Quantum Kinetic Evolution of Marginal Observables

We develop a rigorous formalism for the description of the evolution of observables of quantum systems of particles in the mean-field scaling limit. The corresponding asymptotics of a solution of the initial-value problem of the dual quantum BBGKY hierarchy is constructed. Moreover, links of the evolution of marginal observables and the evolution of quantum states described in terms of a one-particle marginal density operator are established. Such approach gives the alternative description of the kinetic evolution of quantum many-particle systems to generally accepted approach on basis of kinetic equations.Comment: 18 page

PRACTICE OF USING PODCASTS AND VIDEOCASTS IN INTEGRATED BUSINESS ENGLISH TEACHING

The paper aims to consider and assess (from theoretical and practical standpoints) the implementation of podcasts and videocasts in the integrated teaching of two courses: Business English and Knowledge Management. The use of the above technologies enhances the learning motivation of students, provides them with possibilities to realize their intellectual and creative potential and contributes to their more efficient professional training

Роль неправительственных организаций в противодействии жестокому обращению с детьми в современной Украине

У статті розглядається проблема жорстокого поводження з дітьми. Висвітлюються форми насильства. Досліджено основні причини недбалого ставлення до дітей,розглядається вплив жорстокого поводження на розвиток дитини. Визначена роль неурядових організацій у вирішенні цієї проблеми.In the article the problem of child maltreatment is examined. Shows the forms of violence. Major causes of child abuse and neglect are determined, the influence of maltreatment on growth and development of child is briefly reviewed. An exceptional important role of non-governmental in decision this problem are analyzed.В статье рассматривается проблема жестокого обращения с детьми. Освещаются формы насилия. Исследовано основные причины небрежного обращения с детьми, рассматривается влияние жестокого обращения на развитие ребенка. Выявлена роль неправительственных организаций в решении этой проблемы

The Generalized Star Product and the Factorization of Scattering Matrices on Graphs

In this article we continue our analysis of Schr\"odinger operators on arbitrary graphs given as certain Laplace operators. In the present paper we give the proof of the composition rule for the scattering matrices. This composition rule gives the scattering matrix of a graph as a generalized star product of the scattering matrices corresponding to its subgraphs. We perform a detailed analysis of the generalized star product for arbitrary unitary matrices. The relation to the theory of transfer matrices is also discussed

Lab-Scale Study of the Calcium Carbonate Dissolution and Deposition by Marine Cyanobacterium Phormidium subcapitatum

Suggestions that calcification in marine organisms changes in response to global variations in seawater chemistry continue to be advanced (Wilkinson, 1979; Degens et al. 1985; Kazmierczak et al. 1986; R. Riding 1992). However, the effect of [Na+] on calcification in marine cyanobacteria has not been discussed in detail although [Na+] fluctuations reflect both temperature and sea-level fluctuations. The goal of these lab-scale studies therefore was to study the effect of environmental pH and [Na+] on CaCO3 deposition and dissolution by marine cyanobacterium Phormidium subcapitatum. Marine cyanobacterium P. subcapitatum has been cultivated in ASN-III medium. [Ca2+] fluctuations were monitored with Ca(2+) probe. Na(+) concentrations were determined by the initial solution chemistry. It was found that the balance between CaCO3 dissolution and precipitation induced by P. subcapitatum grown in neutral ASN III medium is very close to zero. No CaCO3 precipitation induced by cyanobacterial growth occurred. Growth of P. subcapitatum in alkaline ASN III medium, however, was accompanied by significant oscillations in free Ca(2+) concentration within a Na(+) concentration range of 50-400 mM. Calcium carbonate precipitation occurred during the log phase of P. subcapitatum growth while carbonate dissolution was typical for the stationary phase of P. subcapitatum growth. The highest CaCO3 deposition was observed in the range of Na(+) concentrations between 200-400 mM. Alkaline pH also induced the clamping of P. subcapitatum filaments, which appeared to have a strong affinity to envelop particles of chemically deposited CaCO3 followed by enlargement of those particles size. EDS analysis revealed the presence of Mg-rich carbonate (or magnesium calcite) in the solution containing 10-100 mM Na(+); calcite in the solution containing 200 mM Na(+); and aragonite in the solution containing with 400 mM Na(+). Typical present-day seawater contains xxmM Na(+). Early (Archean) seawater was likely less saline. The division of marine cyanobacterium P. subcapitatum is associated with periodic deposition and dissolution of CaCO3, the rhythms and intensity of which are dependent on concentrations of both OH(-) and Na(+). Thus, the role of present-day marine cyanobacteria in the global carbonate cycle might be reduced to aggregation and recrystallization of available CaCO3 particles in marine water rather than long-term precipitation and accumulation of CaCO3 deposits. For lower Na(+) concentrations, precipitation of carbonates by cyanobacteria would be even less significant. These results suggest that the lack of calcified cyanobacteria in stromatalite-bearing Precambrian sequences can be explained not only by high dissolved inorganic carbon concentrations but also by lower salinity, as well as possible lower pH compared to present-day oceans

