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We present a mixed finite element method for a model of the flow in a Hele-Shaw cell of 2-D fluid droplets surrounded by air driven by surface tension and actuated by an electric &...
This work describes the modeling and simulation of planar electrowetting on dielectric (EWOD) devices that move fluid droplets by modulating surface tension effects. The fluid dynam...
Using asymptotics, we derive explicit, simplified formulas for integrals representing the force dipole interaction energy per unit length between line defects (steps) of the same sign that form pertur...
The ring of projective invariants of eight ordered points on the line is a quotient of the polynomial ring on V , where V is a fourteen-dimensional representation of S8, by an ideal I8, so the modular...
Consider the projective coordinate ring of the GIT quotient (P1)n//SL(2), with the usual linearization, where n is even. In 1894, Kempe proved that this ring is generated in degree one. In [HMSV2]we s...
The ring of projective invariants of n ordered points on the projective line is one of the most basic and earliest studied examples in Geometric Invariant Theory. It is a remarkable fact and the point...
A central question in invariant theory is that of determining the relations among invariants. Geometric invariant theory quotients come with a natural ample line bundle, and hence often a natural proj...
A UNIVERSAL ARONSZAJN LINE     UNIVERSAL  ARONSZAJN LINE       2015/8/17
The purpose of this note is to define an Aronszajn line ηC and prove that under the assumption of PFA it is universal for the class of Aronszajn lines. Moreover ηC can be easily described in terms of ...
We generalize a theorem of Knuth relating the oriented spanning trees of a directed graph G and its directed line graph LG. The sandpile group is an abelian group associated to a directed graph, whose...
The ring of projective invariants of n ordered points on the projective line is one of the most basic and earliest studied examples in Geometric Invariant Theory. It is a remarkable fact and the poin...
We consider the ring of invariants of n points on the projective line. The space (P 1) n//PGL2 is perhaps the first nontrivial example of a Geometry Invariant Theory quotient. The constructio...
The following divisors in the space Sym12 P1 of twelve points on P1 are actually the same: (A) the possible locus of the twelve nodal bers in a rational elliptic bration (i.e. a pencil of plane cu...
A central question in invariant theory is that of determining the relations among invariants. Geometric invariant theory quotients come with a natural ample line bundle, and hence often a natural pr...
In this paper, we seek the conjugate gradient direction closest to the direction of the scaled memoryless BFGS method and propose a family of conjugate gradient methods for unconstrained optimizatio...

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