bluuebunny/crossref_metadata_2025 huggingface dataset:
X–ray Single Crystal Structure and Raman Spectrum of Ammonium Hexafluoroarsenate
Authors: Goreshnik E. , Mazej Z.
Published: June 2007

The structure of ammonium hexafluoroarsenate, NH4AsF6, has been determined by X‐ray diffraction using a single crystal grown from saturated solution in anhydrous HF. NH4AsF6 crystallizes rhombohedral with the KOsF6 structure type, with a = 7.459(3) Å, c = 7.543(3) Å (at 200 K), Z = 3, space group $R{\bar 3}$ (No. 148). No phase transition was observed in the 100 K–296 K temperature range. The structure is dominated by regular AsF6 octahedra and disordered NH4+ cations. Raman spectrum of a single crystal of NH4AsF6 shows the bands at 372 cm−1, 572 cm−1, 687 cm−1 (AsF6−) and at 3240 cm−1 and 3360 cm−1 (NH4+).
The Intrinsic Shape of the cubic cP124 Clathrate Structure
Authors: von Schnering Hans Georg , Zürn Anke , Chang Jen‐Hui , Baitinger Michael , Grin Yuri
Published: June 2007

It is shown how the Periodic Nodal Surface PNS D*&Y** separates perfectly the two partial structures of the cubic cP124 type. Condensed metal‐centered [M@E20] pentagonal dodecahedra of covalently bonded E atoms form a 3‐connected net. This partial structure is embedded in a zeolite‐type labyrinth containing chains of the remaining metal atoms. The shape of this ensemble represents the principle of the intrinsic curvature of solids. The relations of the structure to the β‐manganese structure are discussed in detail. Furthermore, some details concerning the electron balance in the covalent E100 net are reported.
Organoalkoxochlorogallane
Authors: Chamazi Navabeeh Nami , Heravi Majid M. , Neumüller Bernhard
Published: June 2007

Organoalkoxochlorogallanes

Me2GaCl was treated with nBuOH and iBuOH in a molar ration of 1:2, respectively. However, only one equivalent of the alcohol reacted with MeGaCl2 to give [MeGa(Cl)OnBu]3 (1) or [MeGa(Cl)OiBu]3 (2). 1 and 2 were characterized by NMR and IR techniques as well as by X‐ray structure determinations. According to that 1 and 2 form trimers in solution and the solid state. In solution both isomers Cs and C3v were observed while the trimers exist only as Cs isomers in the solid state which exhibit strongly distorted boat conformations with a disorder of the Cl/Me position at one of the gallium atoms.
Reaktion von (R,R)‐(N,N′)‐Diisopropylcyclohexyl‐1,2‐diamin mit Me2MCl (M = Ga, In)
Authors: Chamazi Navabeeh Nami , Heravi Majid M. , Breyhan Thees , Neumüller Bernhard
Published: June 2007

Reaction of (R,R)‐(N,N′)‐Diisopropylcyclohexyl‐1,2‐diamine with Me2MCl (M = Ga, In)

(R,R)‐(N,N′)‐Diisopropylcyclohexyl‐1,2‐diamine (H2L) was reacted with Me2GaCl and Me2InCl in boiling toluene, respectively. In both cases the salt [Me2M(H2L)][Me2MCl2] [M = Ga (1), In (2)] was formed. 1 and 2 were characterized by NMR and vibrational spectroscopy. In addition, an X‐ray structure determination was applied on 2. According to the spectroscopical and structural findings 1 and 2 consist of cations [Me2M(H2L)]+ and anions [Me2MCl2]−.
Single Crystal of a Prussian Blue Analog based on Rubidium Manganese Hexacyanoferrate
Authors: Tokoro Hiroko , Shiro Motoo , Hashimoto Kazuhito , Ohkoshi Shin‐ichi
Published: June 2007

A dark brown single crystal of rubidium manganese hexacyanoferrate, Rb0.61Mn[Fe(CN)6]0.87·1.7H2O, was obtained by the slow diffusion method. X‐ray single crystal analysis showed that this compound crystallized in the cubic system of space group $Fm{\bar 3}m$ with cell constants of a = b = c = 10.5354(4) Å, Z = 4, and R1 = 0.0449. The CN groups bridge octahedral FeC6 and MnN0.87O0.13. Rb and non‐coordinated water (so‐called zeolitic water) exist in the interstitial sites of the cubic lattice.
Characterization and Crystal Structure of some Schiff Base Copper(II) Complexes derived from Enantiomeric Pairs of Chiral Amines
Authors: Fernández‐G. Juan M. , Ausbun‐Valdés Cecilia , González‐Guerrero Erika E. , Toscano Rubén A.
Published: June 2007

Copper(II) complexes of three chiral enantiomeric pairs of o‐hydroxy Schiff bases derived from (R)‐(+)‐1‐phenylethylamine and (S)‐(‐)‐1‐phenylethylamine, were prepared and characterized. Elemental analyses, specific rotation, i.r., electronic, cd and mass spectra,and some X‐ray crystal structures were obtained. The X‐ray study of four complexes shows that the geometry around the metal atom is distorted square planar. Epr studies of all these complexes in DMF solution at 77 K suggest that their geometries in solution are slightly different to that observed in the solid state by X‐ray crystallography. Although, cd spectra only show charge transfer absorptions, the data confirm the enantiomeric character of the three pairs of the obtained complexes.
Synthesis, Structure and Selective Chlorination of Bis(N‐borane‐dimethylaminopropyl)telluride
Authors: Beckmann Jens , Fleige Emanuel , Schnurbusch Nicolai
Published: June 2007

