Arithmetic progressions consisting of unlike powers

In this paper we present some new results about unlike powers in arithmetic progression. We prove among other things that for given $k\geq 4$ and $L\geq 3$ there are only finitely many arithmetic progressions of the form $(x_0^{l_0},x_1^{l_1},...,x_{k-1}^{l_{k-1}})$ with $x_i\in{\Bbb Z},$ gcd$(x_0,x_1)=1$ and $2\leq l_i\leq L$ for $i=0,1,...,k-1.$ Furthermore, we show that, for L=3, the progression $(1,1,...,1)$ is the only such progression up to sign.Comment: 16 page

Renormalised nonequilibrium quantum field theory: scalar fields

We discuss the renormalisation of the initial value problem in quantum field theory using the two-particle irreducible (2PI) effective action formalism. The nonequilibrium dynamics is renormalised by counterterms determined in equilibrium. We emphasize the importance of the appropriate choice of initial conditions and go beyond the Gaussian initial density operator by defining self-consistent initial conditions. We study the corresponding time evolution and present a numerical example which supports the existence of a continuum limit for this type of initial conditions.Comment: 18 pages in revtex4, 5 figure

Out of Equilibrium Non-perturbative Quantum Field Dynamics in Homogeneous External Fields

The quantum dynamics of the symmetry broken lambda (Phi^2)^2 scalar field theory in the presence of an homogeneous external field is investigated in the large N limit. We choose as initial state the ground state for a constant external field J .The sign of the external field is suddenly flipped from J to - J at a given time and the subsequent quantum dynamics calculated. Spinodal instabilities and parametric resonances produce large quantum fluctuations in the field components transverse to the external field. This allows the order parameter to turn around the maximum of the potential for intermediate times. Subsequently, the order parameter starts to oscillate near the global minimum for external field - J, entering a novel quasi-periodic regime.Comment: LaTex, 30 pages, 12 .ps figures, improved version to appear in Phys Rev

A strengths-based case management service for people with serious mental illness in Israel: A randomized controlled trial

Case management services for people with serious mental illness are generally found to be effective, but controlled and randomized studies assessing such services are scarce. The aim of the present study was to assess the effectiveness of a new strengths-based case management (SBCM) service in Israel, using a randomized controlled approach. The sample consisted of 1276 individuals with serious mental illness, who consume psychiatric rehabilitation services (PRS) in the community, and were randomly assigned to receive or not to receive the SBCM service in addition to treatment-as-usual PRS. Quality of life, goal setting and attainment, unmet needs, self-efficacy, interpersonal relationships, symptom severity, and service utilization were assessed by clients at onset and after 20 months. Results show that SBCM participants improved in self-efficacy, unmet needs, and general quality of life, and set more goals than the control group. SBCM participants also consumed fewer services at follow-up. Results suggest that SBCM services are effective in helping individuals with serious mental illness set personal goals and use PRS in a better and more focused manner

Green's function for a Schroedinger operator and some related summation formulas

Summation formulas are obtained for products of associated Lagurre polynomials by means of the Green's function K for the Hamiltonian H = -{d^2\over dx^2} + x^2 + Ax^{-2}, A > 0. K is constructed by an application of a Mercer type theorem that arises in connection with integral equations. The new approach introduced in this paper may be useful for the construction of wider classes of generating function.Comment: 14 page

Self-adjoint Lyapunov variables, temporal ordering and irreversible representations of Schroedinger evolution

In non relativistic quantum mechanics time enters as a parameter in the Schroedinger equation. However, there are various situations where the need arises to view time as a dynamical variable. In this paper we consider the dynamical role of time through the construction of a Lyapunov variable - i.e., a self-adjoint quantum observable whose expectation value varies monotonically as time increases. It is shown, in a constructive way, that a certain class of models admit a Lyapunov variable and that the existence of a Lyapunov variable implies the existence of a transformation mapping the original quantum mechanical problem to an equivalent irreversible representation. In addition, it is proved that in the irreversible representation there exists a natural time ordering observable splitting the Hilbert space at each t>0 into past and future subspaces.Comment: Accepted for publication in JMP. Supercedes arXiv:0710.3604. Discussion expanded to include the case of Hamiltonians with an infinitely degenerate spectru

Semigroup evolution in Wigner Weisskopf pole approximation with Markovian spectral coupling

We establish the relation between the Wigner-Weisskopf theory for the description of an unstable system and the theory of coupling to an environment. According to the Wigner-Weisskopf general approach, even within the pole approximation (neglecting the background contribution) the evolution of a total system subspace is not an exact semigroup for the multi-channel decay, unless the projectors into eigesntates of the reduced evolution generator $W(z)$ are orthogonal. In this case these projectors must be evaluated at different pole locations $z_\alpha\neq z_\beta$. Since the orthogonality relation does not generally hold at different values of $z$, for example, when there is symmetry breaking, the semigroup evolution is a poor approximation for the multi-channel decay, even for a very weak coupling. Nevertheless, there exists a possibility not only to ensure the orthogonality of the $W(z)$ projectors regardless the number of the poles, but also to simultaneously suppress the effect of the background contribution. This possibility arises when the theory is generalized to take into account interactions with an environment. In this case $W(z)$, and hence its eigenvectors as well, are {\it independent} of $z$, which corresponds to a structure of the coupling to the continuum spectrum associated with the Markovian limit.Comment: 9 pages, 3 figure

The cultural and geopolitical dimensions of nation-building in the Ukraine

Ukraine belongs among those young countries where the beginnings of democratisation and nation-building approximately coincided. While the development of nation states in Central Europe was usually preceded by the development of nations, the biggest dilemma in the Ukraine is whether a nation-state programme — parallel to the aim of state-building — is able to bring unfinished nation-building to completion. Ukraine sways between the EU and Russia with enormous amplitude. The alternating orientation between the West and the East can be ascribed to superpower ambitions reaching beyond Ukraine. Eventually, internal and external determinants are intertwined and mutually interact with one another. The aim of the paper is to explain the dilemmas arising from identity problems behind the Ukraine’s internal and external orientation

Pressure dependence of the spin gap in BaVS_3

We carried out magnetotransport experiments under hydrostatic pressure in order to study the nature of the metal-insulator transition in BaVS$_3$. Scaling relations for $\rho(T,H,p)$ are established and the pressure dependence of the spin gap is determined. Our new results, in conjunction with a re-analysis of earlier specific heat and susceptibility data, demonstrate that the transition is weakly second order. The nature of the phase diagram in the $T$--$p$--$H$ space is discussed.Comment: 5 pages, 5 figures, submitted to PRB Rap. Co