Thermochemistry of the ternary solid complex Gd(C5H8NS2)3(C12H8N2)

The novel ternary solid complex Gd(C₅H₈NS₂)₃(C₁₂H₈N₂) has been obtained from the reaction of hydrous gadolinium chloride, ammonium pyrrolidinedithiocarbamate (APDC), and 1,10-phenanthroline (o-phen · H₂O) in absolute ethanol. The complex was described by an elemental analysis, TG-DTG, and an IR spectrum. The enthalpy change of the complex formation reaction from a solution of the reagents, Δ_r H _m ^ϑ (sol), and the molar heat capacity of the complex, c _m , were determined as being − 15.174 ± 0.053 kJ/mol and 72.377 ± 0.636 J/(mol K) at 298.15 K by using an RD496-III heat conduction microcalorimeter. The enthalpy change of a complex formation from the reaction of the reagents in a solid phase, Δ_r H _m ^ϑ (s), was calculated as being 52.703 ± 0.304 kJ/mol on the basis of an appropriate thermochemical cycle and other auxiliary thermodynamic data. The thermodynamics of the formation reaction of the complex was investigated by the reaction in solution. Fundamental parameters, the activation enthalpy (ΔH _≠ ^ϑ ), the activation entropy (ΔS _≠ ^ϑ ), the activation free energy (ΔG _≠ ^ϑ ), the apparent reaction rate constant (k), the apparent activation energy (E), the preexponential constant (A), and the reaction order (n), were obtained by the combination of the thermochemical data of the reaction and kinetic equations, with the data of thermokinetic experiments. The constant-volume combustion energy of the complex, Δ_c U, was determined as being −17588.79 ± 8.62 kJ/mol by an RBC-II type rotatingbomb calorimeter at 298.15 K. Its standard enthalpy of combustion, Δ_c H _m ^ϑ , and standard enthalpy of formation, Δ_f H _m ^ϑ , were calculated to be −17604.28 ± 8.62 and −282.43 ± 9.58 kJ/mol, respectively. The text was submitted by the authors in English.     

Ca(1)(-)(x)Na(2)(x)Al(2)B(2)O(7): a structure with tunable density of Na(+) vacancies

A series of samples with the composition Ca(1)(-)(x)Na(2)(x)Al(2)B(2)O(7) (0 < x < or = 1) was investigated and a hexagonal structure with unusually large range of homogeneity (at least from x = 0.01 to 0.95) was revealed. The hexagonal phase consists of [Al(2)B(2)O(7)](infinity)(2)(-) lamellae stacked along the c axis, as in CaAl(2)B(2)O(7) and Na(2)Al(2)B(2)O(7). Nevertheless, the configuration and stacking sequence of the [Al(2)B(2)O(7)](infinity)(2)(-) lamellae are different in these three structures. In the hexagonal structure of Ca(1)(-)(x)()Na(2)(x)()Al(2)B(2)O(7), Ca and half Na cations (Na1) statistically occupy the same crystallographic site which is located between the [Al(2)B(2)O(7)](infinity)(2)(-) lamellae, the other half Na cations (Na2) distribute in the planes bisecting the [Al(2)B(2)O(7)](infinity)(2)(-) lamellae. Depending on the composition, the site occupation factor of Na2 site can vary in the same range as x, leading to a tunable density of Na(+) vacancies in the structure. The AlO(4) tetrahedra and BO(3) triangles in the structure tilt in appropriate ways to improve the bond valence sum of Na2 cations which are not sufficiently bonded to the anions.     

Regioselective Borylation of Porphyrins by C?H Bond Activation under Iridium Catalysis to Afford Useful Building Blocks for Porphyrin Assemblies

Highly regioselective and efficient borylation of a variety of porphyrins has been achieved by reaction with bis(pinacolato)diboron through C? H bond activation under iridium catalysis on the basis of the synthetic protocol developed by Miyaura, Hartwig, and Smith. A boryl group can be selectively introduced at sterically uncongested positions in the peripheral aryl groups of porphyrin substrates whose peripheral β‐positions are sterically hindered. Curiously, β substituents adjacent to the aryl group to be borylated have unexpectedly large effects on the regioselectivity, because the iridium catalyst can discriminate between subtle steric differences. Chemoselective borylation was also achieved for several functionalized porphyrins. This borylation protocol can be applied to various monomeric and oligomeric functional porphyrins, hence offering an efficient route to elaborate multiporphyrin‐based molecular constructs.     

Periodic,multiplicative number-theoretical functions

D. Leitmann andD. Wolke [3] proved that multiplicative functions, which are restrictions of continuous, periodic functionsF: with irrational period, are constant equal to 0 or 1. In this note a simpler proof for this result is given.     

Zwei Bemerkungen über transzendente Zahlen

In the first part theorems ofBaker are used to prove the transcendence of special values of power series whose coefficients are values of certain ordinary Dirichlet series with coefficients forming a periodic sequence of algebraic numbers. Especially the transcendence of (z)+C is shown for all rationalz which are not integers, denoting the logarithmic derivative of the gamma function andC Euler's constant. In the second part the intimate connection betweenSchanuel's conjecture and the arithmetic nature of ,s=3,4,5... is studied where (n) denotes the number of distinct representation ofn in the forma ^b with positive integersa, b. This function was recently introduced byGolomb.     

