Ghost-matter mixing and feigenbaum universality in string theory

Branelike vertex operators, defining backgrounds with ghost-matter mixing in Neveu-Schwarz-Ramond superstring theory, play an important role in a world-sheet formulation of D branes and M theory, being creation operators for extended objects in the second quantized formalism. We show that the dilaton beta function in ghost-matter mixing backgrounds becomes stochastic. The renormalization group (RG) equations in ghost-matter mixing backgrounds lead to non-Markovian Fokker-Planck equations whose solutions describe superstrings in curved spacetimes with branelike metrics. We show that the Feigenbaum universality constant δ=4.669 ..., describing transitions from order to chaos in a huge variety of dynamical systems, appears analytically in these RG equations. We find that the appearance of this constant is related to the scaling of relative spacetime curvatures at fixed points of the RG flow. In this picture, the fixed points correspond to the period doubling of Feigenbaum iterational schemes.

     

High-Q whispering gallery modes in a spherical shell dielectric resonator: Characterization at microwave frequencies

We present a numerical and experimental characterization of high-Q whispering gallery resonant modes excited in a fused quartz spherical shell operated in the 18-26.5 GHz band; easy coupling and selection of modes is a most advantageous feature of the proposed structure with respect to ordinary bulk resonators. The numerical results, based on a finite element algorithm, well match experimental data, which also show the capability of our device to perform gaseous spectroscopy measurements. Received 25 October 2002 Published online 4 February 2003     

Reliability Estimation of Classification Algorithms. I. Introduction to the Problem. Point Frequency Estimates

The study deals with estimating the reliability of classification algorithms. The present article (the first of three) examines the statistical methods used for point estimation of the reliability of classifiers in the frequency approach. The estimation results are applicable to the small-sample case, which is of considerable importance in practice.     

Simulation of Convective Flow of an Electrically Conducting Fluid in a Cavity

A new quasi-hydrodynamic algorithm is proposed for numerical analysis of convective flows in the presence of a homogeneous external magnetic field. The Marangoni convection problem in a square cross-section cavity is solved.     

Lubin–Tate Formal Groups over the Ring of Integers of a Multidimensional Local Field

Some isomorphism criteria for Lubin–Tate formal groups over the ring of integers of a multidimensional local field are given. Bibliography: 4 titles.     

Embedding of Nonprimary Subgroups in the Symmetric Group S 9

The nonprimary subgroups of the symmetric group S ₉ are investigated. Embedding properties of these subgroups are listed in a table. Properties such as abnormality, pronormality, paranormality, weak normality, etc. were checked with the help of a computer. Algorithms and codes of the first author were used for this purpose. The research leans upon the technique of Burnside marks, as well as upon pertinent information on the table of marks of S ₉ from the computer algebra package GAP. The subgroups were investigated up to conjugacy; the total number of conjugacy classes of nonprimary subgroups of S ₉ is 432. Some subgroups were additionally checked by other programs based on the double coset method. Bibliography: 24 titles.     

Heuristic Rejection in Interval Global Optimization

Based on the investigation carried out in Ref. 1, this paper incorporates new studies about the properties of inclusion functions on subintervals while a branch-and-bound algorithm is solving global optimization problems. It is found that the relative place of the global minimum value within the inclusion function value of the objective function at the current interval indicates mostly whether the given interval is close to a minimizer point. This information is used in a heuristic interval rejection rule that can save a considerable amount of computation. Illustrative examples are discussed and an extended numerical study shows the advantages of the new approach.