Prädikatives und funktionales Denken in der Wahrscheinlichkeitsrechnung

In order to emphasize functional thinking in mathematical education, arguments are brought forward for an early and frequent use of tree diagrams in teaching stochastics. Since set and tree diagrams can be regarded as two sides of the same matter, Bayes’ theorem, which is strongly associated with predicative set diagrams, need not be dealt with explicitly any longer. Set diagrams are replaced by tree diagrams that are labelled in detail and by tree inversion as a functional instrument of dealing with conditioned probabilities. This technique is demonstrated by three typical problems in the context of conditioned probability. Finally, two letters by Pascal to Fermat are analysed in order to illustrate that predicative and functional approaches were already pursued in the early stages of probability calculus in the 17^th century.     

3rd International Conference on Trace Element Speciation in Biomedical,Nutritional and Environmental Sciences

3rd International Conference on Trace Element Speciation in Biomedical, Nutritional and Environmental Sciences     

LD泵浦的声光调Q腔内倍频激光器

研制成用ＬＤ泵浦的声光调Ｑ的Ｎｄ：ＹＶＯ４－ＫＴＰ腔内倍频激光器，得到了ＴＥＭ００模、频率高达１００ｋＨｚ的稳定的５３２ｕｍ绿激光脉冲系列输出，阈值泵浦功率为２７ｍＷ；在连续５７０ｍＷ的泵浦功率下，绿激光脉冲的峰值功率达１１００Ｗ，脉宽为４．６ｕｓ；输出功率稳定，在±５℃的工作温度变化下，输出功率变化小于±２％。此种器件可望得到广泛的应用。     

On the existence of equilibrium states in local quantum field theory

It is shown that any local quantum field theory admits thermodynamical equilibrium states (KMS-states) for all positive temperatures provided it satisfies a nuclearity condition, proposed by Wichmann and one of the authors, which restricts the admissible number of local degrees of freedom.Dedicated to E. H. Wichmann on the occasion of his 60th birthday     

On digital smoothing filters: A brief review of closed form solutions and two new filter approaches

The concept of smoothing noisy data using appropriate polynomials turns out to be equivalent to the application of suitable nonrecursive digital filters having the following properties: They process the data in such a way that the moments are conserved up to a desired order while the energy of their impulse response is minimum. Flatness constraints of their frequency response at =0 are equivalent to the moment condition. By using orthogonal polynomials, an explicit solution is known from the literature. A second approach which uses a special decomposition also yields closed form solutions. The realization is simplified, especially in the case where a large number of moments is supposed to be conserved.     

A comparison of some hierarchal agglomerative clustering algorithms for structure—property correlation

Six different hierarchal clustering algorithms were used to cluster eleven sets of compounds for which associated property data were available. The effectiveness of the clustering in each case was assessed by inspection of the resulting tree diagram representing the classification and by the utility of the classification for molecular property prediction. The best predictions were generally obtained by using the algorithm proposed by Ward while the widely-used nearest neighbour algorithm performed very badly. Unstandardised data gave better results than standardised data although the difference was less when structurally related, rather than structurally disparate, groups of compounds were tested.     

The prism algorithm for two-electron integrals

A new approach to the evaluation of two-electron repulsion integrals over contracted Gaussian basis functions is developed. The new scheme encompasses 20 distinct, but interrelated, paths from simple shell-quartet parameters to the target integrals, and, for any given integral class, the path requiring the fewest floating-point operations (FLOPS ) is that used. Both theoretical (FLOP counting) and practical (CPU timing) measures indicate that the method represents a substantial improvement over the HGP algorithm.     

Zur Kenntnis von Natrium-hexafluoromanganat(III)

Sodium hexafluoromanganate(III) has been synthesized by heating equimolecular quantities of Na₂MnF₅ and NaF in argon atmosphere. The compound is monoclinic witha=5.56 (1) Å,b=5.84 (1) Å,c=8.10 (2) Å, =90.7 (2) andZ=2. It is a high spin complex with _eff and the deformation of the octahedra is evident from its IR-spectra. Two enantiotropic transitions (at 562 and 653°C) and the melting point at 800°C have been observed.

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8. Mitt.: Mh. Chem.106, 483 (1975).     

Pyrolysis of homoadamant-3-ene

Pyrolysis of homoadamant-3-ene ($\text{5}$), generated from 1-adamantylcarbene ($\text{7}$), leads to the same three olefins ($\text{2}$, $\text{3}$, and $\text{4}$) that are produced from pyrolysis of 3-homoadamantyl acetate ($\text{1}$).