2,703 research outputs found
Construction of Doubly Periodic Solutions via the Poincare-Lindstedt Method in the case of Massless Phi^4 Theory
Doubly periodic (periodic both in time and in space) solutions for the
Lagrange-Euler equation of the (1+1)-dimensional scalar Phi^4 theory are
considered. The nonlinear term is assumed to be small, and the
Poincare-Lindstedt method is used to find asymptotic solutions in the standing
wave form. The principal resonance problem, which arises for zero mass, is
solved if the leading-order term is taken in the form of a Jacobi elliptic
function. It have been proved that the choice of elliptic cosine with fixed
value of module k (k=0.451075598811) as the leading-order term puts the
principal resonance to zero and allows us constructed (with accuracy to third
order of small parameter) the asymptotic solution in the standing wave form. To
obtain this leading-order term the computer algebra system REDUCE have been
used. We have appended the REDUCE program to this paper.Comment: 16 pages, LaTeX 2.09. This paper have been published in the
Electronic Proceedings of the Fourth International IMACS Conference on
Applications of Computer Algebra (ACA'98) {Prague (Czech Republic)} at
http://math.unm.edu/ACA/1998/sessions/dynamical/verno
An extension of Buchberger's criteria for Groebner basis decision
Two fundamental questions in the theory of Groebner bases are decision ("Is a
basis G of a polynomial ideal a Groebner basis?") and transformation ("If it is
not, how do we transform it into a Groebner basis?") This paper considers the
first question. It is well-known that G is a Groebner basis if and only if a
certain set of polynomials (the S-polynomials) satisfy a certain property. In
general there are m(m-1)/2 of these, where m is the number of polynomials in G,
but criteria due to Buchberger and others often allow one to consider a smaller
number.
This paper presents two original results. The first is a new characterization
theorem for Groebner bases that makes use of a new criterion that extends
Buchberger's Criteria. The second is the identification of a class of
polynomial systems G for which the new criterion has dramatic impact, reducing
the worst-case scenario from m(m-1)/2 S-polynomials to m-1.Comment: 20 pages, 2 figure
On the Killing form of Lie Algebras in Symmetric Ribbon Categories
As a step towards the structure theory of Lie algebras in symmetric monoidal
categories we establish results involving the Killing form. The proper
categorical setting for discussing these issues are symmetric ribbon
categories
Shifting Ethnic Identities in Spain and Gaul, 500-700: From Romans to Goths and Franks
Traditional scholarship on post-Roman western culture has tended to examine the ethnic identities of Goths, Franks, and similar groups while neglecting the Romans themselves, in part because modern scholars have viewed the concept of being Roman as one denoting primarily a cultural or legal affiliation. As this book demonstrates, however, early medieval \u27Romanness\u27 also encompassed a sense of belonging to an ethnic group, which allowed Romans in Iberia and Gaul to adopt Gothic or Frankish identities in a more nuanced manner than has been previously acknowledged in the literature
Romans, barbarians, and Franks in the writings of Venantius Fortunatus
This paper aims to contribute to the broader discussion of strategies of identification and of Romanness by exploring the changing meaning of Roman, barbarian, and Frankish identity in the writings of Venantius Fortunatus. A close examination of the cultural, ethnic and political nuances of these terms in Fortunatus\u27s works highlights the ways he used the resources available to him within his social context to promote Roman identity as still prestigious and as compatible with a barbarian‐ruled society
The Growth of Gothic Identity in Visigothic Spain: The Evidence of Textual Sources
In recent years, scholars have made significant progress in understanding the transition from a Roman world to a medieval world in Spain. New archaeological excavations have added to our knowledge of the early medieval landscape, and increasingly analytical discussions of the labels used to describe people and objects have brought new depth to both historical and archaeological studies. In place of black and white visions of Goth vs. Roman and continuity vs. discontinuity, it has become more common to see Visigothic Spain as a complex mix of elements on their own terms. What it was like be a Roman in ancient Spain, and a Visigoth in medieval Spain, is far clearer now than it was twenty years ago. However, one area that has been underexplored is the mental landscape: how did Hispano-Romans come to think of themselves, and be thought of by others, as Goths? How did the mental transition from identifying as Roman to identifying as Gothic happen
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