This paper discusses the mean-field limit for the quantum dynamics of $N$ identical bosons in $\mathbf R^3$ interacting via a binary potential with Coulomb type singularity. Our approach is based on the theory of quantum Klimontovich solutions define...
We provide sufficient conditions under which a utility function may be recovered from a finite choice experiment. Identification, as is commonly understood in decision theory, is not enough. We provide a general recoverability result that is widely a...
We provide an epistemological analysis of the developments of relativistic cosmology from 1917 to 2006, based on the seminal articles by Einstein, de Sitter, Friedmann, Lemaitre, Hubble, Gamow and other main historical figures of the field. It appe...
We provide a detailed analysis of the problems and prospects of superstring theory c. 1986, anticipating much of the progress of the decades to follow....
ADHM Yang-Mills instantons are extended field theoretical objects. These are more general than the more familiar 't Hooft Yang-Mills instantons. Their counter parts exist in string theory in terms of sigma models. Nearly three decades ago Witten cons...
We calculate the $\mathcal{O}(\langle H^{\dagger} H \rangle^{2} / Λ^{4} )$ corrections to LEP electroweak precision data using the geometric formulation of the Standard Model Effective Field Theory (SMEFT). We report our results in simple-to-use int...
We reply to the comment by K. Aryanpour, Th. Maier and M. Jarrell (cond-mat/0301460) on our paper (Phys. Rev. B {\bf 65} 155112 (2002)). We demonstrate using general arguments and explicit examples that whenever the correlation length is finite, lo...
We study several aspects of the behaviours produced by instruction sequences under execution in the setting of the algebraic theory of processes known as ACP. We use ACP to describe the behaviours produced by instruction sequences under execution and...
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Numerical range of a Hermitian operator X is defined as the set of all possible expectation values of this observable among a normalized quantum state. We analyze a modification of this definition in which the expectation value is taken among a certa...
For any positive real number $s$, we study the scattering theory in a unified way for the fractional Schrödinger operator $H=H_0+V$, where $H_0=(-Δ)^\frac s2$ and the real-valued potential $V$ satisfies short range condition. We prove the existence...
This paper studies the utility maximization on the terminal wealth with random endowments and proportional transaction costs. To deal with unbounded random payoffs from some illiquid claims, we propose to work with the acceptable portfolios defined v...
Using analytical calculations and computer simulations we consider both the lateral diffusion of a membrane protein and the fluctuation spectrum of the membrane in which the protein is embedded. The membrane protein interacts with the membrane shap...
We investigate how the dynamics of a single chain influences the kinetics of early stage phase separation in a symmetric binary polymer mixture. We consider quenches from the disordered phase into the region of spinodal instability. On a mean field...
A novel freestyle rap software, MCMChaos 0.0.1, based on rap music transcriptions created in previous research is presented. The software has three different versions, each making use of different mathematical simulation methods: collapsed gibbs samp...
A fundamental problem that the bearing rigidity theory studies is to determine when a framework can be uniquely determined up to a translation and a scaling factor by its inter-neighbor bearings. While many previous works focused on the bearing rigid...
Let $(X,ω)$ be a closed symplectic manifold. A loop $φ: S^1 \to \mathrm{Diff}(X)$ of diffeomorphisms of $X$ defines a fibration $π: P_φ \to S^2$. By applying Gromov-Witten theory to moduli spaces of holomorphic sections of $π$, Lalonde, McDuff a...
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Misner space, also known as the Lorentzian orbifold $R^{1,1}/boost$, is one of the simplest examples of a cosmological singularity in string theory. In this lecture, we review the semi-classical propagation of closed strings in this background, wit...
It is a basic property of the entropy in statistical physics that is concave as a function of energy. The analog of this in representation theory would be the concavity of the logarithm of the multiplicity of an irreducible representation as a func...