On the Birationality of the Bicanonical Map of a Surface Section of a Threefold

Let (?, ?) be a polarized threefold of log-general type. The birationality of the bicanonical map of a smooth surface S ∈ |?| is studied. This problem was previously considered and partially solved by the first and fourth author, who gave a satisfactory classification unless h¹(𝒪_?) = 0 and p_g(S) = 3, 4, 5. This article focuses on the remaining cases which are the hardest, settling the problem.     

Projective line over the finite quotient ring GF(2)[x]/〈x 3 ™ x〉 and quantum entanglement: The Mermin “magic” square/pentagram

In 1993, Mermin gave surprisingly simple proofs of the Bell-Kochen-Specker (BKS) theorem in Hilbert spaces of dimensions four and eight respectively using what has since been called the Mermin-Peres “magic” square and the Mermin pentagram. The former is a 3×3 array of nine observables commuting pairwise in each row and column and arranged such that their product properties contradict those of the assigned eigenvalues. The latter is a set of ten observables arranged in five groups of four lying along five edges of the pentagram and characterized by a similar contradiction. We establish a one-to-one correspondence between the operators of the Mermin-Peres square and the points of the projective line over the product ring GF(2) ⊗ GF(2). Under this map, the concept mutually commuting transforms into mutually distant, and the distinguishing character of the third column’s observables has its counterpart in the distinguished properties of the coordinates of the corresponding points, whose entries are either both zero divisors or both units. The ten operators of the Mermin pentagram correspond to a specific subset of points of the line over GF(2)[x]/〈x³ ™ x〉. But the situation in this case is more intricate because there are two different configurations that seem to serve our purpose equally well. The first one comprises the three distinguished points of the (sub)line over GF(2), their three “Jacobson” counterparts, and the four points whose both coordinates are zero divisors. The other con.guration features the neighborhood of the point (1, 0) (or, equivalently, that of (0, 1)). We also mention some other ring lines that might be relevant to BKS proofs in higher dimensions. __________ Translated from Teoreticheskaya i Matematicheskaya Fizika, Vol. 151, No. 2, pp. 219–227, May, 2007.     

Singular problem for a third-order nonlinear ordinary differential equation arising in fluid dynamics

Results concerning singular Cauchy problems, smooth manifolds, and Lyapunov series are used to correctly state and analyze a singular “initial-boundary” problem for a third-order nonlinear ordinary differential equation defined on the entire real axis. This problem arises in viscous incompressible fluid dynamics and describes self-similar solutions to the boundary layer equation for the stream function with a zero pressure gradient (plane-parallel flow in a mixing layer). The analysis of the problem suggests a simple numerical method for its solution. Numerical results are presented.     

全能近似分析简介

根据无限的“无有终了”的事实,应当把无尽小数看作无穷数列简写,采用这种观点就可以得到实数的运算法则;如果用康托（Cantor,G）的“无限是现实的、完成了的、存在着的整体”的“实无限”观点就得不到这个法则．点是针对误差界的足够小,其中没有大小的点叫做理想点,有大小的点叫做近似点．理想点具有无法点出的性质．近似点的集合能够组成线段,但理想点的集合不能组成线段．绝对准确地讨论没有大小的理想瞬时上的速度没有实际意义,理想的瞬时速度依赖于近似瞬时的速度．对于点、线、面、实数、函数、导数、积分、积分变换、实数集等数学名词都需要提出近似、理想、全能近似三类技术术语,应用对立统一法则去阐述数学理论．     

Charakterisierung der Protonen in polykristallinen Parawolframaten durch 1H‐MAS‐NMR‐Untersuchungen

Characterization of the Protons in Polycrystalline Paratungstates using ¹H MAS NMR Investigations ¹H MAS NMR experiments are used to characterize the non‐acid protons of the anions in polycrystalline paratungstates by means of the measured isotropic chemical shift values. The investigation of various hydrates of ammonium paratungstate allows a direct proof of protons in NH₄ ions and in water molecules while protons of the anions are not detectable. However, for both the potassium and the sodium paratungstates ¹H MAS NMR investigations detected the protons of water molecules and the non‐acid protons of the paratungstate anions. Additional ¹H broad‐line NMR experiments at 173 K support the interpretation of the results obtained by the ¹H MAS NMR investigations. For the NMR signal of the non‐acid protons of the paratungstate anion in the ¹H MAS NMR spectra of the potassium salt line‐splitting appears. This refers to the existence of two nonidentical positions of the protons in the crystal lattice and is in agreement with the results of the X‐ray structural analysis.     

X射线荧光光谱法测定化探样品中主、次和痕量组分

采用粉末样品压片制样,用PW2440X射线荧光光谱仪对化探样品中氯、溴、硫、氧化钠、氧化镁、三氧化二铝、二氧化硅、磷、氧化钾、氧化钙、钛、锰、三氧化二铁、钴、铌、锆、钇、锶、铷、铅、钍、锌、铜、镍、钒、铬、钡、镧、铈、钕、钪、镓、砷、铪等34个组分进行测定。讨论了微量元素的背景选择和谱线重叠校正及氯测定的问题。使用经验系数法和康普顿散射线作内标校正基体效应,经标准物质检验,分析结果与标样值吻合,用GBW 07308国家一级标准物质作精密度试验,统计结果RSD（n=12）除砷、钒、镍、铜〈6．0％,溴、硫、铈、铪、钕、钪、氧化钠、镧、铬、钴和钍〈14．0％以外,其余各组分均小于3．0％。     

The Efficiency of a Microcolumn of Rice Bran for On‐line Trace Enrichment in FI‐AAS,a Highly Selective System for On‐line Preconcentration and Determination of Copper

A flow injection flame atomic absorption spectrometry system incorporating a microcolumn of rice bran was designed, and its capability for on‐line trace enrichment of copper, cadmium and lead was studied. Analytes were deposited on the microcolumn by processing a standard or solution of analytes on the column. Injection of 250 μL of nitric acid (1 mol/L) then served to elute the retained species to FAAS. The procedure was successfully applied for determination of copper in tap water, well water and multivitamin tablets. The accuracy was assessed through recovery experiments and independent analysis by furnace‐AAS. A sample volume of 20 mL of copper resulted in a preconcentration factor of 96; precision value at the 20 μg/L was 4.1%.     

Theory of polymer brushes grafted to finite surfaces

In this work, a model based in strong‐stretching theory for polymer brushes grafted to finite planar surfaces is developed and solved numerically for two geometries: stripe‐like and disk‐like surfaces. There is a single parameter, , which represents the ratio between the equilibrium brush height and the grafting surface size, that controls the behavior of the system. When is large, the system behaves as if the polymer were grafted to a single line or point and the brush adopts a cylindrical or spherical shape. In the opposite extreme when it is small, the brush behaves as semi‐infinite and can be described as a planar undeformed brush region and an edge region, and the line tension approaches a limiting value. In the intermediate case, a brush with non‐uniform height and chain tilting is observed, with a shape and line tension depending on the value of . Relative stability of disk‐shaped, stripe‐shaped, and infinite lamellar micelles is analyzed based in this model. © 2018 Wiley Periodicals, Inc. J. Polym. Sci., Part B: Polym. Phys. 2018 , 56, 663–672     

导电高分子膜的电化学阻抗谱研究进展

本文结合近年来导电高分子的电化学阻抗谱（EIS）的研究进展,综述了几个EIS理论模型在导电高分子膜研究中的应用和发展。