Analyzing specific cases of an operator inequality

AbstractLet H and K be Hilbert spaces, and suppose A ε B(H) and B ε B(K) are self-adjoint operators with dist(σ(A), σ(B))≥ δ > 0. In 1983 Bhatia, Davis, and McIntosh showed that for any Q εB(K,H) we must have (π;2)‖AQ−QB‖≥δ‖Q‖. In this paper we specialize their inequality to the case where A, Q, and B are 2 × 2 or 3 × 3 matrices, and give sharp estimates. Doing so, we illustrate one way that bounds on the norm of the Schur product of two matrices have applications to perturbation theory. By specializing the Fourier transform used in the proof of the theorem above, we also obtain sharp estimates in two Fourier interpolation problems

Production and Characterization of Biodegradable Nanofibers via Forcespinning™ Technology

Among the myriad of methods for polymer nanofiber production, there are only a few methods that can produce submicron range fibers in bulk from melt or solution samples. The Forcespinning™ method allows a substantial increase in sample yield; this greatly reduces the time needed to produce bulk quantities of fibers which may be critical in many fields of research and industry, in particularly in fields relating to biopolymers. The aim of the first study was to utilize this method to form non-woven mats of polycaprolactone (PCL) nanofibers and to quantitatively analyze the production and characterization of the produced fibers. The morphology and degree of crystallinity were characterized by SEM, DSC, and XRD. Additionally, as a second project, microcrystalline cellulose fibers were successfully regenerated from the ionic liquid 1-ethyl-3-methylimidazolium acetate using the Forcespinning™ method. Similarly, the cellulose fibers were subjected to various characterization techniques such as SEM, XRD, TGA, and FITR

The Consequences of Remote and Hybrid Instruction During the Pandemic

Using testing data from 2.1 million students in 10,000 schools in 49 states (plus D.C.), we investigate the role of remote and hybrid instruction in widening gaps in achievement by race and school poverty. We find that remote instruction was a primary driver of widening achievement gaps. Math gaps did not widen in areas that remained in-person (although there was some widening in reading gaps in those areas). We estimate that high-poverty districts that went remote in 2020-21 will need to spend nearly all their federal aid on academic recovery to help students recover from pandemic-related achievement losses

Combat damage assessment team A-10/GAU-8 low angle firings versus simulated Soviet tank company (Array 25) : (LAVP lot no. AJD79A181-001) (4 December 1979)

This report describes LAVP firings of the A-10/GAU-8 weapon system on 4 December 1979 against a Soviet tank company simulated by 10 combat loaded M-47 tanks. The pilots making the firing passes attacked at low altitude and used correspondingly low dive angles in order to simulate movement through a hostile air defense system. Ammunition used in the attacks comprised 30mm armor piercing incendiary (API) rounds which proved to be effective damage agents against substantial areas of the US MK 47 tanks used as targets. The pilots in ten successful firing passes fired a total of 381 rounds fo which 139 impacted the targets. Of the projectiles impacting on targets, 22 achieved perforations of the armored envelope. The simulated Soviet tank company was destroyed as a combat formation based on the assessment of damage to individual tankssupported by A-10 System Program Office, Wright-Patterson Air Force Base, Ohio.http://archive.org/details/combatdamageasse80012stolA-10 System Program Office Wright-Patterson Air Force Base OhioN

Developmental programming: Interaction between prenatal BPA and postnatal overfeeding on cardiac tissue gene expression in female sheep

Peer Reviewedhttp://deepblue.lib.umich.edu/bitstream/2027.42/136004/1/em22071.pdfhttp://deepblue.lib.umich.edu/bitstream/2027.42/136004/2/em22071_am.pd

Combat Damage Assessment Team, A-10/GAU-8 Special Report for Array Low Angle Firings Versus Simulated Soviet Firings of Tank Company (10 March 1978)

This report describes firings of the A-10/GAU-8 weapon system on 10 March 1978 against a Soviet tank company simulated by ten combat loaded M-47 tanks. The pilots attacked at low altitudes and dive angles simulating operations in hostile air defense environment. GAU-8 30mm Armor Piercing Incendiary Ammunition was fired achieving 253 impacts on the targets. The impacts included 43 perforations of the armored envelopes and inflicted damage totaling eight immobilized tanks four of which were catastrophically killed.A-10 System Program Office Wright-Patterson Air Poree Bas

Convergence of genetic influences in comorbidity

Abstract Background Predisposition to complex diseases is explained in part by genetic variation, and complex diseases are frequently comorbid, consistent with pleiotropic genetic variation influencing comorbidity. Genome Wide Association (GWA) studies typically assess association between SNPs and a single-disease phenotype. Fisher meta-analysis combines evidence of association from single-disease GWA studies, assuming that each study is an independent test of the same hypothesis. The Rank Product (RP) method overcomes limitations posed by Fisher assumptions, though RP was not designed for GWA data. Methods We modified RP to accommodate GWA data, and we call it modRP. Using p-values output from GWA studies, we aggregate evidence for association between SNPs and related phenotypes. To assess significance, RP randomly samples the observed ranks to develop the null distribution of the RP statistic, and then places the observed RPs into the null distribution. ModRP eliminates the effect of linkage disequilibrium and controls for differences in power at tested SNPs, to meet RP assumptions in application to GWA data. Results After validating modRP based on both positive and negative control studies, we searched for pleiotropic influences on comorbid substance use disorders in a novel study, and found two SNPs to be significantly associated with comorbid cocaine, opium, and nicotine dependence. Placing these SNPs into biological context, we developed a protein network modeling the interaction of cocaine, nicotine, and opium with these variants. Conclusions ModRP is a novel approach to identifying pleiotropic genetic influences on comorbid complex diseases. It can be used to assess association for related phenotypes where raw data is unavailable or inappropriate for analysis using other approaches. The method is conceptually simple and produces statistically significant, biologically relevant results.http://deepblue.lib.umich.edu/bitstream/2027.42/112931/1/12859_2012_Article_5068.pd