bluuebunny/crossref_metadata_2025 huggingface dataset:
Zur Theorie der Windkanalturbulenz1. Mitteilung
Authors: Tollmien W. , Schäfer Manfred
Published: May 2007

Nach einem Überblick über frühere Arbeiten wird durch Linearisierung der hydrodynamischen Differentialgleichungen ein mathematisches Modell der Windkanalturbulenz aufgestellt, ohne die übliche Annahme der Isotropie zu machen. Für das Randwertproblem der linearisierten hydrodynamischen Differentialgleichungen wird eine Integrationstheorie entwickelt. Dabei ergibt sich eine Trennung der Strömung in eine Potential— und Diffusionsströmung. Mittelwerte dieser Strömungen werden diskutiert.
Der Kompressibilitätseinfluß für dünne wenig gekrümmte Profile bei Unterschallgeschwindigkeit .
Authors: Hantzsche W. , Wendt H.
Published: May 2007

Für die Berechnung von höheren Näherungen kompressibler Unterschallströmungen um dünne wenig gekrümmte Profile wird ein Verfahren angegeben, das von der Prandtlschen Näherung für schlanke Profile ausgeht und für alle unterkritischen Machschen Zahlen gilt. Dazu wird die Stromfunktion nach einem Parameter entwickelt, der die Abweichung der Profilform in Dicke, Wölbung und Anstellwinkel von einem‐ geraden nichtangestellten Streckenprofil charakterisiert. Das erste Glied der Reihe stellt die ungestörte Parallelströmung dar. Die beiden ersten Glieder entsprechen der Prandtlschen Näherung. Die neue Verbesserung für etwas dickere Profile ergibt sich durch Hinzunahme des dritten Gliedes. Die Methode wurde in einigen Beispielen für die maximale Übergeschwindigkeit und den Auftrieb ausgewertet, die beide stärker mit der Machschen Zahl anwachsen als nach der Prandtlschen Formel.
Strömungen über Bodenerhebungen auf der rotierenden Erde
Authors: Rothstein W.
Published: May 2007

Die von H. Görtler aufgestellten Gleichungen für die Strömung einer volumbeständigen Flüssigkeitsschicht konstanter Dichte über Bodenerhebungen auf der rotierenden Erde werden für den Fall endlich ausgedehnter Bodenerhebungen behandelt. Dabei wird jedoch zunächst der in jenen Gleichungen erfaßte Reibungseinfluß vernachlässigt. Als Beispiele werden durchgerechnet ein Berg mit kreisförmigen und ein Berg mit elliptischen Höhenlinien.
Zur Kinematik des Rollgleitens
Authors: Grü Gerhard
Published: May 2007

Zur Klärung der kinematischen Verhältnisse beim Rollgleiten werden die beiden Polkurvenscharen, die raumfesten Spurkurven und die für den sich bewegenden Körper, körperfesten Rollkurven für alle Bewegungszustände vom reinen Gleiten bis zum reinen Rollen bestimmt.
Bemerkungen zur Entwicklung gegebener Funktionen nach Legendreschen Polynomen mit Anwendung auf die numerische Integration gewöhnlicher linearer Differentialgleichungen
Authors: Fehlberg Erwin
Published: May 2007

Teil I: Zur Berechnung der Koeffizienten, die bei der Entwicklung gegebener Funktionen nach Legendreschen Polynomen auftreten, wird die zu entwickelnde Funktion abschnittsweise durch Parabeln 4ter Ordnung ersetzt und das Produkt dieser Näherungsparabeln mit den entsprechenden Legendreschen Polynomen exakt integriert.

Teil II: Für die gewöhnliche lineare Differentialgleichung 2‐ter Ordnung wird die erste Randwertaufgabe numerisch gelöst, indem die Koeffizienten der Differentialgleichung nach Legendreschen Polynomen entwickelt werden und für die Lösung eine nach Legendreschen Polynomen fortschreitende Reihe mit unbestimmten Koeffizienten angesetzt wird. Die Berechnung der allgemeinen Lösung wird so auf die Auflösung eines linearen Gleichungensystems zurückgeführt. Die spezielle Lösung der Randwertaufgabe kann numerisch so angegeben werden, daß darin die rechte Seite der Differentialgleichung sowie die Randwerte noch völlig offen bleiben.
Breakdown of Laminar Shearing Flows for Second‐Order Fluids in Channels of Critical Width
Authors: Coleman Bernard D. , Mizel Victor J.
Published: May 2007

The flow of a general incompressible second‐order viscoelastic fluid is described by a third‐order nonlinear vectorial partial differential equation. We here discuss the theory of that equation for the case in which the fluid is flowing between two parallel plates with separation h. We show that for certain critical channell‐widths has flow which is initially a laminar shearing flow cannot remain so. In fact, for these critical values of h, if there is any flow at all the departure from shearing flow must appear instantly in the first time‐derivative of the velocity. This result, which has no analogue in the Navier‐Stokes theory, sheds light on a nonexistence theorem obtained by Coleman, Duffin, and Mizel [6] for the linear equation describing second‐order fluids in shearing flow.
On Bending of a Parallelogram Plate
Authors: Aggarwala B. D.
Published: May 2007

Bending of a parallelogram plate under various kinds of loading has been investigated. The following kinds of loads are considered (1) Isolated load at the center of the plate, (2) Uniform load, (3) Load distributed over a central circular area, (4) Isolated load at an arbitrary point of the plate, (5) Load distributed over an arbitrary circular area of the plate. Various numerical results are given.
Upper and Lower Bounds for the Frequencies of Rectangular Cantilever Plates
Authors: Bazley N. W. , Fox D. W. , Stadter J. T.
Published: May 2007

