Almost Commuting Orthogonal Matrices

We show that almost commuting real orthogonal matrices are uniformly close to exactly commuting real orthogonal matrices. We prove the same for symplectic unitary matrices. This is in contrast to the general complex case, where not all pairs of almost commuting unitaries are close to commuting pairs. Our techniques also yield results about almost normal matrices over the reals and the quaternions.Comment: 13 pages, 3 figure

Damping of Electron Density Structures and Implications for Interstellar Scintillation

The forms of electron density structures in kinetic Alfven wave turbulence are studied in connection with scintillation. The focus is on small scales $L \sim 10^8-10^{10}$ cm where the Kinetic Alfv\'en wave (KAW) regime is active in the interstellar medium. MHD turbulence converts to a KAW cascade, starting at 10 times the ion gyroradius and continuing to smaller scales. These scales are inferred to dominate scintillation in the theory of Boldyrev et al. From numerical solutions of a decaying kinetic Alfv\'en wave turbulence model, structure morphology reveals two types of localized structures, filaments and sheets, and shows that they arise in different regimes of resistive and diffusive damping. Minimal resistive damping yields localized current filaments that form out of Gaussian-distributed initial conditions. When resistive damping is large relative to diffusive damping, sheet-like structures form. In the filamentary regime, each filament is associated with a non-localized magnetic and density structure, circularly symmetric in cross section. Density and magnetic fields have Gaussian statistics (as inferred from Gaussian-valued kurtosis) while density gradients are strongly non-Gaussian, more so than current. This enhancement of non-Gaussian statistics in a derivative field is expected since gradient operations enhance small-scale fluctuations. The enhancement of density gradient kurtosis over current kurtosis is not obvious, yet it suggests that modest fluctuation levels in electron density may yield large scintillation events during pulsar signal propagation in the interstellar medium. In the sheet regime the same statistical observations hold, despite the absence of localized filamentary structures. Probability density functions are constructed from statistical ensembles in both regimes, showing clear formation of long, highly non-Gaussian tails

Management Education Benchmarking Designing Customized And Flexible MBA Programs

To meet the challenges of the 21st century B-schools are revising curriculum, delivery and outcome assessment modalities. Today, the proportion of electives and other specialty offerings in many MBA programs now constitutes more than 50% of the total curriculum. However, this focus on customization, integration and flexibility is not without its own challenges including quality assurance and implementation. Benchmarking, which involves the assessment of a variety of inputs including student satisfaction, the business community and the accreditation process represents, one approach for meeting these challenges. The purpose of this paper is twofold: 1) to benchmark trends and challenges in MBA programs geared towards the working adult and 2) to outline a process for implementing more flexibility and customization in MBA curriculums. The results of a student satisfaction survey of MBA graduates revealed that a customized curriculum yielded greater insights and enhanced job related capabilities than a generalized curriculum

Radiation tolerance of nanocrystalline ceramics: insights from Yttria Stabilized Zirconia.

Materials for applications in hostile environments, such as nuclear reactors or radioactive waste immobilization, require extremely high resistance to radiation damage, such as resistance to amorphization or volume swelling. Nanocrystalline materials have been reported to present exceptionally high radiation-tolerance to amorphization. In principle, grain boundaries that are prevalent in nanomaterials could act as sinks for point-defects, enhancing defect recombination. In this paper we present evidence for this mechanism in nanograined Yttria Stabilized Zirconia (YSZ), associated with the observation that the concentration of defects after irradiation using heavy ions (Kr(+), 400 keV) is inversely proportional to the grain size. HAADF images suggest the short migration distances in nanograined YSZ allow radiation induced interstitials to reach the grain boundaries on the irradiation time scale, leaving behind only vacancy clusters distributed within the grain. Because of the relatively low temperature of the irradiations and the fact that interstitials diffuse thermally more slowly than vacancies, this result indicates that the interstitials must reach the boundaries directly in the collision cascade, consistent with previous simulation results. Concomitant radiation-induced grain growth was observed which, as a consequence of the non-uniform implantation, caused cracking of the nano-samples induced by local stresses at the irradiated/non-irradiated interfaces

Can a Lattice String Have a Vanishing Cosmological Constant?

We prove that a class of one-loop partition functions found by Dienes, giving rise to a vanishing cosmological constant to one-loop, cannot be realized by a consistent lattice string. The construction of non-supersymmetric string with a vanishing cosmological constant therefore remains as elusive as ever. We also discuss a new test that any one-loop partition function for a lattice string must satisfy.Comment: 14 page

Comparing the Efficacy of Defusion, Self-as-Context, and Distraction Strategies For Getting Rid of Possessions

Interventions for hoarding disorder need to target difficulty letting go of items to reduce clutter and improve functioning. The present studies were designed to test the efficacy of brief cognitive interventions for letting go of possessions and self-report outcomes. Participants (N = 67 in Study 1; N = 110 in Study 2) received training on defusion or distraction in Study 1 and defusion, self-as-context, or distraction in Study 2 and completed measures at pre- and postintervention. Study 1 found no differences between defusion and distraction on saving, self-rated discomfort with discarding, or perceived importance of the target belonging. In Study 2, participants provided most favorable feedback for self-as-context compared to defusion and distraction, indicating promise of this strategy. Nonetheless, findings from both studies overall provide minimal support for use of present procedures to reduce saving. Limitations include use of non-clinical samples and single-item variables to obtain participant feedback