Kolmogorov-Burgers Model for Star Forming Turbulence

The process of star formation in interstellar molecular clouds is believed to be controlled by driven supersonic magnetohydrodynamic turbulence. We suggest that in the inertial range such turbulence obeys the Kolmogorov law, while in the dissipative range it behaves as Burgers turbulence developing shock singularities. On the base of the She-Leveque analytical model we then predict the velocity power spectrum in the inertial range to be E_k ~ k^{-1.74}. This result reproduces the observational Larson law, ~ l^{0.74...0.76}, [Larson, MNRAS 194 (1981) 809] and agrees well with recent numerical findings by Padoan and Nordlund [astro-ph/0011465]. The application of the model to more general dissipative structures, with higher fractal dimensionality, leads to better agreement with recent observational results.Comment: revised, new material added, 8 page

Discrete Logarithms in Generalized Jacobians

D\'ech\`ene has proposed generalized Jacobians as a source of groups for public-key cryptosystems based on the hardness of the Discrete Logarithm Problem (DLP). Her specific proposal gives rise to a group isomorphic to the semidirect product of an elliptic curve and a multiplicative group of a finite field. We explain why her proposal has no advantages over simply taking the direct product of groups. We then argue that generalized Jacobians offer poorer security and efficiency than standard Jacobians

Inequalities in premature mortality in Britain: observational study from 1921 to 2007

Objective To report on the extent of inequality in premature mortality as measured between geographical areas in Britain. Design Observational study of routinely collected mortality data and public records. Population subdivided by age, sex, and geographical area (parliamentary constituencies from 1991 to 2007, pre-1974 local authorities over a longer time span). Setting Great Britain. Participants Entire population aged under 75 from 1990 to 2007, and entire population aged under 65 in the periods 1921-39, 1950-3, 1959-63, 1969-73, and 1981-2007. Main outcome measure Relative index of inequality (RII) and ratios of inequality in age-sex standardised mortality ratios under ages 75 and 65. The relative index of inequality is the relative rate of mortality for the hypothetically worst-off compared with the hypothetically best-off person in the population, assuming a linear association between socioeconomic position and risk of mortality. The ratio of inequality is the ratio of the standardised mortality ratio of the most deprived 10% to the least deprived 10%. Results When measured by the relative index of inequality, geographical inequalities in age-sex standardised rates of mortality below age 75 have increased every two years from 1990-1 to 2006-7 without exception. Over this period the relative index of inequality increased from 1.61 (95% confidence interval 1.52 to 1.69) in 1990-1 to 2.14 (2.02 to 2.27) in 2006-7. Simple ratios indicated a brief period around 2001 when a small reduction in inequality was recorded, but this was quickly reversed and inequalities up to the age of 75 have now reached the highest levels reported since at least 1990. Similarly, inequalities in mortality ratios under the age of 65 improved slightly in the early years of this century but the latest figures surpass the most extreme previously reported. Comparison of crudely age-sex standardised rates for those below age 65 from historical records showed that geographical inequalities in mortality are higher in the most recent decade than in any similar time period for which records are available since at least 1921. Conclusions Inequalities in premature mortality between areas of Britain continued to rise steadily during the first decade of the 21st century. The last time in the long economic record that inequalities were almost as high was in the lead up to the economic crash of 1929 and the economic depression of the 1930s. The economic crash of 2008 might precede even greater inequalities in mortality between areas in Britain

Improving and Assessing Information Literacy Skills through Faculty-Librarian Collaboration

This article addresses ways to assess the effectiveness of integrating information literacy into college courses by taking a close look at a partnership developed between Dr. Amy Dailey and the reference librarians at Gettysburg College

Calculation of material properties and ray tracing in transformation media

Complex and interesting electromagnetic behavior can be found in spaces with non-flat topology. When considering the properties of an electromagnetic medium under an arbitrary coordinate transformation an alternative interpretation presents itself. The transformed material property tensors may be interpreted as a different set of material properties in a flat, Cartesian space. We describe the calculation of these material properties for coordinate transformations that describe spaces with spherical or cylindrical holes in them. The resulting material properties can then implement invisibility cloaks in flat space. We also describe a method for performing geometric ray tracing in these materials which are both inhomogeneous and anisotropic in their electric permittivity and magnetic permeability

Graph-theoretical conditions for inscribability and Delaunay realizability

We present new graph-theoretical conditions for inscribable polyhedra and Delaunay triangulations. We establish several sufficient conditions of the following general form: if a polyhedron has a sufficiently rich collection of Hamiltonian subgraphs, then it is inscribable. These results have several consequences:All 4-connected polyhedra are inscribable.All simplical polyhedra in which all vertex degrees are between 4 and 6, inclusive, are inscribable.All triangulations without chords or nonfacial triangles are realizable as Delaunay triangulations.We also strengthen some earlier results about matchings in inscribable polyhedra. Specifically, we show that any nonbipartite inscribable polyhedron has a perfect matching containing any specified edge, and that any bipartite inscribable polyhedron has a perfect matching containing any two specified disjoint edges. We give examples showing that these results are best possible

Combined pyrolysis and radiochemical gas chromatography for studying the thermal degradation of polymers

Pyrolysis gas chromatography and radioactive tracer techniques have been used independently to study the thermal degradation of polymers. In these laboratories the two techniques have been combined to elucidate some of the mechanisms of the thermal degradation of epoxy resins and polyimides. This paper describes the apparatus developed for this work

CFD Mixing Analysis of Jets Injected from Straight and Slanted Slots into Confined Crossflow in Rectangular Ducts

A CFD study was performed to analyze the mixing potential of opposed rows of staggered jets injected into confined crossflow in a rectangular duct. Three jet configurations were numerically tested: (1) straight (0 deg) slots; (2) perpendicular slanted (45 deg) slots angled in opposite directions on top and bottom walls; and (3) parallel slanted (45 deg) slots angled in the same direction on top and bottom walls. All three configurations were tested at slot spacing-to-duct height ratios (S/H) of 0.5, 0.75, and 1.0; a jet-to-mainstream momentum flux ratio (J) of 100; and a jet-to-mainstream mass flow ratio of 0.383. Each configuration had its best mixing performance at S/H of 0.75. Asymmetric flow patterns were expected and predicted for all slanted slot configurations. The parallel slanted slot configuration was the best overall configuration at x/H of 1.0 for S/H of 0.75

Properties of perturbative multi-particle amplitudes in ϕk\phi^k and O(N)O(N) theories

Threshold amplitudes are considered for multi-particle production in $\phi^k$ and $O(N) ~\phi^4$ theories. It is found that the disappearance of tree-level threshold amplitudes of $2$ on-shell particles producing a large number of particles occurs in $\phi^k$ theory only for $k=3$ and $k=4$. The one-loop correction to the threshold amplitude for a highly virtual scalar particle decaying into $n$ particles in an $O(N)$ model is derived.Comment: 7 pages, LaTex, TPI-MINN-92/60-