We present mathematical transformations which allow us to calculate the spin dynamics of an ultrasmall nanoscale molecular magnet consisting of a dimer system of classical (high) Heisenberg spins. We derive exact analytic expressions (in integral form) for the timedependent spin autocorrelation function and several other quantities. The properties of the time-dependent spin autocorrelation func...

Relying on a mathematical analogy of the pure states of the two-qubit system of quantum information theory with four-component spinors we introduce the concept of the intrinsic entanglement of spinors. To explore its physical sense we study the entanglement capabilities of the spin representation of (pseudo-) conformal transformations in (3+1)dimensional Minkowski space-time. We find that only ...

The mathematical and numerical least squares solution of a general linear system of equations is discussed. Perturbation and differentiability theorems for pseudoinverses are given. Computational procedures for calculating least squares solutions using orthonormal transformations, multiplying matrices by a matrix of orthonormal basis vectors for the null-space of a given matrix, sequential proc...

Circle packing can be seen as the art of placing tangent circles on the plane, leaving as little unoccupied space as possible. Circle packing is a very attractive field of mathematics, from several points of view. It contains interesting and complex questions, both mathematical and algorithmical, and keeps its properties through a wide range of geometric transformations. There are several ways ...

We provide optimal control laws by using tools from stochastic calculus of variations and the mathematical concept of δ−sensitivity. The analysis relies on logarithmic transformations of the value functions and the use of linearly solvable Partial Differential Equations(PDEs). We derive the corresponding optimal control as a function of the δ−sensitivity of the logarithmic transformation of the...

The gravity-driven film flow has been analyzed along a vertical wall subjected to a convective boundary condition. The Boussinesq approximation is applied to simplify the buoyancy term, and similarity transformations are used on the mathematical model of the problem under consideration, to obtain a set of coupled ordinary differential equations. Then the reduced equations are solved explicitly ...

In this paper we discuss how semantic annotations can be used to introduce mathematical algorithmic information of the underlying imperative code to enable compilers to produce code transformations that will enable better performance. By using this approaches not only good performance is achieved, but also better programmability, maintainability and portability across different hardware archite...

A Darboux-transformed surface gravitational acceleration of the constant gravitational acceleration for a body endowed with an atmospheric layer is shown to turn the atmospheric free fall with quadratic resistance in the opposite motion, i.e., a free rising. Although the atmosphere of such a body may look completely normal, it is the time dependence of its gravitational field that produces this...

The article surveys and extends variational formulations of the thermodynamic free energy and discusses their information-theoretic content from the perspective of mathematical statistics. We revisit the well-known Jarzynski equality for nonequilibrium free energy sampling within the framework of importance sampling and Girsanov change-of-measure transformations. The implications of the differe...