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 ($\text{1}$).     

Some estimates of theH ∞-uniform distribution

The sequences (y _n )=(a+blogn+ _n ) are uniformly distributed in the sense of the summation methodH . In the present paper the speed of convergence of this procedure is estimated for these, sequences and for some other sequences. For the sequences (a+blogn) theH -means converge considerably faster than logarithmic means.     

On quadratic and sesquilinear functionals

LetX be a leftA-module, whereA is either a complex Banach *-algebra with an identity element or the field of quaternions. The main result of this note is that forQ, anA-quadratic functional defined onX, there exists a sesquilinear functionalB such thatB(x,x)=Q(x) holds for allxX.     

Local limits and harmonic functions for nonisotropic random walks on free groups

Summary Nearest neighbour random walks on the homogeneous tree representing a free group withs generators (2s) are investigated. By use of generating functions and their analytic properties a local limit theorem is derived. A study of the harmonic functions corresponding to the random walk leads to properties that characterize ther-harmonic function connected with the local limits.     

Coloring of universal graphs

LetG be a graph andr a cardinal number. Extending the theorem of J. Folkman we show that if eitherr or clG are finite then there existsH with clH = clG andH (G) _r ¹ . Answering a question of A. Hajnal we show that countably universal graphU ₃ satisfiesU ₃ (U₃) _r ¹ for every finiter.     

Sets of tiles with a prescribed number of tilings

Summary For every k2 and r1 there exists a set of k prototiles that admits exactly r distinct tilings. All the tilings obtained are periodic.     

Automated carbohydrate synthesis to drive chemical glycomics

This feature article describes the development of the first automated solid-phase oligosaccharide synthesizer. A series of chemical challenges had to be addressed to accomplish this breakthrough and provide rapid access to oligosaccharides of biological significance. Accelerated synthesis of glycoconjugates promises to greatly impact the emerging field of glycobiology. Chemical glycomics uses synthetic carbohydrates and analogs to study their role in recognition, signal transduction pathways and other events of fundamental biomedical significance and shapes up to become the next major wave in biomedical research. The automated synthesis of a novel malaria vaccine candidate is discussed to illustrate the medical potential of chemical glycomics.