Aeolian Tones of a Honeycomb Lattice Cell

Aeroacoustic resonant oscillations (aeolian tones) are studied for flow past two plates forming a cross in a square cross section channel. Possible oscillation modes are classified on the basis of admissible symmetry groups and the existence of the modes is proved. The infinite linear system of equations for these modes obtained by the sewing method was simplified and studied numerically. Curves of eigenfrequency versus plate length are constructed. The form of the eigenfunctions is studied.     

Scientific heritage of Boris Lukich Laptev (4/23/05–1/15/89)

Biographical information on the eminent Soviet geometer Boris Lukich Laptev (4/23/05–1/15-89) is given as well as a survey of his research in the areas of differential geometry and history of mathematics.Translated from Itogi Nauki i Tekhniki, Seriya Problemy Geometrii, Vol. 21, pp.27–42, 1989.     

A datalogger to identify vocalizing dolphins

A datalogger was developed to identify vocalizing dolphins within socially interacting captive groups. Every 50 ms the logger stores data on the level and frequency of detected sound. Dataloggers are temporarily attached to dolphins by suction cups for data collection sessions lasting up to 45 min. Later, computer analysis of data from the dataloggers reveals which dolphin produced each vocalization recorded during the session. Results from use of dataloggers with two captive bottlenose dolphins (Tursiops truncatus) at the New England Aquarium in Boston, MA are presented. The possible use of dataloggers with wild dolphins is discussed.     

Structure of norbornene-fused 3,1-oxazine double cycloadducts

Pentacyclic isoxazolines were obtained by the cycloaddition of benzonitrile oxide to norbornene-azetidinone-fused 3,1-oxazines. The constitutions of two of the isomers obtained, and the configurations and conformations of all products, were determined by means of ¹H and ¹³C NMR spectroscopy and DNOE experiments.     

Galactic model of element formation

A cosmological model is presented that produces He, C, O, D, Li, Be, and B in their observed abundances without a Big Bang. The elements are produced during the 1.5-Gy formation period of a galaxy, with C, O, and other heavy elements produced by stars of M>12 M₃ , He by stars of 6 M_s<M<12 M_s, and D, Li, Be, and B by cosmic-ray reactions in a nearly pure H plasma halo. Thus, the model shows that the major elements used in astrophysical studies can be produced during galactic formation by exactly the same processes known to function today at much lower rates     

A decomposition theorem for convexity spaces

We utilize the unifying framework of families of convexity spaces for the treatment of various notions of planar convexity and the associated convex hulls. Our major goal is to prove the refinement and decomposition theorems for families of convexity spaces. These general theorems are then applied to two examples: restricted-oriented convex sets andNESW-convex sets. The applications demonstrate the usefulness of these general theorems, since they give rise to simple algorithms for the computation of the associated convex hulls of polygons.     

Asymptotic expansion of the logistic midrange

Using the symbolic computation program MAPLE, we compute several terms of an asymptotic expansion for the distribution function of the logistic midrange.