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Article Excerpt
ACOUSTIC BAND PASS AND BAND GAP BY DISCRETE MEDIA AT MICRO AND NANO SCALES, Hasson Tavossi, Department of Physics, Astronomy, and Geosciences, Valdosta State University, 1500 N. Patterson St. Valdosta, GA 31698. Acoustic properties of models of crystals, when measured at macroscopic scale, are found experimentally to have remarkable similarities with the same wave properties observed at atomic and nano-scales. It can be shown that, elastic moduli and other wave properties such as; band-pass, forbidden band, wave tunneling, attenuation, cutoff-frequency, and dispersion, depend on the similar structural factors as for phonons in crystals. Acoustic properties of the macroscopic models of discrete media, in the length scale range; 1.5 mm to 30 um, and the frequency range; from audible to ultrasonic frequencies, are studied. The Band-pass, band-gap, attenuation, and dispersion expressed in wave-number (ka), show similar characteristics as phonons in solids. These findings can lead to a better understanding of the wave properties of solids at nanoscales. The readily analyzable wave models at large scale are convenient tools to verify experimentally the models for complex binary composites. In conclusion, experimental findings and numerical results for wave properties of discrete structures at large scale are compared with atomic scale wave behavior of solids, for a wide range of frequencies, from audible to ultrasound, to show the common characteristics with the phonons behavior in solids.
THE SEMIGROUP OF IDEMPOTENT P-ENDOMORPHISMS OF VECTOR LATTICE V([DELTA], H), Dr. Shinemin Lin, Savannah State University. It is well known that all finite dimensional vector spaces are equivalent if they have the same dimension. However it is not the case of vector lattices. Schein proved in 1969 that for two nontrivial Boolean algebras A and B, A [equivalent] B if and only if END(A)[equivalent]END (B). In this paper, first of all I constructed the matrix representation of the semigroup of idempotent p-endomorphisms of the finite vector lattices; secondly I generalized the structures to infinite dimensional vector lattice, and finally I proved the similar result as Schien's theorem for the vector lattices. The main theorem is as following. Given two nontrivial vector lattices A and B, the following statements are equivalent.
a) A [equivalent].B,
b) The root system of A [equivalent] the root system of B
GEOMETRIC ILLUSTRATION OF ALGEBRAIC FORMULA AND THE METHOD OF EXHAUSTION, Ms. Hamilton, Michelle A, Savannah State University. The historical origins of what we now call mathematical concepts--those that deal with number, magnitude, and form-all related to the development of Geometry. The geometrical investigations provided the foundations of the development of much of modern mathematics. Geometry had its origin in Egypt. The agricultural plots along the Nile were taxed according to area, so that when the annual flooding of the river swept away part of a plot and its owner applied for a corresponding reduction in his taxes, it is necessary for surveyors to determine how much land had been lost. Obviously, this would have required the invention of elementary techniques of geometrical measurement. In this research, I will use geometrical algebra to illustrate the algebraic formula for some popular formulas that are used to calculate the area of regular regions. Finally I will use the Method of Exhaustion to show how those Greeks calculate and the area of circles.
DOCUMENTING ACADEMIC PROGRAM'S LEARNING OUTCOMES ASSESSMENT, Arvind C. Shah, Georgia Southwestern State University, Americus, GA 31709. Assessment is one of the most important instruments used to evaluate academic programs. Assessment is a continuing process to collect and document the evidences and to determine program viability. Often...
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