The reaction of Te powder, NaBH4 and Me2N(CH2)3Cl·HCl provided the title compound [H3BNMe2(CH2)3]2Te (1), whose selective chlorination with SO2Cl2 lead to the formation of [ClH2BNMe2(CH2)3]2TeCl2 (2) and [Cl3BNMe2(CH2)3]2TeCl2 (3), respectively. Compounds 1–3 were characterized by multinuclear NMR spectroscopy and single crystal X‐ray diffraction.
The Response of Laminar Skin Friction, Temperature and Heat Transfer to Fluctuations in the Stream Velocity in the Presence of a Transverse Magnetic Field I
Authors: Suryaprakasarao U.
Published: June 2007

Exact solutions are obtained for the flow of a viscous incompressible and electrically conducting fluid in the presence of a transverse magnetic field under the following conditions: (1) the fluid flows past an infinite porous flat plate subjected to uniform suction; (2) the free stream velocity oscillates in magnitude but not in direction; and (3) the magnetic Reynolds number is small. The response of the skin friction, temperature and heat transfer to the fluctuating stream is studied for variations in the magnetic field as well as the frequency of the fluctuating stream. The limiting cases of large frequencies of the fluctuating stream and large magnetic fields are also discussed. It is found that the magnitudes of the skin friction, the wall temperature and the heat flux at the wall increase both with the increase in the magnetic field and the increase in the frequency of the fluctuating stream.
Über Eindeutigkeit und praktische Berechnung der Lösungen von Randwertaufgaben in der Theorie der orthogonal‐anisotropen Platten
Authors: Töpfer Hans‐Joachim
Published: June 2007

Für die Differentialgleichung der orthogonal‐anisotropen Platte

wird die Eindeutigkeit der Lösungen gewisser gemischter Randwertaufgaben bewiesen. Das Hilfsmittel ist eine Greensche Formel erster Art.

Des weiteren werden Aussagen über die Strucktur einer allgemeinen regulären Lösung gemacht und eine singuläre Grundlösung hergeleitet, die der Definition Greenscher Funktionen zugrunde gelegt wird und mit deren Hilfe man eine Integraldarstellung der Lösungen von Randwertaufgaben bekommt.

Ein erprobtes numerisches Verfahren zur Konstruktion regulärer Lösungen von Randwertaufgaben wird beschrieben, das von der Entwickelbarkeit solcher Lösungen nach einem System von Lösungspolynomen Gebrauch macht. Zur Bestimmung der Entwicklungskoeffizienten wird das Verfahren der Randkollokation angewandt.
Instationäre Wärmeleitungsvorgänge in stückweise homogenen Medien
Authors: Engl Walter
Published: June 2007

Der Temperatursprung an der Oberfläche von konzentrischen Kugeln und geschichteten Platten wird mit der Methode der Laplace‐Transformation behandelt. Zur Lösung der physikalisch allein interessierenden Frage nach der Zeitdauer des Ausgleichvorganges ist die vollständige Kenntnis des räumlichen Temperaturfeldes nicht erforderlich. Vielmehr braucht man nur die Funktion anzugeben, die das Anwachsen der Temperatur im Kugel‐bzw. Plattenmittelpunkt beschreibt. Diese Spezialisierung kann schon an der Unterfunktion durchgeführt werden, worin der besondere Vorteil der Laplace‐Transformation liegt. Durch eine Messung des Ausgleichsprozesses an geschichteten Platten wird das theoretische Ergebnis gut bestätigt.
Eine einheitliche Darstellung der Lösungen der Tricomischen Gleichung
Authors: Lanckau Eberhard
Published: June 2007

Die Tricomische Differentialgleichung ist als einfache Differentialgleichung von gemischtem Typ sowohl für rein mathematische Untersuchungen als auch für die näherungsweise Berechnung von Strömungen mit Schalldurchgang bedeutungsvoll. Mit Hilfe der Bergmanschen Operatorenmethode läßt sich aus einer analytischen Funktion („Grundfunktion”︁) durch geeignete Integralausdrücke eine Lösung der Tricomischen Gleichung herstellen. Die bereits in großer Anzahl bekannten Partikularlösungen der Tricomischen Gleichung erweisen sich als einfache Spezialfälle dieser Lösung.
Fehlerabschätzungen mit Hilfe eines Vergleichssatzes
Authors: Schmidt Jochen W.
Published: June 2007

Zur näherungsweisen Lösung der Fixpunktaufgabe wird ein allgemeiner Vergleichssatz formuliert und auf das Polygonzugverfahren bei gewöhnlichen Differentialgleichungen und auf ein Analogon dazu für das charakteristische Anfangswertproblem bei hyperbolischen Differentialgleichungen angewendet. Es ergeben sich Fehlerabschätzungen [(3.17) und (4.16)], welche nur Größen enthalten, die sich aus der rechten Seite und der Näherungslösung ermitteln lassen.
Das Verhalten wellenförmiger Störungen einer ebenen Poiseuilleschen Strömung bei kleinem Parameter Re α
Authors: Szablewski W.
Published: June 2007

Im Rahmen einer Entwicklung der Lösung der Störungsdifferentialgleichung nach Potenzen des Parameters Re α wird die in Re α lineare Lösung explizit angegeben. Es ergeben sich u. a. das Spektrum der Eigenwerte bzw. der Dämpfung und Phasengeschwindigkeit der Wellen, ferner die mittlere induzierte Schubspannung und die mittlere Verformung des Grundprofils der Strömung.
Rayleigh‐Näherungen für Simultan‐Iteration an betragsgleichen Eigenwerten einer Matrix
Authors: Zurmühl R.
Published: June 2007

Bei Iteration an betragsgleichen oder betragsnahen Eigenwerten (Simultan‐Iteration) einer reellen Matrix lassen sich Näherungswerte der dominanten Eigenwerte als Lösungen gewisser Normalgleichungen gewinnen. Für diese Näherungen wird gezeigt, daß sie Rayleigh‐Charakter haben in dem Sinne, daß ihre Fehler von zweiter Ordnung klein sind gegenüber den Vektor‐Verunreinigungen.
General Stability Analysis of Orthotropic Sandwich Panels for four Different Boundary Conditions (Extension of the March‐Ericksen Approach)
Authors: Chang C. C. , Ebcioglu I. K. , Haight C. H.
Published: June 2007

