bluuebunny/crossref_metadata_2025 huggingface dataset:
Über die Realisierung und Konvergenz von Mehrschrittverfahren zur iterativen Lösung nichtlinearer Gleichungen
Authors: Schwetlick H.
Published: June 2007

Es wird zunächst der Begriff einer konsistenten m‐Schritt‐Approximation für die Ableitung einer n‐dimensionalen Vektorfunktion F definiert. Indem die beim Newton‐Verfahren benutzten Ableitungen durch solche Approximationen ersetzt werden, entstehen ableitungsfreie Verfahren zur Nullstellenbestimmung von F, die bei geeigneter Wahl von gewissen Diskretisierungsparametern lokal sogar mit einer Ordnung größer als eins konvergieren. Auf der Grundlage einer Idee von Danilin und Pšeničnyî werden konkrete Realisierungen von Mehrschrittapproximationen angegeben, die sich in aufeinanderfolgenden Iterationsschritten nur um eine Matrix vom festen Rang (1 ≦ l ≦ n) unterscheiden. Als Sonderfall ordnet sich ein als „stabilisiertes Sekantenverfahren”︁ bezeichnetes Verfahren vom Rang‐Eins‐Typ ein, das sich in einigen numerischen Beispielen dem Verfahren von Broyden deutlich überlegen zeigt. Abschließend wird ein spezielles gedämpftes m‐Schritt‐Verfahren angegeben und dessen globale Konvergenz bewiesen.
Experiences with Orthogonal Polynomials and „Best”︁ Numerical Integration Formulas on a Triangle; with Particular Reference to Finite Element Approximations
Authors: Moan T.
Published: June 2007

Für einen Dreiecksbereich wird eine Folge homogener orthogonaler Polynome in natürlichen Dreieckskoordinaten konstruiert. Sie werden insbesondere auf gemeinsame Nullstellen und Punkte, in denen ihre Funktionswerte in Abhängigkeit von der Ordnung minimal werden, untersucht. Es wird gezeigt, daß es eine Beziehung zwischen den Grundpunkten der „besten”︁ numerischen Quadraturformel und den gemeinsamen Nullstellen der orthogonalen Polynome gibt. Außerdem werden einige neue symmetrische Formeln für die numerische Quadratur über einem Dreieck angegeben und wichtige Anwendungen der orthogonalen Polynome in der Approximationstheorie aufgezeigt.

Kurz erörtert wird noch das Wesen der Approximation durch finite Elemente. Beim Studium der sich bei dieser‐Methode ergebenden Fehlerverteilung spielen orthogonale Polynome eine wichtige Rolle. Es werden Punkte vorherbestimmt, in denen der Fehler in den dominierenden Ableitungen des Energiefunktionals minimal ist.
Extremum Principles Governing an Anisotropic Viscoelastic Model
Authors: Breuer S.
Published: June 2007

Zur Charakterisierung der Deformationen eines anisotropen visko‐elastischen Modells werden zwei Extremalprinzipe aufgestellt. Die darin enthalten Funktionale werden als das elastische Potential und als mit dem Modell assoziierte komplementäre Energien interpretiert.
Certain Irrotational, Plane, Unsteady Gasdynamic Flows
Authors: Colwell D. J. , Talbot R. F.
Published: June 2007

Eine bestimmte ebene, instationäre und drehungsfreie gasdynamische Strömung wird in natürlichen Koordinaten formuliert und untersucht. Die Einführung eines Strömungsparameters β gestattet die Unterscheidung von drei Strömungstypen, je nachdem ob β = β(t), β = β0 = const oder β = 0 ist. Für die ersten beiden werden Methoden zur Lösung der Grundgleichungen angegeben und an einem Beispiel erläutert. Der Fall β = 0 führt auf eine Klasse von Strömungen, die bereits von anderen Autoren betrachtet worden ist.
On the Stability of Thermally Stratified Plane Poiseuille Flow
Authors: Tveitereid M.
Published: June 2007

Die Stabilität einer thermisch geschichteten ebenen Poiseuille‐Strömung wird in bezug auf kleine Störungen betrachtet. Für verschiedene Werte der Prandtl‐Zahl wird die Wechselwirkung zwischen der üblichen Tollmien‐Schlichtingschen Instabilitätsform und der thermischen Stabilitäts‐ (bzw. Instabilitäts‐) form untersucht. Das Problem wird als Eigenwertproblem gelöst. An den Ergebnissen erscheint als Wichtigstes, daß die kritische Reynolds‐Zahl als nahezu linear abhängig von der Prandtl‐Zahl gefunden wird und immer eine kritische Reynolds‐Zahl existiert, gleichgültig, in welchem Maße die Flüssigkeit durch ein lineares Temperaturprofil stabilisiert ist.
Newton‐ und Hermite‐Interpolation mit Čebyšev‐Systemen
Authors: Mühlbach G.
Published: June 2007

Zur Lösung von Interpolationsproblemen sind dividierte Differenzen besonders geeignete Hilfsmittel. Bei Polynominterpolation im Sinne von Newton oder Hermite lassen sie sich rekursiv berechnen. Damit können die entsprechenden Interpolationspolynome numerisch einfach (ohne Lösung linearer Gleichungssysteme) bestimmt werden. In der vorliegenden Note wird gezeigt, daß gleiches auch für verallgemeinerte dividierte Differenzen und die Interpolation mit Funktionen geeigneter Čebyšev‐Systeme gilt.
Creep‐Plastic Effects in Sheet Bending
Authors: Seth B. R.
Published: June 2007

Plastische Kriechwirkungen in biegsamen Blechen werden als Übergangs‐Phänomen behandelt, ohne daß ad‐hoc‐Annahmen — wie über eine bestimmte Fließbedingung oder ein Kriechverformungsgesetz — gemacht werden. Man findet, daß ein Kriechübergang in der Ausdehnungszone vor sich geht und dabei die zweite Invariante des Spannungszustandes eine Rolle spielt, mit deren Hilfe man gewöhnlich die Grenze des Plastizitätsgebietes bestimmt. Die Kontraktionszone erfährt eine elastisch‐plastische Verformung. Die Untersuchung liefert außerdem die Grenze zwischen den beiden Zonen.
Zur Thermodynamik der plastischen Verformung
Authors: Kafka V.
Published: June 2007

