A Nightmare

The lake was unusually calm that particular June day, when my Mother and Father started on their daily fishing trip. I bade them farewell from the dock, and reluctantly started back to the cottage. Although I did not have the patience for fishing, it seemed that there should be something more exciting to look forward to than a game of solitaire. Resigning myself to this entertainment, I settled down on the screened porch with my cards and the radio. I played the necessary unsuccessful game, and my luck began to change. I triumphantly placed the last ace on the stack which won the game

Grandma Brown

Sit down, Grandma. There\u27s no need for you to help. I can finish the Turkey myself, said Effie Brown to her mother-in-law. Hmm! Sitting down was all she\u27d done since she\u27d been here. As for finishing the turkey, Effie always cooked the meat too brown and dry, so hard you couldn\u27t eat it, thought Grandma Brown

Rational points on ellipsoids and modular forms

The theory of modular forms and spherical harmonic analysis are applied to establish new best bounds towards the counting and equidistribution of rational points on spheres and other higher dimensional ellipsoids, in what may be viewed as a textbook display of the 'unreasonable effectiveness' of modular forms.Comment: 28 page

Windings of prime geodesics

The winding of a closed oriented geodesic around the cusp of the modular orbifold is computed by the Rademacher symbol, a classical function from the theory of modular forms. For a general cusped hyperbolic orbifold, we have a procedure to associate to each cusp a Rademacher symbol. In this paper we construct winding numbers related to these Rademacher symbols. In cases where the two functions coincide, access to the spectral theory of automorphic forms yields statistical results on the distribution of closed (primitive) oriented geodesics with respect to their winding

Coherent large-scale structures in high Reynolds number supersonic jets

The flow structure of a 50.8 mm (2 in) diameter jet operated at a full expanded Mach number of 1.37, with Reynolds numbers in the range 1.7 to 2.35 million, was examined for the first 20 jet diameters. To facilitate the study of the large scale structure, and determine any coherence, a discrete tone acoustic excitation method was used. Phase locked flow visualization as well as laser velocimeter quantitative measurements were made. The main conclusions derived from this study are: (1) large scale coherent like turbulence structures do exist in large Reynolds number supersonic jets, and they prevail even beyond the potential core; (2) the most preferential Strouhal number for these structures is in the vicinity of 0.4; and (3) quantitatively, the peak amplitudes of these structures are rather low, and are about 1% of the jet exit velocity. Finally, since a number of unique problems related to LV measurements in supersonic jets were encountered, a summary of these problems and lessons learned therefrom are also reported