The authors use a recently developed procedure for lower bounds and the Rayleigh ‐ Ritz procedure for upper bounds to estimate frequencies of free vibration of thin rectangular cantilever plates. The applicability of the lower bound procedure is demonstrated, and calculations are given for a symmetry class of normal modes. The lower bounds seem to be the first rigorously obtained for this problem. The upper bounds are improvements over previously published rigorous results.
Integrabilität und Integration überbestimmter Systeme partieller Differentialgleichungen
Authors: Apostolatos N. , Kulisch U.
Published: May 2007

Frühere Arbeiten ([1], [2], [3]) der Verfasser beschäftigten sich bereits mit der Integration überbestimmter Systeme partieller Differentialgleichungen. Darin wurden jedoch nur solche Probleme behandelt, bei denen ein Teil der Gleichungen quasilinear ist. In der vorliegenden Arbeit werden allgemein Systeme partieller Differentialgleichungen untersucht, bei denen die Anzahl der Gleichungen größer ist als die Anzahl der gesuchten Funktionen. Im ersten Teil wird die Frage der Existenz von Lösungen solcher Systeme sowie die ihrer vollständigen Integrabilität behandelt. Der zweite Teil bringt zwei Methoden zur Integration vollständig integrabler Systeme mittels gewöhnlicher Differentialgleichungen. Eine Fortsetzung der vorliegenden Arbeit beschäftigt sich mit einigen Anwendungen der Integrabilitäts‐ und Integrationstheorie auf die Behandlung von Anfangswertproblemen bei partiellen Differentialgleichungen.
Die Ausgangsgestalt Eulerscher Elastika bei gegebenem Belastungs‐ und Deformationszustand
Authors: Löbel G.
Published: May 2007

In der Theorie der Deformation von Körpern unterscheidet man zwei Grundaufgaben: die Ermittlung des Deformationszustandes bei vorgegebenem Ausgangszustand, d. h. des Zustandes vor der Belastung, und die Ermittlung des Ausgangszustandes bei vorgegebenem Deformationszustand.

Die vorliegende Arbeit demonstriert die zweite Aufgabe anhand Eulerscher Elastika, unter Beschränkung auf konstante Krümmung im Deformationszustand. Es wird gezeigt, daß im Falle geometrisch nichtlinearer Biegedeformationen die beiden Aufgaben zu grundsätzlich verschiedenen Ergebnissen führen.

Praktische Bedeutung kommt den Ergebnissen bei der Herstellung von Kolbendichtungsringen für verschiedenste Aggregate, vorzugsweise jedoch für Kompressoren und Motoren, zu.
Slow Steady Flow of an Idealized Elastico‐Viscous Incompressible Fluid of Oldroyd Type Through a Straight Tube with an Arbitrary Cross‐section
Authors: Ramacharyulu N. Ch. Pattabhi
Published: May 2007

In this paper, slow steady flow of an idealized elastico‐viscous liquid through a straight tube is discussed. Perturbation technique is employed to linearize the equations of motion and state. We observe that the flow, under the influence of a constant pressure gradient down the axis of the tube, is a rectilinear flow over which a secondary flow is superposed in planes perpendicular to the length of the tube. The basic equations derived are solved with the function theoretic method. The solution for any arbitrary cross‐section of the tube is obtained. The case of a tube with an elliptic‐limacon cross‐section is given as an example.
The Axisymmetric Response of a Complete Cylindrical Shell to Shock Loads
Authors: Stadler W. , Wang J. T. S.
Published: May 2007

The bending theory of thin shells is used to obtain the dynamic response of a complete cylindrical shell of finite length. The shell is subjected to axisymmetric dynamic loads, normal to the shell surface. The effects of the inertial load in the longitudinal direction are assumed to be negligible. The general solution is exact within the theory, and it is presented in a concise form, which simplifies its application to specific boundary‐value problems. The natural frequencies are calculated from transcendental equations obtained by the application of the respective boundary conditions to the general solution. An illustrative example of a clamped cylindrical shell subjected to a uniform shock with linear decay is presented, including numerical results.
Hydrodynamic Stability of a Laminar Boundary Layer with Transverse Curvature Effect
Authors: Rao G. N. V.
Published: May 2007

A study of the hydrodynamic stability of the boundary layer with transverse curvature has been made on the basis of linear theory. Defining ζ as the transverse curvature parameter, (essentially the ratio of boundary layer thickness to the radius of transverse curvature), it is found that axisymmetric mode of disturbance is the most critical up to O(ζ). The transverse curvature itself is found to be destabilizing but the velocity profile due to it can in certain cases make the flow stable. In fact, for the boundary layer flow on a circular cylinder moving axially, it is found that all small disturbances will be damped out if the Reynolds number based on the radius is less than about 11 000.
Profile in ebener Scherströmung
Authors: Sockel H.
Published: May 2007

Bei nahezu konstanter Scherung der inkompressiblen reibungsfreien Grundströmung kann man dieser beliebige Potentialströmungen überlagern. Daher ist es auch möglich, die Methode der Singularitätenbelegung zur Darstellung der Strömung um Profile heranzuziehen. Die auf eine einzelne Singularität wirkende Kraft und der Einfluß der Singularitäten auf die Profilkräfte werden berechnet. Kennt man Wirbel‐ und Quellverteilung für ein Profil in Parallelströmung mit konstanter Geschwindigkeit, so kann man damit sofort die Beiwerte für Auftrieb und Moment für dasselbe Profil in einer Scherströmung in erster Näherung ermitteln. Für die angestellte ebene Platte wird eine exakte Lösung angegeben.
A note on the vibration of thin inhomogeneous plates
Authors: Komkov V.
Published: May 2007

The basic equations of motion and/or of static deflection of inhomogeneous plates are reduced to the generalized form of Hamilton's equations. An existence of corresponding variational principles is demonstrated directly from these equations.
Minimale Gerschgorin‐Kreise
Authors: Elsner L.
Published: May 2007

