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

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

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

Higgs diphoton rate enhancement from supersymmetric physics beyond the MSSM

We show that supersymmetric "new physics" beyond the MSSM can naturally accommodate a Higgs mass near 126 GeV and enhance the signal rate in the Higgs to diphoton channel, while the signal rates in all the other Higgs decay channels coincide with Standard Model expectations, except possibly the Higgs to Z-photon channel. The "new physics" that corrects the relevant Higgs couplings can be captured by two supersymmetric effective operators. We provide a simple example of an underlying model in which these operators are simultaneously generated. The scale of "new physics" that generates these operators can be around 5 TeV or larger, and outside the reach of the LHC.Comment: 24 pages, 4 figure