separately. It is surprising how much students can learn using only the tools of highschool geometry. Specifically, one can prove that with independently distributed reservation prices...