Homotopy moment maps

Associated to any manifold equipped with a closed form of degree >1 is an `L-infinity algebra of observables' which acts as a higher/homotopy analog of the Poisson algebra of functions on a symplectic manifold. In order to study Lie group actions on these manifolds, we introduce a theory of homotopy moment maps. Such a map is a L-infinity morphism from the Lie algebra of the group into the observables which lifts the infinitesimal action. We establish the relationship between homotopy moment maps and equivariant de Rham cohomology, and analyze the obstruction theory for the existence of such maps. This allows us to easily and explicitly construct a large number of examples. These include results concerning group actions on loop spaces and moduli spaces of flat connections. Relationships are also established with previous work by others in classical field theory, algebroid theory, and dg geometry. Furthermore, we use our theory to geometrically construct various L-infinity algebras as higher central extensions of Lie algebras, in analogy with Kostant's quantization theory. In particular, the so-called `string Lie 2-algebra' arises this way.Comment: Final version will appear in Advances in Mathematics. Results concerning equivariant cohomology strengthened. In particular, we exhibit the explicit relationship between equivariant de Rham cocycles of arbitrary degree and homotopy moment maps. 62 pages. Comments are welcome. arXiv admin note: text overlap with arXiv:1402.0144 by other author

Nonadiabatic effects in the dynamics of atoms confined in a cylindric time-orbiting-potential magnetic trap

In a time-orbiting-potential magnetic trap the neutral atoms are confined by means of an inhomogeneous magnetic field superimposed to an uniform rotating one. We perform an analytic study of the atomic motion by taking into account the nonadiabatic effects arising from the spin dynamics about the local magnetic field. Geometric-like magnetic-fields determined by the Berry's phase appear within the quantum description. The application of a variational procedure on the original quantum equation leads to a set of dynamical evolution equations for the quantum average value of the position operator and of the spin variables. Within this approximation we derive the quantum-mechanical ground state configuration matching the classical adiabatic solution and perform some numerical simulations.Comment: 12 pages, 4 figure

Microstructural characterization of AISI 431 martensitic stainless steel laser-deposited coatings

High cooling rates during laser cladding of stainless steels may alter the microstructure and phase constitution of the claddings and consequently change their functional properties. In this research, solidification structures and solid state phase transformation products in single and multi layer AISI 431 martensitic stainless steel coatings deposited by laser cladding at different processing speeds are investigated by optical microscopy, Scanning electron microscopy (SEM), energy dispersive spectroscopy (EDS), orientation imaging microscopy (OIM), ternary phase diagram, Schaeffler and TTT diagrams. The results of this study show how partitionless solidification and higher solidification rates alter the microstructure and phase constitution of martensitic stainless steel laser deposited coatings. In addition, it is shown that while different cladding speeds have no effect on austenite–martensite orientation relationship in the coatings, increasing the cladding speed has resulted in a reduction of hardness in deposited coatings which is in contrast to the common idea about obtaining higher hardness values at higher cladding speeds.

Pengaruh Fraksi Penipisan (P) Air Tanah Tersedia Pada Berbagai Fase Tumbuh Terhadap Pertumbuhan, Hasil Dan Efisiensi Penggunaan Air Tanaman Kedelai (Glycine Max [L] Merr.)

