An Arithmetic Reduction of Finite Rank 3 Geometries with Linear Spaces as Plane Residues and with Dual Linear Spaces as Point Residues

Let be a rank three incidence geometry of points, lines and planes whose planes are linear spaces and whose point residues are dual linear spaces (notice that we do not require anything on the line residues). We assume that the residual linear spaces of belong to a natural class of finite linear spaces, namely those linear spaces whose full automorphism group acts flag-transitively and whose orders are polynomial functions of some prime number. This class consists of six families of linear spaces. In the amalgamation of two such linear spaces imposes an equality on their orders leading, in particular, to a series of diophantine equations, the solutions of which provide a reduction theorem on the possible amalgams of linear spaces that can occur in .We prove that one of the following holds (up to a permutation of the words point and plane):A) the planes of and the dual of the point residues belong to the same family and have the same orders,B) the diagram of is in one of six families,C) the diagram of belongs to a list of seven sporadic cases.Finally, we consider the particular case where the line residues of are generalized digons.     

298.15K下Li2B4O7-H2O体系水蒸汽分压及渗透系数的等压测定和离子相互作用模型

在已有研究含硼体系的文献中仅考虑了硼酸根B4O7^-2或B(OH)4^-和H3BO3的存在，而对Li2B4O7-H2O体系具有多种硼物种聚合平衡体系的热力学性质的研究尚未见报道．本文用等压法研究了Li2B4O7-H2O体系于298．15K下浓度由稀到过饱和溶液的平衡气相蒸汽压及渗透系数．考虑了水溶液中多种硼物种的存在，以Pitzer方程为基础，建立了可描述该含硼体系的离子相互作用模型。     

In Situ Study of the Surface Oxidation of FeCr Alloys Using Grazing Incidence X‐ray Absorption Spectroscopy (GIXAS)

The surface oxidation of FeCr alloys with 18, 28, and 43 mass‐% Cr was investigated in situ using grazing‐incidence X‐ray absorption spectroscopy (GIXAS) at the chromium and iron K‐edges. Oxidation in air was monitored in situ in the temperature range from 290 K to 680 K. The standard GIXAS data analysis is extended for the treatment of a single layer model in order to estimate the chromium concentrations of the oxide layer and of the near‐interface substrate as well as the oxide layer thickness. XANES analysis shows transitions from b.c.c. Fe to corundum type Fe₂O₃ and from b.c.c. Cr to corundum type Cr₂O₃. The initial oxide layers are 1.1‐1.4 nm thick and contain 60‐90 mass‐% chromium, while the near‐interface substrate is depleted in Cr. During heating, iron oxide growth dominates up to 560‐600 K. Then the chromium oxide layer loses its passivation effect and Cr oxidation sets in.     

Boiling Temperature and Reversed Deliquescence Relative Humidity Measurements for Mineral Assemblages in the NaCl + NaNO3 + KNO3 + Ca(NO3)2 + H2O System

Boiling temperature measurements have been made at ambient pressure for saturated ternary solutions of NaCl + KNO₃ + H₂O, NaNO₃ + KNO₃ + H₂O, and NaCl + Ca(NO₃)₂ + H₂O over the full composition range, along with those of the single salt systems. Boiling temperatures were also measured for the four component NaCl + NaNO₃ + KNO₃ + H₂O and five component NaCl + NaNO₃ + KNO₃ + Ca(NO₃)₂ + H₂O mixtures, where the solute mole fraction of Ca(NO₃)₂, x{Ca(NO₃)₂}, was varied between 0 and 0.25. The maximum boiling temperature found for the NaCl + KNO₃ + H₂O system is ≈134.9 ^∘C; for the NaNO₃ + KNO₃ + H₂O system is ≈165.1 ^∘C at x(NaNO₃) ≈ 0.46 and x(KNO₃) ≈ 0.54; and for the NaCl + Ca(NO₃)₂ + H₂O system is 164.7 ± 0.6 ^∘C at x{NaCl} ≈ 0.25 and x{Ca(NO₃)₂} ≈ 0.75. The NaCl + NaNO₃ + KNO₃ + Ca(NO₃)₂ + H₂O system forms molten salts below their maximum boiling temperatures and the temperatures corresponding to the cessation of boiling (dry-out temperatures) of these liquid mixtures were determined. These dry-out temperatures range from ≈300 ^∘C when x{Ca(NO₃)₂} = 0 to ≥ 400 ^∘C when x{Ca(NO₃)₂} = 0.20 and 0.25. Mutual deliquescence/efflorescence relative humidity (MDRH/MERH) measurements were also made for the NaNO₃ + KNO₃ and NaCl + NaNO₃ + KNO₃ salt mixture from 120 to 180 ^∘C at ambient pressure. The NaNO₃ + KNO₃ salt mixture has a MDRH of 26.4% at 120 ^∘C and 20.0% at 150 ^∘C. This salt mixture also absorbs water at 180 ^∘C, which is higher than expected from the boiling temperature experiments. The NaCl + NaNO₃ + KNO₃ salt mixture was found to have a MDRH of 25.9% at 120 ^∘C and 10.5% at 180 ^∘C. The investigated mixture compositions correspond to some of the major mineral assemblages that are predicted to control brine composition due to the deliquescence of salts formed in dust deposited on waste canisters in the proposed nuclear repository at Yucca Mountain, Nevada.     

