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.

Several authors have found, however, that a more general

biquadratic transformation can significantly reduce the number of terms needed (see MacLeod [1993]).

Many from previously reported pseudodifferential circuit solutions were focused on

biquadratic (second-order) active filters, [6]-[9] for instance.

Chang, "Single FDCCII-based current-mode universal

biquadratic filter," in Proc.

After generation of the determinant of natural frequencies matrix for the system (H.4)-(H.5) we will write the following characteristic

biquadratic equation of fourth order for system (H.4)-(H.5) in the form:

The governing equations on the physical domain are discretized by using finite element method based on the Galerkin weight residual method with

biquadratic interpolation functions and the equations resulting from the discretization are solved using iterative method called segregate solution algorithm.

Maheshwari, "Multi input multi output

biquadratic universal filter using Dual-X Current Conveyor (DXCCII)," in Proceedings of the International Conference on Computer and Communication Technology (ICCCT '10), pp.

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).

We use Lagrangian quadrilateral elements with

biquadratic interpolation for the velocities and bilinear interpolation for the pressures.

The examples were generated using the IFISS software package [14] and discretized with with a div-stable [Q.sub.2]-[Q.sub.1] finite element discretization (

biquadratic velocities, bilinear pressures) on a uniform mesh of velocity element width 2/[2.sup.l-1] (giving velocity nodal mesh width 2/[2.sup.l]).

Tungjitkusolmun, "Voltage-mode multifunction

biquadratic filters using new ultra-low-power differential difference current conveyors", Radioengineering, vol.

Horng, "Voltage-Mode Highpass, Bandpass, Lowpass and Notch

Biquadratic Filters Using Single DDCC," Radioengineering, vol.