Least-Squares Fitting of Algebraic Spline Surfaces

We present an algorithm for fitting implicitly defined algebraic spline surfaces to given scattered data. By simultaneously approximating points and associated normal vectors, we obtain a method which is computationally simple, as the result is obtained by solving a system of linear equations. In addition, the result is geometrically invariant, as no artificial normalization is introduced. The potential applications of the algorithm include the reconstruction of free-form surfaces in reverse engineering. The paper also addresses the generation of exact error bounds, directly from the coefficients of the implicit representation.     

Computer-Assisted Solution of Chemical Problems—The Historical Development and the Present State of the Art of a New Discipline of Chemistry

The topic of this article is the development and the present state of the art of computer chemistry, the computer-assisted solution of chemical problems. Initially the problems in computer chemistry were confined to structure elucidation on the basis of spectroscopic data, then programs for synthesis design based on libraries of reaction data for relatively narrow classes of target compounds were developed, and now computer programs for the solution of a great variety of chemical problems are available or are under development. Previously it was an achievement when any solution of a chemical problem could be generated by computer assistance. Today, the main task is the efficient, transparent, and non-arbitrary selection of meaningful results from the immense set of potential solutions—that also may contain innovative proposals. Chemistry has two aspects, constitutional chemistry and stereochemistry, which are interrelated, but still require different approaches. As a result, about twenty years ago, an algebraic model of the logical structure of chemistry was presented that consisted of two parts: the constitution-oriented algebra of be- and r-matrices, and the theory of the stereochemistry of the chemical identity group. New chemical definitions, concepts, and perspectives are characteristic of this logic-oriented model, as well as the direct mathematical representation of chemical processes. This model enables the implementation of formal reaction generators that can produce conceivable solutions to chemical problems—including unprecedented solutions—without detailed empirical chemical information. New formal selection procedures for computer-generated chemical information are also possible through the above model. It is expedient to combine these with interactive methods of selection. In this review, the Munich project is presented and discussed in detail. It encompasses the further development and implementation of the mathematical model of the logical structure of chemistry as well as the experimental verification of the computer-generated results. The article concludes with a review of new reactions, reagents, and reaction mechanisms that have been found with the PC-programs IGOR and RAIN.     

Polarographie schwefelhaltiger Proteine

Zusammenfassung An kristallisierten Enzymen des biologischen Stoffwechsel wird gezeigt, daß bei der Polarographie nur die schwefelhaltigen Proteine katalytische Wasserstoffwellen geben. Von den in der Literatur beschriebenen Doppelstufen der Proteine besitzt nur die im negativeren Potentialbereich liegende Welle die eigentliche katalytische Funktion. Die erste Vorwelle von Proteinen verschwindet, wenn die polarographische Messung bei 0° C durchgeführt wird.In Proteinen sind nur Disulfidgruppen katalytisch wirksam. Sogenannte reine Sulfhydryl-Enzyme haben keinen katalytischen Effekt. Typische SH-Enzyme können jedoch polarographisch als p-Chloromercuribenzoatkomplexe gemessen werden.Durch Harnstoffzusatz bei der polarographischen Messung von Proteinen gelingt es, zwischen maskierten und freien Sulfhydryl- oder Disulfidgruppen an Enzymen zu definieren.Auszug aus der Dissertationsschrift H. Katzlmeier, Technische Hochschule München (1959).     

The trace to subsets ofR n of Besov spaces in the general case

R ⁿ. , , , F R ⁿ, F , R ⁿ R ⁿ . ^p,q (Rⁿ), >0, 1, q, — ( ) Rⁿ. , ^p,q (Rⁿ) ^F Rⁿ. , q B ^p,q (F), = – (n–)/, >0, — « », ad — F, . , . : , F=R ^d,F— « » F— R ⁿ, « », F. .

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This work has been supported in part by the Swedish Natural Science Research Council.     

Analysis of polynuclear aromatic hydrocarbons by glass capillary gas chromatography using simultaneous flame ionization and electron capture detection

The possibility of simultaneous application of an electron capture (ECD) and a flame ionization detector (FID) connected to a glass capillary column for analyzing polynuclear aromatic hydrocarbons (PNA) has been investigated. The ECD/FID ratio is determined for 46 PNA compounds. The ratios vary from 0.02 to 117 with relative standard deviations better than 20 percent determined from 10 replicate analyses. The results suggest that the method may be used for obtaining additional evidence in identifying PNA in environmental samples. Impurities and transformation products in the standard were identified by computerized glass capillary gas chromatography/mass spectrometry. Quinones and diones are responsible for the high EC-response determined in some trace components in the standard. An application of the method is shown for PNA from particulates in urban atmospheres.     

