Inverse eigenvalue problem for discrete three-diagonal Sturm-Liouville operator and the continuum limit

In present article the self-contained derivation of eigenvalue inverse problem results is given by using a discrete approximation of the Schroedinger operator on a bounded interval as a finite three-diagonal symmetric Jacobi matrix. This derivation is more correct in comparison with previous works which used only single-diagonal matrix. It is demonstrated that inverse problem procedure is nothing else than well known Gram-Schmidt orthonormalization in Euclidean space for special vectors numbered by the space coordinate index. All the results of usual inverse problem with continuous coordinate are reobtained by employing a limiting procedure, including the Goursat problem -- equation in partial derivatives for the solutions of the inversion integral equation.Comment: 19 pages There were made some additions (and reformulations) to the text making the derivation of the results more precise and understandabl

Small-Energy Analysis for the Selfadjoint Matrix Schroedinger Operator on the Half Line

The matrix Schroedinger equation with a selfadjoint matrix potential is considered on the half line with the most general selfadjoint boundary condition at the origin. When the matrix potential is integrable and has a first moment, it is shown that the corresponding scattering matrix is continuous at zero energy. An explicit formula is provided for the scattering matrix at zero energy. The small-energy asymptotics are established also for the corresponding Jost matrix, its inverse, and various other quantities relevant to the corresponding direct and inverse scattering problems.Comment: This published version has been edited to improve the presentation of the result

Survey Manual for Comprehensive Urban Planning: The Use of Opinion Surveys and Sampling Techniques in the Planning Process

This study examines the applications of scientific public opinion and survey sampling techniques to comprehensive planning and other urban planning programs. The survey manual deals with two major elements: a case study in Providence, Rhode Island, which illustrates the process of conducting a survey and the kinds of findings and results which may be obtained; and a methodology section which focuses on the techniques and methods used in survey research. Research design, survey methodology, organization of data collection, the plan for data processing and preparation of the final report are discussed. Scientific survey sampling is shown to be a useful instrument for obtaining information on a variety of urban problems, including opinions on quality of public facilities, reasons for moving, support for Urban Renewal and Model Cities programs, and evaluation of social welfare programs.The State of Alask

The fastest unbound star in our Galaxy ejected by a thermonuclear supernova

Hypervelocity stars (HVS) travel with velocities so high, that they exceed the escape velocity of the Galaxy. Several acceleration mechanisms have been discussed. Only one HVS (US 708, HVS 2) is a compact helium star. Here we present a spectroscopic and kinematic analysis of US\,708. Travelling with a velocity of $\sim1200\,{\rm km\,s^{-1}}$, it is the fastest unbound star in our Galaxy. In reconstructing its trajectory, the Galactic center becomes very unlikely as an origin, which is hardly consistent with the most favored ejection mechanism for the other HVS. Furthermore, we discovered US\,708 to be a fast rotator. According to our binary evolution model it was spun-up by tidal interaction in a close binary and is likely to be the ejected donor remnant of a thermonuclear supernova.Comment: 16 pages report, 20 pages supplementary material

Reconstruction of the optical potential from scattering data

We propose a method for reconstruction of the optical potential from scattering data. The algorithm is a two-step procedure. In the first step the real part of the potential is determined analytically via solution of the Marchenko equation. At this point we use a diagonal Pad\'{e} approximant of the corresponding unitary $S$-matrix. In the second step the imaginary part of the potential is determined via the phase equation of the variable phase approach. We assume that the real and the imaginary parts of the optical potential are proportional. We use the phase equation to calculate the proportionality coefficient. A numerical algorithm is developed for a single and for coupled partial waves. The developed procedure is applied to analysis of $^{1}S_{0}$ $NN$, $^{3}SD_{1}$ $NN$, $P31$ $\pi^{-} N$ and $S01$ $K^{+}N$ data.Comment: 26 pages, 8 figures, results of nucl-th/0410092 are refined, some new results are presente

Nitrogen and phosphorus limitation of oceanic microbial growth during spring in the Gulf of Aqaba

