q-series and L-functions related to half-derivatives of the Andrews--Gordon identity

Studied is a generalization of Zagier's q-series identity. We introduce a generating function of L-functions at non-positive integers, which is regarded as a half-differential of the Andrews--Gordon q-series. When q is a root of unity, the generating function coincides with the quantum invariant for the torus knot.Comment: 21 pages, related papers can be found from http://gogh.phys.s.u-tokyo.ac.jp/~hikami

Nonlinear spectroscopic studies using sum- and difference-frequency generation

A detailed study is presented of resonant sum- and difference-frequency generation for the mixed-crystal system azulene in naphthalene. The S0 -> S1, S0 -> S2 and S1 -> S2 transitions of azulene provide the 3 needed dipoles for the existence of c(2), and a relatively small static elec. field was used to break the interference between the waves generated in the 2 crystal sublattices. Second-order nonlinear processes can occur sep. in each sublattice. All the theor. predicted resonances, except the DICE effect, were obsd. The generated field intensity satd. at higher fields, and in certain circumstances exhibited hysteresis as a function of the d.c. field strength. The line-narrowing capabilities of these new forms of spectroscopy were explored

Resonant nonlinear spectroscopy in strong fields

A method is presented to describe multiple resonant nonlinear spectra in the presence of strong laser fields. The Liouville equation for the d. operator of the mol. system is transformed to a time-independent linear equation system. This can be easily solved rigorously by numerical methods or, after partitioning into a strong-field part and a perturbation, the soln. can be obtained anal. by a novel perturbative approach. The results account for power broadening. Rabi splitting of signals, and power-induced extra resonances, the latter being related to the pure dephasing-induced resonances in the weak-field limit. The method can be applied to a large no. of multiple resonant nonlinear spectroscopies, esp. CARS, CSRS, coherent Rayleigh scattering and sum- or difference-frequency generation

Long-Term Data Reveal a Population Decline of the Tropical Lizard Anolis apletophallus, and a Negative Affect of El Nino Years on Population Growth Rate

Climate change threatens biodiversity worldwide, however predicting how particular species will respond is difficult because climate varies spatially, complex factors regulate population abundance, and species vary in their susceptibility to climate change. Studies need to incorporate these factors with long-term data in order to link climate change to population abundance. We used 40 years of lizard abundance data and local climate data from Barro Colorado Island to ask how climate, total lizard abundance and cohort-specific abundance have changed over time, and how total and cohort-specific abundance relate to climate variables including those predicted to make the species vulnerable to climate change (i.e. temperatures exceeding preferred body temperature). We documented a decrease in lizard abundance over the last 40 years, and changes in the local climate. Population growth rate was related to the previous years’ southern oscillation index; increasing following cooler-wetter, la niña years, decreasing following warmer-drier, el nino years. Within-year recruitment was negatively related to rainfall and minimum temperature. This study simultaneously identified climatic factors driving long-term population fluctuations and climate variables influencing short-term annual recruitment, both of which may be contributing to the population decline and influence the population’s future persistence

On the harmonic measure of stable processes

Using three hypergeometric identities, we evaluate the harmonic measure of a finite interval and of its complementary for a strictly stable real L{\'e}vy process. This gives a simple and unified proof of several results in the literature, old and recent. We also provide a full description of the corresponding Green functions. As a by-product, we compute the hitting probabilities of points and describe the non-negative harmonic functions for the stable process killed outside a finite interval

The Uq(sl^(2/1))1U_q(\hat{sl}(2/1))_1-module V(Λ2)V(\Lambda_2) and a Corner Transfer Matrix at q=0

The north-west corner transfer matrix of an inhomogeneous integrable vertex model constructed from the vector representation of $U_q\bigl(sl(2/1)\bigr)$ and its dual is investigated. In the limit $q\to0$, the spectrum can be obtained. Based on an analysis of the half-infinite tensor products related to all CTM-eigenvalues $\geq -4$, it is argued that the eigenvectors of the corner transfer matrix are in one-to-one correspondance with the weight states of the $U_q\bigl((\hat{sl}(2/1)\bigr)_1-$module $V(\Lambda_2)$ at level one. This is supported by a comparison of the comlete set of eigenvectors with a nondegenerate triple of eigenvalues of the CTM-Hamiltonian and the generators of the Cartan-subalgebra of $U_q\bigl(sl(2|1)\bigr)$ to the weight states of $V(\Lambda_2)$ with multiplicity one.Comment: 28 pages, revtex accepted for publication in Nuclear Physics

Thermodynamic Bethe Ansatz for the subleading magnetic perturbation of the tricritical Ising model

We give further support to Smirnov's conjecture on the exact kink S-matrix for the massive Quantum Field Theory describing the integrable perturbation of the c=0.7 minimal Conformal Field theory (known to describe the tri-critical Ising model) by the operator $\phi_{2,1}$. This operator has conformal dimensions $(7/16,7/16)$ and is identified with the subleading magnetic operator of the tri-critical Ising model. In this paper we apply the Thermodynamic Bethe Ansatz (TBA) approach to the kink scattering theory by explicitly utilising its relationship with the solvable lattice hard hexagon model. Analytically examining the ultraviolet scaling limit we recover the expected central charge c=0.7 of the tri-critical Ising model. We also compare numerical values for the ground state energy of the finite size system obtained from the TBA equations with the results obtained by the Truncated Conformal Space Approach and Conformal Perturbation Theory.Comment: 22 pages, minor changes, references added. LaTeX file and postscript figur