Die Theorie minimaler Gerschgorin‐Kreise wird auf den Fall erweitert, daβ mehrere Kreise mit gleichem Mittelpunkt von den übrigen getrennt werden können. Wie im Falle eines Kreises ergibt sich auch hier, daβ der kleinste Gerschgorin‐Radius Λo Eigenwert einer gewissen Matrix ist. Die Resultate können zur Fehlerabschätzung beim Jacobi‐Verfahren bei gehäuften Eigenwerten benutzt werden. Hinreichende Kriterien für die Trennbarkeit, die Porsching angegeben hat, sind auf diesen Fall übertragbar.
Der Einfluß starker Unstetigkeitsfronten auf Unterschallströmungen um Profile
Authors: Rues D.
Published: May 2007

Es wird der Einfluß einer starken Unstetigkeitsfront auf das Feld einer inkompressiblen Strömung um ein Profil untersucht. Das Strömungsfeld wird getrennt auf beiden Seiten der Unstetigkeitsfront mit Hilfe der linearisierten Gleichungen berechnet. Diese beiden Felder werden auf der Front durch die Forderung nach gleichem Druck und gleicher u‐Komponente der Geschwindigkeit aneinander angeschlossen. Als numerische Beispiel wird der Einfluß der Unstetigkeitsfront auf die Strömung um ein Parabelbogenprofil behandelt.
Thermal stresses in a polygonal cylinder with a circular hole under internal heat generation
Authors: Takeuti Yoitiro , Sekiya Tsuyoshi
Published: May 2007

This paper is concerned with a treatment of thermoelastic problems for a multiply connected cross section in polygonal cylinder under uniform internal heat generation. In the first part of this paper a general theory is presented for thermal stress analysis in multiply connected region which has been subjected different temperature distribution of unsteady or steady state. As examples of the above theory, in the second part, approximate numerical solutions are obtained by the point‐matching method for the thermal stress distribution of the polygonal cylinder with a central circular hole having the thermally insulated outer boundary under uniform heat generation.
Heat conduction in fluids with substructure
Authors: Kline K. A. , Allen S. J.
Published: May 2007

The basic equations for a theory of fluids with concentrated suspensions are applied to the problem of viscous flow between two heated plates.

The velocity, stresses and heat transfer are determined.
Optimale Formen des dünnwandigen geschlossenen Querschnittes eines Balkens bei Berücksichtigung von Stabilitätsbedingungen
Authors: Z̊yczkowski M.
Published: May 2007

Es wird allgemein das Problem der optimalen dünnwandigen Querschnittsform eines Balkens unter reiner Biegung gestellt. Als Optimalitätskriterium wird minimale Querschnittsfläche angenommen, unter den Nebenbedingungen: Beschränkte Spannungen, Kippstabilität des ganzen Balkens und lokale Wandstabilität. Gelöst wird eine vereinfachte Aufgabe, bei der Doppelsymmetrie, konstante Profildicke h und gegebene Breite b, aber verschiedenartige Nebenbedingungen vorliegen. Die minimalen Ausmaße h und b werden aus den Stabilitäts‐bedingungen bestimmt.
Über Näherungsverfahren zur Lösung einer singulären linearen Integrodifferentialgleichung
Authors: Schleiff M.
Published: May 2007

In der vorliegenden Arbeit wird die Konvergenz der Abschnittsmethode und der Kollokationsmethode von Multhopp zur numerischen Lösung einer singulären linearen Integrodifferentialgleichung nachgewiesen, die in der Tragflügel‐ und Propellertheorie und in der Elastizitätstheorie vorkommt. Beim Konvergenzbeweis wird wesentlich von der umkehrbar eindeutigen Abbildung des Hilbertraums L2[0, π] auf den Folgenraum l2 der Fourierkoeffizienten Gebrauch gemacht.
Large Elastic Deformations of an Infinite Plate Having a Square or Triangular Hole with Rounded Corners under Biaxial Tension
Authors: Tamate O. , Miyata H.
Published: May 2007

This paper deals with the stresses and diplacements of elastic media, based upon the theory of finite elasticity, perforated by a square or triangular hole with rounded corners subjected to biaxial tension at infinity. The material is assumed to be in the state of plane strain. The method of successive approximation is used in connection with the complex variable method of plane elasticity.

Numerical results due to the second‐order elasticity are given for hoop stresses and displacements along the edge of hole, and compared with those predicted by classical theory of elasticity.
A Method for the Solution of Conduction Heat Transfer with Non‐linear Heat Generation
Authors: Na T. Y. , Tang S. C.
Published: May 2007

The equation governing the one‐dimensional heat conduction with non‐linear heat generation is transformed from a boundary value to an initial value problem by using a method of transformation recently presented by Na [2], [3]. The resulting equation is then integrated numerically by the Runge‐Kutta method. Critical values of a parameter are found which serve as a limit for the existence of steady‐state solutions.
Zur physikalisch‐nichtlinearen Theorie der drehsymmetrisch belasteten Rotationsschalen
Authors: De Boer R.
Published: May 2007

Mit einem nichtlinearen Stoffgesetz wird der durch Randstörungen verursachte Biegezustand von Rotationsschalen untersucht. Nach Aufstellen der allgemeinen Grundgleichungen wird zur näherungsweisen Lösung der Differentialgleichungen die Geckelersche Näherung benutzt. Danach wird eingehend die Kreiszylinderschale unter drehsymmetrischer Beanspruchung behandelt.
Eigenwerteinschließung bei gewöhnlichen Differentialgleichungen über ein Differenzenverfahren
Authors: Schönheinz H.
Published: May 2007

