Some results on the Krein parameters of an association scheme

We consider association schemes with d classes and the underlying Bose- Mesner algebra, A. Then, by taking into account the relationship between the Hadamard and the Kronecker products of matrices and making use of some matrix techniques over the idempotents of the unique basis of minimal orthogonal idempotents of A , we prove some results over the Krein parameters of an association scheme

Using directional curvatures to visualize folding patterns of the GTM projection manifolds

In data visualization, characterizing local geometric properties of non-linear projection manifolds provides the user with valuable additional information that can influence further steps in the data analysis. We take advantage of the smooth character of GTM projection manifold and analytically calculate its local directional curvatures. Curvature plots are useful for detecting regions where geometry is distorted, for changing the amount of regularization in non-linear projection manifolds, and for choosing regions of interest when constructing detailed lower-level visualization plots

Steady and Stable: Numerical Investigations of Nonlinear Partial Differential Equations

Excerpt: Mathematics is a language which can describe patterns in everyday life as well as abstract concepts existing only in our minds. Patterns exist in data, functions, and sets constructed around a common theme, but the most tangible patterns are visual. Visual demonstrations can help undergraduate students connect to abstract concepts in advanced mathematical courses. The study of partial differential equations, in particular, benefits from numerical analysis and simulation

Sign Rules for Anisotropic Quantum Spin Systems

We present new and exact ``sign rules'' for various spin-s anisotropic spin-lattice models. It is shown that, after a simple transformation which utilizes these sign rules, the ground-state wave function of the transformed Hamiltonian is positive-definite. Using these results exact statements for various expectation values of off-diagonal operators are presented, and transitions in the behavior of these expectation values are observed at particular values of the anisotropy. Furthermore, the effects of sign rules in variational calculations and quantum Monte Carlo calculations are considered. They are illustrated by a simple variational treatment of a one-dimensional anisotropic spin model.Comment: 4 pages, 1 ps-figur

Small grid embeddings of 3-polytopes

We introduce an algorithm that embeds a given 3-connected planar graph as a convex 3-polytope with integer coordinates. The size of the coordinates is bounded by $O(2^{7.55n})=O(188^{n})$. If the graph contains a triangle we can bound the integer coordinates by $O(2^{4.82n})$. If the graph contains a quadrilateral we can bound the integer coordinates by $O(2^{5.46n})$. The crucial part of the algorithm is to find a convex plane embedding whose edges can be weighted such that the sum of the weighted edges, seen as vectors, cancel at every point. It is well known that this can be guaranteed for the interior vertices by applying a technique of Tutte. We show how to extend Tutte's ideas to construct a plane embedding where the weighted vector sums cancel also on the vertices of the boundary face

P-wave excited baryons from pion- and photo-induced hyperon production

We report evidence for $N(1710)P_{11}$, $N(1875)P_{11}$, $N(1900)P_{13}$, $\Delta(1600)P_{33}$, $\Delta(1910)P_{31}$, and $\Delta(1920)P_{33}$, and find indications that $N(1900)P_{13}$ might have a companion state at 1970\,MeV. The controversial $\Delta(1750)P_{31}$ is not seen. The evidence is derived from a study of data on pion- and photo-induced hyperon production, but other data are included as well. Most of the resonances reported here were found in the Karlsruhe-Helsinki (KH84) and the Carnegie-Mellon (CM) analyses but were challenged recently by the Data Analysis Center at GWU. Our analysis is constrained by the energy independent $\pi N$ scattering amplitudes from either KH84 or GWU. The two $\pi N$ amplitudes from KH84 or GWU, respectively, lead to slightly different $\pi N$ branching ratios of contributing resonances but the debated resonances are required in both series of fits.Comment: 22 pages, 28 figures. Some additional sets of data are adde

