Low temperature absorption spectra of TcO 4 − and ReO 4 − in KClO4

The low temperature spectra of TcO ₄ ^– and ReO ₄ ^– both show two band systems with pronounced vibrational structures. The bands are identified as¹ A ₁¹ T ₂ transitions. No other bands are observed with certainty. It seems likely that the KClO₄ crystals contain KReO₄ crystallites. They are therefore not pure mixed crystals. It is concluded that the virtual orbital (2e) used in the construction of the low lying states resembles an atomic nd orbital more and more when going from n=3, Mn to n=5, Re.

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Zusammenfassung Die Tieftemperaturspektren von TcO ₄ ^– und ReO ₄ ^– zeigen beide zwei Bandensysteme mit ausgeprägten Schwingungsstrukturen. Die Banden werden als ¹ A ₁¹ T ₂-Übergänge identifiziert. Keine anderen Banden werden mit Sicherheit beobachtet. Es scheint wahrscheinlich, daß die KClO₄-Kristalle KReO₄-Kristallite enthalten und deswegen keine reinen Mischkristalle sind. Es wird geschlossen, daß das virtuelle Orbital (2e), welches zur Konstruktion der tiefliegenden Zustände gebraucht wird, in der Reihe n=3, Mn bis n=5, Re immer weitgehender einem nd-Atomorbital ähnelt.

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Nachwuchsstipendiat, Schweizerischer Nationalfonds.     

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.     

Rectangles inscribed in symmetric continua

LetQ be any rectangle and letK ^d (d 2) be a continuum which is either symmetric across a hyperplane or symmetric through a pointz K. We show thatK contains the vertices of a rectangle similar toQ which exhibits the same symmetry as doesK.     

The development of a sampler-sensor using a vanadium-oxinate-polymer film for the selective and direct determination of atmospheric ethanol

The development of a sensor for the direct and selective determination of atmospheric ethanol is in the initial stages. The sensor takes advantage of the selective chemical reaction between ethanol and vanadium oxinate. This reaction occurs in an organic medium where a red colored complex is the product. This reaction is determined spectrophotometrically where the absorbance maxima is 475 nm. The focus of this paper is to discuss the parameters necessary to develop a solid sorbent sampling-sensor which can be used to determine atmospheric ethanol.     

Quantum groups in the higgs phase

In the Higgs phase we may be left with a residual finite symmetry groupH of the condensate. The topological interactions between the magnetic and electric excitations in these so-called discreteH gauge theories are completely described by the Hopf algebra or quantum groupD(H). In 2+1 dimensional space time we may add a Chern-Simons term to such a model. This deforms the underlying Hopf algebraD(H) into the quasi-Hopf algebraD (H) by means of a 3-cocycle onH. Consequently, the finite number of physically inequivalent discreteH gauge theories obtained in this way are labelled by the elements of the cohomology groupH ³(H,U(1)). We briefly review the above results in these notes. Special attention is given to the Coulomb screening mechanism operational in the Higgs phase. This mechanism screens the Coulomb interactions, but not the Aharonov-Bohm interactions.Translated from Teoreticheskaya i Matematicheskaya Fizika, Vol. 98. No. 3, pp. 509–523, March, 1994     

Conjectures on the Quotient Ring by Diagonal Invariants

We formulate a series of conjectures (and a few theorems) on the quotient of the polynomial ring in two sets of variables by the ideal generated by all S _n invariant polynomials without constant term. The theory of the corresponding ring in a single set of variables X = {x ₁, ..., x _n} is classical. Introducing the second set of variables leads to a ring about which little is yet understood, but for which there is strong evidence of deep connections with many fundamental results of enumerative combinatorics, as well as with algebraic geometry and Lie theory.     

Primeness of the enveloping algebra of a Cartan type Lie superalgebra

We show that a primeness criterion for enveloping algebras of Lie superalgebras discovered by Bell is applicable to the Cartan type Lie superalgebras , even. Other algebras are considered but there are no definitive answers in these cases.

     

Processes of flats induced by higher dimensional processes III

Stationary processes of k-flats in ^d can be thought of as point processes on the Grassmannian _k ^d of k-dimensional subspaces of ^d . If such a process is sampled by a (d–k+ j)-dimensional space F, it induces a process of j-flats in F. In this work we will investigate the possibility of determining the original k-process from knowledge of the intensity measures of the induced j-processes. We will see that this is impossible precisely when 1<k<d–1 and j=0,...,2[r/2]–1, where r is the rank of the manifold _k ^d . We will show how the problem is equivalent to the study of the kernel of various integral transforms, these will then be investigated using harmonic analysis on Grassmannian manifolds.The research of the first and third authors was supported in part by NSF grants DMS-9207019 and DMS-9304284. The research of the second author was supported in part by NFR contract number R-RA 4873-306 and the Swedish Academy of Sciences.