335 research outputs found
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 and and a parameter , we
choose at random a vector subspace of dimension . We show that the
set of -tuples of singular values of all unit vectors in fills
asymptotically (as tends to infinity) a deterministic convex set
that we describe using a new norm in .
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
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