Confluent operator algebras and the closability property

Certain operator algebras A on a Hilbert space have the property that every densely defined linear transformation commuting with A is closable. Such algebras are said to have the closability property. They are important in the study of the transitive algebra problem. More precisely, if A is a two-transitive algebra with the closability property, then A is dense in the algebra of all bounded operators, in the weak operator topology. In this paper we focus on algebras generated by a completely nonunitary contraction, and produce several new classes of algebras with the closability property. We show that this property follows from a certain strict cyclicity property, and we give very detailed information on the class of completely nonunitary contractions satisfying this property, as well as a stronger property which we call confluence.Comment: Preliminary versio

MODELLING THE ELECTRON WITH COSSERAT ELASTICITY

Interactions between a finite number of bodies and the surrounding fluid, in a channel for instance, are investigated theoretically. In the planar model here the bodies or modelled grains are thin solid bodies free to move in a nearly parallel formation within a quasi-inviscid fluid. The investigation involves numerical and analytical studies and comparisons. The three main features that appear are a linear instability about a state of uniform motion, a clashing of the bodies (or of a body with a side wall) within a finite scaled time when nonlinear interaction takes effect, and a continuum-limit description of the body–fluid interaction holding for the case of many bodies

One-sided Cauchy-Stieltjes Kernel Families

This paper continues the study of a kernel family which uses the Cauchy-Stieltjes kernel in place of the celebrated exponential kernel of the exponential families theory. We extend the theory to cover generating measures with support that is unbounded on one side. We illustrate the need for such an extension by showing that cubic pseudo-variance functions correspond to free-infinitely divisible laws without the first moment. We also determine the domain of means, advancing the understanding of Cauchy-Stieltjes kernel families also for compactly supported generating measures

A Multiscale Model of Partial Melts 1: Effective Equations

In this paper a model for partial melts is constructed using two-scale homogenization theory. While this technique is well known to the mathematics and materials communities, it is relatively novel to problems in the solid Earth. This approach begins with a grain scale model of the medium, coarsening it into a macroscopic one. The emergent model is in good agreement with previous work, including D. McKenzie's, and serves as verification. This methodology also yields a series of Stokes problems whose solutions provide constitutive relations for permeability and viscosity. A numerical investigation of these relations appears in a companion paper.Comment: 55 pages. Submitted to JGR Solid Eart

A Multiscale Model of Partial Melts 2: Numerical Results

In a companion paper, equations for partially molten media were derived using two-scale homogenization theory. One advantage of homogenization is that material properties, such as permeability and viscosity, readily emerge. A caveat is that the dependence of these parameters upon the microstructure is not self-evident. In particular, one seeks to relate them to the porosity. In this paper, we numerically solve ensembles of the cell problems from which these quantities emerge. Using this data, we estimate relationships between the parameters and the porosity. In particular, the bulk viscosity appears to be inversely proportional to the porosity. Finally, we synthesize these numerical estimates with the models. Our hybrid numerical--analytical model predicts that the compaction length vanishes with porosity.Comment: 50 pages, submitted to JGR Solid Eart

The Psyche Gravity Investigation

The objective of the NASA Psyche mission gravity science investigation is to map the mass distribution within asteroid (16) Psyche to elucidate interior structure and to resolve the question of whether this metal-rich asteroid represents a remnant metal core or whether it is a primordial body that never melted. Measurements of gravity will be obtained via the X-band telecommunication system on the Psyche spacecraft, collected from progressively lower mapping altitudes. Orbital gravity will allow an estimate of GM to better than 0.001 km3 s−2. A spherical harmonic model of gravity to degree and order 10 will be achievable and, in concert with spherical harmonic data sets from topography and magnetometry, as well as surface composition data, will provide information regarding the spatial and radial distribution of mass that will be used to constrain the origin and evolution of (16) Psyche

Laws of large numbers for eigenvectors and eigenvalues associated to random subspaces in a tensor product

Given two positive integers $n$ and $k$ and a parameter $t\in (0,1)$, we choose at random a vector subspace $V_{n}\subset \mathbb{C}^{k}\otimes\mathbb{C}^{n}$ of dimension $N\sim tnk$. We show that the set of $k$-tuples of singular values of all unit vectors in $V_n$ fills asymptotically (as $n$ tends to infinity) a deterministic convex set $K_{k,t}$ that we describe using a new norm in $\R^k$. Our proof relies on free probability, random matrix theory, complex analysis and matrix analysis techniques. The main result result comes together with a law of large numbers for the singular value decomposition of the eigenvectors corresponding to large eigenvalues of a random truncation of a matrix with high eigenvalue degeneracy.Comment: v3 changes: minor typographic improvements; accepted versio

African ancestry allelic variation at the MYH9 gene contributes to increased susceptibility to non-diabetic end-stage kidney disease in Hispanic Americans

Recent studies identified MYH9 as a major susceptibility gene for common forms of non-diabetic end-stage kidney disease (ESKD). A set of African ancestry DNA sequence variants comprising the E-1 haplotype, was significantly associated with ESKD. In order to determine whether African ancestry variants are also associated with disease susceptibility in admixed populations with differing genomic backgrounds, we genotyped a total of 1425 African and Hispanic American subjects comprising dialysis patients with diabetic and non-diabetic ESKD and controls, using 42 single nucleotide polymorphisms (SNPs) within the MYH9 gene and 40 genome-wide and 38 chromosome 22 ancestry informative markers. Following ancestry correction, logistic regression demonstrated that three of the E-1 SNPs are also associated with non-diabetic ESKD in the new sample sets of both African and Hispanic Americans, with a stronger association in Hispanic Americans. We also identified MYH9 SNPs that are even more powerfully associated with the disease phenotype than the E-1 SNPs. These newly associated SNPs, could be divided into those comprising a haplotype termed S-1 whose association was significant under a recessive or additive inheritance mode (rs5750248, OR 4.21, P < 0.01, Hispanic Americans, recessive), and those comprising a haplotype termed F-1 whose association was significant under a dominant or additive inheritance mode (rs11912763, OR 4.59, P < 0.01, Hispanic Americans, dominant). These findings strengthen the contention that a sequence variant of MYH9, common in populations with varying degrees of African ancestry admixture, and in strong linkage disequilibrium with the associated SNPs and haplotypes reported herein, strongly predisposes to non-diabetic ESKD