Die Eigenwertaufgabe bei gewöhnlichen Differentialgleichungen 2. Ordnung mit Sturmschen Randbedingungen wird nach einem Differenzenverfahren näherungsweise gelöst. Mit den so erhaltenen Näherungen lassen sich Einschließungen für die gesuchten Eigenwerte angeben. Die Herleitung dieser Einschließungen beruht auf einer äquivalenten Formulierung des verwendeten Differenzenverfahrens als Quadraturformelmethode bei Integralgleichungen. Dadurch kann ein Einschließungssatz für Eigenwertprobleme bei Integralgleichungen angewendet werden.
A Queueing Problem with Arrivals in Batches of Variable Size and Service Rate Depending on Queue Length
Authors: Murari K.
Published: May 2007

This paper deals with the behavior of a first‐come‐first‐served single channel queueing system with batch arrivals of variable size and a service rate biased towards maintaining the queue length at a pre‐assigned fixed number N. Laplace transform of the distribution function for queue length is obtained. Further, an approximate value of the generating function for queue length is obtained explicitly. Finally, some particular cases are discussed.
A Many Server Queueing Problem with Variable Departures
Authors: Sharda
Published: May 2007

The present paper studies the behaviour of a queueing system in which arrivals form a Poisson distribution and departures occur in batches of variable size. Service is accomplished in M parallel channels and each channel has the same fixed capacity of serving at the most K units. Service is ordered and instantaneous. The distribution functions for the queue length for different cases are obtained. Steady state behaviour and a few particular cases are discussed.
A Frequency Domain Approach to the Problem of the Existence of Periodic Motion in Autonomous Nonlinear Feedback Systems
Authors: Noldus E.
Published: May 2007

A sufficient condition for the existence of periodic motion is derived, for a class of autonomous, nonlinear feedback systems. The criterion is stated in terms of the frequency response of the linear part of the system, and the parameters, characterizing the nonlinearity. In this way, a relationship is established, with commonly used frequency domain theorems, in the stability analysis of the same type of systems.
Combined Natural and Forced Convection Hydromagnetic Flow in Vertical Channels
Authors: Das U. N.
Published: May 2007

The combined natural and forced convection fully developed flow and heat transfer of an electrically conducting fluid with and without temperature dependent heat sources in a vertical channel has been studied under the influence of transverse applied magnetic field and external circuit. The two plane walls of the channel are having the same temperature gradient along their lengths but both are art different temperatures. The system of non‐linear integro‐differential equations have been solved by an iteration method and the shearing stress and Nusselt number at the walls have been calculated. It has been found that the temperature dependent heat sources impose oscillatory behaviour on the temperature profiles and the heat transfer between the wall and the adjacent fluid changes its direction for different ranges of values of the heat source per unit volume. The magnetic field reduces the velocity but increases the temperature and the presence of linear variation of the wall temperature helps in cooling the walls.
On the Contact Problem of Thin Elastic Shells
Authors: DeSilva C. N. , Tsai P. J.
Published: May 2007

The general problem of the contact of two thin elastic shells is considered within the framework of the Kirchhoff‐Love theory by using the contact surfaces as reference. The constitutive equations are shown to have the form given by the Reissner theory when the middle surface is used as reference. The special form of the governing equations when the classical Marguerre shallow shell assumption is made is proposed for solving contact problems. As an example, the contact problem of two spherical shells is solved to yield the variation of contact pressure and the load with the radius of the contact area.
On the Residual Deformation of Elasto‐Plastically Bent Thin Circular Plate After Perfect Unloading
Authors: Ohashi Y. , Kawashima K.
Published: May 2007

An analysis on the residual deformation after perfect unloading from a large deflection was performed for a supported thin circular plate under uniform lateral load. In the analysis, different from the usual method, the equilibrium and compatibility conditions in the unloading process were considered under the influence of the deformed state at the beginning of unloading. The Kirchhoff's hypothesis for the bending of thin plate and the Masing model without the Bauschinger effect for unloading process as well as the Mises' yield condition of material were postulated.

The results of analysis were discussed in comparing with those of the corresponding experiment as well as the analysis on the unusual method for obtaining residual deformation.
A Reciprocal Theorem in the Linear Theory of Directed Continuous Media
Authors: Kline K. A.
Published: May 2007

A linear theory of directed viscoelastic media is developed using the Stieltjes convolution. A dynamic reciprocity relationship is proved.
A three dimensional elasticity solution for rectangular prism under end loads
Authors: Sundara K. T. , Iyengar Raja , Prabhakara M. K.
Published: May 2007

Für ein Rechteckprisma, an dessen Enden vorgegebene Kräfte wirken, wird auf der Grundlage der die dreidimensionale Elastizitätstheorie beherrschenden Gleichungen das Problem des dreidimensionalen elastischen Verhaltens gelöst. Die Lösung hat die Form eines Galerkin‐Vektors, dessen Komponenten in Doppel‐Fourier‐Reihen entwickelt sind, die der zugrunde liegenden biharmonischen Gleichung genügen und so gewählt sind, daß sie alle Randbedingungen befriedigen. Es werden Rechteckprismen mit symmetrischen oder exzentrischen Normalkräften an den Enden untersucht und für typische Fälle numerische Ergebnisse angegeben. Die gewonnenen Ergebnisse werden mit denen der zweidimensionalen Theorie verglichen.
Ein Runge‐Kutta‐Verfahren mit variablem Parameter α
Authors: Scholz S.
Published: May 2007

Der bei dem Runge‐Kutta‐Verfahren 2. Ordnung frei wählbare Parameter α wird nach einer gewissen Vorschrift von Schritt zu Schritt neu bestimmt, und zwar so, daß sich die Verfahrensordnung auf 3 beziehungsweise 4 erhöht. Da man hierzu Informationen über den Fehler der Näherungslösung bis zu dem jeweiligen Schritt benötigt, müssen Näherungsrechnung und Fehler(ab)schätzung direkt miteinander gekoppelt werden.
Asymptotic Theory of Wave‐Motion in Rods (Longitudinal Wave‐Motion)
Authors: Nariboli G. A.
Published: May 2007

