Acyclic Systems of Permutations and Fine Mixed Subdivisions of Simplices

A fine mixed subdivision of a $(d-1)$ -simplex $T$ of size $n$ gives rise to a system of  ${d \atopwithdelims ()2}$ permutations of $[n]$ on the edges of $T$ , and to a collection of $n$ unit $(d-1)$ -simplices inside $T$ . Which systems of permutations and which collections of simplices arise in this way? The Spread Out Simplices Conjecture of Ardila and Billey proposes an answer to the second question. We propose and give evidence for an answer to the first question, the Acyclic System Conjecture. We prove that the system of permutations of $T$ determines the collection of simplices of $T$ . This establishes the Acyclic System Conjecture as a first step towards proving the Spread Out Simplices Conjecture. We use this approach to prove both conjectures for $n=3$ in arbitrary dimension.     

Elucidation of phototransformation reactions of the X‐ray contrast medium iopromide under simulated solar radiation using UPLC‐ESI‐QqTOF‐MS

The highly polar, nonionic X‐ray contrast agent iopromide (C₁₈H₂₄N₃O₈I₃; 791 Da) is resistant to microbial degradation during the activated sludge process in wastewater treatment plants and hence is released into the aquatic environment. Against this background, the present study was conducted to evaluate the phototransformation, potentially constituting the most relevant removal mechanism in rivers and streams. The photolysis of the iodinated aromatic compound was investigated in a Suntest solar simulator using aqueous solutions. Following a 120‐min irradiation period, an almost complete primary degradation of iopromide gave rise to a series of photoproducts that were chromatographed on a reversed‐phase UPLC and subsequently characterized by a combination of accurate mass measurements on a ESI‐QqToF‐MS instrument and H/D‐exchange experiments. This analytical approach facilitated confident identification of eight prominent products with the following elemental compositions and molecular weights: C₁₈H₂₅N₃O₉I₂ (681 Da); C₁₈H₂₅N₃O₈I₂ (665 Da); C₁₇H₂₃N₃O₈I₂ (651 Da); C₁₈H₂₄N₃O₉I (553 Da); C₁₇H₂₄N₃O₈I (525 Da); C₁₅H₂₀N₃O₆I (465 Da); C₁₄H₁₈N₃O₆I (451 Da); and C₁₈H₂₅N₃O₉ (427 Da). Their formation was the result of four principal photoreactions: (1) gradual, and eventually complete, deiodination of the aromatic ring; (2) substitution of the halogen by a hydroxyl group; (3) N‐dealkylation of the amide in the hydroxylated side chain; and (4) oxidation of a methylene group in the hydroxylated side chain to the corresponding ketone. In conclusion, the findings of the artificial sunlight irradiation experiments indicated that in real environmental settings iopromide might suffer partial or even complete deiodination. Copyright © 2009 John Wiley & Sons, Ltd.     

The Application of Diffusing-Wave Spectroscopy to Monitor the Phase Behavior of Emulsion-Polysaccharide Systems

Droplet aggregation is an important cause of instability in emulsions because it may, on one hand, lead to an increased creaming rate, resulting in fast separation of a concentrated emulsion phase (creamed layer). On the other hand, it may also lead to the formation of a stabilizing, droplet-based network. Early detection of instability is often difficult due to the high turbidity and viscosity of more concentrated food emulsions. The applicability of diffusing-wave spectroscopy (DWS) for monitoring droplet aggregation and creaming was studied using a model system consisting of a protein-stabilized emulsion, to which a soluble polymer ("thickener") was added. This addition leads to an increased solvent viscosity and may induce droplet aggregation. In addition, the redistribution process of emulsion droplets in aggregating concentrated emulsions was directly observed by confocal scanning laser microscopy (CSLM). By DWS the decrease of the droplet mobility caused by the viscosity increase of the continuous phase could be separated from the effect of droplet aggregation. Moreover, a distinction could be made between aggregation, leading to increased creaming rates and that leading to the formation of a stabilizing droplet network. The potential of DWS for in situ measurement of the stability of concentrated emulsions is discussed. Copyright 2000 Academic Press.     

Heterocyclic variants of the 1,5-benzodiazepine system. V. Derivatives of 2-(ortho-R1-anilino)-4-(p-R2-phenyl)-3H-1,5-benzodiazepines

Mono-N-methylation of 2-(ortho-R₁-anilino)-4-(p-R₂-phenyl)-3H-1,5-benzodiazepines IV is achieved in moderate yield with sodium hydride in methyl iodide. Reaction of the N-methyl derivatives I with methoxyacetyl chloride gave the compounds II and III . The structure of all products was confirmed by ir, ¹H-nmr and mass spectrometry.     

A Straightforward Synthesis of Six‐Membered‐Ring Heterocyclic α‐Aminophosphonic Acids from N‐Acyliminium Ions

A convenient synthesis of phosphonic analogues of pipecolic acid and its heterocyclic analogues is reported. The major step of the elaborated procedure is the introduction of the phosphonate group into the skeleton of the appropriate cyclic amide through N‐acyliminium ions. The former ones were obtained by preparation of the hemiaminals or their methyl ethers from the N‐protected cyclic amides. Finally, the reaction with trimethyl phosphite in the presence of BF₃·OEt₂ afforded the desired phosphonates, which were converted into phosphonic acids by the hydrolysis of phosphonate moiety with simultaneous cleavage of the nitrogen protecting groups.     

邻苯二酚显色树脂相分光光度法同时测定地下水中微量铁(Ⅲ)和钼(Ⅵ)

研究了铁（Ⅲ）和钼（Ⅵ）与邻苯二酚在ｐＨ ６．２０ 微酸性介质中反应生成的有色配合物与７１７型强碱性阴离子交换树脂的交换吸附,探讨了树脂相分光光度法同时测定铁（Ⅲ）和钼（Ⅵ）的实验条件。铁（Ⅲ）和钼（Ⅵ）树脂相有色配合物的最大吸收波长分别为５２０ ｎｍ 和４００ ｎｍ ,表观摩尔吸光系数ε为４．１×１０４ Ｌ／（ｍ ｏｌ·ｃｍ ）和９．０×１０４ Ｌ／（ｍ ｏｌ·ｃｍ ）,符合Ｂｅｅｒ定律的范围为０～２．２ ｍ ｇ·Ｌ－ １和０～１．６ ｍ ｇ·Ｌ－ １。此法用于地下水中微量铁和钼的测定,相对标准偏差为３．３ ％ 和３．２ ％ 。     

甘氨酸钙络合物的熔融法合成及表征

以甘氨酸和氢氧化钙为原料,采用熔融法合成了甘氨酸钙络合物,最佳合成条件为:原料摩尔比n甘氨酸:nCa(OH)2=2:1,在熔融状态下,反应温度150℃左右,反应时间40min,并通过元素分析、红外光谱、X-射线粉末衍射、差热-热重等实验手段对该络合物进行了表征,确定其化学式为Ca(NH2CH2COO)2,所得产品的产率达94.1%.