γ-sets and other singular sets of real numbers

A family of $\text{J}$ of open subsets of the real line is called an ω-cover of a set X iff every finite subset of X is contained in an element of $\text{J}$. A set of reals X is a γ-set iff for every ω-cover $\text{J}$ of X there exists $\text{〈D}{}_{\mathrm{n}}\text{: n < ω〉?}\text{J}{}^{\mathrm{\omega }}$ such that

In this paper we show that assuming Martin's axiom there is a γ-set X of cardinality the continuum.     

Poly(ethylene glycol) as Impregnator for Silica Gel in Salting-Out Thin-Layer Chromatography of Some Co(III) Complexes

Silica gel impregnated with poly(ethylene glycol) of different molecular mass (400, 1000, 1540, 4000, and 5500) was investigated for salting-out thin-layer chromatography of 15 mixed aminocarboxylato Co(III) complexes using eight ammonium sulphate solutions as mobile phases. Regularities established earlier for non-impregnated adsorbents are also valid in this work. Poly(ethylene glycol) of high molecular mass increases the hydrophobicity of the adsorbent. Positive linear dependence of R_M values and of salting-out efficiency on average poly(ethylene glycol) molecular mass was usually observed. In contrast with non-impregnated silica gel, separation was achieved between complexes with the smallest hydrocarbon groups.     

端基含葡氨糖衍生物的聚乳酸的合成与表征

端基含葡氨糖衍生物的聚乳酸的合成与表征张国栋冯新德（北京大学高分子科学与工程系北京１００８７１）顾忠伟（国家计生委科研所药化室北京１０００８１）关键词壳多糖，聚乳酸，生物医用材料，化学修饰自从发现高分子量聚乳酸在人体内能够降解，并把这类材料引入...     

Low detection limit spectrophotometry

An efficient, more sensitive and accurate spectrophotometric process is possible and can be used to obtain qualitative or quantitative results for analytes at limiting concentrations lower than usual. Transmission measurements (incident light power, P₀, or transmitted, P) are performed with a fluorescence spectrometer. One cell only is used to measure standards or unknown solutions, placed between the standard holder cuvette and the emission monochromator of the instrument. The source of the radiant power (P₀) is not the xenon lamp but the fluorescence or scattered radiation from the holder cuvette filled with an appropriate solution. The analyte concentration is found from a calibration graph, based upon Beer’s law or the approximate formula P₀−P=2.303P₀εbc, which is valid for dilute solutions. Determination of iron in a reference material, using 1,10-phenanthroline as the chromogenic reagent, was chosen as an example to demonstrate the suitability of the proposed method and clarify several important statistical questions. Also discussed is why and to what extent molecular fluorescence methods are more sensitive than molecular absorption methods.     

热致性液晶聚酯酰亚胺高分子的合成

本文以己二胺，癸二胺和对－亚苯基－双苯偏三酸酯二酐为单体通过溶液聚合反应制备了聚酯酰亚胺系列共聚物．采用ＩＲ，ＷＡＸＤ，ＤＳＣ和偏光显微镜研究了共聚物的结构和液晶性能，结果表明，聚合物具有热致液晶性，且随二胺单体摩尔组成的变化，共聚物的熔点Ｔｍｌ和玻璃化转变温度Ｔ８呈规律性变化．     

Acetylenic/cyanoacetylenic complexes: simulation of the Titan’s atmosphere chemistry

The structures and energies of the 1:1 acetylene/cyanoacetylene, acetylene/dicyanoacetylene and cyanoacetylene/dicyanoacetylene complexes in solid argon matrices have been investigated using FT-IR spectroscopy and ab initio calculations, at the B3LYP/6-31G** level of theory. For the three complexes, predicted frequency shifts for the L shaped structures, characterized by a hydrogen bond between the nitrogen of the cyano group and the acetylenic proton, were found to be in good agreement with those experimental. Only in the case of acetylene/cyanoacetylene complex, we obtained a second minimum with a T shaped structure characterized by an interaction between the proton of cyanoacetylene and the Π system of acetylene. It appears clearly that HC₃N acts as an electrophile or as a nucleophile in these complexes.     

