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Articles 4081 - 4083 of 4083
Full-Text Articles in Physical Sciences and Mathematics
Equation Of State Of Nacl And Its Use As A Pressure Gauge In High-Pressure Research, Daniel L. Decker
Equation Of State Of Nacl And Its Use As A Pressure Gauge In High-Pressure Research, Daniel L. Decker
Faculty Publications
The pressure as a function of lattice parameter and temperature has been calculated for NaCl over a pressure range of 0 to 500 kbar for temperatures between 0degrees and 1500degrees C. The calculation used the Mie-Gruneisen equation of state with Born-Mayer type repulsion terms between first and second nearest neighbors. The Gruneisen constant was expanded about its value at room temperature and atmospheric pressure; the first coefficient in the expansion being evaluated by forcing the calculated thermal expansion at atmospheric pressure to fit the experimental results of Enck. The two empirical parameters in the repulsion terms were evaluated using the …
Diffraction Of Spherical Scalar And Vector Waves At Axial Points Of A Circular Aperture And Disk, Keith Leon Mcdonald
Diffraction Of Spherical Scalar And Vector Waves At Axial Points Of A Circular Aperture And Disk, Keith Leon Mcdonald
Faculty Publications
The following work treats Kottler's saltus problem of diffraction of electromagnetic waves emitted by a Hertzian oscillator source and the analogous Kirchhoff's scalar problem of waves emitted by a point source. The medium is a homogeneous isotropic dielectric. In the vector case a new exact solution of the basic integrals is presented, at axial points only, (a) behind a circular aperture in a "black'' screen, and (b) behind its complementary "black'' disk. The relative time-averaged intensity of energy flow is plotted for the disk only. It is shown that the scalar theory predicts considerably larger values than the electromagnetic theory …
A Note On K-Commutative Matrices, D. W. Robinson
A Note On K-Commutative Matrices, D. W. Robinson
Faculty Publications
Let A and B be square matrices over a field in which the minimum polynomial of A is completely reducible. It is shown that A is k commutative with respect to B for some non-negative integer k if and only if B commutes with every principal idempotent of A. The proof is brief, simplifying much of the previous study of k-commutative matrices. The result is also used to generalize some well-known theorems on finite matrix commutators that involve a complex matrix and its transposed complex conjugate.