On a Parametrization of Purifications of a Qubit

This work provides, constructively, explicit one–one parametrizations of all purifications of a mixed state in dimension 2 and all joint purifications, if any, of two mixed states in the same dimension. The former is parametrized by SO(3, R), while the latter is parametrized by SO(2, R), except when the state being purified is already pure. These parametrizations are derived without any passage to the spectral decompositions of the state(s) being purified. Using this, we show how to calculate certain measures of quantum information. The appendix considers an alternative one–one parametrization of mixed states in C² C², which provides a different explicit construction of joint purifications. PACS: 03.67-a; 03.67-Hk; 03.67-Lx     

Control of Motion of a Body in Formation of a Channel in a Fluid

Mechanics of the formation of a channel by a head of a bending body is considered. Equations are derived of the motion of the body in the channel with its simultaneous formation, which contain the positive feedback. Control is described of various modes of motion and also the transition from one mode to another, including the transition to the motion on account of the feedback. The clarified interrelation of the pressure of the body, its speed, and the responses of the fluid makes it possible to describe the mechanics of the formation and deformation of the channel, which denies the possibility of motion of the body on account of the positive feedback.     

Design of a pH titrator as a component part of a personal computer

Personal computers are becoming almost as common as pocket calculators. In particular, their use in laboratories for measurement and control is growing. The next step after computer-controlled instruments is the development of a personal computer with an instrument as a component part. An automatic pH titrator has been designed. The system presented is based on an Apple Ile. Two plug-in cards are used. One card integrates analogue measurement and analogue-to-digital conversion. The other card controls a syringe driven by a stepper motor. The software control system for the personal pH meter is also described.     

On a nonlinear problem of a sequential control with a parameter

The problem of evasion of a group of moving points from a nonlinear controlled object, whose goal is consecutively approach these points in a prescribed order, is analyzed. The movement of each point is defined uniquely by a scalar parameter chosen at the initial time instant. The controlled object minimizes a certain cost function, and the group of the points, acting cooperatively, maximize this cost function by choosing the parameters. Necessary optimality conditions for parameters are obtained. A model problem of an evasion of moving points from a vehicle is solved.     

Three-Link Mechanism as a Model of a Person on a Swing

Journal of Computer and Systems Sciences International - We model movements of a person swinging on a swing. We consider a flat three-link hinged mechanism as the main mechanical model of the...     

A design of a controller as a component of a robotic manufacturing system

This paper specifies the functional design of a robot or machine tool controller suitable for inclusion in robotic manufacturing systems. The principle interest is the unmanned manufacturing cells which are being developed as major components of new manufacturing facilities. The functional specifications are motivated by recent experiences with the creation of a prototype cell for an open die forging process. There are two key technical design requirements. The first relates to the robot or machine tool being controlled. The controller must direct the machine actions, and, for unmanned operation, the controller must receive and process sensor information for process modification and for fault tolerance. The second relates to communication with the central cell computer (the host). The operation of an unmanned system requires a robot communication channel between the host and the controller; the controller must also respond to a variety of instructions transmitted from the host. Additional controller design requirements are imposed by economics. The proposed controller can be used today, and can develop in an evolutionary manner to meet the needs of future manufacturing systems. The evolutionary development is made possible by modular design, organized in a hierarchical manner.     

Location of a boundary for a diffusion equation of a single server queue

A diffusion-equation model of the M/E_s/1 queue is derived from forward Kolmogorov equations for stages. The derivation results in a new boundary condition. Namely, it is established that an abscissa of a reflecting barrier equals minus squared variance coefficient of service time. That result is then obtained for E_r/M/1 and E_r/E_s/1 queues. Its validity is also illustrated for other systems.     

Implementation of a model of a metainformation-controlled editor of information units with a complex structure

This paper describes the model and methods for implementing an extensible tool for editing information with a complex structure with different levels of abstraction and invariance to technological spaces (subject domains) in a common conceptual framework for carriers of this information; this makes it unnecessary to arrange specialized training for these carriers or involve professional intermediaries.     

Algorithmic selection of a disassembly sequence of a component by a wave propagation method

The design of a product for its entire life-cycle is becoming more and more important. Nowadays, a product is designed with significant considerations for its manufacturability, serviceability, its functionality and even for its disassemblability. This is due to the fact that the modern consumers demand products that are not only functional, but also reliable, easy to repair and also environmentally friendly.For maintenance and re-use, the operation sequencing in disassembly process planning needs of reversible operation selecting.We present a new wave propagation disassembly algorithm of the determined component of a product; the given data are the immediate predecessors of each component.We show that the solution exists and that she is unique in the following conditions: the binary matrix of the immediate predecessors is non-symmetrical and the data does not contain a cycle. A tracked down cycle method in the data is also proposed.     

