194,600 research outputs found
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
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
Existence of three solutions for a first-order problem with nonlinear non-local boundary conditions
Conditions for the existence of at least three positive solutions to the
nonlinear first-order problem with a nonlinear nonlocal boundary condition
given by
&& y'(t) - p(t)y(t) = \sum_{i=1}^m f_i\big(t,y(t)\big), \quad t\in[0,1],
&& \lambda y(0) = y(1) + \sum_{j=1}^n \Phi_j(\tau_j,y(\tau_j)), \quad
\tau_j\in[0,1], are discussed, for sufficiently large . The
Leggett-Williams fixed point theorem is utilized.Comment: outline, 6 page
Apocalypse recalled: the Book of Revelation after Christendom
Author: Harry O. Maier. Title: Apocalypse recalled. Publisher: Minneapolis : Fortress, 2002
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