Die Änderungen der mechanischen Eigenschaften eines realen polykristallinen Materials in isothermer plastischer Verformung werden in dieser Arbeit durch Mikrospannungen beschrieben. Manche formale thermodynamische Beziehungen erhalten auf diese Weise eine konkrete physikalische Bedeutung. Die aus einem solchen Zugang folgenden theoretischen Werten der residualen Energie im Laufe der plastischen Verformung werden mit experimentellen Werten verglichen, und es wird gute Übereinstimmung festgestellt.
Exact Asymptotic Solution for the Initial Post‐Buckling of a Strut on Linear Elastic Foundation
Authors: El Naschie M. S.
Published: June 2007

Im Rahmen einer allgemeinen Verzweigungstheorie wird eine geschlossene asymptotische Lösung für den überkritischen Bereich eines linear‐elastisch gebetteten Druckstabes gebildet. Es wird deutlich gezeigt, daß ein schalenähnliches instabiles überkritisches Verhalten möglich ist. Für eine Winkler‐Bettung erweist sich das Ergebnis implizit als Spezialfall der Pasternak‐Bettung. Darüber hinaus wird für einen sehr langen Druckstab die Möglichkeit einer gedämpften Schwingung als Eigenschwingung untersucht.
Solutions of Boundary Layer Equations Governing Free Convective and Magnetohydrodynamic Flows through Parametric Differentiation
Authors: Nath G.
Published: June 2007

In der vorliegenden Arbeit wird die Methode der parametrischen Differentiation angewendet, um ein System nichtlinearer Gleichungen zu lösen, das zwei‐ und dreidimensionale freie, konvektive Grenzschichströmungen bzw. eine zweidimensionale magnetohydrodynamische Grenzschichtströmung beherrscht. Der Hauptvorteil dieser Methode besteht darin, daß die nichlinearen Gleichungen auf lineare reduziert werden und die Nichtlinearität auf ein System von Gleichungen erster Ordnung beschränkt wird, das, verglichen mit den ursprünglichen Nichtlinearen Gleichungen, viel leichter gelöst werden kann. Ein anderer Vorzug der Methode ist, daß sie es ermöglicht, die Lösung von einer bekannten, zu einem bestimmten Parameterwert gehörigen Lösung aus durch schrittweises Vorgehen die Lösung für den gesamten Parameterbereich zu erhalten. Die mit dieser Methode gewonnenen Ergebnisse stimmen gut mit den entsprechenden, mit anderen numerischen Verfahren erzielten überein.
Zur Theorie der ersten Integrale bei gesteuerten mechanischen Systemen
Authors: Müller P. C. , Popp K.
Published: June 2007

Die Theorie der ersten Integrale wird auf gesteuerte dynamische Systeme erweitert. Es werden notwendige und hinreichende Bedingungen für die Existenz dieser Bewegungsinvarianten angegeben. Hierbei spielt der regelungstheoretische Begriff der Steuerbarkeit eine wesentliche Rolle. Bei mechanischen Systemen lassen sich die Zusammenhänge zwischen Impuls‐, Drall‐ und Energie‐Integralen sowie der Steuerbarkeit und den Eigenbewegungen anschaulich erklären. Anhand von Beispielen wird die Bedeutung dieser neuen systemtheoretischen Verbindung Klassischer Dynamik mit moderner Regelungstheorie demonstriert.
Rotary Oscillations of Spheroids and Disks in an Elastico‐Viscous Fluid
Authors: Kanwal R. P. , Pasha M. L.
Published: June 2007

Es wird eine Theorie für die Strömung einer elastoviskosen Flüssigkeit aufgestellt, in der ein axialsymmetrischer Körper Drehschwingungen ausführt. Ziel ist die Behandlung des Scheiben‐Elastoviskosimeters. Zu diesem Zweck Lösen wir die Randwertaufgabe für Rotationsellipsoide und leiten daraus durch Grenzübergang die Lösung für die Scheibe her. Es werden die Werte sowohl der Geschwindigkeit im Strömungsfeld als auch des Drehmoments, das die umströmten Körper erleiden, abgeleitet.
Torsion of Anisotropic Micropolar Elastic Cylinders
Authors: Ieşan D.
Published: June 2007

Die vorliegende Arbeit beschäftigt sich mit dem Torsionsproblem homogener und orthotroper Balken in Rahmen der linearen Theorie mikropolarer Elastizität. Das Problem wird mittels dreier Torsionsfunktionen gelöst. Es wird ein Existenzsatz bewiesen.
Die Stabilität einer Bewegung bezüglich einer Menge
Authors: Lilov L.
Published: June 2007

Bei vielen Aufgaben entsteht das Problem der Stabilität einer Bewegung nicht bezüglich eines isolierten Punktes, sondern bezüglich einer Menge von Punkten. Eine solche Aufgabe ist z. B. die Untersuchung der Stabilität der kleinen Schwingungen eines beliebigen nichtholonomen Systems um die Mannigfaltigkeit seiner Gleichgewichtslagen. Nach der Einführung des Begriffs ‘Definitheit einer Funktion bezüglich einer Menge’ werden Sätze bewiesen, die hinreichende Bedingungen für Stabilität, asymptotische Stabilität und Instabilität einer Bewegung bezüglich einer Menge liefern.
Monotone Einschließung von Lösungen nichtlinearer Gleichungssysteme durch überlinear konvergente Mehrschrittverfahren
Authors: Mönch W.
Published: June 2007

Zur monotonen Einschließung von Lösungen nichtlinearer Gleichungssysteme werden überlinear konvergente Mehrschrittverfahren vom Newton‐Typ angegeben, die sich gegenüber dem Ausgangsverfahren durch eine höhere Effektivität auszeichnen. Durch eine intervallmäßige Auswertung der Ableitung kann auf sonst übliche Voraussetzungen über ihre Monotonie verzichtet werden.
Convective Heat Transfer in Micropolar Fluid Flow Through a Horizontal Parallel Plate Channel
Authors: Maiti G.
Published: June 2007

Using the basic equations of heat conducting micropolar fluid, free and forced convective heat transfer through the horizontal parallel plate channel flow is studied. The micro‐rotation due to the spinning of fluid particles stabilises the flow, and cools the boundaries by controlling heat transfer.
Stability Analysis of Stochastic Large‐Scale Systems
Authors: Michel A. N.
Published: June 2007