Alkane isomers: presence in petroleum ether and complexity

The presence and absence of alkane isomers in petroleum and petroleum derivatives depend on the complexity of these structures. It was assumed that the more complex the structure is the less probable it is that that the molecule can be detected in any petroleum derivative. Complexity is a vague concept, which has not been defined in quantitative terms yet, and therefore there is no experimental method, which could be used to determine ‘complexity’. Mass spectrometry and infrared spectroscopy in combination with gas chromatography were used to identify the various structural isomers of alkanes in petroleum ether. The isomers were categorised in quantitative terms by using topological indices and linear discriminant analysis. It was found that alkanes possessing a more complex, highly branched structure are less probable to be detected in petroleum ether than isomers with a simpler backbone structure. It was proposed that the experimental ‘measure’ of the complexity of isomer_i should be proportional to 1/C_i , where C_i , denotes the concentration of isomer_i in a (primary) petroleum derivative.     

Comparisons of the vector method and tensor method for simulating liquid crystal devices

In calculating the director configuration in a liquid crystal device, two methods are commonly employed: a vector model and a tensor model. In this paper, we compare and contrast these methods for liquid crystal devices consisting of a layer of liquid crystal sandwiched between two plates. We compare the reliability and accuracy of the results, the speed of computation and the complexity of implementations of each method.     

肝素非还原端饱和结构的紫外吸收研究及在肝素寡糖测序中的应用

为了进一步探讨非还原端饱和结构的肝素寡糖在UV 232 nm的吸收情况, 制备了4种饱和结构的肝素二糖, 并用离子对反相液相色谱/离子阱飞行时间质谱(RPIP-LC/MS-IT-TOF)光电二极管阵列检测器分析了它们在UV 232 nm的吸收情况. 分析结果表明, 饱和结构的肝素二糖在UV 232 nm的检出限为9 μg(S/N=10), UV 232 nm/UV 206 nm约为不饱和结构肝素二糖UV 232 nm的7%~40%. 结果还表明, 肝素二糖UV 232 nm的吸收强度受亚硫酸基团(SO₃^2?)影响较大. 另外, 通过比较不饱和结构的肝素/硫酸类肝素(Hep/HS)标样二糖发现, 含N-未取代葡萄糖胺(GlcNH₃⁺)基团的二糖在UV 232 nm的吸收值较低. 最后, 通过简单的UV检测方法, 结合 HNO₂(pH=4.0)裂解法和RPIP-LC/MS-IT-TOF分析, 简化了含GlcNH₃⁺肝素六糖的测序方法. 本研究为以后用 HNO₂(pH=1.5)裂解法对混合组分N-硫酸化的肝素寡糖结构序列分析提供了可能.     

Radiation damage in polymer films from grazing‐incidence X‐ray scattering measurements

Grazing‐incidence X‐ray scattering (GIXS) is widely used to analyze the crystallinity and nanoscale structure in thin polymer films. However, ionizing radiation will generate free radicals that initiate crosslinking and/or chain scission, and structural damage will impact the ordering kinetics, thermodynamics, and crystallinity in many polymers. We report a simple methodology to screen for beam damage that is based on lithographic principles: films are exposed to patterns of X‐ray radiation, and changes in polymer structure are revealed by immersing the film in a solvent that dissolves the shortest chains. The experiments are implemented with high throughput using the standard beam line instrumentation and a typical GIXS configuration. The extent of damage (at a fixed radiation dose) depends on a range of intrinsic material properties and experimental variables, including the polymer chemistry and molecular weight, exposure environment, film thickness, and angle of incidence. The solubility switch for common polymers is detected within 10–60 s at ambient temperature, and we verified that this first indication of damage corresponds with the onset of network formation in glassy polystyrene and a loss of crystallinity in polyalkylthiophenes. Therefore, grazing‐incidence X‐ray “patterning” offers an efficient approach to determine the appropriate data acquisition times for any GIXS experiment. © 2016 Wiley Periodicals, Inc. J. Polym. Sci., Part B: Polym. Phys. 2016 , 54, 1074–1086     

K-Theory for the Integer Heisenberg Groups

We give a closed formula for topological K-theory of the homogeneous space N/, where is the standard integer lattice in the simply connected Heisenberg Lie group N of dimension 2n+1, n . The main tools in our calculations are obtained by computing diagonal forms for certain incidence matrices that arise naturally in combinatorics.