Banach convolution algebras of functions II

LetG be a noncompact, locally compact group. By means of generalized dyadic decompositions ofG, translation invariant Banach spacesF(B, B, X) of (classes of) measurable functions onG are constructed, e. g. certain weighted amalgams ofL ^p -spaces. Basic properties of these spaces are derived and connections with spaces considered in the literature are indicated. As a main result, sufficient conditions are given which imply that a space of this type is a Banach algebra with respect to convolution.With 1 Figure     

Eine mehrdimensionale Version der Ungleichung von le Veque

In this short note we give a proof of le Veque's inequality $$D_N \leqq (6/\pi ^2 )\sum\limits_{h = 1}^\infty {h - 2\left| {(1/N)\sum\limits_{k = 1}^N {e^{2\pi ihx_k } |2)1/3} } \right|} $$ for dimensions≧2.     

Aufeinanderfolgende Elemente in multiplikativen Zahlenmengen

LetM be a multiplicative set with 1M andmnM if and only ifmM,nM for (m,n)=1. It is shown by elementary means that there exists the asymptotic density of the setM(M–1) for every multiplicative setM. The density is positive if and only ifM possesses a positive density and 2M for some . This result is slightly generalized to sums over multiplicative functionsf with |f|1.     

A method of bisection for discounted Markov decision problems

We describe in this paper how to introduce the concept of bisection into Dynamic Programming of stationary Markovian decision processes with infinite horizon. The combination of these two methods delivers a new class of algorithms. A basic bisection algorithm is given. Its rate of convergence is rather independent of the input data, especially the discount factor or contracting factor. If in any method of successive approximations we have > 0.5, then the bisection method has a faster convergence than the successive approximations. Bisection is especially advantageous if is close to unity. The computation of two inventory control problems with the basic algorithm of bisection is presented. The second example has a discount factor=0.9994. Using Howard's automobile replacement problem the new method is compared with value iteration, policy iteration andPorteus' method of extrapolations. Among them bisection turned out to be the most powerful procedure. The combination withPorteus' method of extrapolation is not as efficient as the bisection method alone. We also investigate how to combine the bisection method with monotone extrapolation when the transition matrices do not have equal row sums.

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Zusammenfassung In dieser Arbeit wird die Idee der Bisektion in die Dynamische Optimierung stationärer Markovscher Entscheidungsprozesse mit unendlichem Planungshorizont eingeführt. Die Verbindung dieser beiden Methoden schafft eine neue Klasse von Algorithmen. Ein Basisalgorithmus, der selbst Ausgangspunkt zahlreicher Verfeinerungen und Spezialisierungen bildet, wird vorgestellt. Seine Konvergenzgeschwindigkeit ist nahezu unabhängig von Input-Daten, speziell dem Diskontfaktor bzw. der Lipschitz-Konstanten. Die Bisektion ist immer dann schneller als die Methode der sukzessiven Approximation, falls>0,5 ist. Deshalb ist das neue Verfahren besonders bei Problemen mit schwacher Kontraktionseigenschaft, d.h. nahe bei eins, geeignet. Der Rechenverlauf des Basisalgorithmus wird anhand zweier Lagerhaltungsmodelle diskutiert von denen das zweite eine Lipschitz-Konstante=0.9994 besitzt. Am Beispiel des Howardschen Autoersatzproblems zeigt sich, daß das Bisektionsverfahren im Vergleich mit der Wertiteration, Politikiteration undPorteus' Extrapolationsverfahren das schnellste Verfahren ist. Die Kombination der Bisektion mit der Extrapolationsmethode ist ungünstiger als die Bisektion allein. Es wird noch untersucht, wie die Bisektion mit der monotonen Extrapolation verbunden werden kann, wenn die Zustands-übergangsmatrizen keine konstanten Zeilensummen besitzen.

     

A comparison of two approaches to the optimal positioning of a new product in an attribute space

This paper is concerned with the optimal positioning of a new product in an attribute space. A deterministic optimization model that relies on the axiom of choice is compared with the model byShocker/Srinivasan [1974] that incorporates a probabilistic measure of choice. Investigating the assumptions and the construction of both models, it is shown that the probability function byShocker/Srinivasan is based on a controversial assumption and incorporates a parameter that has not been given an economic explanation. Furthermore, both models are applied to complex configurations. It is demonstrated that the optimal positions for the new product resulting from the model byShocker/Srinivasan depend heavily on the parameter just mentioned and may run contrary to plausible consequences of the axiom of choice.

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Zusammenfassung Für die optimale Gestaltung neuer Produkte, d.h. ihrer Positionierung in einem Raum von Produkteigenschaften, wird ein Modell angeboten, das auf einer deterministischen Kaufentscheidung beruht, ein anderes, das eine stochastische Kaufentscheidung unterstellt. Es wird gezeigt, daß der zuletzt genannte Modelltyp stark von der Spezifikation eines ökonomisch bisher nicht erklärten Parameters abhängt und z.T. Konsequenzen aufweist, die dem Wahlaxiom zuwider laufen, auf das das erstgenannte Modell aufbaut. Durch einen Vergleich auch komplexer Konfigurationen von Käuferbeurteilungen neuer Produkte wird gezeigt, welche Gestaltungsentscheidungen auf der Grundlage der beiden Modelle zur Optimierung einer Zielfunktion zu treffen sind.