Chern classes and extraspecial groups

The mod-p cohomology ring of the extraspecial p-group of exponent p is studied for odd p. We investigate the subquotient ch(G) generated by Chern classes modulo the nilradical. The subring of ch(G) generated by Chern classes of one-dimensional representations was studied by Tezuka and Yagita. The subring generated by the Chern classes of the faithful irreducible representations is a polynomial algebra. We study the interplay between these two families of generators, and obtain some relations between them

GENERALIZATIONS OF AN INVERSE FREE KRYLOV SUBSPACE METHOD FOR THE SYMMETRIC GENERALIZED EIGENVALUE PROBLEM

Symmetric generalized eigenvalue problems arise in many physical applications and frequently only a few of the eigenpairs are of interest. Typically, the problems are large and sparse, and therefore traditional methods such as the QZ algorithm may not be considered. Moreover, it may be impractical to apply shift-and-invert Lanczos, a favored method for problems of this type, due to difficulties in applying the inverse of the shifted matrix. With these difficulties in mind, Golub and Ye developed an inverse free Krylov subspace algorithm for the symmetric generalized eigenvalue problem. This method does not rely on shift-and-invert transformations for convergence acceleration, but rather a preconditioner is used. The algorithm suffers, however, in the presence of multiple or clustered eigenvalues. Also, it is only applicable to the location of extreme eigenvalues. In this work, we extend the method of Golub and Ye by developing a block generalization of their algorithm which enjoys considerably faster convergence than the usual method in the presence of multiplicities and clusters. Preconditioning techniques for the problems are discussed at length, and some insight is given into how these preconditioners accelerate the method. Finally we discuss a transformation which can be applied so that the algorithm extracts interior eigenvalues. A preconditioner based on a QR factorization with respect to the B-1 inner product is developed and applied in locating interior eigenvalues

Center and representations of infinitesimal Hecke algebras of sl_2

In this paper, we compute the center of the infinitesimal Hecke algebras Hz associated to sl_2 ; then using nontriviality of the center, we study representations of these algebras in the framework of the BGG category O. We also discuss central elements in infinitesimal Hecke algebras over gl(n) and sp(2n) for all n. We end by proving an analogue of the theorem of Duflo for Hz.Comment: Final form, to appear in "Communications in Algebra"; 35 pages, laTe

Commentary on Bessen and Meurer\u27s Patent Failure: An Industry Perspective

The paper is from a 2008 Symposium at the University of Georgia devoted to the book by James Bessen and Michael J. Meurer, Patent Failure: How Judges, Bureaucrats, and Lawyers Put Innovators At Risk . The paper provides an Overall Comment as to the conclusions of the book, Topical Comments as to specific items in the book, and then concludes with the author\u27s proposals for Patent Reform to Foster Innovation.The Overall Comment notes that the conclusions of the Bessen-Meurer book are sound. The U.S. patent system is not working for innovators or consumers. But the problems of the U.S. patent system go beyond the imperfect notice problem noted by the book\u27s authors. Not addressed by the book is the question of to what extent, if any, is patent ownership essential for innovation. References cited in the book suggest that patents owned by innovators are only infrequently important for innovation, and patents owned by others than the innovator can be impediments to innovation. The policy suggestion that flows the foregoing is that a patent system that fosters innovation requires high standards for patentability that result in fewer marginal patents to impede innovation.The Topical Comments note, among other things, that the Court of Appeals for the Federal Circuit was established (in 1982) despite the recommendation against a specialist patent court by the Hruska Commission in 1975, and that it almost immediately lowered the standards for patentability in the United States despite assurances to the contrary.The Two Fundamental Patent Reforms proposed by the author are (1) restoration to patent law of a self-correcting structure like that which applies to most other areas of federal law, and (2) enabling the United States Patent & Trademark Office to obtain final decisions as to the patentability of applications it has examined. The former reform can be accomplished by adopting the Nard-Duffy proposal for parallel appellate tracks for patent appeals or by restoring appellate jurisdiction in patent infringement cases to the regular courts of appeals. The latter reform can be achieved by abolishing all forms of continuing patent applications except for divisional applications filed pursuant to a 35 U.S.C. § 121 requirement for restriction so as to eliminate the ability of patent applicants to evade such final decisions

Chiral-Yang-Mills theory, non commutative differential geometry, and the need for a Lie super-algebra

