Primes of the form <Emphasis Type="Italic">x</Emphasis><Superscript>2</Superscript> + (<Emphasis Type="Italic">x</Emphasis> + 1)<Superscript>2</Superscript>. Proper divisors of composites of the same form

The aim of the present paper is to characterize prime numbers of the form n = x ² + (x + 1)² and to obtain certain proper divisors of composite numbers of the same form, i.e. divisors d of n such that 1 < d < n.      

Longitudinal dispersion in a duct with moving walls

The dispersion of a diffusing substance along a channel or pipe is augmented if the channel walls (resp. pipe wall) are moving in the lateral direction. The fluid in the present theoretical investigation is supposed to be inviscid. The longitudinal dispersion enhancement is evaluated analytically and the expressions for various movements of the walls are given in simple formulas.

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Zusammenfassung In der vorliegenden Arbeit wird die Dispersion einer flüssigen Substanz in einem symmetrischen Kanal studiert, dessen ebene Wände sich in der vertikalen Richtung bewegen. Es zeigt sich, daß die longitudinale Dispersion damit vergrößert wird. Die Flüssigkeit wird als reibungsfrei angenommen. Die Lösung wird in analytischer Form dargestellt und an verschiedenen Bewegungen der Kanalwände angewendet. Die Lösung wurde auch für den achsensymmetrischen Fall erweitert.

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In memoriam Prof. Erich Leiter, Technical University of Vienna, Austria     

An implicit characteristic-flux-averaging method for the euler equations for real gases

A formulation of an implicit characteristic-flux-averaging method for the unsteady Euler equations with real gas effects is presented. Incorporation of a real gas into a general equation of state is achieved by considering the pressure as a function of density and specific internal energy. The Ricmann solver as well as the flux-split algorithm are modified by introducing the pressure derivatives with respect to density and internal energy. Expressions for calculating the values of the flow variables for a real gas at the cell faces are derived. The Jacobian matrices and the eigenvectors are defined for a general equation of state. The solution of the system of equations is obtained by using a mesh-sequencing method for acceleration of the convergence. Finally, a test case for a simple form of equation of state displays the differences from the corresponding solution for an ideal gas.     

Molecular dynamics simulations of stretched gold nanowires: the relative utility of different semiempirical potentials

The mechanical elongation of a finite gold nanowire has been studied by molecular dynamics simulations using different semiempirical potentials for transition metals. These potentials have been widely used to study the mechanical properties of finite metal clusters. Combining with density functional theory calculations along several atomic-configuration trajectories predicted by different semiempirical potentials, the authors conclude that the second-moment approximation of the tight-binding scheme (TB-SMA) potential is the most suitable one to describe the energetics of finite Au clusters. They find that for the selected geometries of Au wires studied in this work, the ductile elongation of Au nanowires along the [001] direction predicted by the TB-SMA potential is largely independent of temperature in the range of 0.01-298 K. The elongation leads to the formation of monatomic chains, as has been observed experimentally. The calculated force-versus-elongation curve is remarkably consistent with available experimental results.     

Bonding configurations and collective patterns of Ge atoms adsorbed on Si(111)-(7 x 7)

We report scanning tunneling microscopy observations of Ge deposited on the Si(111)-(7 x 7) surface for a sequence of submonolayer coverages. We demonstrate that Ge atoms replace so-called Si adatoms. Initially, the replacements are random, but distinct patterns emerge and evolve with increasing coverage, until small islands begin to form. Corner adatom sites in the faulted half unit cells are preferred. First-principles density functional calculations find that adatom substitution competes energetically with a high-coordination bridge site, but atoms occupying the latter sites are highly mobile. Thus, the observed structures are indeed more thermodynamically stable.     

Metal complexes of the diuretic drug furosemide

New complexes of the formulaeM(fur)₂·2H₂O (M = Mn, Cu, Zn),M(fur)₂·3H₂O (M = Co, Ni, Cd), Hg₂(fur)₃Cl₂·2H₂O, Pd(fur)Cl·H₂O and Rh(fur)₃·3H₂O, wherefurH = 4-chloro-N-(2-furfuryl)-5-sulfamoylanthranilic acid, have been prepared and characterized by conductivity measurements, X-ray powder patterns, thermal methods, effective magnetic moments as well as by IR, ligand field,¹H-NMR and ESR spectroscopic studies. The anionfur ^– shows a chelated bidentate O(carboxylato), N(imino)-coordinating behaviour.

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Metallkomplexe der diuretischen Droge Furosemid

Zusammenfassung Neue Komplexe der Verbindungen:M(fur)₂·2H₂O (M = Mn, Cu, Zn),M(fur)₂·3H₂O (M = Co, Ni, Cd), Hg₂(fur)₃Cl₂·2H₂O, Pd(fur)Cl·H₂O und Rh(fur)₃·3H₂O, wobeifurH 4-chlor-N-(2-furfuryl)-5-sulfamoylanthanilsäure ist, wurden dargestellt. Die Komplexe wurden durch Leitfähigkeitsmessungen, Röntgen-Pulver-Aufnahmen, thermogravimetrische Analysen, Messungen des effektiven magnetischen Dipolemomentes sowie durch spektroskopische Untersuchungen (IR,¹H-NMR und ESR) charakterisiert. Das Anionfur ^– zeigt das Verhalten einer Chelat-bidentat-O(carboxylato),N(imino)-Koordination.

     

Coordination complexes of l-azetidine-2-carboxylic acid with platinum(II) and palladium(II)

Summary The complexes K[Pt(l-aze)Cl₂, [Pt(l-aze)₂] and [Pd(l-aze)₂] (l-aze = l-azetidine-2-carboxylate) were prepared. X-ray structures show that [Pt(l-aze)₂] and [Pd(l-aze)₂] are isomorphous, having a planar tetragonal geometry with a trans configuration around the Pt and Pd atoms. Slight puckerings of the MN(1)N(11)O(11) chelate ring (M = Pt or Pd) and the azetidine ring were observed. The circular dichroism (c.d.) spectra of the complexes in aqueous solution agree with the structures found in the solid state as far as the hexadecant rule is concerned, giving, for the trans configuration of [M(l-ia)₂] (where ia = imino acid), the profile of the c.d. signs for the three predominant d-d transitions as: +,-,-. I.r., conductivity and n.m.r. measurements are also reported and are in accord with the proposed structures.     

Coordination complexes of 3,4-dihydroxyphenylpropionic acid (dihydrocaffeic acid) with copper(II), nickel(II), cobalt(II) and iron(III)

Summary The preparation of complexes of 3,4-dihydroxyphenylpropoionic acid (hydrocaffeic acid): K₂[Cu₂(hydcafH)₂-Cl₂]·2KCl·2MeOH, K₂[Co(hydcafH)₂]·2KCl, K₂[Ni₂(hydcafH)₂Cl₂]·2KCl·2MeOH and Fe₂ (hydcafH)₂Cl₂·2KCl·2H₂O was achieved. Spectroscopic and magnetic studies are commensurate with tetrahedral structures for the prepared complexes in which the catechol-like coordination is present.     

An analytical expression for the van der Waals interaction in oriented-attachment growth: a spherical nanoparticle and a growing cylindrical nanorod

A mathematical derivation of an analytical expression is presented to evaluate the van der Waals interaction between a sphere and a cylindrical rod. This expression then is applied to study the growth of one-dimensional nanostructures, such as nanorods, using a common growth mechanism in colloidal chemistry, the oriented attachment growth mechanism. Parameters associated with the dimensions and the separation of nanoparticles and nanorods are varied in calculations to assess their influence on the magnitude of the van der Waals interaction.