Determinants of Block Tridiagonal Matrices

An identity is proven that evaluates the determinant of a block tridiagonal matrix with (or without) corners as the determinant of the associated transfer matrix (or a submatrix of it).Comment: 8 pages, final form. To appear on Linear Algebra and its Application

Identities and exponential bounds for transfer matrices

This paper is about analytic properties of single transfer matrices originating from general block-tridiagonal or banded matrices. Such matrices occur in various applications in physics and numerical analysis. The eigenvalues of the transfer matrix describe localization of eigenstates and are linked to the spectrum of the block tridiagonal matrix by a determinantal identity, If the block tridiagonal matrix is invertible, it is shown that half of the singular values of the transfer matrix have a lower bound exponentially large in the length of the chain, and the other half have an upper bound that is exponentially small. This is a consequence of a theorem by Demko, Moss and Smith on the decay of matrix elements of inverse of banded matrices.Comment: To appear in J. Phys. A: Math. and Theor. (Special issue on Lyapunov Exponents, edited by F. Ginelli and M. Cencini). 16 page

Hedin's equations and enumeration of Feynman's diagrams

Hedin's equations are solved perturbatively in zero dimension to count Feynman graphs for self-energy, polarization, propagator, effective potential and vertex function in a many-body theory of fermions with two-body interaction. Counting numbers are also obtained in the GW approximation.Comment: Revised published version, 3 pages, no figure

On conformally recurrent manifolds of dimension greater than 4

Conformally recurrent pseudo-Riemannian manifolds of dimension n>4 are investigated. The Weyl tensor is represented as a Kulkarni-Nomizu product. If the square of the Weyl tensor is nonzero, a covariantly constant symmetric tensor is constructed, that is quadratic in the Weyl tensor. Then, by Grycak's theorem, the explicit expression of the traceless part of the Ricci tensor is obtained, up to a scalar function. The Ricci tensor has at most two distinct eigenvalues, and the recurrence vector is an eigenvector. Lorentzian conformally recurrent manifolds are then considered. If the square of the Weyl tensor is nonzero, the manifold is decomposable. A null recurrence vector makes the Weyl tensor of algebraic type IId or higher in the Bel - Debever - Ortaggio classification, while a time-like recurrence vector makes the Weyl tensor purely electric.Comment: Title changed and typos corrected. 14 page

Selberg integrals in 1D random Euclidean optimization problems

We consider a set of Euclidean optimization problems in one dimension, where the cost function associated to the couple of points $x$ and $y$ is the Euclidean distance between them to an arbitrary power $p\ge1$, and the points are chosen at random with flat measure. We derive the exact average cost for the random assignment problem, for any number of points, by using Selberg's integrals. Some variants of these integrals allows to derive also the exact average cost for the bipartite travelling salesman problem.Comment: 9 pages, 2 figure

Ab-initio self-energy corrections in systems with metallic screening

The calculation of self-energy corrections to the electron bands of a metal requires the evaluation of the intraband contribution to the polarizability in the small-q limit. When neglected, as in standard GW codes for semiconductors and insulators, a spurious gap opens at the Fermi energy. Systematic methods to include intraband contributions to the polarizability exist, but require a computationally intensive Fermi-surface integration. We propose a numerically cheap and stable method, based on a fit of the power expansion of the polarizability in the small-q region. We test it on the homogeneous electron gas and on real metals such as sodium and aluminum.Comment: revtex, 14 pages including 5 eps figures v2: few fixe

High Angular Resolution Observations of Four Candidate BLAST High-Mass Starless Cores

We discuss high-angular resolution observations of ammonia toward four candidate high-mass starless cores (HMSCs). The cores were identified by the Balloon-borne Large Aperture Submillimeter Telescope (BLAST) during its 2005 survey of the Vulpecula region where 60 compact sources were detected simultaneously at 250, 350, and 500 micron. Four of these cores, with no IRAS-PSC or MSX counterparts, were observed with the NRAO Very Large Array (VLA) in the NH3(1,1) and (2,2) spectral lines. Our observations indicate that the four cores are cold (Tk <~ 14K) and show a filamentary and/or clumpy structure. They also show a significant velocity substructure within ~1km/s. The four BLAST cores appear to be colder and more quiescent than other previously observed HMSC candidates, suggesting an earlier stage of evolution.Comment: Submitted to the Astrophysical Journal on January 22, 2010. Accepted for publication on April 15, 2010. The paper has 21 pages and 17 figures

Another proof of Gell-Mann and Low's theorem

The theorem by Gell-Mann and Low is a cornerstone in QFT and zero-temperature many-body theory. The standard proof is based on Dyson's time-ordered expansion of the propagator; a proof based on exact identities for the time-propagator is here given.Comment: 5 page

A Review

Ovarian cancer is the most common cause of death among gynecological malignancies. We discuss different types of clinical and nonclinical features that are used to study and analyze the differences between benign and malignant ovarian tumors. Computer-aided diagnostic (CAD) systems of high accuracy are being developed as an initial test for ovarian tumor classification instead of biopsy, which is the current gold standard diagnostic test. We also discuss different aspects of developing a reliable CAD system for the automated classification of ovarian cancer into benign and malignant types. A brief description of the commonly used classifiers in ultrasound-based CAD systems is also given