A checklist of chromosome numbers of South Asian reptiles

The chromosome numbers of 119 species of reptiles that occur in the south Asian region are listed. The inventory includes three crocodiles, 13 turtles, 54 lizards and 49 snakes. This represents about a fourth of the known species of the subcontinent. Cytogenetic information in many cases offers clues to the detection of cryptic species overlooked by morphological taxonomists

The herpetofauna of the Babuyan Islands, Northern Philippines

We document 52 species of amphibians and reptiles from the Babuyan Islands in the northern Philippines. Among these records, 12 species are endemic to the Babuyan Islands and another 18 are endemic to the Philippines. Prevalence of endemic forms in the island group is high, with 1–3 island-endemic species present in each of the major islands. The present-day assemblage of herpetofauna in the island group is attributed to dispersal from Luzon and subsequent diversification. No evidence of successful southward colonization of species from Taiwan is found. Based on data from our own surveys, and to enable future work, we provide an updated list of the species from the Babuyan and Batanes Island groups. Molecular phylogenetic studies are recommended to gain more insights into the evolutionary history of the island-endemic forms and the biogeography of the small islands between Luzon and Taiwan

Convergence of simulated annealing by the generalized transition probability

We prove weak ergodicity of the inhomogeneous Markov process generated by the generalized transition probability of Tsallis and Stariolo under power-law decay of the temperature. We thus have a mathematical foundation to conjecture convergence of simulated annealing processes with the generalized transition probability to the minimum of the cost function. An explicitly solvable example in one dimension is analyzed in which the generalized transition probability leads to a fast convergence of the cost function to the optimal value. We also investigate how far our arguments depend upon the specific form of the generalized transition probability proposed by Tsallis and Stariolo. It is shown that a few requirements on analyticity of the transition probability are sufficient to assure fast convergence in the case of the solvable model in one dimension.Comment: 11 page

Molecular Clouds as Cosmic Ray Laboratories

We will here discuss how the gamma-ray emission from molecular clouds can be used to probe the cosmic ray flux in distant regions of the Galaxy and to constrain the highly unknown cosmic ray diffusion coefficient. In particular we will discuss the GeV to TeV emission from runaway cosmic rays penetrating molecular clouds close to young and old supernova remnants and in molecular clouds illuminated by the background cosmic ray flux.Comment: to appear on Proceedings of 25th Texas Symposium on Relativistic Astrophysic

Free Boson Representation of Uq(sl^3)U_q(\widehat{sl}_3)

A representation of the quantum affine algebra $U_{q}(\widehat{sl}_3)$ of an arbitrary level $k$ is constructed in the Fock module of eight boson fields. This realization reduces the Wakimoto representation in the $q \rightarrow 1$ limit. The analogues of the screening currents are also obtained. They commute with the action of $U_{q}(\widehat{sl}_3)$ modulo total differences of some fields.Comment: 12 pages, LaTeX, RIMS-920, YITP/K-101

A Quantum Deformation of the Virasoro Algebra and the Macdonald Symmetric Functions

A quantum deformation of the Virasoro algebra is defined. The Kac determinants at arbitrary levels are conjectured. We construct a bosonic realization of the quantum deformed Virasoro algebra. Singular vectors are expressed by the Macdonald symmetric functions. This is proved by constructing screening currents acting on the bosonic Fock space.Comment: 15 pages, latex fil

Heisenberg realization for U_q(sln) on the flag manifold

We give the Heisenberg realization for the quantum algebra $U_q(sl_n)$, which is written by the $q$-difference operator on the flag manifold. We construct it from the action of $U_q(sl_n)$ on the $q$-symmetric algebra $A_q(Mat_n)$ by the Borel-Weil like approach. Our realization is applicable to the construction of the free field realization for the $U_q(\widehat{sl_n})$ [AOS].Comment: 10 pages, YITP/K-1016, plain TEX (some mistakes corrected and a reference added

Macdonald operators and homological invariants of the colored Hopf link

Using a power sum (boson) realization for the Macdonald operators, we investigate the Gukov, Iqbal, Kozcaz and Vafa (GIKV) proposal for the homological invariants of the colored Hopf link, which include Khovanov-Rozansky homology as a special case. We prove the polynomiality of the invariants obtained by GIKV's proposal for arbitrary representations. We derive a closed formula of the invariants of the colored Hopf link for antisymmetric representations. We argue that a little amendment of GIKV's proposal is required to make all the coefficients of the polynomial non-negative integers.Comment: 31 pages. Published version with an additional appendi