Varieties of binary systems

Varieties of Simultaneous Sums of Powers for binary forms

The problem of simultaneous decomposition of binary forms as sums of powers of linear forms is studied. For generic forms the minimal number of linear forms needed is found and the space parametrizing all the possible decompositions is described. These results are applied to the study of rational curves.

On invariant notions of Segre varieties in binary projective spaces

Invariant notions of a class of Segre varieties S(m)(2) of PG(2m − 1, 2) that are direct products of m copies of PG(1, 2), m being any positive integer, are established and studied. We first demonstrate that there exists a hyperbolic quadric that contains S(m)(2) and is invariant under its projective stabiliser group GS(m)(2). By embedding PG(2 m − 1, 2) into PG(2m − 1, 4), a basis of the latte...

Assessments of applicability of Q and RMi systems in binary tunnels of Bakhtiari dam_ Iran

The main rock mass classification systems make use of similar rock mass parameters. Due to lack of comprehensive estimation systems, determining the real specifications of jointed rocks faces some difficulties. A vast number of parameters with various degrees of impact are involved in such definitions. Combination impact of all the effective parameters is to be figured out in order to come up w...

Prediction of Liquid-Liquid Equilibria of Binary Systems Containing Alcohols Using EoS-GE Models

Prym Varieties and Integrable Systems

A new relation between Prym varieties of arbitrary morphisms of algebraic curves and integrable systems is discovered. The action of maximal commutative subalgebras of the formal loop algebra of GLn defined on certain infinite-dimensional Grassmannians is studied. It is proved that every finite-dimensional orbit of the action of traceless elements of these commutative Lie algebras is isomorphic...