The method of representing a subsystem's performance map by one or more biquadratic
or bicubic functions is described, and the role of the performance map within the peak-shifting optimal control algorithm is documented.
Eighty 4-node, biquadratic
displacement, linear pore pressure with reduced integration elements were used to mesh the poroelastic model of articular cartilage and 1475 4-node, bilinear axisymmetric elements to mesh the remaining elastic parts in the axisymmetric model after mesh sensitivity checks were performed.
With concrete examples he begins with cubic equations, turning to complex numbers, biquadratic
equations, equations of degree n and their properties, including plausibility and proof, the search for additional solution formulas, equations that can be reduced in degree, including the decomposition of integer polynomials and Eisenstein's irreducibilty criterion, the construction of regular polygons, the Galois group of an equation, and algebraic structures and Galois theory, including groups and fields, the fundamental theorem, and Artin's version of the fundamental theory.
For example, even Gray's "diary entries" read like this: "We have invented a totally new numerico-exponential calculus", and "Began the theory of cubic and biquadratic
Watt told his son, "You should divide your lesson into 2 parts, one to be dedicated to Geometry and the other to the higher parts of Algebra such as cubic & Biquadratic
Equations, the summation of series, the squaring of curves, and other applications of Algebra to geometry.
Now designers can point and click to create square wave oscillators, a voltage-controlled sample and hold circuit, and a sum/difference stage with biquadratic
If additional information is available to allow the coil performance to be a function of both indoor wet-bulb and outdoor unit coil entering air temperature, a biquadratic
form of the equation may be used (Equation 21).
Within each element the velocity component was approximated by using quadratic interpolation function, the temperature by biquadratic
function, while the pressure was approximated by a linear function.
For system based optimization, Austin (1993) used biquadratic
polynomial models of chillers and cooling towers to optimize the condenser-water temperature setpoint.
The equation of the torus generated by the tool corner radius can be expressed as a biquadratic
equation in the unknown z (Coxeter, 1989):
Examples include simultaneous surface resolution in quadratic and biquadratic
Galois extensions, asymptotic behavior of cohomology, conic divisor classes over a normal monoid algebra, Rees algebras of the second syzygy module of the residue field of a regular local ring, a local global principle for the elementary unimodular vector group, picture invariants and the isomorphism problem for complex semisimple Lie algebras, arithmetic rank of certain Segre products, and strong semistability and Hilbert-Kunz multiplicity for singular plane curves.
4 includes upgraded versions of the bilinear filter and biquadratic
filter CAMs, enabling the creation of non-inverting low-pass filters.