Vladimir Sotirov (Sofia)

A Gentle Introduction to Descent

!! Ui // X The modules Mi are “restrictions“ or pullbacks of M along Ui → X, and are compatible in that if Mi,j is the pullback of Mi over Ui along Ui ×X Uj → Ui, then we have isomorphisms Mi,j ∼= Mj,i that satisfy a coherence condition known as the cocycle condition. We say that modules over affine schemes have the property of descent for a family {Ui → X} if any family of compatible modules M...

Properties of the Dual Cone of Monomial-positive Immanants

We investigate a cone in the symmetric group algebra introduced by Stembridge [2]. It is dual to the cone of monomial-positive immanants of n × n matrices with indeterminate entries. We present a new set of relations between elements of the dual cone, and use these relations to show that the cone is finitely generated for n = 6, generalizing Stembridge’s result for n = 5.

Distinguish Between Benign and Malignant Prostate Using the Trace Element Con- tent Ratios in Prostatic Tissue as Tumor Markers

Mathews Journal of Cancer Science Distinguish Between Benign and Malignant Prostate Using the Trace Element Content Ratios in Prostatic Tissue as Tumor Markers Vladimir Zaichick1, Sofia Zaichick2 1Department of Radionuclide Diagnostics, Medical Radiological Research Centre, Russia. 2Department of Medicine, University of Illinois College of Medicine, USA. Corresponding Author: Vladimir Zaichick,...

Involutions on Standard Young Tableaux and Divisors on Metric Graphs

We elaborate upon a bijection discovered by Cools, Draisma, Payne, and Robeva in [CDPR12] between the set of rectangular standard Young tableaux and the set of equivalence classes of chip configurations on certain metric graphs under the relation of linear equivalence. We present an explicit formula for computing the v0-reduced divisors (representatives of the equivalence classes) associated to...

Distinguishing malignant from benign prostate using content of 17 chemical elements in prostatic tissue