Gluing Solutions

2017 ◽  
Author(s):  
Philip Isett
Keyword(s):  
Stress Tensor ◽  
Compact Support ◽  
Smooth Solution ◽  
Continuous Solution ◽  
Total Momentum ◽  
Frame Of Reference ◽  
Galilean Transformation ◽  
Hölder Continuous ◽  
Pressure Form ◽  
Original Frame

This chapter deals with the gluing of solutions and the relevant theorem (Theorem 12.1), which states the condition for a Hölder continuous solution to exist. By taking a Galilean transformation if necessary, the solution can be assumed to have zero total momentum. The cut off velocity and pressure form a smooth solution to the Euler-Reynolds equations with compact support when coupled to a smooth stress tensor. The proof of Theorem (12.1) proceeds by iterating Lemma (10.1) just as in the proof of Theorem (10.1). Applying another Galilean transformation to return to the original frame of reference, the theorem is obtained.

Approaches to reforming contemporary religious discourse†

2013 ◽  
Vol 6 (2) ◽  
pp. 172-188
Author(s):  
Ahmad Kamal Abou Al-Majd
Keyword(s):  
Religious Orientation ◽  
Religious Discourse ◽  
Frame Of Reference ◽  
Main Subject ◽  
The Past ◽  
Original Frame ◽  
The Mind ◽  
Working Out

This article attempts to attenuate the exaggerated polarization in contemporary religious discourse in Egyptian society emanating from two flawed positions: a wrong conception of ‘applying Shari'a‘; and a wrong intention whereby deliberate cultural exclusion is practised to eradicate any religious orientation. The main subject of this article are manifestations of deviation of this discourse from the orientation of the original frame of reference of religion: (1) The call for Islam through scaring and intimidation; (2) the tendency to be tough on people, thus increasing obligatory duties and decreasing what is permissible; (3) inattention to the objectives of Shari'a and focusing on its literal aspect; (4) inattention to priorities; (5) belittling the role of the mind in Islamic conceptualization; (6) immersion in the past; and (7) Muslims' relationship with others. Nevertheless, rationalizing ‘religious discourse’ and working out a kind of consensus seems to be of utmost importance.

Two-dimensional plastic flow of a Bingham solid

1947 ◽  
Vol 43 (3) ◽  
pp. 383-395 ◽  
Author(s):  
J. G. Oldroyd
Keyword(s):  
Stress Tensor ◽  
Plastic Flow ◽  
Equations Of State ◽  
Variable Viscosity ◽  
Frame Of Reference ◽  
Two Dimensional ◽  
Tensor Form ◽  
Yield Value ◽  
Image Position ◽  
Strain Tensors

The rheological equations of state for an isotropic Bingham solid may be written in tensor form:whereThe notation is explained fully in a previous paper (1). The frame of reference is essentially Eulerian. Primes denote deviatoric components of the stress, strain and rate of strain tensors, pik, εik and eik (for example, ). The dilatation is denoted by Δ. The rigidity and bulk moduli μ and κ are, if not constants, essentially scalar functions of the stress tensor. The variable viscosity η involves two constants, the yield value ϑ and the reciprocal mobility η1.

The global Hölder-continuous solution of isentropic gas dynamics

1993 ◽  
Vol 123 (2) ◽  
pp. 231-238 ◽  
Author(s):  
Yun-Guang Lu
Keyword(s):  
Cauchy Problem ◽  
Gas Dynamics ◽  
Continuous Solution ◽  
Hölder Continuous ◽  
Vanishing Viscosity ◽  
Equations Of Gas Dynamics ◽  
The Cauchy Problem ◽  
Isentropic Gas Dynamics ◽  
Isentropic Gas

SynopsisThis paper considers the Cauchy problem for the isentropic equations of gas dynamics in Euler coordinates ρt + (ρu)x = 0, (ρu)t + (ρu)2 + P(ρ))x=0 and gives the Hölder-continuous solution by applying the method of vanishing viscosity.

scholarly journals Hölder Continuous Euler Flows in Three Dimensions with Compact Support in Time

2017 ◽  
Author(s):  
Philip Isett
Keyword(s):  
Weak Solutions ◽  
Compact Support ◽  
Main Lemma ◽  
Three Dimensions ◽  
Nonlinear Pdes ◽  
Hölder Continuous ◽  
Nonlinear Phase ◽  
Nonuniqueness Of Solutions ◽  
Fluid Dynamics Equations ◽  
Onsager’S Conjecture

Motivated by the theory of turbulence in fluids, the physicist and chemist Lars Onsager conjectured in 1949 that weak solutions to the incompressible Euler equations might fail to conserve energy if their spatial regularity was below 1/3-Hölder. This book uses the method of convex integration to achieve the best-known results regarding nonuniqueness of solutions and Onsager's conjecture. Focusing on the intuition behind the method, the ideas introduced now play a pivotal role in the ongoing study of weak solutions to fluid dynamics equations. The construction itself—an intricate algorithm with hidden symmetries—mixes together transport equations, algebra, the method of nonstationary phase, underdetermined partial differential equations (PDEs), and specially designed high-frequency waves built using nonlinear phase functions. The powerful “Main Lemma”—used here to construct nonzero solutions with compact support in time and to prove nonuniqueness of solutions to the initial value problem—has been extended to a broad range of applications that are surveyed in the appendix. Appropriate for students and researchers studying nonlinear PDEs, this book aims to be as robust as possible and pinpoints the main difficulties that presently stand in the way of a full solution to Onsager's conjecture.

