Experiments on Jet Flows and Jet Noise Far- Field Spectra and Directivity Patterns

Jet flows and jet noise far-field spectral and direction pattern

Kadison-Kastler stable factors

A conjecture of Kadison and Kastler from 1972 asks whether sufficiently close operator algebras in a natural uniform sense must be small unitary perturbations of one another. For n≥3 and a free, ergodic, probability measure-preserving action of SL<sub>n</sub>(Z) on a standard nonatomic probability space (X,μ), write M=(L<sup>∞</sup>(X,μ)⋊SL<sub>n</sub>(Z))⊗¯¯¯R, where R is the hyperfinite II1-factor. We show that whenever M is represented as a von Neumann algebra on some Hilbert space H and N⊆B(H) is sufficiently close to M, then there is a unitary u on H close to the identity operator with uMu∗=N. This provides the first nonamenable class of von Neumann algebras satisfying Kadison and Kastler’s conjecture. We also obtain stability results for crossed products L<sup>∞</sup>(X,μ)⋊Γ whenever the comparison map from the bounded to usual group cohomology vanishes in degree 2 for the module L<sup>2</sup>(X,μ). In this case, any von Neumann algebra sufficiently close to such a crossed product is necessarily isomorphic to it. In particular, this result applies when Γ is a free group

A remark on the similarity and perturbation problems

In this note we show that Kadison's similarity problem for C*-algebras is equivalent to a problem in perturbation theory: must close C*-algebras have close commutants?Comment: 6 Pages, minor typos fixed. C. R. Acad. Sci. Canada, to appea

C*-algebras nearly contained in type I algebras

In this paper we consider near inclusions $A\subseteq_\gamma B$ of C$^*$-algebras. We show that if $B$ is a separable type I C*-algebra and $A$ satisfies Kadison's similarity problem, then $A$ is also type I and use this to obtain an embedding of $A$ into $B$.Comment: 17 Page

Deficient maturation of aspects of attention and executive functions in early onset schizophrenia

The few existing long-term, neuropsychological follow-up studies of early onset schizophrenia (EOS) patients have reported relative stability in some cognitive functions but abnormal developmental trajectories in verbal memory, set shifting, aspects of attention, and speed of information processing throughout late adolescence into early adulthood. The current 5-year follow-up study compared the development of specific cognitive functions in EOS patients (N = 17) from the time of first-episode to chronic phase with that of healthy controls (N = 38) and secondarily to patients with other early onset, non-organic, non-affective psychoses (EOP) (N = 11). Speed of processing of executive functions, set shifting, and attention improved significantly in the healthy controls and reflected continuous functional maturation during late adolescence and early adulthood. The developmental progression of attention and set shifting but not speed of processing of executive functions was significantly subnormal in EOS patients. Other specific cognitive functions that had attained functional maturity in the healthy controls before or around the time of the baseline assessment showed normal development in EOS patients during the follow-up period, indicating stable cognitive deficits. These results suggest post-onset developmental deficits in two out of the three aspects of attention and executive functions that have protracted maturational trajectories and that overlap the age of onset of EOS. No significant difference in the development of any specific cognitive function was found between the EOS and EOP group

C*-algebras nearly contained in type I algebras

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Course of intelligence deficits in early onset, first episode schizophrenia: a controlled, 5-year longitudinal study

Only few prospective longitudinal studies have assessed the course of intelligence deficits in early onset schizophrenia (EOS), and these have used different age appropriate versions of Wechsler Intelligence Scales and age appropriate norms. The post-psychotic development of intelligence in EOS has predominantly been characterized as relatively stable in these studies. However, comparisons of IQs from different test versions based on the different norms may not permit unequivocal interpretations. The objective of the current study was to compare the development of intelligence in EOS patients (N = 10) from their first psychotic episode to 5 years of post onset with that of healthy controls (N = 35) and patients who at baseline had been diagnosed with other non-affective psychoses (N = 8). The same version of a Wechsler Intelligence Scale was administered at both baseline and follow-up assessments, and the same norms were used to derive IQs at baseline and follow-up. Significantly smaller change in mean full scale intelligence quotient (FSIQ) was found in diagnostically stable EOS patients compared with healthy controls during the follow-up period. However, no statistically significant difference in mean FSIQ change was observed between patients with EOS and patients with other non-affective psychoses, although this result must be interpreted with caution due to the small sample sizes. The results suggest abnormally slow acquisition of new intellectual information and skills in EOS patients during the first 5 years after full clinical presentation

Perturbations of nuclear C*-algebras

Kadison and Kastler introduced a natural metric on the collection of all C*-subalgebras of the bounded operators on a separable Hilbert space. They conjectured that sufficiently close algebras are unitarily conjugate. We establish this conjecture when one algebra is separable and nuclear. We also consider one-sided versions of these notions, and we obtain embeddings from certain near inclusions involving separable nuclear C*-algebras. At the end of the paper we demonstrate how our methods lead to improved characterisations of some of the types of algebras that are of current interest in the classification programme.Comment: 45 page

Settling velocity of microplastic particles having regular and irregular shapes

The settling velocities of 66 microplastic particle groups, having both regular (58) and irregular (eight) shapes, are measured experimentally. Regular shapes considered include: spheres, cylinders, disks, square plates, cubes, other cuboids (square and rectangular prisms), tetrahedrons, and fibers. The experiments generally consider Reynolds numbers greater than 102, extending the predominant range covered by previous studies. The present data is combined with an extensive data set from the literature, and the settling velocities are systematically analyzed on a shape-by-shape basis. Novel parameterizations and predictive drag coefficient formulations are developed for both regular and irregular particle shapes, properly accounting for preferential settling orientation. These are shown to be more accurate than the best existing predictive formulation from the literature. The developed method for predicting the settling velocity of irregularly-shaped microplastic particles is demonstrated to be equally well suited for natural sediments in the Appendix