Derivative of the exponential mapping for infinite dimensional lie groups

It is proved that for infinite dimensional Lie groups in the sense of the differential calculus of Frölicher and Kriegl the derivative of the exponential mappings is given by the formula d(exp)(X)Y=d_exp(X)(e) ₀ ¹ Ad_exp(–tX) Y dt, where stands for the left translation ande is the neutral element.This work was supported by the Alexander von Humboldt-Stiftung.     

Constrained minimax approximation and optimal preconditioned for Toeplitz matrices

A good preconditioner is extremely important in order for the conjugate gradients method to converge quickly. In the case of Toeplitz matrices, a number of recent studies were made to relate approximation of functions to good preconditioners. In this paper, we present a new result relating the quality of the Toeplitz preconditionerC for the Toeplitz matrixT to the Chebyshev norm (f– g)/f, wheref and g are the generating functions forT andC, respectively. In particular, the construction of band-Toeplitz preconditioners becomes a linear minimax approximation problem. The case whenf has zeros (but is nonnegative) is especially interesting and the corresponding approximation problem becomes constrained. We show how the Remez algorithm can be modified to handle the constraints. Numerical experiments confirming the theoretical results are presented.     

A statistical model for the optimization of dsc performance in the evaluation of drugs for preformulation studies

Differential scanning calorimetry (DSC) is a thermal analytical tool for preformulation studies. Extrapolated melting temperature (T_P) and heat of fusion (ΔH_f) can be used as parameters for optimizing the DSC performance. Two model pharmaceuticals acetaminophen and nicotinamide are used in this study. Using a factorial design for the experimental model and matrix analysis the results, the effect of sample mass, heating rate and the nitrogen flow rate were evaluated on the ΔH_f values and T_P values. Two levels for each of the procedural variables were used as a balanced experimental design with two sample sizes, two heating rates and two nitrogen flow rates. It was found that the change in the heating rate caused significant changes in the ΔH_f values but not the T_p values for acetaminophen. However, no significant effect was found for the T_p value but ΔH_f value was affected to a certain extent for nicotinamide.     

Microwave assisted low temperature synthesis of sodium zirconium phosphate (NaZr<Subscript>2</Subscript>P<Subscript>3</Subscript>O<Subscript>12</Subscript>)

Sodium zirconium phosphate [NaZr₂P₃O₁₂], a potential ceramic matrix for fixation of high level nuclear waste, was synthesized by heating the mixture of sodium carbonate [Na₂CO₃], zirconyl nitrate hydrate [ZrO(NO₃)₂·5H₂O] and ammonium dihydrogen phosphate [NH₄H₂PO₄] in air, in a resistance heated furnace and a microwave heating system respectively in the temperature range 450 to 650°C. The mixture heated for 1 h in a resistance furnace at 450°C yielded a poorly crystalline NaZr₂P₃O₁₂ [NZP]. Increasing the temperature to 650°C produced a highly crystalline product. The same mixture heated in a microwave oven at 450°C for 1 h however, yielded the most crystalline NZP.In an alternate method, the mixture of sodium dihydrogen phosphate (NaH₂PO₄), zirconium dioxide (ZrO₂) and diammonium hydrogen phosphate [(NH₄)₂HPO₄] heated in resistance furnace at 650°C for the same period did not react in air. It also did not yield the pure product at 450°C when heated in microwave assembly for 1 h.The authors thank the Board of Research in Nuclear Sciences (BRNS) of the Department of Atomic Energy (DAE) for the financial support for this work under the project No. 2000/37/19/BRNS/1959 dtd09-02-02.     

A Review on the Potential and Limitations of Recyclable Thermosets for Structural Applications

Abstract

The outstanding performance of conventional thermosets arising from their covalently cross-linked networks directly results in a limited recyclability. The available commercial or close-to-commercial techniques facing this challenge can be divided into mechanical, thermal, and chemical processing. However, these methods typically require a high energy input and do not take the recycling of the thermoset matrix itself into account. Rather, they focus on retrieving the more valuable fibers, fillers, or substrates. To increase the circularity of thermoset products, many academic studies report potential solutions which require a reduced energy input by using degradable linkages or dynamic covalent bonds. However, the majority of these studies have limited potential for industrial implementation. This review aims to bridge the gap between the industrial and academic developments by focusing on those which are most relevant from a technological, sustainable and economic point of view. An overview is given of currently used approaches for the recycling of thermoset materials, the development of novel inherently recyclable thermosets and examples of possible applications that could reach the market in the near future.     

Thioacetylacetone: structural and vibrational assignments.

