Solutions of mKdV in classes of functions unbounded at infinity

In 1974 P. Lax introduced an algebro-analytic mechanism similar to the Lax L-A pair. Using it we prove global existence and uniqueness for solutions of the initial value problem for mKdV in classes of smooth functions which can be unbounded at infinity, and may even include functions which tend to infinity with respect to the space variable. Moreover, we establish the invariance of the spectrum and the unitary type of the Schr{\"o}dinger operator under the KdV flow and the invariance of the spectrum and the unitary type of the impedance operator under the mKdV flow for potentials in these classes.Comment: 35 pages, new results about spectra and eigenfunctions of Schr\"odinger operators added, new references adde

Spin wave spectrum of the quantum ferromagnet on the pyrochlore lattice Lu2V2O7

Neutron inelastic scattering has been used to probe the spin dynamics of the quantum (S=1/2) ferromagnet on the pyrochlore lattice Lu2V2O7. Well-defined spin waves are observed at all energies and wavevectors, allowing us to determine the parameters of the Hamiltonian of the system. The data are found to be in excellent overall agreement with a minimal model that includes a nearest- neighbour Heisenberg exchange J = 8:22(2) meV and a Dzyaloshinskii-Moriya interaction (DMI) D =1:5(1) meV. The large DMI term revealed by our study is broadly consistent with the model developed by Onose et al. to explain the magnon Hall effect they observed in Lu2V2O7 [1], although our ratio of D=J = 0:18(1) is roughly half of their value and three times larger than calculated by ab initio methods [2].Comment: 5 pages, 4 figure

Transitions in coral reef accretion rates linked to intrinsic ecological shifts on turbid-zone nearshore reefs

Nearshore coral communities within turbid settings are typically perceived to have limited reef-building capacity. However, several recent studies have reported reef growth over millennial time scales within such environments and have hypothesized that depth-variable community assemblages may act as equally important controls on reef growth as they do in clear-water settings. Here, we explicitly test this idea using a newly compiled chronostratigraphic record (31 cores, 142 radiometric dates) from seven proximal (but discrete) nearshore coral reefs located along the central Great Barrier Reef (Australia). Uniquely, these reefs span distinct stages of geomorphological maturity, as reflected in their elevations below sea level. Integrated age-depth and ecological data sets indicate that contemporary coral assemblage shifts, associated with changing light availability and wave exposure as reefs shallowed, coincided with transitions in accretion rates at equivalent core depths. Reef initiation followed a regional ∼1 m drop in sea level (1200–800 calibrated yr B.P.) which would have lowered the photic floor and exposed new substrate for coral recruitment by winnowing away fine seafloor sediments. We propose that a two-way feedback mechanism exists where past growth history influences current reef morphology and ecology, ultimately driving future reef accumulation and morphological change. These findings provide the first empirical evidence that nearshore reef growth trajectories are intrinsically driven by changes in coral community structure as reefs move toward sea level, a finding of direct significance for predicting the impacts of extrinsically driven ecological change (e.g., coral-algal phase shifts) on reef growth potential within the wider coastal zone on the Great Barrier Reef

Commensurate to incommensurate magnetic phase transition in Honeycomb-lattice pyrovanadate Mn2V2O7

We have synthesized single crystalline sample of Mn$_2$V$_2$O$_7$ using floating zone technique and investigated the ground state using magnetic susceptibility, heat capacity and neutron diffraction. Our magnetic susceptibility and heat capacity reveal two successive magnetic transitions at $T_{N1} =$ 19 K and $T_{N2} =$ 11.8 K indicating two distinct magnetically ordered phases. The single crystal neutron diffraction study shows that in the temperature ($T$) range 11.8 K $\le T \le$ 19 K the magnetic structure is commensurate with propagation vector $k_1 = (0, 0.5, 0)$, while upon lowering temperature below $T_{N2} =$ 11.8 K an incommensurate magnetic order emerges with $k_2 = (0.38, 0.48, 0.5)$ and the magnetic structure can be represented by cycloidal modulation of the Mn spin in $ac-$plane. We are reporting this commensurate to incommensurate transition for the first time. We discuss the role of the magnetic exchange interactions and spin-orbital coupling on the stability of the observed magnetic phase transitions.Comment: 8 pages, 7 figure

Context Dependence, MOPs,WHIMs and procedures Recanati and Kaplan on Cognitive Aspects in Semantics

After presenting Kripke’s criticism to Frege’s ideas on context dependence of thoughts, I present two recent attempts of considering cognitive aspects of context dependent expressions inside a truth conditional pragmatics or semantics: Recanati’s non-descriptive modes of presentation (MOPs) and Kaplan’s ways of having in mind (WHIMs). After analysing the two attempts and verifying which answers they should give to the problem discussed by Kripke, I suggest a possible interpretation of these attempts: to insert a procedural or algorithmic level in semantic representations of indexicals. That a function may be computed by different procedures might suggest new possibilities of integrating contextual cognitive aspects in model theoretic semanti

Nonperturbative renormalization group in a light-front three-dimensional real scalar model

The three-dimensional real scalar model, in which the $Z_2$ symmetry spontaneously breaks, is renormalized in a nonperturbative manner based on the Tamm-Dancoff truncation of the Fock space. A critical line is calculated by diagonalizing the Hamiltonian regularized with basis functions. The marginal ($\phi^6$) coupling dependence of the critical line is weak. In the broken phase the canonical Hamiltonian is tachyonic, so the field is shifted as $\phi(x)\to\varphi(x)+v$. The shifted value $v$ is determined as a function of running mass and coupling so that the mass of the ground state vanishes.Comment: 23 pages, LaTeX, 6 Postscript figures, uses revTeX and epsbox.sty. A slight revision of statements made, some references added, typos correcte

Dynamical phase transition for a quantum particle source

We analyze the time evolution describing a quantum source for noninteracting particles, either bosons or fermions. The growth behaviour of the particle number (trace of the density matrix) is investigated, leading to spectral criteria for sublinear or linear growth in the fermionic case, but also establishing the possibility of exponential growth for bosons. We further study the local convergence of the density matrix in the long time limit and prove the semiclassical limit.Comment: 24 pages; In the new version, we added several references concerning open quantum systems and present an extended result on linear particle production in the fermionic cas

Closed Recirculating Seawater Systems for Holding Intermolt Blue Crabs: Literature Review, Systems Design and Construction

Three closed recirculating seawater systems designed for holding intermolt stage blue crabs are described and illustrated. Pertinent literature dealing with design criteria for closed systems is discussed. The biology of the blue crab is reviewed in relation to data required for design purposes. Cost and capacity of the systems are presented including provision for solar heating. Areas where future work is needed are identified.https://aquila.usm.edu/gcrl_publications/1010/thumbnail.jp

The operationalized psychodynamic diagnostics system. Clinical relevance, reliability and validity

In this paper, we present a multiaxial system for psychodynamic diagnosis, which has attained wide usage in Germany in the last 10 years. First we will discuss the 4 operationalized psychodynamic diagnostics (OPD) axes: illness experience and treatment assumptions, relationships, mental conflicts, and structure, then clinical applications will be outlined. Focus psychodynamic formulations can be employed both with inpatients and with outpatients. Studies show good reliability in a research context and acceptable reliability for clinical purposes. Validity will be separately summarized as content, criterion, and construct validity. Validity studies indicate good validity for the individual axes. Numerous studies on the OPD indicate areas of possible improvement, for example for clinical purposes the OPD should be more practically formulated