This work contains a general stability analysis of orthotropic sandwich panels including a revised formulation of the March‐Ericksen energy method as well as the more exact differential equation method. Certain special cases are formulated using the revised March‐Ericksen method and some approximations applicable to this method are indicated. Buckling coefficient curves are plotted for various boundary conditions using the energy method. The appendices give a detailed derivation of the differential equations of the problem and a solution of these equations for the buckling coefficient of a simply‐supported panel.
On a Functional Equation in Finite Deformation
Authors: Seth B. R.
Published: June 2007

The finite deformation of a rectangular plate into a cylindrical shell gives rise to a functional equation whose general solution gives a variety of shapes into which the plate can be bent. Particular cases include the known forms which are circular, parabolic and one given by rn cos n θ = an, n = (3 – 2 σ)−1. The elliptic and hyperbolic forms are found possible only for incompressible plates. An incompressible plate can therefore be bent into a cylinder whose section is any given conic. Five new shapes are obtained in terms of elliptic integrals and three in terms of hyperelliptic integrals. It is found that tractions have to be applied to the curved surfaces in addition to the edge forces and couples in all cases except when the form is circular.
The Response of Laminar Skin Friction, Temperature and Heat Transfer to Fluctuations in the Stream Velocity in the Presence of a Transverse Magnetic Field‐II
Authors: Suryaprakasarao U.
Published: June 2007

Exact solutions are obtained for the flow of a viscous incompressible and electrically conducting fluid in the presence of a transverse magnetic field under the following conditions: (1) the fluid flows past an infinite porous flat plate subjected to uniform suction; (2) the free stream velocity oscillates in magnitude but not in direction; (3) the magnetic Reynolds number is equal to the viscous Reynold number; and (4) the Alfvén velocity is less than the suction velocity. The response of the skin friction, temperature and heat transfer at the plate to the fluctuating stream is studied for the variations in the frequency of the fluctuating stream. It is found that there is an increase in the magnitudes of the skin friction, wall temperature and heat flux at the wall due to an increase in the frequency of the fluctuating stream.
Two Dimensional Flow of Power Law Fluids in the Inlet Length of a Straight Channel
Authors: Kapur J. N. , Gupta R. C.
Published: June 2007

The method of Goldstein [1], Bogue [2] and Schiller [3] has been extended to discuss the two dimensional flow of both pseudoplastic and dilatant fluids in the inlet length of a straight channel. The pressure drop has been obtained and compared with that obtained from kinetic energy end‐correction. Analytical expressions have been obtained for the inlet length and the boundary layer thickness. For certain values of the flow behaviour index, all the results have been illustrated by graphs.
Die Hohlplatte, eine schubweiche Platte
Authors: Giencke Ernst
Published: June 2007

Am Beispiel der Hohlplatte wird gezeigt, wie weit die Schubsteifigkeit quer zur Haupttragrichtung das Kräftespiel in einer Platte beeinflußt. Es wird die ringsum gelagerte und die seitlich freie Platte behandelt.
Elastic‐plastic Transition in Shells and Tubes under Pressure
Authors: Seth B. R.
Published: June 2007

Elastic‐plastic transition is obtained in current literature with the help of a semi‐empirical yield condition like that of Tresca or Von Mises. The stresses are obtained from the elastic solution and then substituted in the yield condition to get the transition surface. The possibility of treating it as a transition or turning point phenomenon in finite deformation has not been explored. When the plastic state tends to set in, the stressstrain relations undergo a change. This should be reflected in our equations. The linear classical theory cannot do it. If we adopt the theory of finite deformation, the equations of equilibrium give rise to non‐linear differential equations whose turning points can give the elastic‐plastic transition. The asymptotic solution at these points then give the displacements and the stresses, and no semi‐empirical yield condition is necessary. The yield stress can be related to the elastic coefficients in the transition range through the tension‐stretch result in finite deformation. This method is applied to the plastic deformation of shells and tubes under pressure.
Die ebene laminare Strömung in einem Halbraum bei kleiner Reynolds‐Zahl
Authors: Förste J.
Published: June 2007

Aus einem Kanal mit parallelen ebenen Wänden ströme eine inkompressible zähe Flüssigkeit in einen Halbraum, die Strömung sei laminar und stationär.

Das Druck‐ und Geschwindigkeitsfeld sowie die Stromfunktion werden durch Lösung des zugehörigen Randwertproblems der Stokesschen Gleichungen ermittelt. Dabei werden die Randbedingungen so gewählt, daß an festen Wänden die Haftbedingung erfüllt ist, und im Unendlichen die Flüssigkeit ruht. In einem Spezialfall wird die Lösung graphisch dargestellt.
Längswirbel in ebener Poiseuillescher Strömung
Authors: Szablewski W.
Published: June 2007

Der Mechanismus der Wechselwirkung zwischen Längswirbeln und einer ebenen Poiseuilleschen Grundströmung wird in linearer sowie erster nichtlinearer Näherung explizit beschrieben. Auf entsprechende beim Umschlag laminarer in turbulente Strömungen in Erscheinung tretende Phänomene wird hingewiesen.
Berechnung vielgliedriger Schwingerketten II. Deformationsgrößen und Kraftgrößen‐Methode
Authors: Marguerre K. , Uhrig R.
Published: June 2007

Die Arbeit zeigt, wie man mit Hilfe kinetischer Steifigkeiten und Nachgiebigkeiten die Deformationsgrößen und die Kraftgrößen‐Gleichungen für die Schwingerkette gewinnen kann, und wie man am zweckmäßigsten eliminiert, um die Eigenwerte schematisch und ohne numerische Schwierigkeiten zu bestimmen.
The Coaxial Disc Viscometer
Authors: Hutson V.
Published: June 2007