Thioacetylacetone and its variously deuterated isotopomers have been investigated using electronic and vibrational spectroscopy combined with quantum chemical calculations. Thioacetylacetone is known for its photochromic properties, but the structures of the initial and final forms have been the subject of a long debate. Analysis of the IR spectra recorded in low-temperature argon and xenon matrices, room-temperature solutions, and in the gas phase has allowed us to establish the nature of the photochromic species and of its precursor. Similar to the case of another beta-thioxoketone, monothiodibenzoylmethane, the photo-product has been assigned to the nonchelated SH exo-rotamer of the (Z)-enethiol tautomeric form, whereas the dominant ground-state species corresponds to the chelated (Z)-enol tautomeric form. Detailed vibrational assignments have been proposed for both forms based on quantum chemical calculations and polarization experiments. In the case of the chelated (Z)-enol species prevailing in the ground state, a second-order perturbative anharmonic analysis at the B3LYP/cc-pVTZ level indicated strong anharmonic effects associated with the intramolecular hydrogen bond, leading to a shift of more than 600 cm-1 of the wavenumber of the OH-stretching vibration. A small fraction of the SH endo-rotameric chelated (Z)-enethiol form was also detected under unperturbed conditions. The (Z)-enethiol form can be converted into the (Z)-enol form by irradiation at 290 nm.     

Ester synthesis catalyzed by Mucor miehei lipase immobilized on magnetic polysiloxane-polyvinyl alcohol particles

Mucor miehei lipase was immobilized on magnetic polysiloxane-polyvinyl alcohol particles by covalent binding with high activity recovered. The performance of the resulting immobilized biocatalyst was evaluated in the synthesis of flavor esters using heptane as solvent. The impact on reaction rate was determined for enzyme concentration, molar ratio of the reactants, carbon chain length of the reactants, and alcohol structure. Ester synthesis was maximized for substrates containing excess acyl donor and lipase loading of 25 mg/mL. The biocatalyst selectivity for the carbon chain length was found to be different concerning the organic acids and alcohols. High reaction rates were achieved for organic acids with 8 or 10 carbons, whereas increasing the alcohol carbon chain length from 4 to 8 carbons gave much lower esterification yields. Optimal reaction rate was determined for the synthesis of butyl caprylate (12 carbons). Esterification performance was also dependent on the alcohol structure, with maximum activity occurring for primary alcohol. Secondary and tertiary alcohols decreased the reaction rates by more than 40%.     

A MATHEMATICAL STUDY OF THE SEVEN GRAPTOLITE BIOZONES OF THE LOWER SILURIAN LONGMAXIAN STAGE IN CHINA

With the aid of matrix theory and computer a series of data can be obtained such as the total number of localities in which r species of graptolites appears, the common number of localities in which both i and j species of graptolites appear, the total number of species of graptolites in one locality, the common number of species of graptolites found in both i and j localities, the total number of zones in which r species of graptolites appears, the common number of zones in which both i and j species appear, the total number of species of graptolites found in one zone, the common number of species of graptolites found in both i and j zones. Based on these data a common problem in biostratigraphy may be solved, that is, in the absence of the zonal graptolite which species of graptolites can be chosen to replace the zonal graptolite, or how to detect the zonal graptolite of a graptolite biozone. The result of matrix treatment not only detects the graptolite biozone but is useful to infer the paleo-biogeo     

石墨炉原子吸收法测定生物样品中镉的几种基体改进剂的比较

本文比较了磷酸二氢铵、氟化铵、硫酸铵、氯化钯、氯铂酸以及氯铂酸与多种有机酸的混合试剂在测定ＧＢＷ猪肝标准物质中镉时基体改进效果，其中，氯铂酸的基体改进能力最强，猪肝标准物质的回收率在９０％     

On the role of localized molecular orbitals in the formation of bond dipoles

The hypothesis of the classical chemistry about bond dipoles resulting from shifts of separate pairs of electrons is proved using the non-canonical method of molecular orbitals (MOs). To this end, a relation is sought between the total charge distribution inside an individual chemical bond of a polyatomic molecule and the square of the respective single localized MO (LMO). General expressions for these MOs are obtained directly on the basis of the Brillouin theorem without invoking additional localization criteria. The two characteristics under comparison are presented in an explicit algebraic form in terms of meaningful components. Reshaping of square of the ‘own’ LMO of the given bond is shown to play the decisive role in the formation of secondary dipoles of initially homopolar bonds (e.g. of C–C and C–H bonds in substituted alkanes), as well as of bonds of relatively low initial polarity. Thus, representability of these dipoles by shifts of the ‘own’ pairs of electrons of respective bonds is supported. For bonds of a high initial polarity, the secondary dipoles are shown to originate mainly from contributions of LMOs of other bonds extending over the antibonding basis orbital of the given bond. Moreover, the actual secondary bond dipole takes an opposite direction vs. that predicted by the shift of the respective ‘own’ pair of electrons in this case. The latter result serves to account for the known low nucleofugality of highly electronegative heteroatoms in the S_N2 reactions.