Replication of Bacteriophage 186 DNA

1972 ◽  
Vol 30 ◽  
pp. 194-195
Author(s):  
Dhruba K. Chattoraj ◽  
Ross B. Inman
Keyword(s):  
Electron Microscopy ◽  
Dna Replication ◽  
Frame Of Reference ◽  
Dna Molecules ◽  
E Coli ◽  
Phage Dna ◽  
Partial Denaturation

Electron microscopy of replicating intermediates has been quite useful in understanding the mechanism of DNA replication in DNA molecules of bacteriophage, mitochondria and plasmids. The use of partial denaturation mapping has made the tool more powerful by providing a frame of reference by which the position of the replicating forks in bacteriophage DNA can be determined on the circular replicating molecules. This provided an easy means to find the origin and direction of replication in λ and P2 phage DNA molecules. DNA of temperate E. coli phage 186 was found to have an unique denaturation map and encouraged us to look into its mode of replication.

Die Spezifität von Begabungsüberzeugungen als Determinante des verbalen und mathematischen Begabungsselbstkonzepts

2002 ◽  
Vol 16 (2) ◽  
pp. 87-97 ◽  
Author(s):  
Jens Möller ◽  
Britta Pohlmann ◽  
Lilian Streblow ◽  
Julia Kaufmann
Keyword(s):  
Reference Model ◽  
Frame Of Reference ◽  
External Frame

Zusammenfassung: Das I/E-Modell (“Internal/External Frame of Reference Model”) von Marsh (1986) postuliert, dass Schülerinnen und Schüler dimensionale Vergleiche der eigenen Leistungen in einem Fach mit den Leistungen in einem anderen Fach anstellen. Diese Vergleiche führen dazu, dass z. B. Schüler mit guten Leistungen in Mathematik ihre verbalen Fähigkeiten niedriger einschätzen. Gegenstand dieser Untersuchung mit N = 1114 Probanden ist die Frage, ob die Überzeugungen von Personen zum Zusammenhang von mathematischer und verbaler Begabung die Effekte dimensionaler Vergleiche moderieren. Analysen zeigten die Bedeutung der Begabungsüberzeugungen der Schülerinnen und Schüler: Negative Zusammenhänge zwischen den Fachleistungen in einem Fach und dem akademischen Selbstkonzept in einem anderen Fach ergaben sich insbesondere für Personen, die annehmen, dass Begabung domänenspezifisch ist, man also entweder mathematisch oder sprachlich begabt ist. Für Schüler mit eher wenig spezifischer Begabungsüberzeugung ergaben sich geringere Effekte dimensionaler Vergleiche.

Values and intergroup perceptions of East Germans and West Germans in 1998 1This research was supported by a grant from the German Research Society (We 1106/3-1).

1999 ◽  
Vol 58 (4) ◽  
pp. 263-272
Author(s):  
Jörg Doll ◽  
Michael Dick
Keyword(s):  
Research Society ◽  
Frame Of Reference ◽  
Control Group ◽  
Perceived Similarity ◽  
The West ◽  
Need For Uniqueness ◽  
German Research ◽  
East German ◽  
Experimental Group ◽  
East West

The studies reported here focus on similarities and dissimilarities between the terminal value hierarchies ( Rokeach, 1973 ) ascribed to different groups ( Schwartz & Struch, 1990 ). In Study 1, n = 65 East Germans and n = 110 West Germans mutually assess the respective ingroup and outgroup. In this intra-German comparison the West Germans, with a mean intraindividual correlation of rho = 0.609, perceive a significantly greater East-West similarity between the group-related value hierarchies than the East Germans, with a mean rho = 0.400. Study 2 gives East German subjects either a Swiss (n = 58) or Polish (n = 59) frame of reference in the comparison between the categories German and East German. Whereas the Swiss frame of reference should arouse a need for uniqueness, the Polish frame of reference should arouse a need for similarity. In accordance with expectations, the Swiss frame of reference significantly reduces the correlative similarity between German and East German from a mean rho = 0.703 in a control group (n = 59) to a mean rho = 0.518 in the experimental group. Contrary to expectations, the Polish frame of reference does not lead to an increase in perceived similarity (mean rho = 0.712).

Wie generell ist das Modell?

2004 ◽  
Vol 18 (3/4) ◽  
pp. 221-230 ◽  
Author(s):  
Susanne R. Schilling ◽  
Jörn R. Sparfeldt ◽  
Detlef H. Rost
Keyword(s):  
Frame Of Reference ◽  
External Frame

Zusammenfassung: Im Rahmen der Genese schulischer Selbstkonzepte postuliert das “Internal/External Frame of Reference”-Modell (I/E-M, Marsh, 1986 ) zwei (gegenläufige) Vergleichsprozesse: Neben sozialen Vergleichen spielen auch dimensionale Vergleiche (Leistungen in verschiedenen Fächern werden einander gegenübergestellt) eine Rolle. Diese sollen zu Kontrasteffekten führen, d. h. zu negativen Pfaden der Leistung in einem Fach (z. B. Mathematik) auf das Selbstkonzept in einem anderen Fach (z. B. Deutsch). Empirische Untersuchungen konzentrierten sich bislang hauptsächlich auf Mathematik und (Mutter-)Sprache. An N = 1632 Gymnasiasten haben wir das I/E-M strukturgleichungsbasiert für zwei sprachliche (Deutsch, Englisch), zwei naturwissenschaftliche (Physik, Mathematik) und zwei nicht eindeutig einer Domäne zugehörige Fächer (Geschichte, Biologie) überprüft. Neben Kontrasteffekten traten auch Assimilationseffekte (positive Pfade der Leistung in einem Fach auf das Selbstkonzept in einem anderen Fach) auf. Zukünftig müsste präzisiert werden, welche Faktoren das Ergebnis dimensionaler Vergleiche (Assimilation oder Kontrast) moderieren.

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