Chemical applications of topology and group theory

The 60 even permutations of the ligands in the five-coordinate complexes, ML ₅, form the alternating group A ₅, which is isomorphic with the icosahedral pure rotation group I. Using this idea, it is shown how a regular icosahedron can be used as a topological representation for isomerizations of the five-coordinate complexes, ML ₅, involving only even permutations if the five ligands L correspond either to the five nested octahedra with vertices located at the midpoints of the 30 edges of the icosahedron or to the five regular tetrahedra with vertices located at the midpoints of the 20 faces of the icosahedron. However, the 120 total permutations of the ligands in five-coordinate complexes ML ₅ cannot be analogously represented by operations in the full icosahedral point group I _h, since I _his the direct product I×C₂ whereas the symmetric group S ₅ is only the semi-direct product A ₅S₂. In connection with previously used topological representations on isomerism in five-coordinate complexes, it is noted that the automorphism groups of the Petersen graph and the Desargues-Levi graph are isomorphic to the symmetric group S ₅ and to the direct product S ₅×S ₂, respectively. Applications to various fields of chemistry are briefly outlined.     

微波－气相－热压法分解高纯铂的研究

本文研究了微波气相热压法新技术分解高纯铂在密闭的聚四氟乙烯高压罐中，以微波瞬间加热混合酸产生的高压、纯净蒸气分解金属铂，此法避免了酸中杂质的沾污以制备供高纯铂分析的试液，提高了痕量杂质分析的准确度和降低检测限     

Reactions of fluorinated acid anhydrides, (CF3CO)2O, (CF3SO2)2O and (FSO2)2O, with organometallic substrates of group 15 (As, Sb and Bi)

(C₆H₅)₃MX₂ (M = As, Sb; X = OCOCF₃ and M = Sb, Bi; X = SO₃F, SO₃CF₃) compounds prepared by the interaction of triphenylmetal(V) substrates with (CF₃CO)₂O, (CF₃SO₂)₂O and (FSO₂)₂O have been characterized by molecular weight determination, elemental and spectroscopic (IR, ¹H and ¹⁹F NMR, mass) analyses.     

Fluorescence decay of tertiary aliphatic amines

The fluorescence decay of the tertiary aliphatic animes trimethylamine (TMA), triethylamine (TEA) and tri-n-propylamine (TPA) in the vapour phase excited between 260 and 215 nm has been shown to consist of a single, wavelength-dependent, component when the first excited state is uniquely excited, but two components when the first and second excited states are simultaneously excited. This dual exponentiality persists at pressures as low as 10 mTorr, and it is argued that the two-component decay does not arise from collisional vibrational relaxation.     

Influence of solvents on the insertion of methacrolein into zirconacyclopropenes

The reaction of Cp₂Zr(L)(η²-Me₃SiC₂) (L = THF, py) with equimolar amounts of H₂C = CMe-CHO at room temperature depends strongly on the ligands L and the solvents that are used. With L = THF, in the THF solution the insertion product

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1 was isolated, whereas by conducting the reaction in n-hexane solution an alkyne substitution with 1,4-coordination of the methacrolein takes place and the binuclear complex [

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2 was obtained. In conttrast, with L = py (a stronger ligand) only a 1:1 ratio of 1 and 2 was observed in both THF and in n-hexane. At 50°C complex 1 was converted into 2 and the alkyne was eliminated quantitatively.

Complexes 1 and 2 were characterized by IR and NMR spectroscopical measurements and 1 by an additional X-ray structure determination.     

Investigation of the limitations of saturated fractional factorial experimental designs,with confounding effects for an HPLC ruggedness test

Summary Recently much attention has been directed to the validation of analytical methods. The level of validation will depend on the method application. If a method is developed for general use, for instance by different analysts, instruments or laboratories, then the effect of these changes need evaluation. This is normally referred to as ruggedness testing, where the limitations of the method to changes in the specified conditions are examined.This paper examines the use of Plackett-Burman fractional factorial experiment designs for ruggedness testing in high performance liquid chromatography (HPLC). The ability of these designs to identify confounding effects is applied to the stability indicating analysis of Salbutamol and its major degradation product, AH4045. The results show that confounding effects, proving extremely pertinent to HPLC, can be identified.The assay proved rugged to most tested changes although not to the use of column packing material from different manufacturers.     

Nonlinear vertical accelerations of a floating torus in regular waves

The longitudinal motions and vertical accelerations of a floating torus as well as wave motion inside the torus are studied by model tests in regular deep-water waves. Comparisons are made with linear and partly with second-order potential-flow theory for the smallest examined experimental wave height-to-wave length ratio 1/120. Reasonable agreement is obtained, in particular for the linear problem. The importance of 3D flow, hydroelasticity and strong hydrodynamic frequency dependency is documented. Experimental precision errors and bias errors, for instance, due to tank-wall interference are discussed. Numerical errors due to viscous effects are found to be secondary. Experiments show that the third and fourth harmonic accelerations of the torus matter and cannot be explained by a perturbation method with the wave steepness as a small parameter.     

A generic framework for time-stepping partial differential equations (PDEs): general linear methods,object-oriented implementation and application to fluid problems

Time-stepping algorithms and their implementations are a critical component within the solution of time-dependent partial differential equations (PDEs). In this article, we present a generic framework – both in terms of algorithms and implementations – that allows an almost seamless switch between various explicit, implicit and implicit–explicit (IMEX) time-stepping methods. We put particular emphasis on how to incorporate time-dependent boundary conditions, an issue that goes beyond classical ODE theory but which plays an important role in the time-stepping of the PDEs arising in computational fluid dynamics. Our algorithm is based upon J.C. Butcher's unifying concept of general linear methods that we have extended to accommodate the family of IMEX schemes that are often used in engineering practice. In the article, we discuss design considerations and present an object-oriented implementation. Finally, we illustrate the use of the framework by applications to a model problem as well as to more complex fluid problems.     

A new design of the elimination and choice translating reality method for multi-criteria group decision-making in an intuitionistic fuzzy environment

The purpose of this paper is to design a new extension of the ELECTRE, known as the elimination and choice translating reality method, for multi-criteria group decision-making problems based on intuitionistic fuzzy sets. This method is widely utilized when a set of alternatives should be identified and evaluated with respect to a set of conflicting criteria by reflecting decision makers’ (DMs’) preferences. However, handling the exact data and numerical measure is difficult to be precisely focused because the DMs’ judgments are often vague in real-life decision problems and applications. A more realistic and practical approach can be to use linguistic variables expressed in intuitionistic fuzzy numbers instead of numerical data to model DMs’ judgments and to describe the inputs in the ELECTRE method. The proposed intuitionsitic fuzzy ELECTRE utilizes the truth-membership function and non-truth-membership function to indicate the degrees of satisfiability and non-satisfiability of each alternative with respect to each criterion and the relative importance of each criterion, respectively. Then, a new discordance intuitionistic index is introduced, which is extended from the concept of the fuzzy distance measure. Outranking relations are defined by pairwise comparisons and a decision graph is depicted to determine which alternative is preferable, incomparable or indifferent in the intuitionistic fuzzy environment. Finally, a comprehensive sensitivity analysis is employed to further study regarding the impact of threshold values on the final evaluation, and a comparative analysis is demonstrated with an application example in flexible manufacturing systems between the proposed ELECTRE method and the existing intuitionistic fuzzy technique for order preference by similarity to ideal solution (IF-TOPSIS) method.