Soft Pion Emission in Semileptonic BB-Meson Decays

An analysis of semileptonic decays of $B$ mesons with the emission of a single soft pion is presented in the framework of the heavy-quark limit using an effective Lagrangian which implements chiral and heavy-quark symmetries. The analysis is performed at leading order of the chiral and inverse heavy mass expansions. In addition to the ground state heavy mesons some of their resonances are included. The estimates of the various effective coupling constants and form factors needed in the analysis are obtained using a chiral quark model. As the main result, a clear indication is found that the $0^{+}$ and $1^{+}$ resonances substantially affect the decay mode with a $D^{\ast}$ in the final state, and a less dramatic effect is also noticed in the $D$ mode. An analysis of the decay spectrum in the $D^{(\ast)}-\pi$ squared invariant mass is carried out, showing the main effects of including the resonances. The obtained rates show promising prospects for studies of soft pion emission in semileptonic $B$-meson decays in a $B$-meson factory where, modulo experimental cuts, about $10^5$ such decays in the $D$ meson mode and $10^4$ in the $D^{\ast}$ mode could be observed per year.Comment: 41 pages, uses revtex, epsf. 16 uuencoded postscript figures appended after `\end{document

NASA/Pratt and Whitney experimental clean combustor program: Engine test results

A two-stage vorbix (vortex burning and mixing) combustor and associated fuel system components were successfully tested in an experimental JT9D engine at steady-state and transient operating conditions, using ASTM Jet-A fuel. Full-scale JT9D experimental engine tests were conducted in a phase three aircraft experimental clean combustor program. The low-pollution combustor, fuel system, and fuel control concepts were derived from phase one and phase two programs in which several combustor concepts were evaluated, refined, and optimized in a component test rig. Significant pollution reductions were achieved with the combustor which meets the performance, operating, and installation requirements of the engine

A model for evolution and extinction

We present a model for evolution and extinction in large ecosystems. The model incorporates the effects of interactions between species and the influences of abiotic environmental factors. We study the properties of the model by approximate analytic solution and also by numerical simulation, and use it to make predictions about the distribution of extinctions and species lifetimes that we would expect to see in real ecosystems. It should be possible to test these predictions against the fossil record. The model indicates that a possible mechanism for mass extinction is the coincidence of a large coevolutionary avalanche in the ecosystem with a severe environmental disturbance.Comment: Postscript (compressed etc. using uufiles), 16 pages, with 15 embedded figure

Semileptonic Decays of Heavy Omega Baryons in a Quark Model

The semileptonic decays of $\Omega_c$ and $\Omega_b$ are treated in the framework of a constituent quark model developed in a previous paper on the semileptonic decays of heavy $\Lambda$ baryons. Analytic results for the form factors for the decays to ground states and a number of excited states are evaluated. For $\Omega_b$ to $\Omega_c$ the form factors obtained are shown to satisfy the relations predicted at leading order in the heavy-quark effective theory at the non-recoil point. A modified fit of nonrelativistic and semirelativistic Hamiltonians generates configuration-mixed baryon wave functions from the known masses and the measured \lcle rate, with wave functions expanded in both harmonic oscillator and Sturmian bases. Decay rates of \ob to pairs of ground and excited \omc states related by heavy-quark symmetry calculated using these configuration-mixed wave functions are in the ratios expected from heavy-quark effective theory, to a good approximation. Our predictions for the semileptonic elastic branching fraction of $\Omega_Q$ vary minimally within the models we use. We obtain an average value of (84$\pm$ 2%) for the fraction of $\Omega_c\to \Xi^{(*)}$ decays to ground states, and 91% for the fraction of $\Omega_c\to \Omega^{(*)}$ decays to the ground state $\Omega$. The elastic fraction of \ob \to \omc ranges from about 50% calculated with the two harmonic-oscillator models, to about 67% calculated with the two Sturmian models.Comment: 52 pages, 8 figure

On the elastic approximation to the vacancy formation energy in metals

Isotropic elastic continuum model application to calculate energy and entropy of vacancy formation in metal crystal

On the size of approximately convex sets in normed spaces

Let X be a normed space. A subset A of X is approximately convex if $d(ta+(1-t)b,A) \le 1$ for all $a,b \in A$ and $t \in [0,1]$ where $d(x,A)$ is the distance of $x$ to $A$. Let \Co(A) be the convex hull and \diam(A) the diameter of $A$. We prove that every $n$-dimensional normed space contains approximately convex sets $A$ with \mathcal{H}(A,\Co(A))\ge \log_2n-1 and \diam(A) \le C\sqrt n(\ln n)^2, where $\mathcal{H}$ denotes the Hausdorff distance. These estimates are reasonably sharp. For every $D>0$, we construct worst possible approximately convex sets in $C[0,1]$ such that \mathcal{H}(A,\Co(A))=\diam(A)=D. Several results pertaining to the Hyers-Ulam stability theorem are also proved.Comment: 32 pages. See also http://www.math.sc.edu/~howard

An ultra-low frequency electromagnetic wave force mechanism for the ionosphere

Ultra-low frequency electromagnetic wave force mechanism for ionospheric anomalie

Extremal Approximately Convex Functions and Estimating the Size of Convex Hulls

A real valued function $f$ defined on a convex $K$ is anemconvex function iff it satisfies $$f((x+y)/2) \le (f(x)+f(y))/2 + 1.$$ A thorough study of approximately convex functions is made. The principal results are a sharp universal upper bound for lower semi-continuous approximately convex functions that vanish on the vertices of a simplex and an explicit description of the unique largest bounded approximately convex function~$E$ vanishing on the vertices of a simplex. A set $A$ in a normed space is an approximately convex set iff for all $a,b\in A$ the distance of the midpoint $(a+b)/2$ to $A$ is $\le 1$. The bounds on approximately convex functions are used to show that in $\R^n$ with the Euclidean norm, for any approximately convex set $A$, any point $z$ of the convex hull of $A$ is at a distance of at most $[\log_2(n-1)]+1+(n-1)/2^{[\log_2(n-1)]}$ from $A$. Examples are given to show this is the sharp bound. Bounds for general norms on $R^n$ are also given.Comment: 39 pages. See also http://www.math.sc.edu/~howard