Chemiluminescence of nitric oxide: The NO (C2Π−A2Σ+) rate constant

A rocket borne scanning $\text{1}\text{4}$-m spectrometer was used to observe the night airglow between 1900 and 2300 Å at a resolution of 15 Å. An attitude control system oriented the payload horizontally near apogee (150 km) and pointed the field of view to the north and parallel with the terminator. Progressions from the δ(0, v″) and γ(0, 0) band system of nitric oxide were observed. The observations of the δ-bands and γ-bands are consistent with the relative intensities produced in the preassociation of ground state atomic oxygen and nitrogen. An observation of the v′ = 0, ε-band progression is suggested and is consistent with the presence of a resonance fluorescence contribution near apogee. The A²Σ⁺ (upper level of the γ-bands) can only be populated by cascade from the C²π state (upper level of the γ-bands) in the preassociation reaction. In the absence of quenching of the A²Σ⁺ state, the emission rate of the γ-bands can be used as a measure of the C?A transition and thus to deduce the branching ratio to the A²Σ⁺ state. This branching ratio is estimated to be 0.21±0.04.     

Comparison theorems and orbit counting in hyperbolic geometry

In this article we address an interesting problem in hyperbolic geometry. This is the problem of comparing different quantities associated to the fundamental group of a hyperbolic manifold (e.g. word length, displacement in the universal cover, etc.) asymptotically. Our method involves a mixture of ideas from both ``thermodynamic' ergodic theory and the automaton associated to strongly Markov groups.

     

Obtaining local reciprocal lattice vectors from finite‐element analysis

Finite‐element analysis is frequently used by engineers at synchrotron beamlines to calculate the elastic deformation of a single crystal undergoing mechanical bending or thermal load. ANSYS^® Workbench? software is widely used for such simulations. However, although ANSYS^® Workbench? software provides useful information on the displacements, strains and stresses within the crystal, it does not yield the local reciprocal lattice vectors that would be required for X‐ray diffraction calculations. To bridge this gap, a method based on the shape functions and interpolation procedures of the software itself has been developed. An application to the double‐crystal bent Laue monochromator being designed for the I12 (JEEP) wiggler beamline at the Diamond Light Source is presented.     

Temperature dependence of the cristobalite α-β inversion

The cristobalite - inversion has been studied using DSC on cristobalites produced by firing high purity quartz with and without addition of a mineraliser. If no mineraliser was used, the inversion temperatures and hysteresis on heating and cooling increased with firing temperature. Firing time had little or no effect on inversion temperature. When a mineraliser was used, the same general trend was observed with increases in firing time at low temperatures leading to splitting of the inversion peak. The amount of mineraliser added had little effect. Tridymite inversions were also observed. The results are explained in terms of the degree of order of the cristobalite structure.We are grateful for the award of an S.E.R.C. CASE award in conjunction with Specialist Refractory Services to SJS. Helpful discussions have been held with Mr. D. W. Bailey and Dr. P. Watkins.     

Hermite–Birkhoff–Obrechkoff four-stage four-step ODE solver of order 14 with quantized step size

A four-stage Hermite–Birkhoff–Obrechkoff method of order 14 with four quantized variable steps, denoted by HBOQ(14)4, is constructed for solving non-stiff systems of first-order differential equations of the form y^′=f(t,y)$y^{\prime }=f(t,y)$ with initial conditions y(_t0)=_y0$y\left(t_0\right)=y_0$. Its formula uses y^′$y^{\prime }$, y^″$y^{″}$ and y^?$y^{?}$ as in Obrechkoff methods. Forcing a Taylor expansion of the numerical solution to agree with an expansion of the true solution leads to multistep- and Runge–Kutta-type order conditions which are reorganized into linear Vandermonde-type systems. To reduce overhead, simple formulae are derived only once to obtain the values of Hermite–Birkhoff interpolation polynomials in terms of Lagrange basis functions for 16 quantized step size ratios. The step size is controlled by a local error estimator. When programmed in C ++, HBOQ(14)4 is superior to the Dormand–Prince Runge–Kutta pair DP(8,7)13M of order 8 in solving several problems often used to test higher order ODE solvers at stringent tolerances. When programmed in Matlab, it is superior to ode113 in solving costly problems, on the basis of the number of steps, CPU time, and maximum global error. The code is available on the URL www.site.uottawa.ca/~remi.     

Compactness of the Space of Minimal Hypersurfaces with Bounded Volume and <Emphasis Type="Italic">p</Emphasis>-th Jacobi Eigenvalue

Given a closed Riemannian manifold of dimension less than eight, we prove a compactness result for the space of closed, embedded minimal hypersurfaces satisfying a volume bound and a uniform lower bound on the first eigenvalue of the stability operator. When the latter assumption is replaced by a uniform lower bound on the p-th Jacobi eigenvalue for \(p\ge 2\) one gains strong convergence to a smooth limit submanifold away from at most \(p-1\) points.     

Bryozoan metabolites: an ecological perspective

This Highlight covers the chemical ecology of bryozoans, primarily the ecological functions of bryozoan natural products. The Highlight is arranged taxonomically, according to the bryozoan Treatise classification (P. Bock, Bryozoa Homepage, 2006, http://bryozoa.net).     

Graded annihilators of modules over the Frobenius skew polynomial ring, and tight closure

This paper is concerned with the tight closure of an ideal in a commutative Noetherian local ring of prime characteristic . Several authors, including R. Fedder, K-i. Watanabe, K. E. Smith, N. Hara and F. Enescu, have used the natural Frobenius action on the top local cohomology module of such an to good effect in the study of tight closure, and this paper uses that device. The main part of the paper develops a theory of what are here called `special annihilator submodules' of a left module over the Frobenius skew polynomial ring associated to ; this theory is then applied in the later sections of the paper to the top local cohomology module of and used to show that, if is Cohen-Macaulay, then it must have a weak parameter test element, even if it is not excellent.