Sufficient conditions for the Lyapunov stability, with probability one, of several classes of (a) continuous‐parameter stochastic composite systems, and, (b) discrete‐parameter stochastic composite systems are established. In all cases the objective is the same: to analyze the stability of large‐scale composite systems in terms of their lower order subsystems and in terms of their interconnecting structure. In order to demonstrate the usefulness of the present approach, several specific examples are considered.
Bemerkungen zum Versuch von Hohenemser
Authors: Betten J.
Published: June 2007

Der Versuch von Hohenemser wird bisweilen zum Nachweis der Gültigkeit der „Deformationszuwachstheorie”︁ bzw. der „Deformationstheorie”︁ herangezogen. Die gute Übereinstimmung der Versuchsergebnisse mit der „Deformations‐theorie”︁, die trotz „peripherem”︁ Belastungsweg gegeben ist, ist vereinbar mit einer vom Verfasser früher angegebenen Integrationsbedingung.

Um eine bessere Anpassungsmöglichkeit an alle im Schrifttum vorliegenden Versuchsergebnisse zu haben, werden zwei verallgemeinerte Spannungs‐Dehnungs‐Beziehungen angegeben, die im Sonderfall zwanglos in den Pragerschen bzw. Neuberschen Ansatz übergehen. Es wird weiterhin gezeigt, daß für die Prandtl‐Reuss‐Theorie mit dem Pragerschen Ansatz und die Henckysche Theorie mit der Neuberschen Charakteristik übereinstimmt.

Weiterhin wird gezeigt, daß auf der Basis der Hill‐Bedingung eine schlechtere Übereinstimmung der Deformations‐zuwachstheorie mit den Versuchsergebnissen von Hohenemser erreicht wird, d. h., die Versuchsrohre verhielten sich eher isotrop als orthotrop anisotrop.

Benutzt man Fließbedingungen, die sowohl die zweite als auch die dritte Invariante berücksichtigen, dann erhält man eine bessere Übereinstimmung mit den Versuchsergebnissen. Schließlich wird noch der Einfluß von Eigenspannungen untersucht.
Stresses in the Plastic Range Around a Circular Hole in an Infinite Sheet Subjected to Equal Biaxial Tension
Authors: Ishikawa H.
Published: June 2007

The stresses in the plastic range around a circular hole in an infinite sheet of strain‐hardening material subjected to equal biaxial tension are found analytically on the basis of the simple deformation theory of plasticity. The stress concentration factor is given by 2Es (Sc · p)/Es(p) where Es(Sc · p) and Es(p) are the secant moduli at points around a circular hole and far removed from the hole.

Der Spannungskonzentrationsfaktor wird durch 2Es(Sc · p)/Es(p) gegeben, wobei Es(Sc · p) und Es(p) die Sekanten‐module an Punkten um eine kreisförmige Öffnung und weit entfernt von der Öffnung sind.
Spinorkalkül und Normalkoordinaten
Authors: Günther P.
Published: June 2007

Es wird eine Methode angegeben, um die Basen in den tangentialen Spinorräumen eines 4‐dimensionalen Riemannschen Raumes mit normalhyperbolischer Signatur einem Normalkoordinatensystem anzupassen. Es werden einfache Differentialgleichungen hergeleitet, welche die Bestimmung der Verbindungsgrößen (Pauli‐Matrizen) und des metrischen Tensors aus dem Krümmungstensor erlauben. Insbesondere werden die Formeln explizit angegeben, welche die Ableitungen des metrischen Tensors in Normalkoordinaten durch den Krümmungstensor und seine kovarianten Ableitungen ausdrücken. Sie sind unabhängig von der Dimension und Signatur des betrachteten Riemannschen Raumes.
Finite Amplitude Thermal Convection in Non‐Newtonian Fluids: Fixed Boundaries
Authors: van der Borght R. , Crawford J. R.
Published: June 2007

In this paper the one‐mode approximation, based on a variational principle of Glansdorff and Prigogine, has been used to integrate numerically the system of non‐linear differential equations describing steady convection, with hexagonal planform, in a non‐Newtonian fluid with rigid boundaries. A description is given of the three methods used to integrate the equations and it is shown that the theoretical results confirm the observed increase in the Nusselt number due to visco‐elastic effects and are in good agreement with the experimental results.
A Cavitating Hydrofoil in a Solid Wall Tunnel
Authors: Ota Terukazu
Published: June 2007

A nonlinear theory is developed for a flow about a flat plate hydrofoil with a finite cavity in a solid wall tunnel applying the Sedov's method treated the mixed boundary value problem in the doubly connected region.
A Variational Principle for Non‐Conservative Dynamical Systems
Authors: Vujanovic B.
Published: June 2007

The purpose of the present paper is to establish a variational principle of Hamilton's type, for purely nonconservative mechanics according to Central Lagrangian Equation. The velocity of variation and the variation of velocity are not commutative as in conservative mechanics. The applications on the nonlinear heat transfer in solids are discussed in detail.
Thermal Effects in Plasticity. Part I: Coupled Theory
Authors: Raniecki B. , Sawczuk A.
Published: June 2007

The coupled thermoplastic behavior is studied within the framework of classical thermodynamics. A classification of thermal effects is given and a pattern for theories allowing for a straightforward interpretation of the observed properties of irreversible deformation is presented. A procedure is outlined for constructing a simple non‐isothermal theory of thermoplasticity. A suitable single internal parameter is introduced. The Ziegler orthogonality principle is used in deriving the equations regarding the temperature, the stress and the rate of plastic strain. Explicit forms of the governing equations for elastic‐plastic materials with an isotropic hardening are derived.
Optimale Steuerung einer Klasse nichtlinearer Aufheizungsprozesse
Authors: Wolfersdorf L. V.
Published: June 2007

Es wird ein Analogon zum Maximum‐Prinzip von Pontrjagin bei einer Klasse von optimalen Prozessen hergeleitet, die durch parabolische Differentialgleichungen 2. Ordnung in einer räumlichen Variablen beschrieben werden.
Thermal Effects in Plasticity. Part II: Uniqueness and Applications
Authors: Raniecki B. , Sawczuk A.
Published: June 2007

The constitutive relations of the theory proposed in the first part of the paper are analyzed as to their consistency. The inversion of the obtained rate relations and the uniqueness of the solution to boundary value problems in coupled thermoplasticity are discussed. Simplified rate relations are derived on neglecting certain couplings. The significance of coupling effects in the stability analysis of thermo‐plastic deformations is outlined.