Field Measurements of Terrestrial and Martian Dust Devils

Surface-based measurements of terrestrial and martian dust devils/convective vortices provided from mobile and stationary platforms are discussed. Imaging of terrestrial dust devils has quantified their rotational and vertical wind speeds, translation speeds, dimensions, dust load, and frequency of occurrence. Imaging of martian dust devils has provided translation speeds and constraints on dimensions, but only limited constraints on vertical motion within a vortex. The longer mission durations on Mars afforded by long operating robotic landers and rovers have provided statistical quantification of vortex occurrence (time-of-sol, and recently seasonal) that has until recently not been a primary outcome of more temporally limited terrestrial dust devil measurement campaigns. Terrestrial measurement campaigns have included a more extensive range of measured vortex parameters (pressure, wind, morphology, etc.) than have martian opportunities, with electric field and direct measure of dust abundance not yet obtained on Mars. No martian robotic mission has yet provided contemporaneous high frequency wind and pressure measurements. Comparison of measured terrestrial and martian dust devil characteristics suggests that martian dust devils are larger and possess faster maximum rotational wind speeds, that the absolute magnitude of the pressure deficit within a terrestrial dust devil is an order of magnitude greater than a martian dust devil, and that the time-of-day variation in vortex frequency is similar. Recent terrestrial investigations have demonstrated the presence of diagnostic dust devil signals within seismic and infrasound measurements; an upcoming Mars robotic mission will obtain similar measurement types

The Projection Method for Reaching Consensus and the Regularized Power Limit of a Stochastic Matrix

In the coordination/consensus problem for multi-agent systems, a well-known condition of achieving consensus is the presence of a spanning arborescence in the communication digraph. The paper deals with the discrete consensus problem in the case where this condition is not satisfied. A characterization of the subspace $T_P$ of initial opinions (where $P$ is the influence matrix) that \emph{ensure} consensus in the DeGroot model is given. We propose a method of coordination that consists of: (1) the transformation of the vector of initial opinions into a vector belonging to $T_P$ by orthogonal projection and (2) subsequent iterations of the transformation $P.$ The properties of this method are studied. It is shown that for any non-periodic stochastic matrix $P,$ the resulting matrix of the orthogonal projection method can be treated as a regularized power limit of $P.$Comment: 19 pages, 2 figure

Industry concentration and strategic trade policy in successive oligopoly

We study a policy game between exporting and importing countries in vertically linked industries. In a successive international Cournot oligopoly, we analyse incentives for using tax instruments strategically to shift rents vertically, between exporting and importing countries, and horizontally, between exporting countries. We show that the equilibrium outcome depends crucially on the relative degree of competitiveness in the upstream and downstream parts of the industry. With respect to national welfare, a more competitive upstream industry may benefit an exporting (upstream) country and harm an importing (downstream) country. On the other hand, a more competitive downstream industry may harm exporting countries.Financial support from the Norwegian Research Council, through the PETROPOL research programme, is gratefully acknowledged. The paper has been greatly improved by the suggestions of two anonymous referees. We also thank Hisashi Hokari and Frode Meland for valuable comments and suggestions

Heavy quarkonium: progress, puzzles, and opportunities

A golden age for heavy quarkonium physics dawned a decade ago, initiated by the confluence of exciting advances in quantum chromodynamics (QCD) and an explosion of related experimental activity. The early years of this period were chronicled in the Quarkonium Working Group (QWG) CERN Yellow Report (YR) in 2004, which presented a comprehensive review of the status of the field at that time and provided specific recommendations for further progress. However, the broad spectrum of subsequent breakthroughs, surprises, and continuing puzzles could only be partially anticipated. Since the release of the YR, the BESII program concluded only to give birth to BESIII; the $B$-factories and CLEO-c flourished; quarkonium production and polarization measurements at HERA and the Tevatron matured; and heavy-ion collisions at RHIC have opened a window on the deconfinement regime. All these experiments leave legacies of quality, precision, and unsolved mysteries for quarkonium physics, and therefore beg for continuing investigations. The plethora of newly-found quarkonium-like states unleashed a flood of theoretical investigations into new forms of matter such as quark-gluon hybrids, mesonic molecules, and tetraquarks. Measurements of the spectroscopy, decays, production, and in-medium behavior of c\bar{c}, b\bar{b}, and b\bar{c} bound states have been shown to validate some theoretical approaches to QCD and highlight lack of quantitative success for others. The intriguing details of quarkonium suppression in heavy-ion collisions that have emerged from RHIC have elevated the importance of separating hot- and cold-nuclear-matter effects in quark-gluon plasma studies. This review systematically addresses all these matters and concludes by prioritizing directions for ongoing and future efforts.Comment: 182 pages, 112 figures. Editors: N. Brambilla, S. Eidelman, B. K. Heltsley, R. Vogt. Section Coordinators: G. T. Bodwin, E. Eichten, A. D. Frawley, A. B. Meyer, R. E. Mitchell, V. Papadimitriou, P. Petreczky, A. A. Petrov, P. Robbe, A. Vair