Bergman kernel and complex singularity exponent

We give a precise estimate of the Bergman kernel for the model domain defined by $\Omega_F=\{(z,w)\in \mathbb{C}^{n+1}:{\rm Im}w-|F(z)|^2>0\},$ where $F=(f_1,...,f_m)$ is a holomorphic map from $\mathbb{C}^n$ to $\mathbb{C}^m$, in terms of the complex singularity exponent of $F$.Comment: to appear in Science in China, a special issue dedicated to Professor Zhong Tongde's 80th birthda

An R^4 non-renormalisation theorem in N=4 supergravity

We consider the four-graviton amplitudes in CHL constructions providing four-dimensional N=4 models with various numbers of vector multiplets. We show that in these models the two-loop amplitude has a prefactor of d^2R^4. This implies a non-renormalisation theorem for the R^4 term, which forbids the appearance of a three-loop ultraviolet divergence in four dimensions in the four-graviton amplitude. We connect the special nature of the R^4 term to the U(1) anomaly of pure N=4 supergravity.Comment: v2: added comments about one-loop UV divergences. Assorted stylistic corrections. Added references. v3: Eq. III.21 corrected and assorted minor corrections and clarifications. Version to be published. v4: minor corrections. 18 pages. one figur

The K\"ahler-Ricci flow on surfaces of positive Kodaira dimension

The existence of K\"ahler-Einstein metrics on a compact K\"ahler manifold has been the subject of intensive study over the last few decades, following Yau's solution to Calabi's conjecture. The Ricci flow, introduced by Richard Hamilton has become one of the most powerful tools in geometric analysis. We study the K\"ahler-Ricci flow on minimal surfaces of Kodaira dimension one and show that the flow collapses and converges to a unique canonical metric on its canonical model. Such a canonical is a generalized K\"ahler-Einstein metric. Combining the results of Cao, Tsuji, Tian and Zhang, we give a metric classification for K\"aher surfaces with a numerical effective canonical line bundle by the K\"ahler-Ricci flow. In general, we propose a program of finding canonical metrics on canonical models of projective varieties of positive Kodaira dimension

Observation of a μs isomer in 134 49In85: Proton-neutron coupling “southeast” of 132 50Sn82

We report on the observation of a microsecond isomeric state in the single-proton-hole, three-neutron-particle nucleus 134In. The nuclei of interest were produced by in-flight fission of a 238U beam at the Radioactive Isotope Beam Factory at RIKEN. The isomer depopulates through a γ ray of energy 56.7(1) keV and with a half-life of T1/2 = 3.5(4) μs. Based on the comparison with shell-model calculations, we interpret the isomer as the Iπ = 5− member of the π0g−1 9/2 ⊗ ν1 f 3 7/2 multiplet, decaying to the Iπ = 7− ground state with a reduced-transition probability of B(E2; 5− → 7−) = 0.53(6) W.u. Observation of this isomer, and lack of evidence in the current work for a Iπ = 5− isomer decay in 132In, provides a benchmark of the proton-neutron interaction in the region of the nuclear chart “southeast” of 132Sn, where experimental information on excited states is sparse

Supersymmetric Many-particle Quantum Systems with Inverse-square Interactions

The development in the study of supersymmetric many-particle quantum systems with inverse-square interactions is reviewed. The main emphasis is on quantum systems with dynamical OSp(2|2) supersymmetry. Several results related to exactly solved supersymmetric rational Calogero model, including shape invariance, equivalence to a system of free superoscillators and non-uniqueness in the construction of the Hamiltonian, are presented in some detail. This review also includes a formulation of pseudo-hermitian supersymmetric quantum systems with a special emphasis on rational Calogero model. There are quite a few number of many-particle quantum systems with inverse-square interactions which are not exactly solved for a complete set of states in spite of the construction of infinitely many exact eigen functions and eigenvalues. The Calogero-Marchioro model with dynamical SU(1,1|2) supersymmetry and a quantum system related to short-range Dyson model belong to this class and certain aspects of these models are reviewed. Several other related and important developments are briefly summarized.Comment: LateX, 65 pages, Added Acknowledgment, Discussions and References, Version to appear in Jouranl of Physics A: Mathematical and Theoretical (Commissioned Topical Review Article

From error bounds to the complexity of first-order descent methods for convex functions

This paper shows that error bounds can be used as effective tools for deriving complexity results for first-order descent methods in convex minimization. In a first stage, this objective led us to revisit the interplay between error bounds and the Kurdyka-\L ojasiewicz (KL) inequality. One can show the equivalence between the two concepts for convex functions having a moderately flat profile near the set of minimizers (as those of functions with H\"olderian growth). A counterexample shows that the equivalence is no longer true for extremely flat functions. This fact reveals the relevance of an approach based on KL inequality. In a second stage, we show how KL inequalities can in turn be employed to compute new complexity bounds for a wealth of descent methods for convex problems. Our approach is completely original and makes use of a one-dimensional worst-case proximal sequence in the spirit of the famous majorant method of Kantorovich. Our result applies to a very simple abstract scheme that covers a wide class of descent methods. As a byproduct of our study, we also provide new results for the globalization of KL inequalities in the convex framework. Our main results inaugurate a simple methodology: derive an error bound, compute the desingularizing function whenever possible, identify essential constants in the descent method and finally compute the complexity using the one-dimensional worst case proximal sequence. Our method is illustrated through projection methods for feasibility problems, and through the famous iterative shrinkage thresholding algorithm (ISTA), for which we show that the complexity bound is of the form $O(q^{k})$ where the constituents of the bound only depend on error bound constants obtained for an arbitrary least squares objective with $\ell^1$ regularization

An Ordovician ostracod palaeopsychrosphere?