On the singular graph and the Weyr characteristic of anM-matrix

LetA be anM-matrix in standard lower block triangular form, with diagonal blocksA _ii irreducible. LetS be the set of indices such that the diagonal blockA is singular. We define the singular graph ofA to be the setS with partial order defined by > if there exists a chain of non-zero blocksA _i, A_ij, , A_l.Let ₁ be the set of maximal elements ofS, and define thep-th level _p ,p = 2, 3, , inductively as the set of maximal elements ofS \( _{1 p-1}). Denote by _p the number of elements in _p . The Weyr characteristic (associated with 0) ofA is defined to be (A) = ( ₁, ₂,, _h ), where ₁ + + _p = dim KerA ^p ,p = 1, 2, , and _h > 0, _h+1 = 0.Using a special type of basis, called anS-basis, for the generalized eigenspaceE(A) of 0 ofA, we associate a matrixD withA. We show that(A) = ( ₁, , _h) if and only if certain submatricesD _p,p+1 ,p = 1, , h – 1, ofD have full column rank. This condition is also necessary and sufficient forE(A) to have a basis consisting of non-negative vectors, which is a Jordan basis for –A. We also consider a given finite partially ordered setS, and we find a necessary and sufficient condition that allM-matricesA with singular graphS have(A) = ( ₁, , _h). This condition is satisfied ifS is a rooted forest.The work of the second-named author was partly supported by the National Science Foundation, under grant MPS-08618 A02.     

Synthesis and properties of aromatic poly(ester amide)s with pendant phosphorus groups

Two series of phosphorus‐containing aromatic poly(ester amide)s with inherent viscosities of 0.46–3.20 dL/g were prepared by low‐temperature solution polycondensation from 1,4‐bis(3‐aminobenzoyloxy)‐2‐(6‐oxido‐6H‐dibenz〈c,e〉〈1,2〉oxaphosphorin‐6‐yl)naphthalene and 1,4‐bis(4‐aminobenzoyloxy)‐2‐(6‐oxido‐6H‐dibenz〈c,e〉〈1,2〉oxaphosphorin‐6‐yl)naphthalene with various aromatic diacid chlorides. All the poly(ester amide)s were amorphous and readily soluble in many organic solvents, such as N,N‐dimethylformamide, N,N‐dimethylacetamide (DMAc), and N‐methyl‐2‐pyrrolidone (NMP). Transparent, tough, and flexible films of these polymers were cast from DMAc and NMP solutions. Their casting films had tensile strengths of 71–214 MPa, elongations to break of 5–10%, and initial moduli of 2.3–6.0 GPa. These poly(ester amide)s had glass‐transition temperatures of 209–239 °C (m‐series) and 222–267 °C (p‐series). The degradation temperatures at 10% weight loss in nitrogen for these polymers ranged from 462 to 489 °C, and the char yields at 800 °C were 55–63%. Most of the poly(ester amide)s also showed a high char yield of 35–45%, even at 800 °C under a flow of air. The limited oxygen indices of these poly(ester amide)s were 35–46. © 2002 John Wiley & Sons, Inc. J Polym Sci Part A: Polym Chem 40: 459–470, 2002; DOI 10.1002/pola.10129     

Thermodynamic properties of hydrated sodium l-threonate Na(C4H7O5)·H2O(s)

Low-temperature heat capacities of the compound Na(C₄H₇O₅)·H₂O(s) have been measured with an automated adiabatic calorimeter. A solid-solid phase transition and dehydration occur at 290-318 K and 367-373 K, respectively. The enthalpy and entropy of the solid-solid transition are Δ_transH_m = (5.75 ± 0.01) kJ mol⁻¹ and Δ_transS_m = (18.47 ± 0.02) J K⁻¹ mol⁻¹. The enthalpy and entropy of the dehydration are Δ_dH_m = (15.35 ± 0.03) kJ mol⁻¹ and Δ_dS_m = (41.35 ± 0.08) J K⁻¹ mol⁻¹. Experimental values of heat capacities for the solids (I and II) and the solid-liquid mixture (III) have been fitted to polynomial equations.