A systematic procedure is developed for constructing dynamical theories of rods, plates, and shells, based on full three‐dimensional equations. The title problem is chosen to bring out the various difficulties. The method of asymptotic expansion, used till now for static problems, is extended to time‐dependent cases. Successive approximations give classical wave equations, the effect of lateral inertia, and the effect of transverse shear. However, two additional objectives are achieved. First, it has been possible to construct a complete and well‐posed “inner problem”; this obviates the necessity of “matching” with “boundary layer” solutions at each stage. Second a modified approach is proposed to construct higher approximations; previously known methods have led to solutions where an initial singularity worsens with higher approximations. The procedure herein developed not only avoids it but gives a physically more realistic solution.
Zur Traglinientheorie des Hubschrauberrotors
Authors: Isay W. H.
Published: May 2007

Es wird eine Methode zur Berechnung der Flügelkräfte eines Hubschrauberrotors im Vorwärtsflug entwickelt. Sie basiert auf der Wirbeltheorie des schräg angeströmten Propellers. In der vorliegenden Arbeit werden die durch die Schlag‐ und Schwenkbewegungen bedingten Lageänderungen der Rotorflügel vernachlässigt. Außerdem werden weder die Effekte der Rückwärtsanströmung noch der Schräganströmung (also des Schiebens) der Flügelblätter berücksichtigt; daher ist die Theorie auf kleinere Fortschrittsgrade beschränkt.
Über den Einfluß konstanter Parameter auf Übergangsvorgänge, Grenzzykel und Stabilitätsgrenzen
Authors: Troch I.
Published: May 2007

Es wird zunächst der Begriff der quasihomogenen Funktion eingeführt und anschließend gezeigt, daß für Differentialgleichungssysteme, die aus solchen Funktionen aufgebaut sind, die Untersuchung der Systeme mit Parametern auf die Untersuchung eines gewissen „Vergleichssystems”︁ zurückgeführt werden kann. Diese Zurückführung geschieht mit Hilfe einer Maßstabtransformation, unter alleiniger Ausnützung der Quasihomogenitätseigenschaften und kann unabhängig davon durchgeführt werden, ob das betreffende System autonom, nichtautonom, von erster oder höherer Ordnung, explizit oder implizit gegeben ist, jedoch zeigen die Untersuchungen, daß sich in Abhängigkeit von der speziellen Bauart des Systems eine Beschränkung hinsichtlich Art und Zahl der auftretenden Parameter ergibt. Anhand von Beispielen wird die Reichweite der Methode illustriert.
Vergleich der Konvergenzgeschwindigkeit des Ritzschen Verfahrens und der Fehlerquadratmethode
Authors: Nitsche J.
Published: May 2007

Als Konvergenzbegriff bei Näherungsverfahren wird das asymptotische Verhalten der Fehlernormen herangezogen. In diesem Sinne erweist sich das Ritzsche Verfahren als mindestens so gut wie die Fehlerquadratmethode. Als Anwendung wird das Sturm‐Liouville‐Problem betrachtet. Hier kann die Konvergenzgeschwindigkeit nach oben und unten abgeschätzt werden. Das Ritz‐Verfahren ist bei der Verwendung trigonometrischer Funktionen als Ansatzfunktionen i.a. besser konvergent.
Two Dimensional Splines and their Extremal Properties
Authors: Ritter K.
Published: May 2007

Let (xν, yμ) be the mesh‐points of a rectangular mesh. We consider the problem of finding functions with the property that the values of the function and of certain of its derivatives at the mesh‐points lie in prescribed intervals. Among all admissible functions satisfying these conditions we are interested in thoses functions which have an additional minimum property. It is shown that the solution of this problem leads to two‐dimensional spline functions.
Slow Flow Past an Insulator in a Perfectly Conducting Liquid
Authors: Buckmaster J. , Ludford G. S. S.
Published: May 2007

The transient plane disturbance of a stream at any angle to the applied magnetic field is studied. For an airfoil, when this angle is comparable to the thickness ratio, the potential disturbance is not comparably small. Such a result persists for non‐vanishing Alfvén numbers, so that the method developed for aligned fields will not succeed. Care is taken to show that the Alfvén waves emitted by a body are not capable of realigning the flow into the direction of the magnetic field, which would be the only way of avoiding the airfoil conclusion.
Über zwei Randwertprobleme des inhomogenen Systems der Cauchy‐Riemannschen Differentialgleichungen mit einer Anwendung auf ein Problem der stationären schallnahen Strömung
Authors: Schubert H. , Schleiff M.
Published: May 2007

Zwei Randwertprobleme eines inhomogenen Systems der Cauchy‐Riemannschen Differentialgleichungen werden in der längs der reellen Achse aufgeschlitzten Vollebene unter völlig verschiedenen Voraussetzungen gelöst. Aus den Integraldarstellungen der Lösungen werden die singulären Integralgleichungen von J. Zierep und K. Oswatitsch für die ebene stationäre schallnahe Strömung hergeleitet. Die Integralgleichung von Oswatitsch läßt sich mit einer anderen Definition des Cauchyschen Hauptwerts des singulären Integrals in die von S. G. Michlin behandelte Klasse von singulären Integralgleichungen einordnen.
Die Beziehungen zwischen den Krümmungen der Zahnoberflächen bei räumlichen Verzahnungen
Authors: Litvin F. L.
Published: May 2007

Es wird eine räumliche Verzahnung zwischen sich kreuzenden und sich schneidenden Achsen unter der Annahme, daß im Gebiet des Kontaktpunktes die erste Ableitung des Übersetzungsverhältnisses Null ist, betrachtet.