Two equal, circular, coaxial discs at a small separation are rotating slowly with equal and opposite angular velocities in a viscous fluid. The purpose of this investigation is to find asymptotically the turning couple on each disc as their separation approaches zero. The problem was formulated by Cooke [2] as an integral equation. This is solved asymptotically by splitting the field into two regions, one being an annulus containing the edges, the other being the rest of the domain, and combining these solutions. Use is then made of a technique related to a variational method to obtain an accurate asymptotic expression for the turning couple from a much less accurate solution of the integral equation.
Das Variationsproblem der allgemeinen linearen Schalentheorie
Authors: Klingbeil E.
Published: June 2007

Die verallgemeinerte lineare Theorie elastischer Schalen nach W. Zerna wird hier als Variationsproblem behandelt. Ausgehend von der allgemeinen Elastizitätstheorie des dreidimensionalen Kontinuums werden die Ausdrücke für die Formänderungsenergie elastischer Schalen gewonnen. Das Prinzip vom Minimum der Formänderungsenergie liefert in den Euler‐Lagrangeschen Differentialgleichungen das vollständige System der Schalengleichungen. Näherugen gestalten sich auf diese Weise besonders übersichtlich. So wird schließlich die bisher übliche Schalentheorie als Näherung der verallgemeinerten gewonnen.
On Take‐off from Circular Orbit by Small Thrust
Authors: Ting Lu , Brofman Sherwood
Published: June 2007

Analytic solutions for the trajectories of taking off from a circular orbit by low thrust at a finite angle to the radial vector are presented. The solution is uniformly valid for the entire time interval measured from the initial instant of take‐off, t = 0, to t = O (1/ϵ) subjected to the upper limit set by the assumption of small thrust, where ϵ is the ratio of thrust to the central force at t = 0. The zero order solution is a function of the “slow” time variable τ = ϵ t. The first order solution is obtained by splitting it into two parts; one is a non‐oscillatory function of τ and the other is an oscillatory function of t with varying periods. With this scheme it is possible to simplify the equations by estimating the order of magnitude of the terms for the entire interval. For the first order solution the non‐oscillatory part is uniquely determined from an integral equation while the oscillatory term cannot be uniquely determined. This indeterminacy is removed by the technique which is equivalent to that of Mitropolsky in the problem of nonlinear oscillation with slowly varying parameters.
Beitrag zum Kontaktproblem zweier Hohlzylinder
Authors: Eschke K.
Published: June 2007

Es wird ein allgemeines Verfahren zur Berechnung des Spannungs‐ und Verformungszustandes bei Schrumpfverbindungen zylindrischer Körper von verschiedener Länge entwickelt. Dabei wird elastisches Material vorausgesetzt, das dem Hookeschen Gesetz gehorcht, und angenommen, daß im Kontaktbereich keine Schubkräfte übertragen werden. Ein numerisches Beispiel zeigt die Anwendungsmöglichkeiten des Verfahrens.
Zeitlicher Verlauf des Kippwinkels einer starren Kreisplatte bei außermittiger Belastung
Authors: Schimmerl J.
Published: June 2007

Ein als unendlicher Halbraum aus Ton angesehener Grundwasserträger soll an seiner horizontalen, überall durchlässigen Oberfläche zum Zeitpunkt t = 0 durch eine stoßfrei aufgebrachte außermittig belastete starre Kreisplatte beansprucht werden. Gesucht sei der zeitliche Verlauf der eingeleiteten Schiefstellung (Kippwinkel) der starren Platte.
The Rotation of a Conducting Liquid in a Uniform Transverse Magnetic Field
Authors: Smith P.
Published: June 2007

The effect of a uniform transverse magnetic field on an incompressible conducting liquid contained in a circular cylinder rotating with constant angular velocity is investigated. The problem is treated as a perturbation one for small magnetic Reynolds and Hartmann numbers. The first order approximation shows that the core of the liquid is slowed down whilst to the second order, perturbations in the circular streamlines appear. However, the latter effects are extremely small for the cases considered here. Some results are presented for a cylinder containing mercury.
Differentialgleichungen orthotroper Platten im geometrisch und beschränkt physikalisch nichtlinearen Bereich
Authors: Müller H.
Published: June 2007

Es wird eine Platte aus einem ebenen Deckblech und außermittigen, orthogonal angeordneten, völlig torsionsweichen und „verschmierbaren”︁ Rippen unter statischer Belastung bei begrenzt zugelassenen endlichen Verschiebungen betrachtet. Für das Deckblech wird ideal elastisches, für die Rippen ideal elastisches‐ ideal plastisches Verhalten gefordert. Wegen der Rippenplastizierung werden die Schnittkräfte aus einem elastischen Anteil und einer „plastischen Korrektur„ zusammengesetzt. Das aufgestellte Differentialgleichungssystem enthält die Scheibenkräfte (Längskräfte und Schubkraft), die Querverschiebung und die Plastizierungstiefen beider Rippenscharen als Unbekannte. Analog zum bekannten Vorgehen bei isotropen Platten wird unter Einführung eines dickenabhängigen Störparameters das Differentialgleichungssystem auf unendlich viele, einfachere Differentialgleichungssysteme von je vier Gleichungen für die Scheibenkräfte und die Querverschiebung und zwei Gleichungen für die Plastizierungstiefen zurückgeführt. Für das erste Gleichungssystem wird die Lösung mittels der gewöhnlichen Differenzenmethode beschrieben, und die Ergebnisse eines Zahlenbeispieles werden mitgeteilt.
Swimming of a Flexible Hydrofoil near a Free Surface
Authors: Reece J. W. , Siekmann J.
Published: June 2007