The response of structural elements to thermal and loading cycles is described and the bounding theorems of the shakedown analysis are recalled.
Symmetric and Asymmetric Theories of Bimodulus Elasticity‐Bending of Cylindrical Panels
Authors: Kamiya N.
Published: June 2007

Some composite materials and high‐polymers behave or may be approximately regarded to behave as bimodulus materials. There are several investigations being conducted on the symmetry of elastic constants appearing in two‐or three‐dimensional stress‐strain relations of these materials, and some experimental results confirm their symmetry while others establish their asymmetry. In this paper, by solving a simple problem based either on the symmetric or asymmetric theory of elasticity, these theoretical differences are discussed. The resulting difference in deflection of laterally loaded cylindrical panels is less than few percent.
Criteria for Pervasive Damping of Mechanical Systems with First Integrals of Motion
Authors: Samin J.‐Cl.
Published: June 2007

This paper determines necessary and sufficient criteria for pervasive (or complete) damping of mechanical systems with first integrals of motion. The pervasiveness of the damping is essential when the stability of a system is investigated through its linearized set of equations of motion by Liapunov's method: the sufficient conditions for asymptotic stability then become necessary conditions. The existence of first integrals of motion restricts the asymptotic stability to a certain class of initial conditions. The pervasiveness of the damping will be considered in the same sense.
Intrinsic Equations of Steady Rotating, Incompressible Viscous Fluid Flow
Authors: Gopalakrishna A. V. , Rao A. Ramachandra
Published: June 2007

The equations governing the flow of a steady rotating incompressible viscous fluid are expressed in intrinsic form along the vortex lines and their normals. Using these equations the effects of rotation on the geometric properties of viscous fluid flows are studied. A particular flow in which the vortex lines are right circular helices is discussed.
On Energy Stored in Linear Viscoelastic Solids
Authors: Breuer Shlomo
Published: June 2007

It is shown that the constitutive equations and the existence of a minimum potential energy principle are insufficient for the unique determination of a stored energy functional in linear viscoelastic solids.
The Generalized Hamilton‐Jacobi Method for Nonholonomic Dynamical Systems of Chetaev's Type
Authors: van Dooren R.
Published: June 2007

An extension of the classical Hamilton‐Jacobi method for dynamical systems subject to nonholonomic constraints of Chetaev's type is established by applying a variational principle for the integral of action. The generalized method is illustrated by an example in which the constraint is nonlinear in the velocity components.
Numerical Similarity Solutions to Stefan Problems
Authors: Milinazzo F. , Bluman G. W.
Published: June 2007

The general similarity solution of the heat equation is used to find approximate numerical solutions of a direct Stefan problem. The constructed algorithm is shown to converge and is illustrated by numerical examples.
Das Pontryaginsche Maximumprinzip für Probleme mit Zustandsbeschränkung. I
Authors: Knoblochi H. W.
Published: June 2007

Die vorliegende Arbeit befaßt sich mit Kontrollproblemen, ben denen die Zustandsvariable x einer Beschränkung der Form γ(x) ≦ 0 unterworfen ist. Die Resultate sind in erster Linie für das Studium optimaler Lösungen von Bedeutung. Sie eröffnen einen neuen, auf einer verfeinerten lokalen Approximation der erreichbaren Menge begründeten Zugang zu notwendigen Bedingungen. Die für die Approximation benötigten Hilfsmittel werden im vorliegender. ersten Teil der Arbeit entwickelt.
Beweis einer Vermutung über n‐Orbiformen kleinsten Inhalts
Authors: Klötzler R.
Published: June 2007

N‐Orbiformen sind ebene konvexe Bereiche, die sich in einem regulären n‐Eck allseitig tangierend drehen lassen. Es wird in dieser Arbeit die Existenz einer n‐Orbiform kleinsten Flächeninhalts nachgewiesen und ihre Gestalt mittels Pontrjaginschem Maximumprinzip bestimmt. Vom J. Focke aufgenommene Untersuchungen zu diesem Problem erfahren damit ihre Vervollständigung.
Zur iterativen Lösung der zweidimensionalen Boussinesq‐Gleichungen
Authors: Gajewski Herbert
Published: June 2007

In vorliegender Arbeit begründen wir ein Iterationsverfahren zur Lösung der Boussinesq‐Approximation der Gleichungen des gekoppelten Wärme‐ und Stofftransports im zweidimensionalen Fall.
Turbulent Anisotropic Diffusion in Fluids
Authors: de Socio L. M. , Salusti E.
Published: June 2007

Anisotropic diffusion of a tracer in a turbulent medium is considered. Once the neighbour concentration has been calculated, the evaluation of the tracer's concentration may be obtained by series expansion in terms of orthonormal functions. The harmonic‐oscillator wave functions are suggested as a suitable choise. The ambiguities arising about the sign of the series coefficients are discussed.
Convective Instability in a Rapidly Rotating Viscoelastic Layer
Authors: Eltayeb I. A.
Published: June 2007

The linear stability of a highly rotating horizontal viscoelastic fluid layer heated from below is studied in the Boussinesq approximation, when the fluid is governed by relations due to Oldroyd. The problem is solved by using singular perturbation methods. The effect of elasticity is shown to destabilize the layer, in general. However, the degree of destabilization depends crucially on the retardation time of the fluid as well as on the type of boundary under consideration. The reason for the destabilization is traced down to the inhibition of viscous dissipation by elasticity.
Das Pontryaginsche Maximumprinzip für Probleme mit Zustandsbeschränkung. II
Authors: Knobloch H. W.
Published: June 2007

