Problem of Measurement Within the Operator Formulation of Hybrid Systems

The basic concepts of classical mechanics are given in operator form. Then ahybrid systems approach with the operator formulation of both quantum andclassical sectors is applied to the case of an ideal nonselective measurement. Itis found that the dynamical equation, consisting of the Schrödinger and Liouvilledynamics, produces noncausal evolution when the initial state of the measured(quantum mechanical) system and measuring apparatus=nclassical mechanicalsystem is chosen to be as demanded in discussions regarding the problem ofmeasurement. Nonuniqueness of possible realizations of the transition from apure noncorrelated to a mixed correlated state is analyzed in detail. It is concludedthat the state of the quantum mechanical system instantaneously collapses becauseof the nonnegativity of probabilities, and a dynamical model of this reductionis proposed.     

General model of microtubules

Nonlinear Dynamics - In the present work, we deal with nonlinear dynamics of microtubules. A new model, describing nonlinear dynamics of microtubules, is introduced. Its advantages over two...     

Solid-contact Cu(II) ion-selective electrode based on 1,2-di-(<Emphasis Type="Italic">o</Emphasis>-salicylaldiminophenylthio)ethane

The development of Cu(II) solid-contact ion-selective electrodes, based on 1,2-di-(o-salicylaldiminophenylthio)ethane as a neutral carrier, is presented. For the electrodes construction, unmodified carbon ink (type 1 electrode) and polymer membrane-modified carbon ink (type 2 electrode) were used as solid support and transducer layer. Also, carbon ink composite polymer membrane electrode (type 3 electrode) was prepared. The analytical performance of the electrodes was evaluated with potentiometry, while bulk and interfacial electrode features were provided with electrochemical impedance spectroscopy. It is shown that modification of carbon ink with polymer membrane cocktail decreases the bulk contact resistance of the transducer layer and polymer membrane, thus enhancing the analytical performance of the electrode in terms of sensitivity, linear range, and stability of potential. The optimized electrodes of types 2 and 3 exhibit a wide linear range with detection limits of 1.8 × 10⁻⁶ and 1.6 × 10⁻⁶ M, respectively. They are suitable for determination of Cu²⁺ in analytical measurements by direct potentiometry and in potentiometric titrations, within pH between 2.3 and 6.5. The electrodes are selective for Cu²⁺ over a large number of tested transition and heavy metal ions.     

Employment of Jacobian elliptic functions for solving problems in nonlinear dynamics of microtubules

We show how Jacobian elliptic functions （JEFs） can be used to solve ordinary differential equations （ODEs） describing the nonlinear dynamics of microtubules （MTs）. We demonstrate that only one of the JEFs can be used while the remaining two do not represent the solutions of the crucial differential equation. We show that a kinkbtype soliton moves along MTs. Besides this solution, we also discuss a few more solutions that may or may not have physical meanings. Finally, we show what kind of ODE can be solved by using JEFs.     

Visualisation methods for complex nematic fields

In analysis of numerically simulated or experimentally obtained nematic textures, data visualisation plays an important role in interpretation and comparison of results. We review both commonly used, and more recently developed visual presentation methods that expose different aspects of the textures, from director field patterns and topological content of nematic defects, to deformation modes and simulated optical effects. We outline the theoretical background and potential uses, with examples that highlight the features of each of the described techniques.     

Pulse perturbation technique for determination of piroxicam in pharmaceuticals using an oscillatory reaction system

A simple and reliable novel kinetic method for the determination of piroxicam (PX) was proposed and validated. For quantitative determination of PX, the Bray-Liebhafsky (BL) oscillatory reaction was used in a stable non-equilibrium stationary state close to the bifurcation point. Under the optimized reaction conditions (T = 55.0°C, [H₂SO₄]₀ = 7.60×10^?2 mol L^?1, [KIO₃]₀ = 5.90×10^?2 mol L^?1, [H₂O₂]₀ = 1.50×10^?1 mol L^?1 and j ₀ = 2.95×10^?2 min^?1), the linear relationship between maximal potential shift ΔE _m , and PX concentration was obtained in the concentration range 11.2–480.5 μg mL^?1 with a detection limit of 9.9 μg mL^?1. The method had a rather good sample throughput of 25 samples h^?1 with a precision RSD = 4.7% as well as recoveries RCV ≤ 104.4%. Applicability of the proposed method to the direct determination of piroxicam in different pharmaceutical formulations (tablets, ampoules and gel) was demonstrated.      

Optimal dispatching strategy on an airline network after a schedule perturbation

It often happens that one or more aeroplanes from an airline fleet are taken out of operation for technical reasons and the airline has to operate on the existing network with a reduced number of planes. This paper presents the results of an effort to define a new ad hoc schedule for this situation, so that the total passenger delay on an airline network is minimized. A network is formed, in which nodes represent flights on a given airline network, and arcs are the total time losses on individual flights. The problem of determining a new routing and scheduling plan for the airline fleet is solved by branch and-bound methods. A numerical example illustrates the efficiency of the model.     

Analysis of Error Propagation from NMR-Derived Internuclear Distances into Molecular Structure ofCyclo-Pro-Gly

Analytical expressions have been derived that translate uncertainties in distance constraints (obtained from NMR investigations) into uncertainties in atom positions in the maximum likelihood (ML) structure consistent with these inputs. As a test of this approach, a comparison was made between test structures reconstructed by the new ML approach, which yields a single structure and a covariance matrix for coordinates, and those reconstructed by metric matrix distance-geometry (MMDG), which yields a family of structures that sample uncertainty space. The test structures used were 560 polyhedra, with edges of arbitrary length containing up to 50 vertices, and one polyhedron, with 100 vertices; randomized distance constraints generated from these structures were used in reconstructing the polyhedra. The uncertainties derived from the two methods showed excellent agreement, and the correlation improved, as expected, with increasingly larger numbers of MMDG structures. This agreement supports the validity of the rapid analytical ML approach, which requires the calculation of only a single structure. As a second test of the ML method, the approach was applied to the determination of uncertainties in the structure of a cyclic dipeptide,cyclo(DL-Pro-Gly) (cPG), derived from NMR cross-relaxation data. The input data were interproton distances calculated from NOEs measured for a solution of the peptide in 2:1 DMSO:H₂O at −40°C (so as to yield large negative NOEs). In order to evaluate effects of the quality of the input spectral parameters on the precision of the resulting NMR structure, information from the covalent geometry of cPG was not used in the structure calculations. Results obtained from the analytical ML approach compared favorably with those from the much slower random-walk variant of the Monte Carlo method applied to the same input data. As a third test, the ML approach was used with synthetic structural constraints for a small protein; the results indicate that it will be feasible to use this rapid method to translate uncertainties associated with a given set of distance restraints into uncertainties in atom positions in larger molecules.     

Presentations for a class of generalized Thompson’s groups

For a given group G and a monomorphism φ:G→G×G there is a group ?_φ(G), introduced by the author, which blends Thompson’s group F with G. Given a presentation of G we determine a presentation of ?_φ(G). In particular, we prove that ?_φ(G) is finitely generated (resp. finitely presented) if G is finitely generated (resp. finitely presented).     

Gaussian-induced rotation in periodic photonic lattices

We numerically investigate time-dependent rotation of counterpropagating mutually incoherent self-trapped Gaussian beams in periodic optically induced fixed photonic lattices. We demonstrate the relation between such rotation and less confined discrete solitonic solutions.