Synthesis and characterization of highly luminescent CdSe-core CdS/Zn0.5Cd0.5S/ZnS multishell nanocrystals

We report on the preparation and structural characterization of CdSe nanocrystals, which are covered by a multishell structure from CdS and ZnS. By using the newly developed successive ion layer adhesion and reaction (SILAR) technique, we could gradually change the shell composition from CdS to ZnS in the radial direction. Because of the stepwise adjustment of the lattice parameters in the radial direction, the resulting nanocrystals show a high crystallinity and are almost perfectly spherical, as was investigated by X-ray diffraction and electron microscopy. Also, due to the radial increase of the respective valence- and conduction-band offsets, the nanocrystals are well electronically passivated. This leads to a high fluorescence quantum yield of 70-85% for the amine terminated multishell particles in organic solvents and a quantum yield of up to 50% for mercapto propionic acid-covered particles in water. Finally, we present experimental results that substantiate the superior photochemical and colloidal stability of the multishell particles.     

Aqueous Solution Chemistry of the Mo(3)PdS(4) Cube: Substitution Reactions and the Double to Single Cube Interconversion Induced by CO, Two Phosphines, Cl(-), Br(-), and NCS(-)

The kinetics of conversion of an edge-linked double cube, in this case [{Mo(3)PdS(4)(H(2)O)(9)}(2)](8+), to the corresponding single cube [Mo(3)(PdX)S(4)(H(2)O)(9)](4+), has been studied for the first time. Reaction is induced by six reagents X = CO, two water-soluble phosphines, Cl(-), Br(-), and NCS(-), which complex at the tetrahedral Pd. The first stage of reaction is fast and is accompanied by color changes, e.g. purple to dark blue in the case of Cl(-), assigned as double to single cube conversion. With X = CO and the two phosphines, when absorbance changes are intense enough for stopped-flow monitoring with reactants at Pd-SCN. On removal of e.g. Cl(-) by chromatography or addition of Ag(+), the double cube re-forms.     

Effect of non-planarity on the spin distribution in the radical anions containing the stilbene or the azobenzene π-system: An ESR and ENDOR Study

The radical anions of 5H-dibenzo[a,d]cycloheptene ( 9 ), 5 H-dibenzo[c,f][1,2]diazepine ( 10 ), 5,6-dihydrodibenzo[a,e]cyclooctene ( 11 ), 5,6-dihydrodibenzo[c,g][1,2]diazocine ( 12 ), and (E)-2,2,5,5-tetramethyl-3,4-diphenylhex-3-ene ( 13 ) were characterized by ESR and ENDOR spectroscopy. Their hyperfine data were compared with those previously reported for radical anions also containing the stilbene or the azobenzene π-system. Whereas the π-spin distribution in the radical anions of the stilbene series is only moderately sensitive to deviations of the π-system from planarity, the radical anions of the azobenzene series respond to steric strain by shifting the π-spin population from the benzene rings to the azo group. This finding is impressively demonstrated by the similar hyperfine data for 9 ^{· ?} and 11 ^{· ?} which contrast with the strongly highly hindered 13 ^{· ?}. A. plausible interpretation is readily provided by the electron affinities of the constituent π-moieties in stilbene and azobenzene. While those of benzene and ethene are both comparatively low, the azo group has a considerably higher electron affinity.     

Hydrolysis and Condensation of Alkyltrimethoxysilanes in Monomolecular Films

Hydrolysis and condensation of monomolecular alkyloxysilane films by the Langmuir technique is presented. Octadecyltrimethoxysilane formed monolayers on aqueous subphases with different properties depending on the bulk pH. At pH 1 a solid condensed film was directly formed with a molecular area of 23 Ų and a surface pressure/surface area variation similar to that on non-ionized stearic acid. At pH 5.6 and 11 several phase transitions were observed during the compression of the monolayer with a final collapse at a molecular area of 20 Ų. Relaxation measurements confirmed the stability of the films for longer than 12 hours at different surface pressures below a critical value.