Using exchange structure analysis to explore argument in text-based computer conferences

Computer conferencing provides a new site for students to develop and rehearse argumentation skills, but much remains to be learnt about how to encourage and support students in this environment. Asynchronous text-based discussion differs in significant ways from face-to-face discussion, creating a need for specially designed schemes for analysis. This paper discusses some of the problems of analysing asynchronous argumentation, and puts forward an analytical framework based on exchange structure analysis, which brings a linguistic perspective to bear on the interaction. Key features of the framework are attention to both interactive and ideational aspects of the discussion, and the ability to track the dynamic construction of argument content. The paper outlines the framework itself, and discusses some of the findings afforded by this type of analysis, and its limitations

Pygmy blue whale movement, distribution and important areas in the Eastern Indian Ocean

This study was conducted as part of AIMS’ North West Shoals to Shore Research Program (NWSSRP) and was supported by Santos as part of the company’s commitment to better understand Western Australia’s marine environment. Hydrophone pressure data from Ocean Bottom Seismometers (OBS) were provided by the CANPASS project, jointly funded by the National Natural Science Foundation of China (NSFC grants 91955210, 41625016), and the China Academy of Science (CAS program GJHZ1776). Instruments were provided by the Australian National instrument pool ANSIR (http://ansir.org.au/). ANSIR, OBS data was also made data available from the Geoscience Australia and Shell. Data was sourced from Australia’s Integrated Marine Observing System (IMOS).Pygmy blue whales in the South-east Indian Ocean migrate from the southern coast of Australia to Indonesia, with a significant part of their migration route passing through areas subject to oil and gas production. This study aimed at improving our understanding of the spatial extent of the distribution, migration and foraging areas, to better inform impact assessment of anthropogenic activities in these regions. Using a combination of passive acoustic monitoring of the NW Australian coast (46 instruments from 2006 to 2019) and satellite telemetry data (22 tag deployments from 2009 to 2021) we quantified the pygmy blue whale distribution and important areas during their northern and southern migration. We show extensive use of slope habitat off Western Australia and only minimal use of shelf habitat, compared to southern Australia where use of the continental shelf and shelf break predominates. In addition, movement behaviour estimated by a state-space model on satellite tag data showed that in general pygmy blue whales off Western Australia were mostly engaged in migration, interspersed with mostly relatively short periods (median = 28hours, range = 2 – 1080hours) of low move persistence (slow movement with high turning angles), which is indicative of foraging. Using the spatial overlap of time and number of whales in area analysis of the satellite tracking data (top 50% of grid cells) with foraging movement behaviour, we quantified the spatial extent of pygmy blue whale high use areas for foraging and migration. We compared these areas to the previously described areas of importance to foraging and migrating whales (Biologically Important Areas; BIAs). In some cases these had good agreement with the most important areas we calculated from our data, but others had only low (5%) to moderate (13%) overlap. Month was the most important variable predicting the number of pygmy blue whale units and number of singers (acting as indices of pygmy blue whale density). Whale density was highest in the southern part of the NW Australian coast and whales were present there between April-June, and November-December, a pattern also confirmed by the satellite tracking data. Available data indicated pygmy blue whales spent up to 124 days in Indonesian waters (34% of annual cycle). Since this area may also be the calving ground for this population, inter-jurisdictional management is necessary to ensure their full protection.Publisher PDFPeer reviewe

Integrable Structure of Conformal Field Theory, Quantum KdV Theory and Thermodynamic Bethe Ansatz

We construct the quantum versions of the monodromy matrices of KdV theory. The traces of these quantum monodromy matrices, which will be called as ``${\bf T}$-operators'', act in highest weight Virasoro modules. The ${\bf T}$-operators depend on the spectral parameter $\lambda$ and their expansion around $\lambda = \infty$ generates an infinite set of commuting Hamiltonians of the quantum KdV system. The ${\bf T}$-operators can be viewed as the continuous field theory versions of the commuting transfer-matrices of integrable lattice theory. In particular, we show that for the values $c=1-3{{(2n+1)^2}\over {2n+3}} , n=1,2,3,...$of the Virasoro central charge the eigenvalues of the ${\bf T}$-operators satisfy a closed system of functional equations sufficient for determining the spectrum. For the ground-state eigenvalue these functional equations are equivalent to those of massless Thermodynamic Bethe Ansatz for the minimal conformal field theory ${\cal M}_{2,2n+3}$; in general they provide a way to generalize the technique of Thermodynamic Bethe Ansatz to the excited states. We discuss a generalization of our approach to the cases of massive field theories obtained by perturbing these Conformal Field Theories with the operator $\Phi_{1,3}$. The relation of these ${\bf T}$-operators to the boundary states is also briefly described.Comment: 24 page