Diffusion of a chemically reactive species of a power-law fluid past a stretching surface

A numerical solution for the steady magnetohydrodynamic (MHD) non-Newtonian power-law fluid flow over a continuously moving surface with species concentration and chemical reaction has been obtained. The viscous flow is driven solely by the linearly stretching sheet, and the reactive species emitted from this sheet undergoes an isothermal and homogeneous one-stage reaction as it diffuses into the surrounding fluid. Using a similarity transformation, the governing non-linear partial differential equations are transformed into coupled nonlinear ordinary differential equations. The governing equations of the mathematical model show that the flow and mass transfer characteristics depend on six parameters, namely, the power-law index, the magnetic parameter, the local Grashof number with respect to species diffusion, the modified Schmidt number, the reaction rate parameter, and the wall concentration parameter. Numerical solutions for these coupled equations are obtained by the Keller-Box method, and the solutions obtained are presented through graphs and tables. The numerical results obtained reveal that the magnetic field significantly increases the magnitude of the skin friction, but slightly reduces the mass transfer rate. However, the surface mass transfer strongly depends on the modified Schmidt number and the reaction rate parameter; it increases with increasing values of these parameters. The results obtained reveal many interesting behaviors that warrant further study of the equations related to non-Newtonian fluid phenomena, especially shear-thinning phenomena. Shear thinning reduces the wall shear stress.     

Motion control of a rotor with a cavity with a viscous fluid

A formulation and solution procedure of optimal control problems for perturbed relative uniform motion of a body with a cavity filled with a viscous incompressible fluid are proposed. In this paper, the case with a cylinder is considered; however, this approach is basically true for the a cavity of an arbitrary form. The formula for the angular velocity of perturbed motion depending on an external perturbing element is devised. After that, we have a possibility to set different optimal control problems and apply the formalism elaborated in the optimal control theory. Two illustrated problems are given.     

Constructing a committee of a system of linear inequalities

A representation of an arbitrary system of strict linear inequalities in R ⁿ as a system of points is proposed. The representation is obtained by using a so-called polarity. Based on this representation an algorithm for constructing a committee of a plane system of linear inequalities is given. A solution of two problems on minimal committee of a plane system is proposed. The obtained solutions to these problems can be found by means of the proposed algorithm. Kobylkin K.S. Born in 1977. Graduated from Ural State University in 2000. At the present time Kobylkin K.S. works at Institute of Mathematics and Mechanics of the Ural Division of the Russian Academy of Sciences. Scientific interests: pattern recognition, mathematical economics. Author of four publications. Member of the Russian Association for Pattern Recognition and Image Analysis and IAPR.     

On the problem of a free drag of a rigid body with a tapered front in a resisting medium

The author constructs a nonlinear mathematical model of a plane-parallel impact of the medium on a rigid body with a front part of the outer surface shaped as a circular cone. Multivariable analysis of the dynamic equations of motion was performed. A new family of phase patterns on the phase cylinder of quasi-velocities has been obtained. This family consists of infinitely numerous topologically inequivalent phase patterns. The sufficient conditions for the stability of an important mode of motion, i.e., rectilinear translational drag, have been obtained, as well as conditions for the presence of the self-oscillatory modes in the system.     

Navigation of a subsatellite of a space cable system

A method for the navigation of an object of a space cable system, a subsatellite, that does not have its own navigation means and is connected with the master space spacecraft of the bunch by an elastic weightless cable is considered. A method for estimating the location of the subsatellite based on information about the tension force of the cable is proposed, and the problems of observability of the location parameters are investigated. The results of simulating the process of estimating the subsatellite location under various conditions are presented (under the presence and absence of measurements of the cable tension and under the assumption that the cable is constantly tensed under the conditions of its loosing, etc.).     

Markovianity of a subset of components of a Markov process

We consider the necessary and sufficient conditions for a group of the components of a stationary vector Gaussian Markov process to possess Markov property. The representation by a linear Itô stochastic differential equation is also given.     

Construction of a model of a continuous light source specified by a fixed set of rays

A physically correct model of a light source specified by a finite set of rays obtained either by processing the measured characteristics of the light source on the Radiant Imaging goniometric system or as a result of the forward stochastic ray tracing in a scene modeling the radiation of a complex light source is constructed. An algorithm for constructing a continuous emitting surface of a light source and its goniometric diagram given a finite set of rays is developed. The model preserves the spectral composition of the source rays in the surface luminance distribution of the radiation light source. An example of the photorealistic rendering of a scene illuminated by a finite set of rays obtained by the computer processing photometric measurement data.