In dem Artikel wird erhalten:

eine Beziehung, die die Normalenkrümmungen der Zahnoberflächen in dem Schnitt miteinander verknüpft, der durch den Vektor der Relativgeschwindigkeit verläuft;

eine Beziehung zwischen den Hauptkrümmungen und Hauptrichtungen beider Zahnoberflächen;

neue Formeln zur Bestimmung der reduzierten Krümmung der Oberflächen.
Vibrations of Rectilinear Plates
Authors: Aggarwala B. D.
Published: May 2007

A simplified version of von Karman equations for vibrations of simply supported rectilinear plates is used to discuss vibrations of various triangular plates. An approximate analysis indicates that, when the amplitude of vibrations is equal to the thickness of the plate, the fundamental frequency is higher by about 40% as compared to the corresponding frequency for infinitesimal vibrations. A heuristic formula is given to calculate the frequencies when more than one mode of vibration is present.
Torsional wave propagation in magneto‐elastic solids with modified Maxwell Stress
Authors: Chakrabarti A.
Published: May 2007

Der Maxwellsche Ansatz für die Spannung im Innern eines homogenen isotropen elastischen Mediums in Gegenwart eines statischen Magnetfeldes wird aus der Bewegungsgrundgleichung der Magnetoelastizität abgeleitet. Man stellt fest, daß das Medium im allgemeinen seine Isotropieeigenschaft verliert. Es wird sodann die Fortpflanzung von Torsionswellen in einem massiven Kreiszylinder und in einem kreiszylindrischen Rohr, beide Male unter der Annahme eines konstanten axialen Magnetfeldes, betrachtet, wobei die Kenntnis der Maxwell‐Spannungen wesentlich ist.
Das Nyquist‐Kriterium für Regelkreise, deren Verhalten durch lineare Funktional‐Differential‐Gleichungen beschrieben wird
Authors: Herz B.
Published: May 2007

Für die untersuchte Klasse von Regelkreisen werden die für die Stabilität entscheidenden charakteristischen Funktionen und eine Übertragungsfunktion F(λ) aufgestellt. Sie erweisen sich als ganz, im allgemeinen jedoch transzendent, bzw. meromorph, im allgemeinen jedoch nichtrational. Die für imaginäre λ‐Werte durch Frequenzgangmessung erhältliche Funktion F(λ) wird hinsichtlich ihr es Wachstumsverhaltens und der Nullstellen‐ und Polverteilung eingehender studiert. Sodann wird eine Neufassung des Nyquist‐Kriteriums angegeben und bewiesen, die vom Benutzer nicht verlangt, daß er a priori Kenntnis über die Vielfachheiten gemeinsamer Nullstellen der Zähler‐ und der Nennerfunktion von F(λ) hat. Der Anwendungsbereich des Nyquist‐Kriteriums wird dadurch auch im klassischen Fall erweitert.
Report of the instrumental techniques committee AOCS, 1971–72
Authors: O’Connor R. T. , Allen R. R. , Brobst K. M. , Herb S. F.
Published: May 2007

As described in this report, the Instrumental Techniques Committee has in various stages of progress several methods which will be proposed for adoption as official methods of the AOCS. For convenience, these proposed methods and their present status are summarized in Table II.
A method for the quantitative determination of ethylene oxide adducts in their aqueous solutions or dispersions
Authors: Schönfeldt N.
Published: May 2007

A method for quantitative determination of ethylene oxide adducts is described. By precipitation in hydrochloric acid solution with a known quantity of ferrocyanic acid, filtration, and titration with zinc sulfate, the consumption of ferrocyanic acid can be determined. From the results a m.d. of less than 8% was calculated, the corresponding figure for adducts containing more than 9 ethylene oxide units does not surpass 5%. The reaction takes place on the ethylene oxide chain in the compound. To precipitate an adduct containing 6 units ethylene oxide approximately one mole of ferrocyanic acid is necessary.
Dietary lipids and arteriosclerosis
Authors: Kaunitz H.
Published: May 2007

A great deal of attention has been given to the question of whether dietary fats in general and certain fats in particular play an important part in such arteriosclerotic complications as heart attacks and strokes. Milk fats have been widely accepted as desirable nutritional fats. Cow milk fat, or butter, contains a wide variety of fatty acid derivatives, including the important, medium chain acids. The structural configuration of butter triglycerides facilitates absorption of the palmitate present in butter. However, there have been objections to the use of butter and other forms of milk fat because of the preoccupation of many investigators with the unproven lipid theory of arteriosclerosis, and because serum cholesterol levels are relatively high after the intake of milk fat. Reevaluation of the lipid theory suggests that cholesterol can hardly be an atherogenic factor. Cholesterol occurs under conditions of tissue repair, and it may well be that the high serum levels in arteriosclerotic conditions are a consequence of such processes. The low serum levels occurring after the consumption of polyunsaturated vegetable oils are often associated with high tissue levels of cholesterol. Long term clinical studies and population surveys suggest that this century’s changes in mortality and morbidity are much less related to dietary factors (other than over‐eating) than is claimed. New insights in the fields of immunology and microbiology may be vastly more important for an understanding of some etiological factors in arteriosclerosis.
Characterization of some new C16 and C17 unsaturated fatty aldehydes
Authors: Kemp Thomas R.
Published: May 2007

The following six volatile fatty aldehydes, including five new compounds have been characterized by spectral analyses (mass spectra presented) and ozonolysis:cis‐7‐hexadecenal,cis‐8‐heptadecenal (previously known),cis,cis‐7,10‐hexadecadienal,cis,cis‐8,11‐heptadecadienal,cis,cis,cis‐7,10,13‐hexadecatrienal,cis,cis,cis‐8,11,14‐heptadecatrienal. Compounds were separated (gas liquid chromatography) from a volatile concentrate prepared by reduced pressure steam distillation of an aqueous cucumber homogenate. These aldehydes were not detected by our methods when the tissue was extracted with CHCl3‐MeOH.
Paper chromatography of lipides
Authors: Schlenk H. , Gellerman Joanne L. , Tillotson Jerry A. , Mangold H. K.
Published: May 2007

Procedures for qualitative and quantitative paper chromatography of lipides have been described in detail, together with some practical applications.

