Interior regularity criteria for suitable weak solutions of the Navier-Stokes equations

We present new interior regularity criteria for suitable weak solutions of the 3-D Navier-Stokes equations: a suitable weak solution is regular near an interior point $z$ if either the scaled $L^{p,q}_{x,t}$-norm of the velocity with $3/p+2/q\leq 2$, $1\leq q\leq \infty$, or the $L^{p,q}_{x,t}$-norm of the vorticity with $3/p+2/q\leq 3$, $1 \leq q < \infty$, or the $L^{p,q}_{x,t}$-norm of the gradient of the vorticity with $3/p+2/q\leq 4$, $1 \leq q$, $1 \leq p$, is sufficiently small near $z$

A geometric condition implying energy equality for solutions of 3D Navier-Stokes equation

We prove that every weak solution $u$ to the 3D Navier-Stokes equation that belongs to the class $L^3L^{9/2}$ and \n u belongs to $L^3L^{9/5}$ localy away from a 1/2-H\"{o}lder continuous curve in time satisfies the generalized energy equality. In particular every such solution is suitable.Comment: 10 page

Partial Regularity of solutions to the Four-dimensional Navier-Stokes equations at the first blow-up time

The solutions of incompressible Navier-Stokes equations in four spatial dimensions are considered. We prove that the two-dimensional Hausdorff measure of the set of singular points at the first blow-up time is equal to zero.Comment: 19 pages, a comment regarding five or higher dimensional case is added in Remark 1.3. accepted by Comm. Math. Phy

Independent analysis of the orbits of Pioneer 10 and 11

Independently developed orbit determination software is used to analyze the orbits of Pioneer 10 and 11 using Doppler data. The analysis takes into account the gravitational fields of the Sun and planets using the latest JPL ephemerides, accurate station locations, signal propagation delays (e.g., the Shapiro delay, atmospheric effects), the spacecrafts' spin, and maneuvers. New to this analysis is the ability to utilize telemetry data for spin, maneuvers, and other on-board systematic effects. Using data that was analyzed in prior JPL studies, the anomalous acceleration of the two spacecraft is confirmed. We are also able to put limits on any secondary acceleration (i.e., jerk) terms. The tools that were developed will be used in the upcoming analysis of recently recovered Pioneer 10 and 11 Doppler data files.Comment: 22 pages, 5 figures; accepted for publication in IJMP

Bacterial adherence and hemolysin production from Escherichia coli induces histamine and leukotriene release from various cells

We investigated the role of bacterial adherence and hemolysin production from Escherichia coli parent and genetically cloned strains as to their eft'ects on bistaJidne release from rat mast cells and leukotriene generation from human polymorphonuclear granulocytes. These mediators were involved in the induction of inftammatory disease processes and led, for example, to enhancement of vascular permeability, chemotaxis (leukotriene 84 [LTB4]), chemoaggregation, lysosomal enzyme release, and smooth muscle contraction, (LTC4, LTD4 , and LTE4). Washed bacteria (E. coli K-12 Ms+ my=; E. coli 536 Ms+ MR= my=) as weil as their culture supematants were analyzed. Washed E. coli K-12 (Hiy+), unlike Hly- strains, induced high amounts of histamine release from rat mast cells and chemotactic activity from human polymorphonuclear granulocytes. Significant leukotriene releasewas obtained with washed E. coli K-12 my+ strains and their bacterial culture supematants. Leukotriene induction was dependent on the amount of hemolysin activity present in the supematant. However, additional soluble factors should also be considered. The presence of hemolysin appeared to aceeierate and enhance the rate of phagocytosis of bacteria by neutrophUs. When E. coli 536 (MS+ MR= Hly=) strains were analyzed, the simultaneous presence of MR+ pili and hemolysin production led to an increase in histamine release as compared with MR- my+ strains. The genetically cloned MR+ my+ E. coli 536 strain induced higher amounts of IeukotrieDes as compared with the wUd-type strain. Our data soggest a potent role for adhesins and hemolysin as virulence factors in inducing the release of inftammatory mediators

On admissibility criteria for weak solutions of the Euler equations

We consider solutions to the Cauchy problem for the incompressible Euler equations satisfying several additional requirements, like the global and local energy inequalities. Using some techniques introduced in an earlier paper we show that, for some bounded compactly supported initial data, none of these admissibility criteria singles out a unique weak solution. As a byproduct we show bounded initial data for which admissible solutions to the p-system of isentropic gas dynamics in Eulerian coordinates are not unique in more than one space dimension.Comment: 33 pages, 1 figure; v2: 35 pages, corrected typos, clarified proof

Use of real-time quantitative reverse transcription polymerase chain reaction for the detection of African horse sickness virus replication in Culicoides imicola

Despite its important role as vector for African horse sickness virus (AHSV), very little information is available on the dissemination of this virus in Culicoides (Avaritia) imicola Kieffer (Diptera: Ceratopogonidae). This study reports on the applicability of a real-time quantitative reverse transcription polymerase chain reaction (RT-qPCR) to detect AHSV in dissected midges. A total of 96 midges were fed on AHSV-infected blood, after which one test group was dissected into head/thorax and abdomen segments immediately after feeding and the other only after 10 days of incubation. The majority of the midges (96%) ingested the virus successfully and there was no significant difference between the virus concentration in the heads/thoraxes and the abdomens immediately after feeding. After incubation, virus was detected in 51% of the midges and it was confined to the abdomen in the majority of these. The fact that virus was detected only in the heads/thoraxes of four Culicoides midges after incubation suggests the presence of a mesenteronal escape barrier. Replication in the salivary glands was not shown. An increase of the mean virus concentration in the abdomen after incubation indicates localised viral replication. The real-time RT-qPCR is recommended for further studies investigating the replication and dissemination of AHSV in Culicoides midges

Hit-and-run algorithms for the indentification of nonredundant linear inequalities

Two probabilistic hit-and-run algorithms are presented to detect nonredundant constraints in a full dimensional system of linear inequalities. The algorithms proceed by generating a random sequence of interior points whose limiting distribution is uniform, and by searching for a nonredundant constraint in the direction of a random vector from each point in the sequence. In the hypersphere directions algorithm tile direction vector is drawn from a uniform distribution on a hypersphere. In tile computalionalb superior coordinate directions algorithm a search is carried out along one of the coordinate vectors. The algorithms are terminated through the use of a Bayesian stopping rule. Computational experience with the algorithms and the stopping rule will be reported