Penelitian bertujuan untuk mengetahui pengaruh fraksi penipisan (p) air tanah tersedia pada berbagai fase tumbuh terhadap pertumbuhan dan efisiensi penggunaan air tanaman kedelai. Penelitian ini dilaksanakan di dalam rumah plastik, laboratorium lapang terpadu, Universitas Lampung pada bulan Oktober 2015 sampai dengan Januari 2016. Penelitian ini menggunakan rancangan Faktorial dalam Acak Lengkap (RAL) dengan 2 faktor perlakuan, yaitu faktor I (Fraksi penipisan air tanah tersedia, p) dan faktor II (fase tumbuh, F). Masing-masing perlakuan terdiri dari 3 taraf, yaitu faktor I terdiri dari P1(0,2), P2(0,4) dan P3(0,6) dari penipisan air tanah tersedia, dan faktor II terdiri dari fase vegetatif aktif (F1), fase pembungaan (F2), dan fase pembentukan polong (F3), dengan ulangan sebanyak 3 kali. Pengukuran evapotranspirasi tanaman acuan dilakukan pada fraksi penipisan 0,2 dari air tanah tersedia dengan menggunakan tanaman rumput. Hasil penelitian menunjukkan bahwa, perlakuan fraksi penipisan (p) air tanah tersedia pada berbagai fase tumbuhtidak berpengaruh terhadap pertumbuhan dan efisiensi penggunaan air tanaman kedelai.Tanaman kedelai pada perlakuan fraksi penipisan (p) air tanah tersedia tidak mengalami cekaman air pada semua perlakuan, karena tanaman sebelum mendekati batas bawah perlakuan segera diberi irigasi dan dikembalikan ke kondisi kapasitas lapang. Produksi tertinggi dengan nilai efisiensi penggunaan air tertinggi dicapai oleh perlakuan fraksi penipisan (0-0,2) air tanah tersedia pada perlakuan fase pembungaan (F2). Tanaman kedelai menghasilkan produksi yang tinggi pada fraksi penipisan 0,4 untuk perlakuan fase pertumbuhan aktif dan fraksi penipisan 0,2 untuk perlakuan fase pembungaan dan fase pengisian polong

Dietary folates and cancer risk in a network of case-control studies

Background Folate deficiency leads to DNA damage and inadequate repair, caused by a decreased synthesis of thymidylate and purines. We analyzed the relationship between dietary folate intake and the risk of several cancers. Patients and methods The study is based on a network of case-control studies conducted in Italy and Switzerland in 1991-2009. The odds ratios (ORs) for dietary folate intake were estimated by multiple logistic regression models, adjusted for major identified confounding factors. Results For a few cancer sites, we found a significant inverse relation, with ORs for an increment of 100μg/day of dietary folate of 0.65 for oropharyngeal (1467 cases), 0.58 for esophageal (505 cases), 0.83 for colorectal (2390 cases), 0.72 for pancreatic (326 cases), 0.67 for laryngeal (851 cases) and 0.87 for breast (3034 cases) cancers. The risk estimates were below unity, although not significantly, for cancers of the endometrium (OR=0.87, 454 cases), ovary (OR=0.86, 1031 cases), prostate (OR=0.91, 1468 cases) and kidney (OR=0.88, 767 cases), and was 1.00 for stomach cancer (230 cases). No material heterogeneity was found in strata of sex, age, smoking and alcohol drinking. Conclusions Our data support a real inverse association of dietary folate intake with the risk of several common cancer

The quantum non-linear Schrodinger model with point-like defect

We establish a family of point-like impurities which preserve the quantum integrability of the non-linear Schrodinger model in 1+1 space-time dimensions. We briefly describe the construction of the exact second quantized solution of this model in terms of an appropriate reflection-transmission algebra. The basic physical properties of the solution, including the space-time symmetry of the bulk scattering matrix, are also discussed.Comment: Comments on the integrability and the impurity free limit adde

First mineralogical maps of 4 Vesta

Before Dawn arrived at 4 Vesta only very low spatial resolution (~50 km) albedo and color maps were available from HST data. Also ground-based color and spectroscopic data were utilized as a first attempt to map Vesta’s mineralogical diversity [1-4]. The VIR spectrometer [5] onboard Dawn has ac-quired hyperspectral data while the FC camera [6] ob-tained multi-color data of the Vestan surface at very high spatial resolutions, allowing us to map complex geologic, morphologic units and features. We here re-port about the results obtained from a preliminary global mineralogical map of Vesta, based on data from the Survey orbit. This map is part of an iterative map-ping effort; the map is refined with each improvement in resolution