This paper represents some of the results obtained from a study which extended an exact linearized potential theory to include the problem of the thrust generated by an oscillating, flexible, flat, two‐dimensional plate of zero thickness moving near the free surface of an ideal incompressible fluid. Of particular interest is the applicability of the model to the problem of a thin flat fish (such as rays) swimming near the surface of a body of water. The theoretical expression for the thrust is presented and it is shown to reduce to that obtained previously by a different method for the case of swimming at an infinite depth. Numerical results are given for swimming at both shallow and infinite depths.
On Nonhomogeneous Elastic Spheres
Authors: Huston R. L.
Published: June 2007

Radial deformation due to body forces and free radial vibration of nonhomogeneous elastic spheres is investigated. The elastic coefficients and the mass density are taken to vary as the n‐th power of the distance from the sphere center. The boundary conditions are general insofar as spherical symmetry is maintained. The stress‐displacement relations of Stojanovitch are used and solutions are obtained through the use of a generalized finite Hankel transform.
Die Äquivalenz der Methode Galerkins mit der Methode von Ritz für nichtlineare Operatoren
Authors: Kodnár R.
Published: June 2007

Die Untersuchung der qualitativen Eigenschaften quasilinearer und nichtlinearer Differentialgleichungen und der in ihnen vorkommenden Operatoren befindet sich noch im Anfangsstadium. Eine systematische Theorie ist bei weitem noch nicht aufgebaut worden, und das Studium der einzelnen Eigenschaften ist in erster Linie auf praktische Ziele, insbesondere auf die Möglichkeit einer unmittelbaren Ausnützung dieser Eigenschaften ausgerichtet.

Der wesentliche Inhalt dieses Aufsatzes besteht in der Untersuchung der Äquivalenz zwischen der Galerkinschen Methode und der Methode von Ritz für das System der quasilinearen Differentialgleichungen v. Kármáns. Auf dieses System führen die geometrisch nichtlinearen Aufgaben der schlanken Wände.
Der Äquivalenzsatz und die parabolische Methode für schallnahe Strömungen
Authors: Zierep Jürgen
Published: June 2007

Der Äquivalenzsatz für schallnahe Strömungen gestattet, die dreidimensionale Umströmung eines dünnen Flügels kleiner Spannweite auf diejenige um einen äquivalenten Rotationskörper zurückzuführen. Es wird gezeigt, daß diese Gesetzmäßigkeit auch von der parabolischen Methode richtig wiedergegeben wird. Hierzu wird die schallnahe Umströmung des Flügels mit der parabolischen Methode bestimmt und bewiesen, daß der zugehörige Raumeinfluß dieser Strömung ebenso groß ist wie derjenige des äquivalenten Rotationskörpers.
New High‐Order Runge‐Kutta Formulas with an Arbitrarily Small Truncation Error
Authors: Fehlberg Erwin
Published: June 2007

New high‐order Runge‐Kutta formulas for systems of first‐ and second‐order differential equations are derived. These new formulas, although similar to earlier formulas of the author, offer the advantage of a greatly reduced truncation error. By the proper choice of a parameter the leading term of the truncation error can be made arbitrarily small (but not zero) without increase of the overall computational expense per step, as compared with the earlier formulas. 24‐digit tables for the new Runge‐Kutta coefficients are presented for 8‐th through 12‐th order formulas. Two examples demonstrate the advantage of the new formulas as expressed in a substantial reduction of the number of required integration steps and, therefore, of the total computer running time as well.
Defektabschätzungen bei Differenzenverfahren
Authors: Schmidt Jochen W.
Published: June 2007

Es wird eine Methode beschrieben, nach der man zu Differenzenverfahren bei bestimmten gewöhnlichen Differentialgleichungen Fehlerschranken errechnen kann, welche nur bekannte Größen erfordern und außerdem die Ordnung der Differenzenverfahren richtig wiedergeben. Hierzu wird wesentlich benutzt, daß sich Randwertaufgabe und Differenzenverfahren als zueinander benachbarte Fixpunktgleichungen darstellen lassen. In die Schranke für die Abweichung ihrer Fixpunkte geht vor allem der Defekt der Näherung ein. Auf seine Abschätzung konzentriert sich ein großer Teil der Ausführungen, wobei insbesondere die geringe Differenzierbarkeit der auftretenden Greenschen Funktion zu berücksichtigen ist. — Einige numerische Beispiele bilden den Abschluß.
Der Spannungs‐ und Verschiebungszustand in homogen‐ und inhomogen‐elastischen Ringen
Authors: Saumweber Eckart
Published: June 2007

In der vorliegenden Arbeit wird der Spannungs‐ und Verschiebungszustand für das ebene Problem für folgende Fälle ermittelt: 1. Für einen aus einzelnen homogenen und elastisch‐isotropen Ringen gleicher Dicke bestehenden Verbundkörper February Für einen Ring, dessen Elastizitätsmodul nach dem Gesetz E = K(r/a)n ( K, an und n sind Konstanten) mit dem Radius r veränderlich ist. 3. Für eine rotierende Scheibe veränderlicher Dicke unter Berücksichtigung von Wärmespannungen; die vorgegebene Scheibe wird durch Teilschieben ersetzt, deren Dickenverlauf mit Hilfe von Potenzgesetzen mit jeweils verschiedenem Exponenten an das vorgegebene Profil angepaßt wird.
An Exact Analysis of Laminar Magnetohydrodynamic Flow in the Entrance Region of a Flat Duct
Authors: Manohar R.
Published: June 2007

A numerical method for obtaining solutions of laminar boundary layer equations for incompressible fluids due to Hartree has been modified here to obtain solutions of the problem of laminar flow of a conducting fluid with constant properties in the entrance region of a semi‐infinite flat duct with a transverse magnetic field. The non‐linear equations governing the flow in the entrance region are solved numerically for various values of Hartmann numbers and the corresponding velocity profiles, pressure distribution and inlet length are obtained. The same method can be applied to other problems of similar nature.
Non‐Newtonian, Non‐Isothermal Liquid Boundary Layers
Authors: Steverding B.
Published: June 2007