Der zweite Teil der Arbeit ist vor allem der Herleitung der notwendigen Bedingungen für optimale Lösungen der in Teil I betrachteten Kontrollprobleme gewidmet. Die Formulierung dieser Bedingungen erfolgt mit Hilfe einer Hamilton‐Funktion, welche die gleiche Gestalt wie bei Problemen ohne Zustandsbeschränkung hat und insbesondere keinen zusätzlichen Lagrangeschen Multiplikator enthält. Die zusätzliche Bedingung an die Zustandsvariable kommt dafür in der Form des Maximumprinzips zum Ausdruck. Eine ausführliche Diskussion eines Beispiels (Abschnitt 7) erläutert die Tragweite unserer Methode.
Evaluation of the Excessive Initial Values in the Twodimensional Operational Calculus
Authors: Berg L.
Published: June 2007

Solving equations by means of operator formulas in some cases more initial values can occur, than are necessary to determine the solution uniquely. Here we describe a method to evaluate these excessive initial values in the general two‐dimensional operational calculus, and we outline the specialization to the discrete, the mixed and the continuous case. This method is based on a generalization of a theorem by W. Jentsch, which is proved previously by means of formal power series. The results about these series concerning their composition, substitution, inversion, and the solution of corresponding polynomial equations may be used also in asymptotics.
Effects of Uniform Suction on the Induced Forces on a Flat Plate in Bounded Shear Flow
Authors: Olunloyo V. O. S.
Published: June 2007

The effect of plate porosity on the induced forces in a bounded shear flow is investigated by allowing uniform suction at the plate. Near the leading edge the comparative ranking of the circulation, Li‐Murray and wall pressures remain the same although logarithmic terms, for the first time, now appear in the inviscid pressure. Far upstream no radical changes occur but the pressure no longer decays far downstream on either side of the plate. In general the wall pressure on the plate overtakes the Li‐Murray component at a slower rate than in any of the cases treated so far. This gives the Li‐Murray approximation a bigger radius of validity near the leading edge than in the corresponding case without suction.
System of Cracks in Elasticity Theory
Authors: Sharfuddin S. M.
Published: June 2007

General methods for solving punch and crack problems in elasticity theory have been developed by Muskhelishvili and others. In this paper general equations concerning a system of cracks have been established making use of Muskhelishvil's method. A closed form solution to the infinite row of collinear cracks has been found and an explicit solution of the problem of an infinite row of parallel cracks has been obtained after reducing it to a Fredholm type of integral equation.
Facile purification of a C‐terminal extended His‐tagged Vibrio mimicus arylesterase and characterization of the purified enzyme
Authors: Lee Ya‐Lin , Chang Rey‐Chang , Shaw Jei‐Fu
Published: June 2007

Vibrio mimicus arylesterase, a 20 kDa protein, is a multifunctional enzyme with thioesterase and chymotrypsin‐like activities. Because an affinity His‐tag (six consecutive histidine affinity tag) directly to the protein caused the loss of enzyme activity, a hexadecapeptide with His‐tag, ADPNSSSVDKLAAALEHHHHHH encoded from vector pET‐20b(+) was constructed to extend from the carboxyl terminus of the arylesterase. This Histagged protein retained enzyme functions. Thermal unfolding behavior of both proteins was almost identical, and their Tm values were near 54°C as monitored by circular dichroism. Tryptic cleavage of the functional His‐tagged enzyme produced two smaller proteins, which still possessed enzyme activity and which suggested that the additional peptide extended on the protein surface. The spacing peptide between His‐tag and arylesterase successfully prevented the interference of the His‐tag to the enzyme functions. The kinetic studies showed that the esterase and thioesterase activities of the His‐tagged enzyme were similar to those of the wild type. On the other hand, the catalytic efficiency of chymotrypsin‐like activity of the His‐tagged protein was two times higher than that of the wild type.
Purification and characterization of a cold‐active protease from psychrotrophic Serratia marcescens AP3801
Authors: Morita Yasutaka , Kondoh Kenji , Hasan Quamrul , Sakaguchi Toshifumi , Murakami Yuji , Yokoyama Kenji , Tamiya Eiichi
Published: June 2007

Protease activity was detected in the culture medium of Serratia marcescens AP3801 grown at 10°C, which was isolated from soil collected from the top of a mountain. The enzyme, designated as CP‐58 protease, was purified to homogeneity from the culture broth by ion exchange and gel filtration chromatographies. The molecular mass of the protease was 58 kDa, and its isoelectric point was close to 6.0. Maximal activity toward azocasein was observed at 40°C and from pH 6.5 to 8.0. The activity was strongly inhibited by 1,10‐phenanthroline, suggesting that the enzyme is a metalloprotease. The N‐terminal amino acid sequence was Ser‐Leu‐Asn‐Gly‐Lys‐Thr‐Asn‐Gly‐Trp‐Asp‐Ser‐Val‐Asn‐Asp‐Leu‐Leu‐Asn‐Tyr‐His‐Asn‐Arg‐Gly‐Asn (or Asp)‐Gly‐Thr‐Ile‐Asn‐Asn‐Lys‐Pro‐Ser‐Phe‐Asp‐Ile‐Ala. A search through databases for sequence homology aligned CP‐58 protease with metalloprotease. The result of the cleavage pattern of oxidized insulin B‐chain suggests that CP‐58 protease has a broader specificity than other proteases against the peptide substrate.
Enantioselective formation of an α, β‐epoxy alcohol by reaction of methyl 13(S)‐hydroperoxy‐9(Z), 11(E)‐octadecadienoate with titanium isopropoxide
Authors: Piazza George J. , Foglia Thomas A. , Nuñez Alberto
Published: June 2007

Methyl 11(R), 12(R)‐epoxy‐13(S)‐hydroxy‐9(Z)‐octadecenoate (threo isomer) was generated from linoleic acid by the sequential action of an enzyme and two chemical reagents. Linoleic acid was treated with lipoxygenase to yield its corresponding hydroperoxide [13(S)‐hydroperoxy‐9(Z), 11(E)‐octadecadienoic acid]. After methylation with CH2N2, the hydroperoxide was treated with titanium (IV) isopropoxide [Ti(O‐i‐Pr)4] at 5°C for 1 h. The products were separated by normal‐phase high‐performance liquid chromatography and characterized with gas chromatography‐mass spectrometry, infrared spectroscopy, and nuclear magnetic resonance spectroscopy. Approximately 30% of the product was methyl 13(S)‐hydroxy‐9(Z), 11(E)‐octadecadienoate. Over 60% of the isolated product was methyl 11(R), 12(R)‐epoxy‐13(S)‐hydroxy‐9(Z)‐octadecenoate. After quenching Ti(O‐i‐Pr)4 with water, the spent catalyst could be removed from the fatty products by partitioning between CH2Cl2 and water. These results demonstrate that Ti(O‐i‐Pr)4 selectively promotes the formation of an α‐epoxide with the threo configuration. It was critically important to start with dry methyl 13(S)‐hydroperoxy‐9(Z),11(E)‐octadecadienoate because the presence of small amounts of water in the reaction medium resulted in the complete hydrolysis of epoxy alcohol to trihydroxy products.
Characterization of new yeast lipases
Authors: Hou Ching T.
Published: June 2007

