Global well-posedness and scattering for the defocusing energy-critical nonlinear Schr\"odinger equation in R1+4\R^{1+4}

We obtain global well-posedness, scattering, uniform regularity, and global $L^6_{t,x}$ spacetime bounds for energy-space solutions to the defocusing energy-critical nonlinear Schr\"odinger equation in $\R\times\R^4$. Our arguments closely follow those of Colliander-Keel-Staffilani-Takaoka-Tao, though our derivation of the frequency-localized interaction Morawetz estimate is somewhat simpler. As a consequence, our method yields a better bound on the $L^6_{t,x}$-norm

The support of the logarithmic equilibrium measure on sets of revolution in R3\R^3

For surfaces of revolution $B$ in $\R^3$, we investigate the limit distribution of minimum energy point masses on $B$ that interact according to the logarithmic potential $\log (1/r)$, where $r$ is the Euclidean distance between points. We show that such limit distributions are supported only on the ``out-most'' portion of the surface (e.g., for a torus, only on that portion of the surface with positive curvature). Our analysis proceeds by reducing the problem to the complex plane where a non-singular potential kernel arises whose level lines are ellipses

The Corrected Log N-Log Fluence Distribution of Cosmological Gamma-Ray Bursts

Recent analysis of relativistically expanding shells of cosmological gamma-ray bursts has shown that if the bursts are cosmological, then most likely total energy (E_0) is standard and not peak luminosity (L_0). Assuming a flat Friedmann cosmology (q_o = 1/2, Lambda = 0) and constant rate density (rho_0) of bursting sources, we fit a standard candle energy to a uniformly selected log N-log S in the BATSE 3B catalog correcting for fluence efficiency and averaging over 48 observed spectral shapes. We find the data consistent with E_0 = 7.3^{+0.7}_{-1.0} X 10^{51} ergs and discuss implications of this energy for cosmological models of gamma-ray bursts.Comment: A five page LateX file that uses the Revtex conference proceedings macro aipbook.sty, and includes three postscript figures using psfig. To Be published in the Proceedings of the Third Hunstville Symposium on Gamma-Ray Bursts, eds. C. Kouveliotou, M.S. Briggs and G.J. Fishman (New York:AIP). Postscript version availible at http://nis-www.lanl.gov/~jsbloom/LOG_S.p

Foreword

Since it was onlined in 2011, Journal of Harmonia has been accessed by thousands of visitors from all over the world. International index institutions, such as the Directory of Open Access Journal (DOAJ), Google Scholar, Mendely, Citeulike, and Worldcat, have been making Harmonia as one of the journals linked there. Likewise, national index institutions, such as the Indonesia Publication Index (IPI/Portal Garuda), Indonesian Scientific Journal Database (ISJD) that make Harmonia a national indexed journal.Based on the facts above, Harmonia needs to adjust while enhancing the quality and quantity to be more tangible to facilitate the readers and the authors of the article. The change of journal subtitle originally named Harmonia: Jurnal Pengetahuan dan Pemikiran Seni to become Harmonia: Journal of Arts Research and Education, with the entire contents of English articles from Volume 14 Number 1 in 2014 is an effort towards the dissemination of the content of Harmonia articles broadly. A manuscript writing guide is adjusted by using one of the standards of writing in the world of publication, namely the American Psychology Association (APA), though it is not entirely adopted. The addition of subtitles ‘education\u27 in the name of the journal affirms that the scope of the journal focuses on the content of the article about art studies and education.Our great appreciation to all the readers, writers and observers of art and art educators who have been supporting the publication of Harmonia. The expectation is that the presence of Harmonia in a new edition can complete the art literature that can contribute to the development of the science of art and art education

The two dimensional Hubbard model:a theoretical tool for molecular electronics

When speaking about molecular electronics, the obvious question which occurs is how does one study it theoretically. The simplest theoretical model suitable for application in molecular electronics is the two dimensional Hubbard model. The aim of the present paper is to introduce this model, and give some examples of the systems which it can describe. After a short mathematically oriented discussion, it will be shown how to calculate the electrical conductivity of a particular planar system: a rectangular lattice with mutually independent conductivities along the two axes,but without using the 2D Hamiltonian. This system could find applications in high Tc studies. It will finally be shown that the electrical conductivity of graphene can be determined not by using the full formalism of the $2D$ Hubbard model, but by a slight reformulation of the Hamiltonian of the 1D Hubbard modelComment: Lecture given at the 16 Int.School of Cond.Matt.Physics,August 29.,-September 3 2010.,Varna (Bulgaria

Is There Really a de Sitter/CFT Duality

In this paper a de Sitter Space version of Black Hole Complementarity is formulated which states that an observer in de Sitter Space describes the surrounding space as a sealed finite temperature cavity bounded by a horizon which allows no loss of information. We then discuss the implications of this for the existence of boundary correlators in the hypothesized dS/cft correspondence. We find that dS complementarity precludes the existence of the appropriate limits. We find that the limits exist only in approximations in which the entropy of the de Sitter Space is infinite. The reason that the correlators exist in quantum field theory in the de Sitter Space background is traced to the fact that horizon entropy is infinite in QFT.Comment: 12 Figures, STIAS Workshop on Quantum Gravit

New BeppoSAX-WFC results on superbursts

Presently seven superbursters have been identified representing 10% of the total Galactic X-ray burster population. Four superbursters were discovered with the Wide Field Cameras (WFCs) on BeppoSAX and three with the All-Sky Monitor and Proportional Counter Array on RXTE. We discuss the properties of superbursters as derived from WFC observations. There are two interesting conclusions. First, the average recurrence time of superbursts among X-ray bursters that are more luminous than 10% of the Eddington limit is 1.5 yr per object. Second, superbursters systematically have higher alpha values and shorter ordinary bursts than most bursters that have not exhibited superbursts, indicating a higher level of stable thermonuclear helium burning. Theory predicts hitherto undetected superbursts from the most luminous neutron stars. We investigate the prospects for finding these in GX~17+2.Comment: Submitted in January 2004 for the Proceedings of the meeting 'X-Ray Timing 2003: Rossi and Beyond', eds. P. Kaaret, F. K. Lamb, & J. H. Swank (Melville, NY: American Institute of Physics

Stability of central finite difference schemes for the Heston PDE

This paper deals with stability in the numerical solution of the prominent Heston partial differential equation from mathematical finance. We study the well-known central second-order finite difference discretization, which leads to large semi-discrete systems with non-normal matrices A. By employing the logarithmic spectral norm we prove practical, rigorous stability bounds. Our theoretical stability results are illustrated by ample numerical experiments