Topological Charge of ADHM Instanton on R^2_{NC}*R^2

We have calculated the topological charge of U(N) instantons on non-degenerate noncommutative space time to be exactly the instanton number k in a previous paper [Mod.Phys.Lett. A18 1691]. This paper, which deals with the degenerate R^2_{NC}*R^2 case, is the continuation of that one. We find that the same conclusion holds in this case, thus complete the answer to the problem of topological charge of noncommutative U(N) instantons.Comment: LaTeX, to appear in Mod. Phys. Lett.

Horizontal non-vanishing of Heegner points and toric periods

Let $F/\mathbb{Q}$ be a totally real field and $A$ a modular \GL_2-type abelian variety over $F$. Let $K/F$ be a CM quadratic extension. Let $\chi$ be a class group character over $K$ such that the Rankin-Selberg convolution $L(s,A,\chi)$ is self-dual with root number $-1$. We show that the number of class group characters $\chi$ with bounded ramification such that $L'(1, A, \chi) \neq 0$ increases with the absolute value of the discriminant of $K$. We also consider a rather general rank zero situation. Let $\pi$ be a cuspidal cohomological automorphic representation over \GL_{2}(\BA_{F}). Let $\chi$ be a Hecke character over $K$ such that the Rankin-Selberg convolution $L(s,\pi,\chi)$ is self-dual with root number $1$. We show that the number of Hecke characters $\chi$ with fixed $\infty$-type and bounded ramification such that $L(1/2, \pi, \chi) \neq 0$ increases with the absolute value of the discriminant of $K$. The Gross-Zagier formula and the Waldspurger formula relate the question to horizontal non-vanishing of Heegner points and toric periods, respectively. For both situations, the strategy is geometric relying on the Zariski density of CM points on self-products of a quaternionic Shimura variety. The recent result \cite{Ts, YZ, AGHP} on the Andr\'e-Oort conjecture is accordingly fundamental to the approach.Comment: Adv. Math., to appear. arXiv admin note: text overlap with arXiv:1712.0214

Radio observations and spectral index study of SNR G126.2+1.6

We present new images of the low radio surface brightness Supernova Remnant (SNR) G126.2+1.6, based on the 408 MHz and 1420 MHz continuum emission and the HI-line emission data of the Canadian Galactic Plane Survey (CGPS). {\bf We find the SNR's flux densities at 408 MHz (9.7$\pm$3.9 Jy) and 1420 MHz (6.7$\pm$2.1 Jy) which have been} corrected for flux densities from compact sources within the SNR. The integrated flux density based spectral index (S$_{\nu}$$\propto$$\nu$$^{-\alpha}$) is 0.30$\pm$0.41. The respective T-T plot spectral index is 0.30 $\pm$0.08. We also find spatial variations of spectral index within the SNR{\bf:0.2-0.6.} HI observations show structures probably associated with the SNR, i.e, features associated with the SNR's southeastern filaments in the radial velocity range of -33 to -42 km$/$s, and with its northwestern filaments in -47 to -52 km$/$s. This association suggests a distance of 5.6 kpc for SNR G126.2+1.6. The estimated Sedov age for G126.2+1.6 is less than 2.1$\times10^{5}$ yr.Comment: 12 pages, 4 figures, 4 tables, accepted by A&

Integrable Systems and Factorization Problems

The present lectures were prepared for the Faro International Summer School on Factorization and Integrable Systems in September 2000. They were intended for participants with the background in Analysis and Operator Theory but without special knowledge of Geometry and Lie Groups. In order to make the main ideas reasonably clear, I tried to use only matrix algebras such as $\frak{gl}(n)$ and its natural subalgebras; Lie groups used are either GL(n) and its subgroups, or loop groups consisting of matrix-valued functions on the circle (possibly admitting an extension to parts of the Riemann sphere). I hope this makes the environment sufficiently easy to live in for an analyst. The main goal is to explain how the factorization problems (typically, the matrix Riemann problem) generate the entire small world of Integrable Systems along with the geometry of the phase space, Hamiltonian structure, Lax representations, integrals of motion and explicit solutions. The key tool will be the \emph{% classical r-matrix} (an object whose other guise is the well-known Hilbert transform). I do not give technical details, unless they may be exposed in a few lines; on the other hand, all motivations are given in full scale whenever possible.Comment: LaTeX 2.09, 69 pages. Introductory lectures on Integrable systems, Classical r-matrices and Factorization problem

The HI absorption distance of HESS J1943+213 favours its extragalactic nature

The H.E.S.S. collaboration (Abramowski et al. 2011) dicovered a new TeV point-like source HESS J1943+213 in the Galactic plane and suggested three possible low-energy-band counterparts: a $\gamma$-ray binary, a pulsar wind nebula (PWN), or a BL Lacertae object. We measure the distance to the radio counterpart G57.76-1.29 of HESS J1943+213. We analyze Very Large Array observations to obtain a reliable HI absorption spectrum.The resulting distance limit is $\ge$ 16 kpc. This distance strongly supports that HESS J1943+213 is an extragalactic source, consistent with the preferred counterpart of the HESS collaboration.Comment: 3 figures, 2 pages, A&A accepte

Classical and Quantum Nonultralocal Systems on the Lattice

We classify nonultralocal Poisson brackets for 1-dimensional lattice systems and describe the corresponding regularizations of the Poisson bracket relations for the monodromy matrix . A nonultralocal quantum algebras on the lattices for these systems are constructed.For some class of such algebras an ultralocalization procedure is proposed.The technique of the modified Bethe-Anzatz for these algebras is developed.This technique is applied to the nonlinear sigma model problem.Comment: 33 pp. Latex. The file is resubmitted since it was spoiled during transmissio

Exergy optimisation for cascaded thermal storage

Cascaded thermal storage, consisting of multiple Phase Change Materials (PCMs) with different melting temperatures, has been proposed to solve the problem of poor heat transfer caused by unavoidable decrease of temperature differences during heat exchange process. This paper conducts a theoretical study of the overall thermal performance for a cascaded thermal storage system. Both heat transfer rate and exergy efficiency are taken into account. The main findings are: the cascaded arrangement of PCMs enhances the heat transfer rate by up to 30%, whilst it does not always improve the exergy efficiency (-15 to +30%). Enhanced heat transfer and reduced exergy efficiency can both be attributed to the larger temperature differences caused by the cascaded arrangement. A new parameter hex (exergy transfer rate) has been proposed to measure the overall thermal performance. It is defined as the product of heat transfer rate and exergy efficiency, representing the transfer rate of the utilisable thermal energy. The simulation results indicate that the cascaded thermal storage has higher overall thermal performance than the single-staged storage despite of higher exergy efficiency loss.Peer reviewe