The problem of solving two‐dimensional, non‐isothermal, non‐Newtonian boundary layer flow is of great importance in treating ablation phenomena of glassy substances. Many organic or inorganic glassy materials are shear thinning especially when they contain gas bubbles. The liquid layer equations for viscous non‐Newtonian flow are integrated in the vicinity of the stagnation point, when non‐Newtonian flow deviations are caused by shear as well as by the pressure gradient. Numerical results for an ablating model substance with the physical properties of a silicaborate glass (Pyrex) but varying shear rate dependency are given at several altitudes.
Two Generalizations of the Stokes Formula for a Porous Sphere
Authors: Gheorghitza St. I.
Published: June 2007

A slow stationary motion of a uniformly flowing viscous liquid in the presence of a porous sphere is considered. First it is assumed that the filtration coefficient has constant values for r ϵ (O, b) and r ϵ (b, a) and that Darcy's law holds in the porous medium. Next, the problem of motion is discussed for the case where the sphere is homogeneous yet the initial value of the gradient exists.

The formulae obtained for the forces acting on the sphere generalize the results obtained previously for a porous homogeneous sphere under the validity of Darcy's law.
Second‐Order Change of Volume in Isotropic Materials Free from Applied Loads
Authors: Wang Áskýc.
Published: June 2007

The apparent elasticities of an isotropic elastic material in undistorted states are obtained from the second‐order elasticity theory. The results are applied to find the second‐order change of volume for an isotropic body free from external loads. In particular, the requirement that the material is hyperelastic is shown to be equivalent to Zener's formula.
Zur Konvergenz der Eigenvektoren beim Jacobi‐Verfahren
Authors: Pasedach Klaus
Published: June 2007

Das Iterationsverfahren von Jacobi dient bekanntlich dazu, gleichzeitig sämtliche Eigenwerte und Eigenvektoren einer hermiteschen Matrix zu approximieren. Hier wird für den Fall lauter einfacher Eigenwerte die Differenz der exakten und genäherten Eigenvektoren abgeschätzt, und zwar sowohl für das klassische als auch für das spezielle zyklische Jacobi‐Verfahren. Für diese Abschätzung wird in Satz 1 der kleinste Abstand zweier Eigenwerte der vorgelegten Matrix benötigt. In Satz 2 dagegen kommt nur der kleinste Abstand zweier Diagonalelemente derjenigen Matrix vor, die im Laufe des Jacobi‐Verfahrens diagonalisiert wird.
Statische Stabilität nichtlinear elastischer Kontinua mit Anwendung auf Schalen
Authors: Neuber H.
Published: June 2007

Durch Untersuchung des indifferenten Gleichgewichtszustandes lassen sich mehrdimensionale Stabilitäts‐probleme im nichtlinear elastischen Bereich auf eine lineare Theorie zurückführen. In vorliegender Arbeit wird diese Theorie für zwei verschiedene nichtlineare Ansätze formuliert und auf Schalen angewandt.
Zur Segmentapproximation mit Polynomen
Authors: Meinardus Günter
Published: June 2007

Ch. L. Lawson hat kürzlich eine Theorie der rationalen Segmentapproximation aufgestellt. In der vorliegenden Note wird untersucht, wie die besten Trennpunkte im Falle der Polynomapproximation berechnet werden können. Hierbei wird ein Monotonieprinzip wesentlich benutzt, über das in der voranstehenden Arbeit berichtet wurde.
Systeme nichtlinearer Integralgleichungen mit positiv definiten Kernen
Authors: Petry W.
Published: June 2007

Für nichtlineare Integralgleichungssysteme vom Hammersteinschen Typ mit symmetrischen positiv definiten Kernen werden zwei Existenzsätze angegeben, die den Sätzen von Hammerstein und Schaefer für eine Integralgleichung äquivalent sind. Die Bedingung der Darstellbarkeit des nichtlinearen Teils des Integralgleichungssystems als Gradient eines Skalars, die bei der Behandlung mittels der Variationsmethode stets auftritt, ist nicht notwendig. Die Sätze werden auf allgemeinere Integralgleichungssysteme übertragen. Zwei Beispiele werden angegeben.
Mechanische Quadraturverfahren durch sukzessive Intervallteilung
Authors: Bandemer H.
Published: June 2007

In Erweiterung der Pólyaschen Definition wird als mechanisches Quadraturverfahren eine Folge linearer Funktionale definiert, in denen neben Funktionswerten auch Werte der Ableitungen aus einem vorgegebenen Intervall vorkommen. Wenn in der Folge die Ableitungsordnungen beschränkt bleiben, sind die bekannten Bedingungen von Stekloff für die Konvergenz noch hinreichend. Es wird untersucht, welche Form die Bedingung der Polynomkonvergenz bei Verfahren annimmt, die auf sukzessiver Intervallteilung beruhen, wobei sich das Romberg‐Verfahren als einfacher Spezialfall erweist.
Die Spannungsfunktionen des Cosserat‐Kontinuums
Authors: Kessel S.
Published: June 2007

Die Gleichgewichtsbedingungen des Cosseratschen Kontinuums werden durch einen vollständigen Spannungsfunktionenansatz identisch erfüllt. Die Spannungsfunktionen eines kinematisch verträglichen Spannungszustandes in einem elastisch isotropen Kontinuum lassen sich aufbauen aus Potentialfunktionen und Lösungen von Helmholtz‐Gleichungen.
Berechnung von Kerbfaktoren gezogener Scheiben bei nichtlinearem Elastizitätsgesetz
Authors: Gajewski H.
Published: June 2007

