Recent developments in perturbation theory

Rayleigh-Schroeder perturbation theory - degenerate and non-degenerate states - quantum chemistry - other perturbation equation

Practolol in Hyperthyroid Cardiac Failure

Practolol (Eraldint), a recently developed beta-adrenergic blocking agent, has been found useful in conjunction with digitalis and diuretics in 6 patients with thyrocardiac disease who had been refractory to therapy. In all cases cardiac failure improved dramatically, suggesting better myocardial efficiency and a return of digitalis responsiveness after practolol. This drug might be a useful therapeutic adjunct in thyrocardiac disease

Late-Time Convection in the Collapse of a 23 Solar Mass Star

The results of a 3-dimensional SNSPH simulation of the core collapse of a 23 solar mass star are presented. This simulation did not launch an explosion until over 600ms after collapse, allowing an ideal opportunity to study the evolution and structure of the convection below the accretion shock to late times. This late-time convection allows us to study several of the recent claims in the literature about the role of convection: is it dominated by an l=1 mode driven by vortical-acoustic (or other) instability, does it produce strong neutron star kicks, and, finally, is it the key to a new explosion mechanism? The convective region buffets the neutron star, imparting a 150-200 km/s kick. Because the l=1 mode does not dominate the convection, the neutron star does not achieve large (>450 km/s) velocities. Finally, the neutron star in this simulation moves, but does not develop strong oscillations, the energy source for a recently proposed supernova engine. We discuss the implications these results have on supernovae, hypernovae (and gamma-ray bursts), and stellar-massed black holes.Comment: 31 pages (including 13 figures), submitted to Ap

Socially Optimal Mining Pools

Mining for Bitcoins is a high-risk high-reward activity. Miners, seeking to reduce their variance and earn steadier rewards, collaborate in pooling strategies where they jointly mine for Bitcoins. Whenever some pool participant is successful, the earned rewards are appropriately split among all pool participants. Currently a dozen of different pooling strategies (i.e., methods for distributing the rewards) are in use for Bitcoin mining. We here propose a formal model of utility and social welfare for Bitcoin mining (and analogous mining systems) based on the theory of discounted expected utility, and next study pooling strategies that maximize the social welfare of miners. Our main result shows that one of the pooling strategies actually employed in practice--the so-called geometric pay pool--achieves the optimal steady-state utility for miners when its parameters are set appropriately. Our results apply not only to Bitcoin mining pools, but any other form of pooled mining or crowdsourcing computations where the participants engage in repeated random trials towards a common goal, and where "partial" solutions can be efficiently verified

Frontostriatal Maturation Predicts Cognitive Control Failure to Appetitive Cues in Adolescents

Adolescent risk-taking is a public health issue that increases the odds of poor lifetime outcomes. One factor thought to influence adolescents' propensity for risk-taking is an enhanced sensitivity to appetitive cues, relative to an immature capacity to exert sufficient cognitive control. We tested this hypothesis by characterizing interactions among ventral striatal, dorsal striatal, and prefrontal cortical regions with varying appetitive load using fMRI scanning. Child, teen, and adult participants performed a go/no-go task with appetitive (happy faces) and neutral cues (calm faces). Impulse control to neutral cues showed linear improvement with age, whereas teens showed a nonlinear reduction in impulse control to appetitive cues. This performance decrement in teens was paralleled by enhanced activity in the ventral striatum. Prefrontal cortical recruitment correlated with overall accuracy and showed a linear response with age for no-go versus go trials. Connectivity analyses identified a ventral frontostriatal circuit including the inferior frontal gyrus and dorsal striatum during no-go versus go trials. Examining recruitment developmentally showed that teens had greater between-subject ventral-dorsal striatal coactivation relative to children and adults for happy no-go versus go trials. These findings implicate exaggerated ventral striatal representation of appetitive cues in adolescents relative to an intermediary cognitive control response. Connectivity and coactivity data suggest these systems communicate at the level of the dorsal striatum differentially across development. Biased responding in this system is one possible mechanism underlying heightened risk-taking during adolescence