Bioassay experiments were performed to identify how growth of key groups within the microbial community was simultaneously limited by nutrient (nitrogen and phosphorus) availability during spring in the Gulf of Aqaba's oceanic waters. Measurements of chlorophyll a (chl a) concentration and fast repetition rate (FRR) fluorescence generally demonstrated that growth of obligate phototrophic phytoplankton was co-limited by N and P and growth of facultative aerobic anoxygenic photoheterotropic (AAP) bacteria was limited by N. Phytoplankton exhibited an increase in chl a biomass over 24 to 48 h upon relief of nutrient limitation. This response coincided with an increase in photosystem II (PSII) photochemical efficiency (F v /F m), but was preceded (within 24 h) by a decrease in effective absorption crosssection (σPSII) and electron turnover time (τ). A similar response for τ and bacterio-chl a was observed for the AAPs. Consistent with the up-regulation of PSII activity with FRR fluorescence were observations of newly synthesized PSII reaction centers via low temperature (77K) fluorescence spectroscopy for addition of N (and N + P). Flow cytometry revealed that the chl a and thus FRR fluorescence responses were partly driven by the picophytoplankton (æ10 μm) community, and in particular Synechococcus. Productivity of obligate heterotrophic bacteria exhibited the greatest increase in response to a natural (deep water) treatment, but only a small increase in response to N and P addition, demonstrating the importance of additional substrates (most likely dissolved organic carbon) in moderating the heterotrophs. These data support previous observations that the microbial community response (autotrophy relative to heterotrophy) is critically dependent upon the nature of transient nutrient enrichment. © Inter-Research 2009

A Cosmological Model with Dark Spinor Source

In this paper, we discuss the system of Friedman-Robertson-Walker metric coupling with massive nonlinear dark spinors in detail, where the thermodynamic movement of spinors is also taken into account. The results show that, the nonlinear potential of the spinor field can provide a tiny negative pressure, which resists the Universe to become singular. The solution is oscillating in time and closed in space, which approximately takes the following form g_{\mu\nu}=\bar R^2(1-\delta\cos t)^2\diag(1,-1,-\sin^2r ,-\sin^2r \sin^2\theta), with $\bar R= (1\sim 2)\times 10^{12}$ light year, and $\delta=0.96\sim 0.99$. The present time is about $t\sim 18^\circ$.Comment: 13 pages, no figure, to appear in IJMP

Inverse spectral problems for Sturm--Liouville operators with matrix-valued potentials

We give a complete description of the set of spectral data (eigenvalues and specially introduced norming constants) for Sturm--Liouville operators on the interval $[0,1]$ with matrix-valued potentials in the Sobolev space $W_2^{-1}$ and suggest an algorithm reconstructing the potential from the spectral data that is based on Krein's accelerant method.Comment: 39 pages, uses iopart.cls, iopams.sty and setstack.sty by IO

Electrostatic and electrokinetic contributions to the elastic moduli of a driven membrane

We discuss the electrostatic contribution to the elastic moduli of a cell or artificial membrane placed in an electrolyte and driven by a DC electric field. The field drives ion currents across the membrane, through specific channels, pumps or natural pores. In steady state, charges accumulate in the Debye layers close to the membrane, modifying the membrane elastic moduli. We first study a model of a membrane of zero thickness, later generalizing this treatment to allow for a finite thickness and finite dielectric constant. Our results clarify and extend the results presented in [D. Lacoste, M. Cosentino Lagomarsino, and J. F. Joanny, Europhys. Lett., {\bf 77}, 18006 (2007)], by providing a physical explanation for a destabilizing term proportional to \kps^3 in the fluctuation spectrum, which we relate to a nonlinear ($E^2$) electro-kinetic effect called induced-charge electro-osmosis (ICEO). Recent studies of ICEO have focused on electrodes and polarizable particles, where an applied bulk field is perturbed by capacitive charging of the double layer and drives flow along the field axis toward surface protrusions; in contrast, we predict "reverse" ICEO flows around driven membranes, due to curvature-induced tangential fields within a non-equilibrium double layer, which hydrodynamically enhance protrusions. We also consider the effect of incorporating the dynamics of a spatially dependent concentration field for the ion channels.Comment: 22 pages, 10 figures. Under review for EPJ

\pi\pi, K\pi and \pi N potential scattering and a prediction of a narrow \sigma meson resonance

Low energy scattering and bound state properties of the \pi N, \pi\pi and K\pi systems are studied as coupled channel problems using inversion potentials of phase shift data. In a first step we apply the potential model to explain recent measurements of pionic hydrogen shift and width. Secondly, predictions of the model for pionium lifetime and shift confirm a well known and widely used effective range expression. Thirdly, as extension of this confirmation, we predict an unexpected medium effect of the pionium lifetime which shortens by several orders of magnitude. The \sigma meson shows a narrow resonance structure as a function of the medium modified mass with the implication of being essentially energy independent. Similarly, we see this medium resonance effect realized for the K\pi system. To support our findings we present also results for the \rho meson and the \Delta(1232) resonance.Comment: 42 pages, 17 PS figures, REFTeX, epsfig.sty needed, submitted to Phys. Re