Mit Hilfe eines Näherungsverfahrens werden die Koeffizienten der Spannungskonzentration gezogener Scheiben mit tiefen und flachen Kerben auf der Grundlage nichtlinearer Spannungs‐Dehnungs‐Beziehungen berechnet.
Modified Matrix Factorizations for Solving Systems of Nonlinear Equations
Authors: Hoy A. , Schwetlick H.
Published: June 2007

The modified Cholesky factorization due to Gill and Murray as well as an adaptation to the case of nonsymmetric LU‐factorizations described in the literature often generate modified Newton directions which are badly scaled. In order to overcome the deficiencies observed a new technique for modifying LU‐factorizations is proposed which avoids extreme differences in the pivot size and, therefore, leads to more balanced directions. Under appropriate assumptions the global convergence is proved. Some numerical examples demonstrate that the new method is suitable to deal with singular points occurring in the intermediate stages of the iterative process.
Ein Runge‐Kutta‐Nyström‐Formelpaar der Ordnung 10(11) für Differentialgleichungen der Form y′ = f(x, y)
Authors: Fehlberg E. , Filippi S. , Gräf J.
Published: June 2007

Es wird ein neues explizites, direktes Runge‐Kutta‐Nyström‐Formelpaar der Ordnung 10(11) mit insgesamt 17 f‐Werten pro Schritt für Anfangswertaufgaben bei gewöhnlichen Differentialgleichungen zweiter Ordnung der speziellen Form y′ = f(x, y) aufgestellt. Die Güte dieses Verfahrens wird anhand von zwei numerischen Beispielen demonstriert.
Monotone Enclosure of Solutions for not Necessarily Convex Operator Equations and Applications to Mildly Nonlinear Boundary Value Problems
Authors: Krätzschmar M.
Published: June 2007

Monotone methods are applied to nonlinear operator equations in order to obtain sequences of upper and lower bounds for solutions. It is shown, that by relaxed regularity conditions to the ordering the sequences converge monotonically and superlinearly, too. The assumptions on the starting points are relaxed by consideration of different orderings in the range of the operator. The results are applied to mildly nonlinear boundary value problems.
Synthesis of Unsymmetrical Bolaform Surfactants with a Sulfonate Group and a Carboxyl Group
Authors: Jiang Yurong , Xu Zhigang , Luan Jimei , Liu Pingqin , Qiao Weihong , Li Zongshi
Published: June 2007

Three unsymmetrical bolaform surfactants with different aromatic rings and a ω‐carboxyalkyl chain were synthesized and their molecular structures were characterized by ESI–MS and1H NMR. The percentages of conversion of alkylation were judged by the iodine value measurements and the effect of reaction temperature on sulfonate content of synthesized products has also been discussed.
Oily Grime Formed on Hard Surfaces of Kitchen Appliances: (Part 2) Kinetics of Oily Grime Removal
Authors: Yamada Kaoru , Tsutsui Takuya , Natsuhara Masahiko , Tanizawa Yoshiaki
Published: June 2007

The oily grime adsorbed to the surfaces of kitchen appliances ages to become difficult to remove using normal dishwashing detergents. Artificial grime models similar to actual grime were prepared using composition data of the oily grime obtained in previous work. To evaluate typical cleaning products, one needs to observe their efficacy against actual and artificial grime using precise and objective evaluation methods. In the present work, the kinetic method was applied to actual kitchen grime. The grime‐removal rate constants were calculated by monitoring absorbance of the cleaning fluids, and the results are discussed based on the compositions of the detergents and grime. One commercial detergent, with pH adjusted to 9.7, consisted mainly of spirit solvent and had two rate constants, k1 (fast) and k2 (slow), which indicated the removal rates of THF‐soluble and THF‐insoluble oily grime, respectively. With a second commercial detergent that contained mainly an alkali agent at pH 11.8, the removal rates were extremely fast for both THF‐soluble and THF‐insoluble grime. The alkalinity worked effectively against both types of grime. The effects on the removal rates of various ingredients that could be added to the cleaning products were also investigated and the overall removal rates were highly dependent on the pH of the fluids and slightly dependent on the kinds of alkalies used. The present kinetic method was found to be useful for evaluating the capability of the detergents. The plural rate constants observed for a single grime sample, which previously were not well understood, could be interpreted in terms of the compositions of the grime.
Dietary Lipids Impacts on Healthy Ageing
Authors: Okuyama Harumi , Yamada Kazuyo , Miyazawa Daisuke , Yasui Yuko , Ohara Naoki
Published: June 2007

Healthy ageing is gaining attention in the lipid nutrition field. As in vivo biomarkers of healthy ageing, we have evaluated the survival, learning/memory performance, and physical potencies in rodents fed a diet supplemented with high‐linoleic acid (LNA, ω6) safflower oil or high‐α‐linolenic acid (ALA, ω3) perilla oil for long periods. The results suggested that perilla oil with a low ω6/ω3 ratio is beneficial for healthy ageing. In order to address this issue further, we determined the survival of stroke‐prone SHR (SHRSP) rats fed a conventional rodent diet supplemented with 10% fat or oil. Survival was longer with ω3‐rich oils compared with ω6‐rich oils. However, some kinds of vegetable oils and hydrogenated oils shortened the survival of SHRSP rats to an unusual degree (ca. 40% compared with that of ω6‐rich oil) that could not be accounted for by the fatty acid and phytosterol composition of the oils. The observed decrease in platelet counts was associated with pathological changes in the kidney and other organs. Dihydro‐vitamin K1 is proposed as a likely candidate as a stroke‐stimulating factor in hydrogenated oils. Thus, factors other than fatty acids (ω6/ω3 balance) and phytosterols must be taken into account when fats and oils are evaluated in relation to healthy ageing.
Enumeration Schemes for Restricted Permutations
Authors: VATTER VINCENT
Published: June 2007