Scattering theory on graphs (2): the Friedel sum rule

We consider the Friedel sum rule in the context of the scattering theory for the Schr\"odinger operator -\Dc_x^2+V(x) on graphs made of one-dimensional wires connected to external leads. We generalize the Smith formula for graphs. We give several examples of graphs where the state counting method given by the Friedel sum rule is not working. The reason for the failure of the Friedel sum rule to count the states is the existence of states localized in the graph and not coupled to the leads, which occurs if the spectrum is degenerate and the number of leads too small.Comment: 20 pages, LaTeX, 6 eps figure

Kirchhoff's Rule for Quantum Wires

In this article we formulate and discuss one particle quantum scattering theory on an arbitrary finite graph with $n$ open ends and where we define the Hamiltonian to be (minus) the Laplace operator with general boundary conditions at the vertices. This results in a scattering theory with $n$ channels. The corresponding on-shell S-matrix formed by the reflection and transmission amplitudes for incoming plane waves of energy $E>0$ is explicitly given in terms of the boundary conditions and the lengths of the internal lines. It is shown to be unitary, which may be viewed as the quantum version of Kirchhoff's law. We exhibit covariance and symmetry properties. It is symmetric if the boundary conditions are real. Also there is a duality transformation on the set of boundary conditions and the lengths of the internal lines such that the low energy behaviour of one theory gives the high energy behaviour of the transformed theory. Finally we provide a composition rule by which the on-shell S-matrix of a graph is factorizable in terms of the S-matrices of its subgraphs. All proofs only use known facts from the theory of self-adjoint extensions, standard linear algebra, complex function theory and elementary arguments from the theory of Hermitean symplectic forms.Comment: 40 page

SMART TECHNOLOGIES (WIKI AND PODCASTS) IN FOREIGN LANGUAGE TEACHING

The article focuses on smart learning technologies such as wiki, video and audio podcasts which are used both online and offline in a foreign language teaching process. These technologies are applied to complement traditional methods of teaching, enhance the learning motivation of students, provide them with possibilities to realize their intellectual and creative potential

A single-mode quantum transport in serial-structure geometric scatterers

We study transport in quantum systems consisting of a finite array of N identical single-channel scatterers. A general expression of the S matrix in terms of the individual-element data obtained recently for potential scattering is rederived in this wider context. It shows in particular how the band spectrum of the infinite periodic system arises in the limit $N\to\infty$. We illustrate the result on two kinds of examples. The first are serial graphs obtained by chaining loops or T-junctions. A detailed discussion is presented for a finite-periodic "comb"; we show how the resonance poles can be computed within the Krein formula approach. Another example concerns geometric scatterers where the individual element consists of a surface with a pair of leads; we show that apart of the resonances coming from the decoupled-surface eigenvalues such scatterers exhibit the high-energy behavior typical for the delta' interaction for the physically interesting couplings.Comment: 36 pages, a LaTeX source file with 2 TeX drawings, 3 ps and 3 jpeg figures attache