Previously, we used a simple, sensitive agar plate method to screen lipase activity from 1229 selected cultures, including 508 bacteria, 479 yeasts, 230 actinomycetes and 12 fungi, that covered many genera and species. About 25% of the cultures tested were lipase‐positive. We also expanded our screening method to focus specifically on the pH dependence and thermostability of these lipase activities. In this report, we have characterized 25 yeast lipases, obtained from our screening program, on the basis of their positional specificity against triglycerides. Lipase was produced by growing cultures on nutrient medium in the presence of vegetable oil at 25°C for 4 d. Of the 25 new yeast lipases analyzed, 19 showed 1,3‐positional specificity and 6 showed random specificity. No 2‐positional specific lipases were found. Among those cultures with highest lipase activity are: Candida silvicola NRRL YB‐2846 (random); Candida sp. 55 (random); Candida sp. 125 (random); Pichia americana NRRL Y‐2156 (1,3‐specific); P. muscicola NRRL Y‐7005 (random); P. petersanii NRRL YB‐3808 (1,3‐specific); and Yarrowia lipolytica NRRL YB‐423 (random). Characterization of Candida sp. strain 55 lipase on its substrate preference showed that this enzyme hydrolyzed soybean oil triglyceride species LLLn, LLL, LLO, and LLP more readily than LOO, LOP, OOO, LOS, and POO, where L=linoleic, Ln=linolenic, O=oleic, P=palmitic, and S=stearin.
Additive effects of acyl‐binding site mutations on the fatty acid selectivity of Rhizopus delemar lipase
Authors: Klein Robert R. , King Gregory , Moreau Robert A. , McNeill Gerald P. , Villeneuve Pierre , Haas Michael J.
Published: June 2007

The fatty acid specificity and pH dependence of triacylglycerol hydrolysis by the Rhizopus delemar lipase acylbinding site mutant Val206Thr+Phe95Asp (Val, valine; Thr, threonine; Phe, phenylalanine; Asp, aspartic acid) were characterized. The activity of the double mutant prolipase was reduced by as much as 10‐fold, compared to the wild‐type prolipase. However, the fatty acid specificity profile of the enzyme was markedly sharpened and was dependent on the pH of the substrate emulsion. At neutral pH, strong preference (10‐fold or greater) for hydrolysis of triacylglycerols of medium‐chainlength fatty acids (C8:0 to C14:0) was displayed by the variant prolipase, with no hydrolysis of triacylglycerols of short‐chain fatty acids (C4:0 to C6:0) and little activity manifested toward fatty acids with 16 or more carbons. At acidic pH values, the fatty acid selectivity profile of the double mutant prolipase expanded to include short‐chain triacylglycerols (C4:0, C6:0). When assayed against a triacylglycerol mixture of tributyrin, tricaprylin and triolein, the Val206Thr+Phe95Asp prolipase displayed a high selectivity for caprylic acid and released this fatty acid at least 25‐fold more efficiently than the others present in the substrate mixture. When presented a mixture of nine fatty acid methyl esters, the wild‐type prolipase showed a broad substrate specificity profile, hydrolyzing the various methyl esters to a similar extent. Contrastingly, the double mutant prolipase displayed a narrowed substrate specificity profile, hydrolyzing caprylic methyl ester at nearly wild‐type levels, while its activity against the other methyl esters examined was 2.5‐ to 5‐fold lower then that observed for the wild‐type enzyme.
Enzymatic synthesis of position‐specific low‐calorie structured lipids
Authors: Akoh Casimir C. , Yee Lisa N.
Published: June 2007

An immobilized sn‐1,3‐specific lipase from Rhizomucor miehei (IM 60) was used to catalyze the interesterification of tristearin (C18:0) and tricaprin (C10:0) to produce low‐calorie structured lipids (SL). Acceptable product yields were obtained from a 1:1 mole ratio of both triacylglycerols with 10% (w/w of reactants) of IM 60 in 3 mL hexane. The SL molecular species, based on total carbon number, were 44.2% C41 and 40.5% C49, with 3.8 and 11.5% unreacted tristearin C57 and tricaprin C27, respectively, remaining in the product mixture. The best yield of C41 species (44.3%) was obtained with zero added water. Tricaprylin (C8:0) was also successfully interesterified with tristearin in good yields at 1:1 mole ratio. Products were analyzed by reverse‐phase high‐performance liquid chromatography with an evaporative light‐scattering detector. Reaction parameters, such as substrate mole ratio, enzyme load, time course, added water, reaction media, and enzyme reuse, were also investigated. Hydrolysis by pancreatic lipase revealed the specific fatty acids present at the sn‐1,3 positions of SL.
Water activity‐adjusted enzymatic partial hydrolysis of phospholipids to concentrate polyunsaturated fatty acids
Authors: Ono Masayo , Hosokawa Masashi , Inoue Yoshikazu , Takahashi Koretaro
Published: June 2007

Selective partial hydrolyses of egg yolk phospholipid and squid skin phospholipid were carried out. By keeping the water activity (aw) of Lipozyme IM at an intermediate level, it was easy to concentrate docosahexaenoic acid (DHA). It was also possible to concentrate both DHA and arachidonic acid (AA) simultaneously to a certain level under this aw range. However, it was impossible to concentrate AA alone when DHA was present. Though there is a limitation in concentrating AA exclusively, the proposed aw‐adjusted hydrolytic reaction is a promising way for preparing phospholipids rich in DHA.
Preparation of highly purified concentrates of eicosapentaenoic acid and docosahexaenoic acid
Authors: Breivik Harald , Haraldsson Gudmundur G. , Kristinsson Björn
Published: June 2007

