Formal Substitution Research Articles

Hybrid Manipulations for the Solution of Systems of Nonlinear Algebraic Equations

where x and f(x) are real ^/-dimensional vectors, and f(x) is defined to be twice continuously differentiable on a bounded region D in R. However the numerical manipulation languages can not handle mathematical operations such as formal differentiations, substitutions or symbolic calculations of determinants. Only very recently, by practical applications of the symbolic and algebraic manipulation languages such as REDUCE 2 [7], it is possible for the computers to treat these mathematical operations. If we introduce both numerical and symbolic manipulations, termed here as hybrid manipulations, new and efficient algorithms can be developed which greatly improve the feasibility of solving the system of nonlinear algebraic equations. For the purpose the author et al. are developing the package NAES (Nonlinear Algebraic Equation's Solver} [14,18,28]. This paper reports on several implementations which incorporate newly developed algorithms into the package.

Electron-transfer, halogen-metal exchange, and direct processes in formal nucleophilic substitutions on alkyl halides by trimethyltinsodium

Electron-transfer, halogen-metal exchange, and direct processes in formal nucleophilic substitutions on alkyl halides by trimethyltinsodium

High-performance liquid chromatography of adamantanols and other cyclic alcohols

Chromatographic elution data for 28 monocyclic and polycyclic alcohols of the adamantane type have been measured, using silica gel as the stationary phase and mixed mobile phases in different concentration ratios. The position of the hydroxyl group has the largest effect on the chromatographic behaviour of polycyclic alcohols. The introduction of an alkyl group into alcohols such as adamantanol results in a decrease in retention time. This decrease is larger when the adamantanol is substituted by several small alkyl substituents (CH 3, C 2H 5) than by one large alkyl group. For polycyclic alcohols having the same formal substitution type, the elution time decreases with increasing size of the basic skeleton. The rate of this decrease depends on the composition of the mobile phase used. The effect of the mobile phase composition on the elution data for the compounds studied is discussed.

The stationary distribution of an asymmetrical model of selection in a random environment

The stationary distribution for the asymmetrical form of the SAS-CFF model of selection in a random environment is presented. Also presented are the conditions for the stable coexistence of K alleles. These conditions are the same as the conditions obtained from the classical constant-fitness model with the formal substitution of geometric mean fitnesses for the constant fitnesses of the classical model. Two examples are explored. In the “equally spaced” example, increases in the degree of asymmetry raise the homozygosity, which is accompanied by loss of alleles from the population. In the “best allele” example, increases in the degree of asymmetry raise the homozygosity without the loss of alleles. In both cases the frequency spectra are altered by the changes in the degree of asymmetry.

Different behaviour of secondary and primary amines towards 1-alkyl-3,4-dinitropyrroles

The reaction of 1-alkyl-3,4-dinitropyrroles with secondary amines gives nucleophilic aromatic cine substitution (formation of 1-alkyl-2-amino-4-nitropyrroles), whereas the reaction with primary amines follows a more complicated pattern, involving mainly a multistep ring-opening and ring-closure process, and also yielding the product of formal direct substitution, but not that of cine substitution.

STUDIES ON PLANT BILE PIGMENTS–6. PHOTOCHEMICALLY ASSISTED REACTION OF A‐DIHYDROBILINDIONE WITH NUCLEOPHILES AS A MODEL FOR PHYTOCHROME INTERCONVERSION

Abstract— –From the A‐dihydrobilindione 3. the pyridinium derivatives 6a, b and analogues therwf have been obtained by a formal nucleophilic substitution. The reaction is rationalized as a photochemically assisted oxidation of 3 with a subsequent regioselective addition of pyridine at C‐5. By thermolysis. 6a.b yields back the parent bilin 3, together with an oxidation product. The significance of the reaction with respect to the phytochrome interconversion is discussed.

Aminohaloborane in Organic Synthesis. VII.1A Directed Aldol Condensation Using Vinyloxyaminochloroborane

Abstract Vinyloxydichloroboranes (1) are scarcely found in literature2 probably because of certain unstable properties. We have found that some vinyloxyamino-chloroboranes (2), which can be prepared by formal substitution of one chlorine atom of 1 with a diethylamino group, are isolable stable compounds.