With the monochain lipides it was found that one developing system serves universally. The long aliphatic chains essentially determine the chromatographic properties so that suitable conditions for chromatographing any lipide or lipide‐like entity are predictable. For the same reason total analysis of natural mixtures cannot be done on one paper chromatogram due to superpositions.

For complete analysis of natural mixtures of fatty acids it is advisable at the present time to combine paper chromatography with some other separation method. Distillation supplements best but requires gram quantities of material while paper chromatography is applicable on gamma or milligram scale. Chain‐length analysis by paper chromatography and low‐temperature chromatography have been introduced and are promising methods to approach a completely micro method for analyzing complex mixtures.
Melting and crystallization of vegetable waxes
Authors: Dodsworth Machado Raul
Published: May 2007

A rapid but sufficiently accurate method is applied to the observation of phase changes in vegetable waxes and is suggested for adoption as a routine procedure. Five indications are obtained in about 20 minutes for each sample: odor, surface appearance, initial melting, melting and crystallization points. A hot stage is used, designed by the author, and made under his supervision at the Instituto de Óleos.

Data are discussed concerning carnuauba (Copernicia cerifera, Mart.) and licuri or ouricuri (Syagrus coronata, Mart., Becc.) waxes. Some results related to carandá (Copernicia australis, Becc.), cuban carnauba, sugar cane,Heliconia farinosa, Raddi.,Heliconia pendula, Wawra., candelilla, and caá‐uassú (Calathea lutea, Mey.) waxes are also included.
Pilot plant development of the alkali cooking process for cottonseed meats. I. Effect of flake, thickness and of time, temperature, and moisture content during cooking
Authors: King W. H. , Knoepfler N. B. , Hoffpauir C. L. , McCourtney E. J.
Published: May 2007

Summary and Conclusions

Results obtained from alkaline cooking experiments show that all of the four variables studied—cooking mousture content, temperature, time and flake thickness—influenced the properties of the resultant meals in varying degrees. Under the experimental conditions used a high initial moisture content, above 18%, is necessary to lower the free gossypol content in the finished meal to less than 0.04%. When this amount of moisture is used, a plastic mass results at the beginning of the process which requires special equipment to supply the mechanical action necessary to break the pigment glands at a low temperature. In the presence of high moisture content and alkali the gossypol, which is released when the glands are ruptured, is bound to the meal. When sufficient initial moisture is present (24–31%), only traces of gossypol (0.010% or less) are found in the extracted crude oil.

High temperatures in the presence of high moisture content reduce the solubility of the meal protein (in 0.02N NaOH). Under the conditions of moisture, temperature, and time of cooking used in the experiments the maximum nitrogen solubility obtained under conditions necessary to produce low free gossypol content was 64%. This differs from results obtained in previous work performed under different conditions. A probable reason for the difference is given based on the interrelationship of the three variables.

The results demonstrated further that finer comminution of the raw meats by rolling to 0.005‐in. thick flakes results in lower free gossypol content in the finished meal and lower gossypol content of the oils as well as more complete removal of the oil by the filtration‐extraction procedure used.
A note on improved isolation of concentrates of linolenic acid and ethyl linolenate from linseed oil
Authors: Parker Winfred E. , Swern Daniel
Published: May 2007

Linolenic acid and ethyl linolenate concentrates (80–85%) have been obtained from linseed oil fatty acids or ethyl esters in 50–60% yield, based on linolenic recovery, by a single urea complex separation at room temperature.
Research on the effects of detergents (Alkylbenzenesulfonates and phosphates) in sewage systems. A progress report
Authors: Justice J. D.
Published: May 2007

Several university research programs on the effects of alkylbenzenesulfonate (ABS) and condensed phosphates on water‐treatment plants and sewage‐treatment plants are reviewed. Methods of analyzing for very small amounts of these materials have been developed. The concentration of condensed phosphates in surface waters was determined, and it was found that even at several times these levels the effect on normal water‐treatment procedures is slight. In sewage treatment plants the presence of ABS is only one of the factors in the frothing problem. Ammonia nitrogen, BOD, and temperature are also involved. Most of the ABS entering an activated sludge process is biologically degraded, and it has no toxic effect on sewage bacteria. At the levels found in surface waters ABS does not have a toxic effect on aquatic life.
Composition of the seed oil of sterculia foetida, Linn
Authors: Varma J. P. , Dasgupta Sharda , Nath Bhola , Aggarwal J. S.
Published: May 2007

Sterculia foetida oil has been found to contain 71.8% of sterculic acid and minor proportions of oleic, linoleic, and saturated acids. The saturated component consists mostly of myristic and palmitic acids.

The oil consists of traces of tristearin (0.8%) and a major quantity of tristerculin (31.4%) together with different amounts of the glycerides of the type GS2U, GSU2, and GU3 of other fatty acids.
Toxic protein from trichloroethylene‐extracted soybean oil meal
Authors: McKinney L. L. , Weakley F. B. , Campbell R. E. , Eldridge A. C. , Cowan J. C. , Picken J. C. , Jacobson N. L.
Published: May 2007

Fractionation studies have been carried out on a specially prepared undenatured toxic trichloroethylene‐extracted soybean oil meal to determine which component of the meal is associated with the toxicity. Calf‐assay of the samples indicated that the toxic factor is associated with the protein.

The toxic factor associated with the protein is labile to strong acid hydrolysis. Measurable destruction of the toxic factors occurs when the protein is treated with alkali at pH 11–12 at 60°C. Because destruction of the toxic factor occurred when the neutral protein dispersion was autoclaved for 1 hr. and was followed by an alkaline treatment simulating the pH conditions encountered in tryptic digestion, it was not possible to evaluate the effect of tryptic digestion upon the toxic factor.

