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The introduction of high-speed circuits to realize an arithmetic function f as a piecewise linear approximation has created a need to understand how the number of segments depends on the interval a is greater or equal to x which is greater or equal to b and the desired approximation error e...

In this paper we prove two conjectures proposed by Janous on an extension to the p-th power-mean of the Erdoes-Debrunner inequality relating the areas of the four sub- triangles formed by connecting three arbitrary points on the sides of a given triangle., Published in the Journal of Inequal. Pure and Appl. Math. v8 n3 p1-16, 2007.

In this papere we prove two conjectures proposed by Janous on an extension to the p-th power-mean of the Erdos-Debrunner inequality relating the areas of the four subtriangles formed by connecting three arbitrary points on the sides of a given triangle.

Bi-orthogonality relationships are established for a vertically heterogeneous porous media in contact with a fluid, a solid, a second porous medium, and a free surface. Fraser's bi-orthgonality relation for propagation of Rayleigh-Lamb modes in a plate with traction free eurfaces is shown to be a special case of the bi-orthogonality relations derived herein in which the medium can be thought of as a porous slab with zero porosity.

The optical field in free electron lasers can sometimes develop sidebands and exhibit very complex behavior. The purpose of this report is to develop a two mode model of the optical field in a free electron laser in which the optical modes are coupled by the free electrons in the laser. This model may be used to study the long term stability of the optical wave and the development of sidebands in the optical field. In this report the equations of motion governing the interaction of an electron with the optical modes will be derived. Free electron lasers, Optical wave.

The consequences of assuming that density is conserved in the problem of determining absolute velocities are investigates. Two questions are considered: (i) the constraints that the density must satisfy to be compatible with assumed geostrophic and hydrostatic dynamics and (ii) whether and to what extent the indeterminacy in this dynamics is removed by this additional assumption. With the dawn of ocean forecasting approaching, the need to know velocity fields for use as initial conditions in a prediction scheme is keenly felt. but direct velocity measurements are still difficult to make, and so we are forced to rely on the classical procedure which consists of inferring the velocity fields from temperature and salinity measurements. Reprints., Published in Journal of Marine Research, v46 p701-714 1988

With the dawn of ocean forecasting approaching, the need to know velocity fields for use as initial conditions in a prediction scheme is keenly felt. But direct velocity measurements are still difficult to make, and so we are forced to rely on the classical procedure which consists of inferring the velocity fields from temperature and salinity measurements. In this procedure, given the density field one must find velocity fields and a pressure field., Prepared in cooperation with Southern Methodist Univ., Dallas, TX.