Absence of species doubling in finite-element quantum electrodynamics

In this Letter, it will be demonstrated explicitly that the finite-element formulation of quantum electrodynamics is free from fermion doubling. We do this by (1) examining the lattice fermion propagator and using it to compute the one-loop vacuum polarization on the lattice, and (2) by an explict computation of vector and axial-vector current anomalies for an arbitrary rectangular lattice in the Schwinger model. There it is shown that requiring that the vector current be conserved necessitates the use of a square lattice, in which case the axial-vector current is anomalous.     

FM Space Depend on Operator T and the Normal Solvability of Operator Polynomial P（T）

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Line strengths and self-broadening coefficients of carbon dioxide isotopologues (CO2 and OCO) near 2.04 μm for the in situ laser sensing of the Martian atmosphere

A diode laser spectrometer was used in the laboratory to study ¹³CO₂ and ¹⁸O¹²C¹⁶O line intensities and self-broadening coefficients near 2.04 μm. The spectral region ranging from 4896 to 4903 cm⁻¹, which is suitable for in situ laser sensing of both isotopologues in the lower Martian atmosphere, was investigated using a distributed feedback GaInSb diode laser. Five lines of the (2 0⁰ 1)_II←(0 0 0) band of ¹³CO₂ and seven lines of the (2 0⁰ 1)_II←(0 0 0) band of ¹⁸O¹²C¹⁶O were carefully revisited. The measured intensities and self-broadening coefficients were thoroughly compared with relevant molecular databases.     

Minimal degree liftings in characteristic 2

In this paper we analyze liftings of hyperelliptic curves over perfect fields in characteristic 2 to curves over rings of Witt vectors. This theory can be applied to construct error-correcting codes; lifts of points with minimal degrees are likely to yield the best codes, and these are the main focus of the paper. We find upper and lower bounds for their degrees, give conditions to achieve the lower bounds and analyze the existence of lifts of the Frobenius. Finally, we exhibit explicit computations for genus 2 and show codes obtained using this theory.     

Representation of holomorphic functions on coverings of pseudoconvex domains in Stein manifolds via integral formulas on these domains

The classical integral representation formulas for holomorphic functions defined on pseudoconvex domains in Stein manifolds play an important role in the constructive theory of functions of several complex variables. In this paper, we will show how to construct similar formulas for certain classes of holomorphic functions defined on coverings of such domains.     

NaCl interaction with interfacially polymerized polyamide films of reverse osmosis membranes: A solid-state Na NMR study

²³Na nuclear magnetic resonance (NMR) spectroscopy of NaCl-exchanged polyamide (PA) films comparable to those of the active skin layer of many reverse osmosis (RO) membranes provides novel insight into the structural environments and dynamical behavior of Na⁺ in such films. Unsupported PA films were synthesized via interfacial polymerization of trimesoyl chloride in hexane and m-phenylenediamine in aqueous solution, and SEM, FT-IR, and ¹³C NMR data demonstrate successful thin film polymerization. Compositional data confirm this conclusion and demonstrate equal Na and Cl incorporation during NaCl exchange from aqueous solution. The ²³Na NMR spectra for freshly made polymer samples exchanged in 1 M NaCl solution show significant relative humidity (RH) dependence. At near 0% RH, there are resonances for crystalline NaCl and rigidly held Na⁺ in the PA. With increasing RH, a resonance for solution-like dynamically averaged Na⁺ appears and above 51% RH is the only signal observed. The slightly negative chemical shift of this resonance suggests a dominantly hydrous environment with some atomic-scale coordination by atoms of the polymer. The greatly reduced ²³Na T₁ relaxation rates for this resonance relative to bulk solution and crystalline NaCl confirm close association with the polymer. Variable temperature ²³Na NMR spectra for a sample equilibrated at 97% RH obtained from −80 to 20 °C show the presence of rigidly held Na⁺ in a hydrated environment at low temperatures and replacement of this resonance by the dynamically averaged signal at temperatures above about −20 °C. The results provide support for the solution–diffusion model for RO membranes transport and demonstrate the capabilities of multi-nuclear NMR methods to investigate molecular-scale structure and dynamics of the interactions between dissolved species and RO membranes.     

关于零级亚纯函数的一类新的奇异方向

本文研究了平面上的亚纯函数的奇异方向,利用Tsuji’s的第二基本定理和几个已有的关于函数增长性估计的引理,证明了平面上的零级亚纯函数至少存在一条T方向,这种方向直接以特征函数为比较函数,克服了Borel方向的定义中关于增长级不能为零的限制.     

On the topological theory of self-dual connections over noncompact Riemann surfaces

A topological action for self-dual connections over noncompact Riemann surfaces is proposed. TheJ formulation and the associated linear system are obtained. A new connection is constructed, depending on a Kac-Moody parameter such that its flatness condition is theJ-equation associated to the self-dual problem. The algebra of infinitesimal Bäcklund transformations depending on this Kac-Moody parameter is constructed.     

Quantitative cerebral magnetic resonance imaging during ACTH treatment of multiple sclerosis

Serial MR scans were performed with the 2DFT imaging method and the filtered backprojection imaging method on 12 patients with multiple sclerosis in acute phase, 4 in a relapsing/remitting form, and 8 in a progressive form, before, during and after ACTH treatment. Both T₁ and T_2mono relaxation times, obtained by fitting transverse magnetization decay curves with a monoexponential function within the apparently normal white matter and the areas of increased signal, were measured. With the backprojection method it was possible to fit the transverse magnetization decay curve with a biexponential function and obtain T_2long and T_2short relaxation times. The T_2mono and T₁ relaxation times of the apparently normal white matter were significantly different from those obtained for volunteers, but no significant differences were found before, during, or after treatment. The transverse magnetization decay curves of the areas of increased signal were better fitted by a biexponential function. No significant changes in these relaxation times were observed after ACTH treatment. These results argue against an anti-oedematous action of ACTH and may suggest that it has an immunosuppressant effect.