Analyses of the toxic protein failed to indicate the nature of the reaction of trichloroethylene with the protein to produce the toxicity.
Infrared absorption of branched‐chain fatty acids and derivatives in the carbon‐hydrogen stretching region
Authors: Guertin Donald L. , Wiberley Stephen E. , Bauer Walter H.
Published: May 2007

An investigation of the lithium fluoride region makes it possible to characterize a number of structural isomers of branched‐chain fatty acids. For example, 2‐methyl, 3‐methyl, and 5‐methyl hexanoic acids may be distinguished. Similarly a number of isomers of octanoic acid may be identified ; 2‐n‐propyl and 2‐isopropyl hexanoic acid may be differentiated. The isomers of 2‐n‐butyl hexanoic acid may also be identified.

Absorption bands at 2960 cm−1 and 2930 cm−1 have been assigned, respectively, to asymmetrical methyl stretching modes and in‐phase vibrations of the methylene group. Absorption at 2870 cm−1 is associated with symmetrical stretching modes of the methyl group. The absorption at 2860 cm−1 has been assigned to the out‐of‐phase vibrations of the methylene group. These assignments correspond to those of Fox and Martin and of Pozefsky and Coggeshall.

The absorption bands at 2930 cm−1 and 2860 cm−1 are stronger than those at 2960 cm−1 and 2870 cm−1 when the ratio of methylene groups to methyl groups equals or exceeds three to one. The one exception to this rule is the case of 2‐methyl hexanoic acid and the corresponding silver salt and di‐soap. An interaction between the methyl group in the two‐position and the acid group has been proposed as an explanation for this case.

As the spectra of the fatty acids and their silver salt and aluminum di‐soap derivatives are identical in the carbon‐hydrogen region, it is obvious that other derivatives of these acids may be identified by reference to the spectra reported.
Isomerization of linoleic, linolenic, and other polyunsaturated acids with potassium tertiary butoxide and its application in the spectrophotometric estimation of these acids
Authors: Sreenivasan B. , Brown J. B.
Published: May 2007

It has been shown that potassium tertiary butoxide isomerizes such unsaturated fatty acids as linoleic, linolenic, arachidonic, and pentaenoic at a temperature of 90°. With 5% potassium‐t‐butanol reagent conjugation of linoleic acid attains a maximum at the end of 2 hrs. and remains steady thereafter even up to 10 hrs. while with linolenic, arachidonic, and pentaenoic acids it is still occurring at the end of such long times of reaction as 48 and 10 hrs., respectively. This continuance of reaction at the end of such long periods with these higher unsaturated acids demonstrates that the isomerization with the tertiary butoxide reagent at 90° is not complicated by side reactions, such as polymerization and deisomerization. All the methods studied give high absorption coefficients in the lower regions of maxima—233 mµ with linolenic, 233 mµ and 268 mµ with arachidonic acids—showing thereby that isomerizations of these acids occur stepwise. Based on this study, a method using 5% potassium‐t‐butanol as reagent, at 90° with a time of reaction of 4 hrs., has been proposed for the estimation of linoleic and linolenic acids. The k233 value for linoleic acid (94.0) obtained by this method compares very well with those by the 6.6% KOH‐glycol and 21% KOH‐glycol methods while with linolenic acid the k233 value (63.2) is higher and k268 value (74.2) lies intermediate between those by the other methods. The proposed method is shown to estimate the linoleic and linolenic acid contents of several typical oils with about the same degree of accuracy as either the 6.6% KOH‐glycol or 21% KOH‐glycol methods.

Appendix. When this paper was ready to be submitted, a note (27) describing the use of tertiary butoxide reagent on the kinetic study of isomerization of linoleic and linolenic acids came to our attention. Extinction coefficients at 235 mµ and 268 mµ are reported for linolenic acid and the values (61.4, 74.2) obtained by isomerization with a molar solution of the reagent at 99.5° and 180 minutes’ time of reaction are about the same order as those reported in this paper. It is of interest to note that these authors have also noted that no destruction of the product occurs at this temperature and time of heating.
Tocopherols as carry‐through antioxidants
Authors: Dugan L. R. , Kraybill H. R.
Published: May 2007

1. Tocopherols have been found to be carry‐through antioxidants in lard.

2. Gamma tocopherol, which is a better antioxidant than alpha tocopherol, is also a better carry‐through antioxidant.

3. Higher levels of tocopherol provide increased carry‐through stability although the AOM stability of lard is decreased.

4. Combinations of BHA with tocopherol in lard provide increased carry‐through stability but do not increase the AOM stability.
Metal ion catalysis of autoxidation in a lard gel
Authors: Ellis R. , Currie G. T. , Gaddis A. M.
Published: May 2007

The prooxidant effects of transition metal compounds upon lard triglycerides in an aqueous heterogeneous model system were examined. Catalytic activity of a metal salt depended on its identity, the phase in which it is dissolved, the buffering salts and pH of the system. The iron and copper inorganic salts dissolved in the aqueous phase were powerful catalysts. Other transition metal salts had little positive effect on autoxidation at acid and neutral pH values. Manganous chloride had an inhibiting action. Freeze‐drying reversed catalysis patterns, and Mn++ and Co++ became the strongest prooxidants. Cobaltous and manganese stearates were the most active of such compounds. Reversals in catalytic activity were due to the formation or disappearance of aquo ions.
2‐trans‐nonenal, the hardened flavor present in hydrogenated peanut oil
Authors: Feenstra W. H. , Meijboom P. W.
Published: May 2007

Oils belonging to linoleic‐oleic acid group may have a characteristic hardening flavor after hardening and refining. This flavor was isolated from hardened peanut oil by degassing and preparative gaschromatography. An investigation into the structure of this flavor showed it to be 2‐trans‐nonenal. The structure was confirmed by comparison with an authentic synthesized product. 10‐Octadecenoic and 11‐octadecenoic acid which are formed during the hardening process (isomerization) of linoleic and oleic acids, are proposed as precursors of the hardening flavor.