ChemInform Abstract: SOLID ELECTROLYTES WITH A GLASS‐LIKE STRUCTURE

AbstractDurch Zusammenschmelzen von Agl mit bis zu 20 Mol‐% Ag,SO4, Ag,CrO4, Ag2MoO4, Ag2WO4, Ag3PO4, Ag3AsO4, Ag2Cr2O7 oder Ag4P2O7 und Abschrecken der Schmelzen in Tropfenform werden glasartige Elektrolyte hergestellt.

Solid Electrolytes with a Glass‐Like Structure

Solid electrolytes formed by a formal partial substitution of iodide in AgI by a variety of oxoanions may be prepared in the vitreous state by fast‐quenching from the melt. Such materials, with few exceptions, are metastable and undergo thermal transitions into poorly conducting phases below the melting point. The conductance of a glassy electrolyte of this class was studied as a function of temperature and frequency. Features such as curved Arrhenius plots and high‐frequency dispersion are compared with similar observations in molten salt systems and the basis of such behavior is discussed.

Zur reaktivität der SiC-bindung in pyridylsilanen

The SiC(heterocyclic)-bonds in 2-trimethylsilylpyridine, in 2,6-bis(trimethylsilyl)pyridine and in 2-bromo-6-trimethylsilylpyridine have differing reactivities. They are essentially less reactive than the SiC-bonds in thiazolyl- and imidazolyl-silanes. This is shown by hydrolysis and transsilylation experiments and by reactions with trichlorogermane. The basicity of the imino-nitrogen and the polarity of the SiC-bond in the particular pyridylsilane are important for these formal electrophilic substitutions.

Evidence for caged intermediate species in a formal nucleophilic aromation substitution

Evidence for caged intermediate species in a formal nucleophilic aromation substitution

Right Haar Measure for Convergence in Probability to Quasi Posterior Distributions

Right Haar Measure for Convergence in Probability to Quasi Posterior Distributions

On the Universality of the Weak Interactions

The universality of weak decay interactions is applied to the introduction of weak interactions using a formal substitution similar to that in the electromagnetic caee. The Latgrangian equation for the no-weak-interaction case is corrected by addition of multipole interaction terms for baryons and bosons and by substitution of universal lepton interaction terms. Thus, the lepton decays of hyperons and beta decays can be described, and almost all the known weak interactions can be derived qualitatively but not quantitatively. (D.L.C.)

Diffusion‐controlled mechanical properties of polyvinyl alcohol and polyvinyl formals

AbstractThe elongation of polyvinyl alcohol and of formalized polyvinyl alcohol films under constant load for a wide range of conditions of temperature and humidity seems to be affected predominantly by the diffusion of water molecules into these polymeric films, as these films have many water‐sensitive bonds. In order to obtain a perspective of the diffusion mechanism of water molecules into these polymer films, the theoretical analysis of creep curves is here worked out. Since the diffusion is a time‐dependent, non‐Fickian process, the time dependence of the diffusion coefficient is considered into our theoretical treatment. It is also assumed that the elongation is caused only by the breaking of hydrogen bonds due to the absorption of water molecules in amorphous regions of the polymer film.To evaluate theoretical equations for the creep curves in accordance with a simple Voigt model, the parameter α for the rate of diffusion is conveniently substituted for by K, the parameter for the rate of elongation. Experiments were performed at temperatures from 20 to 50°C. at 60% R. H., and also at different relative humidities ranging from 40 to 80% at a constant temperature of 30°C. A series of creep curves for PVA and PVF, the latter having a degree of formal substitution ranging from 6% to 42.5% were obtained.In analyzing the observed creep curves by the present theoretical treatment, we can easily compute the values of K through application of the condition for the characteristic inflection point of each curve, i.e., d2γ/dt2 = 0. By use of the values of K thus obtained and by application of the theory of absolute reaction rates, the activation energy and entropy for the diffusion process of water molecules are duly determined. The values thus obtained are also compared with those calculated by Hauser and McLaren. The activation energy and entropy are highest and lowest, respectively for PVF (6%); this is made adequately explicable by the fact that the proportion of amorphous polymer in these films is found to be maximum when the degree of formalization is between 10 and 20%.