Divergence Criterion for a Class of Random Series Related to the Partial Sums of I.I.D. Random Variables

Journal of Theoretical Probability - Let $$ \{X, X_{n};~n \ge 1 \}$$ be a sequence of independent and identically distributed Banach space valued random variables. This paper is devoted to...     

Neue Näherungsgleichung zur einheitlichen Berechnung von Wärmeübertragern

Zusammenfassung Es wird eine für alle Stromführungen einheitliche Näherungsgleichung mit drei oder vier anpaßbaren Parametern zur Berechnung des Korrekturfaktors für die mittlere logarithmische Temperaturdifferenz angegeben. Die anpaßbaren Parameter wurden für etwa 50 verschiedene Stromführungen durch Ausgleichsrechnung bestimmt. Die Genauigkeit der Gleichung ist für die Berechnung im praktisch wichtigen Bereich mehr als ausreichend.

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New approximate equation for uniform heat exchanger design

An approximate equation with three or four empirical parameters for the uniform calculation of the LMTD-correction factor of all heat exchanger configurations is proposed. The empirical parameters have been determined for about 50 different flow configurations using least squares estimation. The accuracy of the equation is more than sufficient for practical design purposes.

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Formelzeichen A Übertragungsfläche - a, b, c, d Parameter der Näherungsgleichung - Wärmekapazitätsstrom - F Korrekturfaktor für die logarithmische mittlere Temperaturdifferenz - k Wärmedurchgangskoeffizient - m, n Zahl der Durchgänge oder Einzelapparate - NTU Anzahl der Übertragungseinheiten (number of transfer units); NTU_i=kA/ _i - P dimensionslose Temperaturänderung - R Wärmekapazitätsstromverhältnis;R ₁=₁/₂;R ₂=₂/₁ - relativer Fehler - Mittelwert von NTU₁ und NTU₂ Indizes 1, 2 Stoffstrom 1, 2 - G Gegenstrom - s Schätzwert Herrn Prof. Dr.-Ing. E.h. K. Stephan zum 65. Geburtstag gewidmet.     

Liquid chromatographic determination of the plasticizer di(2-ethylhexyl) phthalate (DEHP) in PVC plastics

A fast, simple and reliable method for the analysis of DEHP in PVC products was developed using a one-step Soxhlet extraction prior to HPLC determination. The linear range from 1.25 /g to 250 mg/g of DEHP in PVC was found sufficient to cover the normal concentrations encountered. The reliability of the method was established by comparison with the ASTM method and no potential interferent was identified except a large concentration of DIMP.     

Elliptic Genera of Level N and Elliptic Cohomology

Elliptic genera of level N have been defined by F. Hirzebruch,generalising the earlier notion of elliptic genus due to S.Ochanine. We show that there are corresponding elliptic cohomologytheories which are naturally associated to such genera and thatthese are obtained from the level 1 case by algebraic extensionof the coefficient rings from level 1 to level N modular forms.     

On the Left Cell Representations of Iwahori-Hecke Algebras of Finite Coxeter Groups

In this paper we investigate the left cell representations ofthe Iwahori-Hecke algebras associated to a finite Coxeter groupW. Our main result shows that , where w₀ is the element of longest length in W, acts essentiallyas an involution upon the canonical bases of a cell representation.We describe some properties of this involution, use it to furtherdescribe the left cells, and finally show how to realize eachcell representation as a submodule of . Our results rely uponcertain positivity properties of the structure constants ofthe Kazhdan-Lusztig bases of the Hecke algebra and so have notyet been shown to apply to all finite Coxeter groups.     

On two methods of determining the ellipses and ellipsoids of positioning accuracy of robot manipulators

Summary When analysing the problem of the positioning accuracy of robot manipulators it is important to know how far random deviations of the hand may be from the desired position if the joint positioning errors possess a normal distribution. Two methods of determining the ellipses and ellipsoids of probability concentration are compared. The first of them is based on the standard procedure of the probability calculus. The second approximate method consists in finding at first the polygon or polyhedron of the positioning accuracy, and then in finding the ellipse or ellipsoid with principal axes and second order moments coinciding with those of the polygon or polyhedron, respectively. Examples of application demonstrate that these two methods give very close results.

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Zwei Methoden zur Bestimmung der Ellipsen und Ellipsoide der Positioniergenauigkeit von Handhabungsrobotern

Übersicht Bei der Untersuchung der Positioniergenauigkeit von Handhabungsrobotern ist es wichtig, die Größe zufälliger Abweichungen des Greifers von der erstrebten Position zu kennen, wenn die Lagefehler der Verbindungen eine Normalverteilung besitzen. Es werden zwei Methoden zur Bestimmung der Ellipsen bzw. Ellipsoide der Wahrscheinlichkeitsdichte verglichen. Die erste beruht auf dem Standardverfahren der Wahrscheinlichkeitsrechnung. Die zweite Näherungsmethode besteht darin, daß zunächst das Polygon bzw. Polyeder der Positioniergenauigkeit bestimmt wird und danach die Ellipse bzw. das Ellipsoid mit den Hauptachsen und Momenten zweiter Ordnung wie das Polygon oder Polyeder. Beispiele zeigen, daß beide Methoden zu sehr ähnlichen Ergebnissen führen.

     

Electronic and vibrational second-order nonlinear optical properties of protein secondary structural motifs

A perturbation theory approach was developed for predicting the vibrational and electronic second-order nonlinear optical (NLO) polarizabilities of materials and macromolecules comprised of many coupled chromophores, with an emphasis on common protein secondary structural motifs. The polarization-dependent NLO properties of electronic and vibrational transitions in assemblies of amide chromophores comprising the polypeptide backbones of proteins were found to be accurately recovered in quantum chemical calculations by treating the coupling between adjacent oscillators perturbatively. A novel diagrammatic approach was developed to provide an intuitive visual means of interpreting the results of the perturbation theory calculations. Using this approach, the chiral and achiral polarization-dependent electronic SHG, isotropic SFG, and vibrational SFG nonlinear optical activities of protein structures were predicted and interpreted within the context of simple orientational models.     

A configuration interaction study of phosphine using bonded functions

A computational study is made of the effect of basis set upon the energy, properties and inversion barrier of the phosphine molecule. The calculations are performed at both the SCF and CI level. The flexibility of the double zeta basis is discussed in the light of the results.     

Struktur von 7,11-Diphenyl-2,4-diazaspiro[5,5]undecan-1,3,5,9-tetraonen durch LIS-NMR

A semi-quantitative method for determining distances between a possible coordination centre and protons from LIS-NMR values is developed for the title compounds3, although these have four coordination points. This makes it possible to propose structures and conformations for the isomers of3.

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Mit 4 Abbildungen

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H.-H. Otto undH. Yamamura, Ann. Chem., im Druck.