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.     

Optimal Inventory Policies with Service-Level Constraints

In a practical situation it is often difficult to determine the value of the shortage costs for use in in ventory-control systems. However, in cost-minimization problems including service-level constraints, shortage costs are implicitly prevailing. With the purpose of exploring these relations, a continuous review (Q, r) stock-control system is considered, where the order points and lot sizes are computed simultaneously. Instead of explicitly expressing the shortage cost in the objective function, it is taken into consideration through a service-level constraint. The shadow price of this constraint can in some sense be interpreted as the shortage cost corresponding to the requested service level. By changing the value of the service level, interesting relations between shortage costs and service levels can be viewed for different sets of other inventory parameters. In order to investigate the sensitivity for probabilistic variations in the input data, two different probability distributions are used to describe the lead-time demand.     

Enantiomeric separation of amphetamine,methamphetamine and ring substituted amphetamines by means of a β-cyclodextrin-chiral stationary phase

Summary The enantioseparation of amphetamine, methamphetamine and various ring-substituted amphetamines by use of a chiral stationary phase carrying immobilized native -cyclodextrin (-CyD) selectors is reported. The system is evaluated for resolving the specified compounds directly without any derivatization and after derivatization with phenyl isothiocyanate (PITC), naphthyl isothiocyanate (NITC) and 6-aminoquinolyl-N-hydroxysuccinimidyl carbamate (AQC). This direct enantioseparation is compared with the features of indirect separation of diasteromeric derivatives after reaction with the optically pure Marfey's reagent employing a simple non-chiral alkyl-silica (RP-8) column. A selection of those methods best suited for each single amphetamine is given.Seventeen different samples of amphetamine, confiscated by the Swedisch police, were analyzed with respect to their enantiomeric composition. Within this set of samples synthesized by the same method no significant deviation from a racemic ratio could be observed.     

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.     

Study of short-lived silver isotopes with a laser ion source

The continuum part of the⁶Li (a,a)⁶Li (1.47–2.47 MeV) scattering data at E_a=50 MeV are extracted in two discretized bins. Coupled-channel calculations are carried out coupling the 1⁺ ground state of⁶Li with both the resonant, 3⁺ ₁ state, and two non-resonant continuum states. The discretized continuum of the⁶Li (p,p)⁶Li (1.75–3.25 MeV) scattering data at E_p=65 MeV are also analysed on the same footing. In both the cases the effect of coupling is found to be minimal.     

Conversion of sodium lactate to lactic acid with water-splitting electrodialysis

The conversion of sodium lactate to lactic acid with water-splitting electrodialysis was investigated. One way of reducing the power consumption is to add a conductive layer to the acid compartment. Doing this reduced the power consumption by almost 50% in a two-compartment cell, whereas the electric current efficiency was not affected at all. Three different solutions were treated in the electrodialysis unit: a model solution with 70 g/L of sodium lactate and a fermentation broth that had been prefiltered two different ways. The fermentation broth was either filtered in an open ultrafiltration membrane (cut-off of 100,000 Dalton) in order to remove the microorganisms or first filtered in the open ultrafiltration membrane and then in an ultrafiltration membrane with a cut-off of 2000 Dalton to remove most of the proteins. The concentration of sodium lactate in the fermentation broth was 70 g/L, as well. Organic molecules present in the broth (peptides and similar organic material) fouled the membranes and, therefore, increased power consumption. Power consumption increased more when permeate from the more open ultrafiltration membrane was treated in the electrodialysis unit than when permeate from the membrane with the lower cut-off was treated, since there was a higher amount of foulants in the former permeate. However, the electrodialysis membranes could be cleaned efficiently with a 0.1 M sodium hydroxide solution.     

Pion photoproduction on197Au to ground and isomeric states in197Hg

The lifetime of the 331.3 keV 0 ₂ ⁺ state in¹⁰⁰Zr has been measured at the gas-filled recoil separator for fission products JOSEF. By observing the delayed coincidences between theβ-particles populating the level and theE0 conversion electrons from its decay into the ground state, a half-life of 3.37±0.30 ns has been obtained. From the measured lifetime and the relative intensities of the 0 ₂ ⁺ →0 ₁ ⁺ and 0 ₂ ⁺ →2 ₁ ⁺ transitions, values of 0.493±0.015 for theE0 strength parameterρ, and of 16 single particle units forB(E2,2 ₁ ⁺ → 0 ₂ ⁺ ) have been deduced. The enhanced nature of theE0 transitions suggests mixing of the 0 ₁ ⁺ and 0 ₂ ⁺ states which may be estimated by comparing the experimentalB(E2) values for the 2 ₁ ⁺ →0 ₁ ⁺ and 2 ₁ ⁺ →0 ₂ ⁺ transitions with the predictions of the asymmetric VMI model.     

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.     

Fluoreszenzmethoden zur histochemischen Sichtbarmachung von Monoaminen. 6. Identifizierung der fluoreszierenden Produkte aus m-Hydroxyphenyläthylaminen und Formaldehyd

It is known that in tissue slices treated with dry gaseous formaldehyde according to the histochemical technique of HILLARP & FALCK structures containing catecholamines show a green fluorescence in the fluorescence microscope. The m-hydroxyphenylethylamines m-tyramine, m-hydroxyamphetamine and m-hydroxynorephedrine (metaraminol) enclosed in vitro in dry protein films undergo a similar reaction with dry gaseous formaldehyde and form fluorescent products which have been characterized as 6-hydroxy-3,4-dihydro-isoquinolines existing predominantly in the quinoidal form fluorescing at 385/510 nm. By treatment of these protein layers with gaseous hydrogen chloride another form fluorescing at 360/420 nm can be obtained which is not visible in the fluorescence microscope with the usual equipment.