We study the unitary time evolution of a simple quantum Hamiltonian describing two harmonic oscillators coupled via a three-level system. The latter acts as an engine transferring energy from one oscillator to the other and is driven in a cyclic manner by time-dependent external fields. The S-matrix (scattering matrix) of the cycle is obtained in analytic form. The total number of quanta contai...

A variety of converging operations demonstrate key differences between separable dimensions, which can be analyzed independently, and integral dimensions, which are processed in a non-analytic fashion. A recent investigation of response time distributions, applying a set of logical rule-based models, demonstrated that integral dimensions are pooled into a single coactive processing channel, in ...

The accurate calculation of synchrotron radiation from an undulator is a common problem and numerous codes have been developed that describe the radiation from analytic and measured undulator fields. However, for very long undulator systems there is not a suitable code that can handle the amount of data in a convenient manner and which runs in a practically realisable time limit. The developmen...

This paper addresses the problem of how a robot can autonomously improve a manipulation skill in an efficient and secure manner. Instead of using the standard reinforcement learning formulation where all objectives are defined in a single reward function, we propose a generalized formulation that consists of three components: 1) A known analytic cost function; 2) A black-box reward function; 3)...

The field equations of a special class of tetrad theory of gravitation have been applied to tetrad space having three unknown functions of radial coordinate. The spherically symmetric vacuum stress-energy momentum tensor with one assumption concerning its specific form generates two non-trivial different exact analytic solutions for these field equations. For large r, the exact analytic solutio...

Replication is a suitable approach for the provision of fault tolerance and load balancing in distributed systems. Object replication takes place on the basis of well-designed interaction protocols that preserve object state consistency in an application transparent manner. The published analytic performance models may only be applied in single-server process replication schemes and are not sui...

Many years ago in paper [1] some special set-theoretical operation ∆K was introduced. It was used to reduce manipulations with phase prefactors in the Fock space ( Grassmann algebra) to pure set theoretical ones. More detailed discussion of this operation was given in [2], Appendix A. The main purpose of this paper is to show that the operation mentioned makes it easy to obtain very complicated...

A symbolic proof for establishing that a given arithmetic formula Φ computes the zero polynomial (or equivalently, that two given arithmetic formulas compute the same polynomial) is a sequence of formulas, starting with Φ and deriving the formula 0 by means of the standard polynomial-ring axioms applied to any subformula. Motivated by results in proof complexity and algebraic complexity, we inv...

Gibbs phenomenon is the particular manner how a global spectral approximation of a piecewise analytic function behaves at the jump discontinuity. The truncated spectral series has large oscillations near the jump, and the overshoot does not decay as the number of terms in the truncated series increases. There is therefore no convergence in the maximum norm, and convergence in smooth regions awa...

This paper presents a design optimization problem reformulation method based on Singular Value Decomposition (SVD), dimensionality reduction, and unsupervised clustering. The method calculates linear approximations of the associative patterns of symbol co-occurrences in a design problem representation to infer induced interaction/coupling strengths between variables and constraints. Unsupervise...