Zeilberger's enumeration schemes can be used to completely automate the enumeration of many permutation classes. We extend his enumeration schemes so that they apply to many more permutation classes and describe the Maple packageWilfPlus, which implements this process. We also compare enumeration schemes to three other systematic enumeration techniques: generating trees, substitution decompositions, and the insertion encoding.
Expected magnitude of the aerosol shortwave indirect effect in springtime Arctic liquid water clouds
Authors: Lubin Dan , Vogelmann Andrew M.
Published: June 2007

Radiative transfer simulations are used to assess the expected magnitude of the diurnally‐averaged shortwave aerosol first indirect effect in Arctic liquid water clouds, in the context of recently discovered longwave surface heating of order 3 to 8 W m−2 by this same aerosol effect detected at the Barrow, Alaska, ARM Site. We find that during March and April, shortwave surface cooling by the first indirect effect is comparable in magnitude to the longwave surface heating. During May and June, the shortwave surface cooling exceeds the longwave heating. Due to multiple reflection of photons between the snow or sea ice surface and cloud base, the shortwave first indirect effect may be easier to detect in surface radiation measurements than from space.
Chorus source properties that produce time shifts and frequency range differences observed on different Cluster spacecraft
Authors: Chum J. , Santolík O. , Breneman A. W. , Kletzing C. A. , Gurnett D. A. , Pickett J. S.
Published: June 2007

We present an explanation of frequency range differences and time shifts between corresponding chorus elements of whistler mode chorus which have been recently observed on multiple Cluster spacecraft. We show that a nonmoving or quasi‐static source that emits waves in a relatively narrow interval of wave normal angles and that varies both the wave normal angle and frequency during the generation of a single chorus element can reproduce these observations. To validate this model, we perform a ray tracing analysis from a source located close to the geomagnetic equator to simulate the dispersion properties and relative timing of the chorus elements observed at different spacecraft. We demonstrate that the ray tracing simulation leads to patterns which are very similar to those observed.
Two‐dimensional hybrid model of wave and beam heating of multi‐ion solar wind plasma
Authors: Ofman L. , Viñas A. F.
Published: June 2007

We study the heating and the acceleration of protons and heavy ions by waves in the solar wind, as well as the nonlinear influence of heavy ions on the wave structure, using a two‐dimensional (2‐D) hybrid model. Protons and heavy ions are treated kinetically by solving their equations of motion in the self‐consistent electric and magnetic fields of the waves, while electrons are treated as a neutralizing background fluid. We use the 2‐D hybrid code to investigate more realistic 2‐D plasma model than previous 1‐D simulation and analytical studies, which allows parallel as well as obliquely propagating waves and localized driver. Using the hybrid code, we consider for the first time the heating and acceleration of protons and heavy ions by a driven‐input spectrum of Alfvén/cyclotron waves and by heavy ion beam in the multispecies coronal plasma in two spatial dimensions. We find that the ion beam is more efficient in generating temperature anisotropy than the driven wave spectrum in our model. We discuss the observational implication of the results to the solar wind.
Meridional overturning circulation of the deep Pacific estimated assuming the vertical advective‐diffusive balance
Authors: Endoh Takahiro , Hibiya Toshiyuki
Published: June 2007

Assuming the vertical advective‐diffusive balance, we calculate the meridional overturning circulation of the deep Pacific based on the observed density field. In addition to the global distribution of diapycnal diffusivity in the pycnocline, bottom‐intensified mixing that follows a Gaussian distribution with depth is taken into account. When diapycnal diffusivity in the pycnocline is assumed to extend uniformly to the bottom, the northward transport of the Lower Circumpolar Deep Water (LCDW) across the equator is only 1 Sv. When the bottom‐intensified mixing is incorporated, the meridional overturning circulation increases, decreases, or even reverses depending on the vertical gradient of diapycnal diffusivity. The northward transport of the LCDW crossing the equator becomes comparable to the estimates from previous current meter moorings as well as hydrographic surveys only when the mixing extends well above the rough ocean bottom and hence the vertical gradient of diapycnal diffusivity is small.
SUMO junction—what's your function?
Authors: Kerscher Oliver
Published: June 2007

The small ubiquitin‐like modifier, SUMO, can be covalently linked to specific proteins and many substrates carrying this modification have been identified. However, for some proteins, the role that SUMO modification imparts remains obscure. Our understanding of SUMO biology and function has been significantly advanced by the recent discovery of proteins and protein domains that contain SUMO‐interacting motifs (SIMs), which interact non‐covalently with SUMO. Unlike the motifs and domains that mediate ubiquitin binding, the diversity of SIMs seems limited. Nevertheless, SIMs have already increased our understanding of how SUMO affects DNA repair, transcriptional activation, nuclear body formation and protein turnover. This review takes a detailed look at how SIMs were identified, how they specifically bind to SUMO, their crucial roles in multi‐step enzymatic processes, and how they direct the assembly and disassembly of dimeric and multimeric protein complexes.
Arterial adaptations to chronic changes in haemodynamic function: coupling vasomotor tone to structural remodelling
Authors: Dajnowiec Dorota , Langille B. Lowell
Published: June 2007

Healthy mature arteries are usually extremely quiescent tissues with cell proliferation rates much below 1%/day and with extracellular matrix constituents exhibiting half-lives of years to decades. However, chronic physiological or pathological changes in haemodynamic function elicit arterial remodelling processes that may involve substantial tissue synthesis, degradation or turnover. Although these remodelling processes accommodate changing demands placed upon the cardiovascular system by physiological adaptations, they can compromise further perfusion in the context of arterial occlusive disease and they entrench hypertension and may exacerbate its progression. Recent findings indicate that some of the most important such remodelling responses involve the integrated effects of persistently altered vascular tone that feed into restructuring responses, with common signalling pathways frequently interacting in the control of both phases of the response. Current efforts to define these signals and their targets may provide new directions for therapeutic interventions to treat important vascular disorders.