Ostracods are tiny bivalved crustaceans with a fossil record extending into rocks of the Lower Ordovician. They occupy almost all aquatic environments today, from the ocean abyssal planes to damp forest leaf litter. Their stratigraphical record suggests they had diversified into a wide range of marine and non-marine habitats already during the Palaeozoic. Through the Ordovician, ostracods are mostly known from marine shelf depositional settings. These are mostly podocope ostracods that appear to have had a benthic mode of life like their modern counterparts; myodocope ostracods, though known from the Ordovician, likely became pelagic only in the Silurian. As they are considered benthic, and possessed no pelagic larval stage, Ordovician podocope ostracods have been widely used as key biogeographical index species for much of the early Palaeozoic. A fundamental question in the oceanographic evolution of ostracods is: when did a psychrosphere evolve (a fauna inhabiting cool waters below the thermocline)? A psychrospheric ostracod fauna in the Ordovician would question some of their biogeographic utility, given that such taxa might have a much wider dispersal capability than more shallow shelf faunas. Here we describe a new ostracod fauna from a palaeotropical South China plate setting, preserved in Upper Ordovician mudstones and siltstones from northern Vietnam. The fauna contains taxa endemic to the South China palaeoplate, but also yields several taxa at the generic level that are known from European and North American Ordovician settings. We discuss whether these latter taxa might be indicative of a more widely dispersed deeper marine psychrospheric Ordovician ostracod fauna, and the implications this would have on traditional biogeographic models. We also discuss other possibilities for these apparently more cosmopolitan taxa, including homeomorphy, previously unknown palaeogeographical connections, and the possibility of pelagic podocope taxa

Geochemical Assessment of Vulnerability of Groundwater to Contaminant at Phuoc Hiep Landfill Site, Ho Chi Minh City, Vietnam

Abstract A geochemical assessment on vulnerability of groundwater quality and shallow aquifer in the vicinity of the Phuoc Hiep landfill site was carried out with a hydro-chemical approach for identifying various geochemical processes and understanding the impacts of landfill leachate on groundwater quality. Results indicate that hardness, nitrate, fluoride, iron in groundwater and heavy metal in surface water are above the standard for drinking water. Leachate seepage from the landfill is a main contaminant source of groundwater of Na-Cl water type with electrical conductivity (EC) values of 4,275 to 4,575 μS/cm. The pH values of the leachate are between 5.8 and 6.6. Concentrations of Al, Fe and Mn and heavy metals (Pb, Zn and Cu) in the leachate are above the drinking water standards. As a result, the waste leachate has a high content of contaminant that affects groundwater quality in highly productive zones. Two main zones of the aquifer were determined to be most vulnerable using GOD vulnerability model. Thus, these vulnerable zones are not suitable for waste disposal and the aquifer should be protected from leachate

Analysis of host responses to Mycobacterium tuberculosis antigens in a multi-site study of subjects with different TB and HIV infection states in sub-Saharan Africa.

BACKGROUND: Tuberculosis (TB) remains a global health threat with 9 million new cases and 1.4 million deaths per year. In order to develop a protective vaccine, we need to define the antigens expressed by Mycobacterium tuberculosis (Mtb), which are relevant to protective immunity in high-endemic areas. METHODS: We analysed responses to 23 Mtb antigens in a total of 1247 subjects with different HIV and TB status across 5 geographically diverse sites in Africa (South Africa, The Gambia, Ethiopia, Malawi and Uganda). We used a 7-day whole blood assay followed by IFN-γ ELISA on the supernatants. Antigens included PPD, ESAT-6 and Ag85B (dominant antigens) together with novel resuscitation-promoting factors (rpf), reactivation proteins, latency (Mtb DosR regulon-encoded) antigens, starvation-induced antigens and secreted antigens. RESULTS: There was variation between sites in responses to the antigens, presumably due to underlying genetic and environmental differences. When results from all sites were combined, HIV- subjects with active TB showed significantly lower responses compared to both TST(-) and TST(+) contacts to latency antigens (Rv0569, Rv1733, Rv1735, Rv1737) and the rpf Rv0867; whilst responses to ESAT-6/CFP-10 fusion protein (EC), PPD, Rv2029, TB10.3, and TB10.4 were significantly higher in TST(+) contacts (LTBI) compared to TB and TST(-) contacts fewer differences were seen in subjects with HIV co-infection, with responses to the mitogen PHA significantly lower in subjects with active TB compared to those with LTBI and no difference with any antigen. CONCLUSIONS: Our multi-site study design for testing novel Mtb antigens revealed promising antigens for future vaccine development. The IFN-γ ELISA is a cheap and useful tool for screening potential antigenicity in subjects with different ethnic backgrounds and across a spectrum of TB and HIV infection states. Analysis of cytokines other than IFN-γ is currently on-going to determine correlates of protection, which may be useful for vaccine efficacy trials