Theoretical determination of lifetimes of metastable states in Sc III and Y III

Lifetimes of the first two metastable states in Sc^{2+} and Y^{2+} are determined using the relativistic coupled-cluster theory. There is a considerable interest in studying the electron correlation effects in these ions as though their electronic configurations are similar to the neutral alkali atoms, their structures are very different from the latter. We have made a comparative study of the correlation trends between the above doubly ionized systems with their corresponding neutral and singly ionized iso-electronic systems. The lifetimes of the excited states of these ions are very important in the field of astrophysics, especially for the study of post-main sequence evolution of the cool giant stars.Comment: 13 pages, 1 figure and 5 table

The C_2 heat-kernel coefficient in the presence of boundary discontinuities

We consider the heat-kernel on a manifold whose boundary is piecewise smooth. The set of independent geometrical quantities required to construct an expression for the contribution of the boundary discontinuities to the C_{2} heat-kernel coefficient is derived in the case of a scalar field with Dirichlet and Robin boundary conditions. The coefficient is then determined using conformal symmetry and evaluation on some specific manifolds. For the Robin case a perturbation technique is also developed and employed. The contributions to the smeared heat-kernel coefficient and cocycle function are calculated. Some incomplete results for spinor fields with mixed conditions are also presented.Comment: 25 pages, LaTe

Self-replication and splitting of domain patterns in reaction-diffusion systems with fast inhibitor

An asymptotic equation of motion for the pattern interface in the domain-forming reaction-diffusion systems is derived. The free boundary problem is reduced to the universal equation of non-local contour dynamics in two dimensions in the parameter region where a pattern is not far from the points of the transverse instabilities of its walls. The contour dynamics is studied numerically for the reaction-diffusion system of the FitzHugh-Nagumo type. It is shown that in the asymptotic limit the transverse instability of the localized domains leads to their splitting and formation of the multidomain pattern rather than fingering and formation of the labyrinthine pattern.Comment: 9 pages (ReVTeX), 5 figures (postscript). To be published in Phys. Rev.

School violence, school differences and school discourses

This article highlights one strand of a study which investigated the concept of the violenceresilient school. In six inner-city secondary schools, data on violent incidents in school and violent crime in the neighbourhood were gathered, and compared with school practices to minimise violence, accessed through interviews. Some degree of association between the patterns of behaviour and school practices was found: schools with a wider range of wellconnected practices seemed to have less difficult behaviour. Interviews also showed that the different schools had different organisational discourses for construing school violence, its possible causes and the possible solutions. Differences in practices are best understood in connection with differences in these discourses. Some of the features of school discourses are outlined, including their range, their core metaphor and their silences. We suggest that organisational discourse is an important concept in explaining school effects and school differences, and that improvement attempts could have clearer regard to this concept

The Orbiter Stability Experiment on STS-40

The Orbiter Stability Experiment (OSE) was developed to evaluate the steadiness of the STS Orbiter as a potential platform for instrumentation that would image the Sun in its extreme ultraviolet and soft X-ray radiations. We were interested in any high frequency motions of the Orbiter's orientation due to normal operations and manned activities. Preliminary results are presented of the observations. Other than the expected slow motion of the Orbiter within the specified angular deadband of 0.1 degrees during the observations, it was found that high frequency (above 1 Hz) angular motions (jitter) were not detectable at the 0.25 arc sec detection limit of the most sensitive detector, for most of the period of observation. No high frequency motions were recorded during intervals that were identified with vernier thruster firings. However, one short interval with detectable spectral power to a frequency of 10 Hz has been found to date. It has not yet been correlated with a particular activity going on at the time. The results of the observations may also be of value in assessing perturbations to the Orbiter's micro-gravity environment produced by normal operations