Dihedral Quintic Fields with a Power Basis

It is shown that there exist infinitely many dihedral quintic fields with a power basis.</p

Functional Analytic Continuation Techniques with Applications in Field Theory

Often one has data at points inside the holomorphy domain of a Green’s function, or of an Amplitude or Form—Factor, and wants to obtain information about the spectral function i.e. the discontinuity along the cuts. Data may be experimental or theoretical. In QCD for example the perturbation expansion is valid only for unphysicaL values of the energy: one would like to continue this information to the cuts to find the resonance parameters. However, analytic continuation off open contours is extremely unstable. Also, the straightforward continuation of the truncated perturbation expansion will not do, since this is itself analytic and continuation will thus yield exactly the same result. This problem is solved by functional techniques, first by allowing small imprecisions in the data to remove the uniqueness of the continuation, and then by introducing a stabilizing condition suited to the particular physical problem, which will suppress the functions with incorrect behaviour. The stabilizing condition is expressed in terms of a norm giving a measure of the smoothness of the Discrepancy Function -which is the Amplitude with the resonances removed. The minimal norm computed from the data depends on the trial values of the resonance parameters and enables one to select the best values for these. The corresponding optimal amplitude is also constructed. An explicit solution is obtained for the case of a discrete data set; in the continuous case the problem is expressed in terms of a Fredholm integral equation

The Prime Ideal Factorization of 2 in Pure Quartic Fields with Index 2

The prime ideal decomposition of 2 in a pure quartic field with field index 2 is determined explicitly.</p

Diagonal and Low-Rank Matrix Decompositions, Correlation Matrices, and Ellipsoid Fitting

In this paper we establish links between, and new results for, three problems that are not usually considered together. The first is a matrix decomposition problem that arises in areas such as statistical modeling and signal processing: given a matrix $X$ formed as the sum of an unknown diagonal matrix and an unknown low rank positive semidefinite matrix, decompose $X$ into these constituents. The second problem we consider is to determine the facial structure of the set of correlation matrices, a convex set also known as the elliptope. This convex body, and particularly its facial structure, plays a role in applications from combinatorial optimization to mathematical finance. The third problem is a basic geometric question: given points $v_1,v_2,...,v_n\in \R^k$ (where $n > k$) determine whether there is a centered ellipsoid passing \emph{exactly} through all of the points. We show that in a precise sense these three problems are equivalent. Furthermore we establish a simple sufficient condition on a subspace $U$ that ensures any positive semidefinite matrix $L$ with column space $U$ can be recovered from $D+L$ for any diagonal matrix $D$ using a convex optimization-based heuristic known as minimum trace factor analysis. This result leads to a new understanding of the structure of rank-deficient correlation matrices and a simple condition on a set of points that ensures there is a centered ellipsoid passing through them.Comment: 20 page

On the Common Index Divisors of a Dihedral Field of Prime Degree

A criterion for a prime to be a common index divisor of a dihedral field of prime degree is given. This criterion is used to determine the index of families of dihedral fields of degrees 5 and 7

CAML Does Not Modulate Tetherin-Mediated Restriction of HIV-1 Particle Release

Background: Tetherin/BST-2 is a recently-identified potent restriction factor in human cells that restricts HIV particle release following particle formation and budding at the plasma membrane. Vpu counteracts tetherin’s restriction of particle release in a manner that has not yet been fully defined. We recently identified calcium-modulating cyclophilin ligand (CAML) as a Vpu-interacting protein that also restricts particle release. We hypothesized that CAML may act to enhance tetherinmediated restriction of particle release and thereby explain how two distinct factors could be responsible for Vpuresponsive restriction. Methodology/Principal Findings: Endogenous levels of tetherin in human cells correlated well with their restriction pattern and responsiveness to Vpu, while levels of cellular CAML protein did not. Tetherin but not CAML was inducible by interferon in a wide variety of human cells. Stable depletion of human CAML in restrictive HeLa cells had no effect on cell surface levels of tetherin, and failed to relieve tetherin-mediated restriction. Stable depletion of tetherin from HeLa cells, in contrast, rendered HeLa cells permissive and Vpu-unresponsive. Tetherin but not CAML expression in permissive human cells rendered them restrictive and Vpu responsive. Depletion of CAML had no influence on cell surface levels of tetherin. Conclusions/Significance: We conclude that tetherin restricts particle release and does not require CAML for this effect

The determination of integral closures and geometric applications

We express explicitly the integral closures of some ring extensions; this is done for all Bring-Jerrard extensions of any degree as well as for all general extensions of degree < 6; so far such an explicit expression is known only for degree < 4 extensions. As a geometric application we present explicitly the structure sheaf of every Bring-Jerrard covering space in terms of coefficients of the equation defining the covering; in particular, we show that a degree-3 morphism f : Y --> X is quasi-etale if and only if the first Chern class of the sheaf f_*(O_Y) is trivial (details in Theorem 5.3). We also try to get a geometric Galoisness criterion for an arbitrary degree-n finite morphism; this is successfully done when n = 3 and less satifactorily done when n = 5.Comment: Advances in Mathematics, to appear (no changes, just add this info