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Academy of Mathematics and Systems Science, CAS Colloquia & Seminars：t-stabilities and t-structures for the weighted projective line of type (2)
加权投影线 t-稳定性 t-结构
2023/11/13
We focus on the study of t-stabilities on a triangulated category in the sense of Gorodentsev, Kuleshov and Rudakov. We give an equivalent description for the nest t-stabilities on certain triangulate...
MIXED FINITE ELEMENT METHOD FOR ELECTROWETTING ON DIELECTRIC WITH CONTACT LINE PINNING
FINITE ELEMENT CONTACT LINE PINNING
2015/12/11
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 &...
Electrowetting with Contact Line Pinning: Computational Modeling and Comparisons with Experiments
equation Contact Line Pinning
2015/12/11
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...
Formulas for the force dipole interaction of surface line defects in homoepitaxy
Formulas for the force surface line defects homoepitaxy
2015/10/16
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 POINTS ON THE LINE VIA REPRESENTATION THEORY
PROJECTIVE INVARIANTS EIGHT POINTS ON THE LINE VIA
2015/10/14
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...
THE IDEAL OF RELATIONS FOR THE RING OF INVARIANTS OF n POINTS ON THE LINE:INTEGRALITY RESULTS
RELATIONS FOR THE RING INVARIANTS OF n POINTS ON THE LINE INTEGRALITY RESULTS
2015/10/14
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 RELATIONS AMONG INVARIANTS OF POINTS ON THE PROJECTIVE LINE
RELATIONS AMONG INVARIANTS POINTS ON THE PROJECTIVE LINE
2015/10/14
THE RELATIONS AMONG INVARIANTS OF POINTS ON THE PROJECTIVE LINE.
THE IDEAL OF RELATIONS FOR THE RING OF INVARIANTS OF n POINTS ON THE LINE
RELATIONS FOR THE RING INVARIANTS OF n POINTS THE LINE
2015/10/14
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...
THE EQUATIONS FOR THE MODULI SPACE OF n POINTS ON THE LINE
MODULI SPACE n POINTS ON THE LINE
2015/10/14
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...
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 ...
SANDPILE GROUPS AND SPANNING TREES OF DIRECTED LINE GRAPHS
SANDPILE GROUPS SPANNING TREES DIRECTED LINE GRAPHS
2015/8/14
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...
TWELVE POINTS ON THE PROJECTIVE LINE, BRANCHED COVERS, AND RATIONAL ELLIPTIC FIBRATIONS
PROJECTIVE LINE BRANCHED COVERS
2015/7/14
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...