Let Cm×n, Cm×n r , C m ≥ , C m > , and In denote the set of m × n complex matrices, subset of Cm×n consisting of matrices with rank r, set of the Hermitian nonnegative definite matrices of order m, subset of C ≥ consisting of positive-definite matrices and n × n unit matrix, respectively. Without specification, we always assume that m > n >max{r, s} and the given weight matrices M ∈ C > ,N ∈ C ...

The variety of principal minors of n× n symmetric matrices, denoted Zn, is invariant under the action of a group G ⊂ GL(2) isomorphic to (SL(2)) ×Sn. We describe an irreducible G-module of degree 4 polynomials that cuts out Zn set theoretically. This solves the set-theoretic version of a conjecture of Holtz and Sturmfels.

the interaction of magnesium hydrate at the phosphate oxygen atom of the pyrimidine nucleotides (cmp,ump,dtmp) were studied at the hartree-fock level theory. we used lanl2dz basis set for mg and 6-31g* basis set for atoms.the basis set superposition error (bsse) begins to converge for used method/basis set. the gauge-invariant atomic orbital (giao) method and the continuous-set-of-gauge-transfo...

In [AO] the authors study Steiner bundles via their unstable hyperplanes and proved that (see [AO], Tmm 5.9) : A rank n Steiner bundle on Pn which is SL(2,C) invariant is a Schwarzenberger bundle. In this note we give a very short proof of this result based on Clebsch-Gordon problem for SL(2,C)modules.

We use ergodic theory to prove a quantitative version of a theorem of M. A. Berger and Y. Wang, which relates the joint spectral radius of a set of matrices to the spectral radii of finite products of those matrices. The proof rests on a theorem asserting the existence of a continuous invariant splitting for certain matrix cocycles defined over a minimal homeomorphism and having the property th...

We describe the set of all invariant measures on the spaces of universal countable graphs and on the spaces of universal countable triangles-free graphs. The construction uses the description of the S∞-invariant measure on the space of infinite matrices in terms of measurable function of two variables on some special space. In its turn that space is nothing more than the universal continuous (B...

We describe the set of all invariant measures on the spaces of universal countable graphs and on the spaces of universal countable triangles-free graphs. The construction uses the description of the S∞-invariant measure on the space of infinite matrices in terms of measurable function of two variables on some special space. In its turn that space is nothing more than the universal continuous (B...