Because of the complexity of marine lipids, polyunsaturated fatty acid (PUFA) derivatives in highly purified form are not easily prepared by any single fractionation technique. The products are usually prepared as the ethyl esters by esterification of the body oil of fat fish species and subsequent physicochemical purification processes, including short‐path distillation, urea fractionation, and preparative chromatography. Lipase‐catalyzed transesterification has been shown to be an excellent alternative to traditional esterification and short‐path distillation for concentrating the combined PUFA‐content in fish oils. At room temperature in the presence of Pseudomonas sp. lipase and a stoichiometric amount of ethanol without any solvent, efficient transesterification of fish oil was obtained. At 52% conversion, a concentrate of 46% eicosapentaenoic acid (EPA) plus docosahexaenoic acid (DHA) was obtained in excellent recovery as a mixture of mono‐, di‐, and triacylglycerols. The latter can be easily separated from the saturated and monounsaturated ethyl esters and converted into ethyl esters either by conventional chemical means or enzymatically by immobilized Candida antarctica lipase. Urea‐fractionation of such an intermediary product can give an EPA+DHA content of approximately 85%.
Production of high yields of docosahexaenoic acid by Schizochytrium sp. strain SR21
Authors: Yaguchi T. , Tanaka S. , Yokochi T. , Nakahara T. , Higashihara T.
Published: June 2007

The culture conditions for high‐yield production of docosahexaenoic acid (DHA) by Schizochytrium sp. strain SR21 were investigated in a fermenter. With increasing carbon (glucose) and nitrogen (corn steep liquor and ammonium sulfate) sources (up to 12% glucose) in the medium, DHA productivity increased without a decrease in growth rate, i.e., 2.0, 2.7, and 3.3 g DHA/L/d with 6, 10, and 12% glucose, respectively. Eventually, 48.1 g dry cells/L and 13.3 g DHA/L were produced in 4 d with 12% glucose. DHA productivity was decreased with 15% glucose, i.e., 3.1 g/L/d. With 12% glucose, the lipid content was 77.5% of dry cells, and DHA content was 35.6% of total fatty acids. The lipid was composed of about 95% neutral lipid and 5% polar lipid. In polar lipids, the contents of phosphatidylcholine (PC), phosphatidylethanolamine, and phosphatidylinositol were 74, 11, and 5%, respectively. The PC profile was simple, 70% of PC molecules were 1‐palmitoyl‐2‐DHA‐PC and 1.2‐di‐DHA‐PC. These results indicate that Schizochytrium sp. strain 21 is an excellent source for microbial DHA production, including not only the acid form of DHA but also 2‐DHA‐PC.
Industrial high‐performance liquid chromatography purification of docosahexaenoic acid ethyl ester and docosapentaenoic acid ethyl ester from single‐cell oil
Authors: Yamamura R. , Shimomura Y.
Published: June 2007

The use of polyunsaturated fatty acids (PUFA) as medicine or in functional diets requires high purity. An industrial purification method for PUFA from Schizochytrium sp. SR21 oil was investigated. This oil contains fewer unwanted components than fish oils. Docosahexaenoic acid and docosapentaenoic acid ethyl esters (DHA‐E and DPA‐E) were prepared by treatment of this oil with ethanol and 1 N potassium hydroxide in hexane. DHA‐E and DPA‐E were purified by an industrial high‐performance liquid chromatography (HPLC) plant. The separation plant consists of two columns (400 mm i.d., 1,000 mml) with temperature‐controlled water jackets and double‐plunger (four heads) injection and eluent pumps. This plant was computer‐controlled and equipped with an explosion‐prevention system. The packed material was octadecylsilica (reverse‐phase ODS), and the eluent was methyl alcohol/water (98:2). DHA‐E and DPA‐E from single‐cell oil were highly purified by this industrial HPLC method in a one‐step process. The DHA‐E and DPA‐E obtained were better than 99% purity.
Carica papaya latex‐catalyzed synthesis of structured triacylglycerols
Authors: Foglia T. A. , Villeneuve P.
Published: June 2007

One impediment to the industrial use of enzymes in fat and oil transformations is the higher cost often associated with an enzymatic process compared with the corresponding chemical process. Processes that utilize plant enzymes, however, may have advantages because of their lower cost and ready availability. One example of such a plant‐derived enzyme is Carica papaya latex (CPL), the principal source of the protease papain. Recently, it has been shown that this latex also catalyzes the lipolysis of triacylglycerols and that this latex lipase has a selectivity for short‐chain acyl groups as well as a 1,3‐glycerol selectivity. These selectivities can be used in the synthesis of structured triacylglycerols. In this paper we describe the utility of CPL in lipase‐catalyzed reactions, specifically the synthesis of low‐calorie triacylglycerol analogs.
Improvement of palm oil through breeding and biotechnology
Authors: Jalani B. S. , Cheah S. C. , Rajanaidu N. , Darus A.
Published: June 2007

The oil palm Elaeis guineensis is the highest oil‐yielding crop and has the potential to become the major supplier of both edible oil and renewable industrial feedstock. The oil yield from wild groves is presently less than 0.5 t/ha/y. However, through breeding and selection, the oil yield of commercial plantations could reach as much as 8 t/ha/y. New planting materials also have the capability of better oil yields with high iodine value (IV), slow height increment, and larger kernels. The oil also contains considerable amounts of carotenoids (500–700 ppm), vitamin E (600–1000 ppm), and sterols (250–620 ppm). The oil yield of another oil palm species, E. oleifera, is approximately 0.5 t/ha/y with high contents of carotenoids (700–1500 ppm), vitamin E (700–1500 ppm), and sterols (3500–4000 ppm). The above traits could be improved through breeding and biotechnology. Biotechnological efforts at the Palm Oil Institute of Malaysia are directed toward the production of oil with high IV and high monounsaturated fatty acids for edible purposes and industrial uses. Isolation and manipulation of the genes involved in the biosynthesis of fatty acids are the main focus. The aim is to increase the efficiency of conversion of palmitate (C16:0) to oleate (C18:1). Levels of palmitate and oleate are controlled by the enzymes acyl‐acyl carrier protein (ACP) thioesterase and β‐keto acyl ACP synthase II. The chain termination reactions of C16:0 and C18:1 are independent, thus paving the way for the possibility of reducing palmitate levels by switching off the palmitoyl ACP thioesterase gene.
Purification of γ‐linolenic acid from borage oil by a two‐step enzymatic method
Authors: Shimada Yuji , Sugihara Akio , Shibahiraki Masahiro , Fujita Hiroyuki , Nakano Hirofumi , Nagao Toshihiro , Terai Tadamasa , Tominaga Yoshio
Published: June 2007

