[Download] "Section IV: Physics, Mathematics, Computer Science, Engineering and Technology (Briefs)" by Georgia Journal of Science " Book PDF Kindle ePub Free
eBook details
- Title: Section IV: Physics, Mathematics, Computer Science, Engineering and Technology (Briefs)
- Author : Georgia Journal of Science
- Release Date : January 22, 2008
- Genre: Engineering,Books,Professional & Technical,
- Pages : * pages
- Size : 180 KB
Description
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.