Unifying discrete and continuous Weyl-Titchmarsh theory via a class of linear Hamiltonian systems on Sturmian time scales

In this study, we are concerned with introducing Weyl-Titchmarsh theory for a class of dynamic linear Hamiltonian nabla systems over a half-line on Sturmian time scales. After developing fundamental properties of solutions and regular spectral problems, we introduce the corresponding maximal and minimal operators for the system. Matrix disks are constructed and proved to be nested and converge to a limiting set. Some precise relationships among the rank of the matrix radius of the limiting set, the number of linearly independent square summable solutions, and the defect indices of the minimal operator are established. Using the above results, a classification of singular dynamic linear Hamiltonian nabla systems is given in terms of the defect indices of the minimal operator, and several equivalent conditions on the cases of limit point and limit circle are obtained, respectively. These results unify and extend certain classic and recent results on the subject in the continuous and discrete cases, respectively, to Sturmian time scales.Comment: 34 page

Method for removing oxygen impurities from cesium Patent

Heated tungsten filter for removing oxygen impurities from cesiu

The devil is in the definitions

Lk 10:25-37

Reaching DEEP in Math (Developing Educational Excellence and Proficiency in Mathematics)

This paper describes the DEEP in Math Program developed in the academic year 1998-1999 from a collaborative effort of the Louisiana Systemic lnitiative Program (LaSlP) and the Louisiana Department of Education (LDE). It includes evidence of impressive results in low achieving schools and in high-poverty districts targeted by the effort. The plan was for LaSlP to give intensive content and leadership training in Summer 1999 and academic year 1999-2000 to carefully selected. well-qualified math leaders. These leaders were then employed full-time in the 1999-2000 academic year and beyond by their local education authorities to work with all math teachers in a few designated schools at some cohesive subset of grades 3-8

Piezoelectric pump Patent

Piezoelectric pump for supplying fluid at high frequencies to gyroscope fluid suspension syste