In Yang-Mills theory, the charges of the left and right massless Fermions are independent of each other. We propose a new paradigm where we remove this freedom and densify the algebraic structure of Yang-Mills theory by integrating the scalar Higgs field into a new gauge-chiral 1-form which connects Fermions of opposite chiralities. Using the Bianchi identity, we prove that the corresponding covariant differential is associative if and only if we gauge a Lie-Kac super-algebra. In this model, spontaneous symmetry breakdown naturally occurs along an odd generator of the super-algebra and induces a representation of the Connes-Lott non commutative differential geometry of the 2-point finite space.Comment: 17 pages, no figur

The Vertical Structure of Planet-induced Gaps in Proto-Planetary Discs

Giant planets embedded in circumstellar discs are expected to open gaps in these discs. We examine the vertical structure of the gap edges. We find that the planet excites spiral arms with significant (Mach number of a half) vertical motion of the gas, and discuss the implications of these motions. In particular, the spiral arms will induce strong vertical stirring of the dust, making the edge appeared `puffed up' relative to the bulk of the disc. Infra-red observations (sensitive to dust) would be dominated by the light from the thick inner edge of the disc. Sub-millimetre observations (sensitive to gas velocities) would appear to be hot in `turbulent' motions (actually the ordered motion caused by the passage of the spiral arms), but cold in chemistry. Resolved sub-millimetre maps of circumstellar discs might even be able to detect the spiral arms directly.Comment: Revision adds new data, and corrects physical intepretatio

On higher derivative corrections to Wess-Zumino and Tachyonic actions in type II super string theory

We evaluate in detail the string scattering amplitude to compute different interactions of two massless scalars, one tachyon and one closed string Ramond-Ramond field in type II super string theory. In particular we find two scalar field and two tachyon couplings to all orders of $\alpha'$ up to on-shell ambiguity. We then obtain the momentum expansion of this amplitude and apply this infinite number of couplings to actually check that the infinite number of tachyon poles of S-matrix element of this amplitude for the $p=n$ case (where $p$ is the spatial dimension of a D$_p$-brane and $n$ is the rank of a Ramond-Ramond field strength) to all orders of $\alpha'$ is precisely equal to the infinite number of tachyon poles of the field theory. In addition to confirming the couplings of closed string Ramond-Ramond field to the world-volume gauge field and scalar fields including commutators, we also propose an extension of the Wess-Zumino action which naturally reproduces these new couplings in field theory such that they could be confirmed with direct S-matrix computations. Finally we show that the infinite number of massless poles and contact terms of this amplitude for the $p=n+1$ case can be reproduced by Chern-Simons, higher derivative corrections of the Wess-Zumino and symmetrized trace tachyon DBI actions.Comment: 51 pages, some refs and comments added, typos are removed. Almost all ambiguities in BPS and non-BPS effective actions have been addresse

Do Proto-Jovian Planets Drive Outflows?

We discuss the possibility that gaseous giant planets drive strong outflows during early phases of their formation. We consider the range of parameters appropriate for magneto-centrifugally driven stellar and disk outflow models and find that if the proto-Jovian planet or accretion disk had a magnetic field of >~ 10 Gauss and moderate mass inflow rates through the disk of less than 10^-7 M_J/yr that it is possible to drive an outflow. Estimates based both on scaling from empirical laws observed in proto-stellar outflows and the magneto-centrigugal disk and stellar+disk wind models suggest that winds with mass outflow rates of 10^-8 M_J/yr and velocities of order ~ 20 km/s could be driven from proto-Jovian planets. Prospects for detection and some implications for the formation of the solar system are briefly discussed.Comment: AAS Latex, accepted for Ap

Uncovering the kiloparsec-scale stellar ring of NGC5128

We reveal the stellar light emerging from the kiloparsec-scale, ring-like structure of the NGC5128 (Centaurus A) galaxy in unprecedented detail. We use arcsecond-scale resolution near infrared images to create a "dust-free" view of the central region of the galaxy, which we then use to quantify the shape of the revealed structure. At the resolution of the data, the structure contains several hundreds of discreet, point-like or slightly elongated sources. Typical extinction corrected surface brightness of the structure is K_S = 16.5 mag/arcsec^2, and we estimate the total near infrared luminosity of the structure to be M = -21 mag. We use diffraction limited (FWHM resolution of ~ 0.1", or 1.6 pc) near infrared data taken with the NACO instrument on VLT to show that the structure decomposes into thousands of separate, mostly point-like sources. According to the tentative photometry, the most luminous sources have M_K = -12 mag, naming them red supergiants or relatively low-mass star clusters. We also discuss the large-scale geometry implied by the reddening signatures of dust in our near infrared images.Comment: 5 pages, 4 figures, accepted for publication in A&A Letters. A version with high resolution images can be downloaded from http://www.helsinki.fi/~jtkainul/CenALette