γ‐Linolenic acid (GLA) was purified from borage oil by a two‐step enzymatic method. The first step involved hydrolysis of borage oil (GLA content, 22.2 wt%) with lipase, Pseudomonas sp. enzyme (LIPOSAM). A mixture of 3 g borage oil, 2 g water, and 5000 units (U) LIPOSAM was incubated at 35°C with stirring at 500 rpm. The reaction was 91.5% complete after 24 h. The resulting free fatty acids (FFA) were extracted from the reaction mixture with n‐hexane (GLA content, 22.5 wt%; recovery of GLA, 92.7%). The second step involved selective esterification of borage‐FFA with lauryl alcohol by using Rhizopus delemar lipase. A mixture containing 4 g borage‐FFA/lauryl alcohol (1:2, mol/mol), 1 g water, and 1000 U lipase was incubated at 30°C for 20 h with stirring at 500 rpm. Under these conditions, 74.4% of borage‐FFA was esterified, and the GLA content in the FFA fraction was enriched from 22.5 to 70.2 wt% with a recovery of 75.1% of the initial content. To further elevate the GLA content, unesterified fatty acids were extracted, and esterified again in the same manner. By this repeated esterification, GLA was purified to 93.7 wt% with a recovery of 67.5% of its initial content.
Synthesis of (Z)‐3‐hexen‐1‐yl butyrate in hexane and solvent‐free medium using Mucor miehei and Candida antarctica lipases
Authors: Bourg‐Garros S. , Razafindramboa N. , Pavia A. A.
Published: June 2007

(Z)‐3‐Hexen‐1‐yl butyrate is an important flavor and fragrance compound as it represents the model of a natural herbaceous (green) note. Two immobilized lipases from Mucor miehei (Lipozym IM) and from Candida antarctica (Novozym 435) were investigated for their use in the synthesis of (Z)‐3‐hexen‐1‐yl butyrate by direct esterification in n‐hexane. To determine optimal conditions for esterification, we examined the following parameters: temperature, amount of lipase, acid/alcohol ratio, and absence of solvent. In n‐hexane, bioconversion yields reached 95 (after 4 h) and 92% (after 6 h) for, respectively, Lipozym IM [17 (w/w reactants)] and Novozym 435 [2% (w/w reactants)]. In the absence of solvent, at 60°C, Novozym 435‐catalyzed esterification afforded the title compound in 80% yield. Up to 250 g (in hexane) and 160 g (without solvent) of ester were easily prepared, in a single operation, at a laboratory scale, in few hours, using 2% (w/w reactants) lipase.
Synthesis of cocoa butter equivalent by lipase‐catalyzed interesterification in supercritical carbon dioxide
Authors: Liu Kuan‐Ju , Cheng Hong‐Ming , Chang Rey‐Chang , Shaw Jei‐Fu
Published: June 2007

With supercritical carbon dixoide as a reaction medium, the syntheses of cocoa butter equivalent by interesterification with various lipases were investigated. The study showed that among those five lipases tested, lipase IM‐20 from Mucor miehei was the most effective and specific in synthesizing this cocoa butter equivalent product by interesterification. The yields of cocoa butter equivalent are affected by pressure, substrate oil composition, solubility and co‐solvent. The best reaction conditions were: reaction pressure at 1500 psi, triglyceride with high content of POP (P, palmitate; O, oleate) and POO, reaction medium with 5.0% water, and reaction temperature at 50°C. The major component of cocoa butter, POS (S, stearate), can be increased by 6.0% by adding a small amount of carbon dioxide. The yield and melting point of the purified cocoa butter equivalent are 53.0% and 34.3°C, respectively.
Lipase‐catalyzed alcoholysis with supercritical carbon dioxide extraction 1: Influence of flow rate
Authors: Gunnlaugsdottir Helga , Sivik Björn
Published: June 2007

A combined process of lipase (E.C. 3.1.1.3) catalysis and extraction of product with supercritical carbon dioxide was studied. The effect of different flow rates of the extraction fluid on the selective removal of the ethyl esters (EE) synthesized in a lipase‐catalyzed alcoholysis of cod liver oil with ethanol was investigated. The faster the flow rate, the faster the extraction rate and the higher the recovery of EE. For example, after a 270‐min extraction, the total recovery of EE was 1520 mg for a flow rate of 0.3 liter carbon dioxide at atmospheric pressure and room temperature/min (NL/min) as compared to 250 mg when 0.015 NL/min was used. The concentration of EE in the carbon dioxide was found to decrease with increasing flow rate, which indicates that the rate of diffusion of EE limits their extraction at fast flow rates. A high flow rate was found to result in a more selective extraction of EE, i.e., less amounts of other lipid components present in the reaction mixture were coextracted with the EE. Further, by increasing the flow rate, the equilibrium of the reaction was shifted slightly toward ester synthesis. An increase in the flow rate from 0.015 to 0.075 NL/min resulted in an approximately 10% increase in total conversion (from 73 to 82%), whereas only a negligible increase was obtained when the flow rate was increased further to 0.15 NL/min.
Lipase‐catalyzed alcoholysis with supercritical carbon dioxide extraction 2: Phase behavior
Authors: Gunnlaugsdottir Helga , Karlsson Anders Å. , Sivik Björn
Published: June 2007

The phase behavior of systems containing ethanol plus lipid samples with different lipid compositions plus carbon dioxide was studied visually at 40°C and pressures of 0.01, 9, 15, and 23 MPa by means of a high‐pressure sapphire cell. The systems studied represent the main components present in a lipase‐catalyzed alcoholysis reaction of cod liver oil in supercritical carbon dioxide. Two phases, a vapor and a liquid phase, were observed in all systems studied at supercritical conditions.