Abstract:
The rising costs of higher education, along with the learning styles and needs of modern students, are changing the instructional landscape. Students of today do less and less well in the “lecture only” format, and staffing this format with live faculty is extremely expensive. MOOCs and other technology-heavy options are low cost but quite impersonal. Blended instruction has promise, with the ultimate goal of cost-efficient student engagement. This paper reports on a major course transformation to achieve student engagement in a large, formerly lecture-only course. The resulting blended-learning course features clickers, web-based operationalization of students helping students, media-rich interactive online materials, event credit, and newly added student-produced video tutorials. Results show that the addition of the student-produced video tutorials increased the student engagement in the course. 1. Introduction A teenaged-daughter enjoyed watching old Saturday Night Live episodes on Netflix, so her father took her to The Second City comedy club in Chicago to see some budding SNL prospects. The evening cost over $150, compared to an average of less than $1 per SNL episode on Netflix. Why the difference? The cost of live performers, of course. Instructional faculty is live performers in the classroom, and the rising costs of higher education are threatening their existence. One key to their survival is student engagement. The real time, multimodal digitally connected students of today do less and less well in the “lecture only” format [1], a format which has shown an upper limit of about 30% content retention regardless of lecturer [2]. If this format continues to be chosen Massively Open Online Courses (MOOCs) and other technology-assisted options could permanently remove the live performers. This paper reports on a major course transformation, following the guidelines of University of North Texas’ NextGen program. The resulting blended-learning course features clickers, web-based operationalization of students helping students, media-rich interactive online materials, event credit, and newly added student-produced video tutorials. 2. Theoretical Grounding: The Goal of Student Engagement With the shifting landscape of higher education, many colleges and universities have turned to student engagement activities as a way to ensure deep learning occurs among students [3, 4]. Universities want graduates equipped with skills and knowledge necessary for the 21st century career. Through campus-wide strategic planning initiatives that seek to adjust

Abstract:
An ultra-fast laser with central wavelength at 1064？nm and 10？ps pulse duration？was used to tightly focus laser radiation？with a microscope objective inside the volume of nucleated Lithium Aluminosilicate (LAS) glass-ceramic. The nonlinear absorption？of the LAS glass-ceramic was measured？for different laser parameters and a thermal simulation was performed to determine the temperature field inside the laser-modified area. After laser processing,？the samples were crystallized in a furnace and the effect of the laser-induced modifications on the microstructure was analyzed with SEM. The SEM analysis shows an increase in the length and size of whisker-shaped？β-spodumene crystals in the laser-modified area. By increasing the dimension of these whisker-shaped crystals, the flexural strength of LAS can be improved locally.？First？four-point bending flexural tests were performed to examine the influence on the mechanical properties.

Abstract:
We survey a new paradigm in signal processing known as "compressive sensing". Contrary to old practices of data acquisition and reconstruction based on the Shannon-Nyquist sampling principle, the new theory shows that it is possible to reconstruct images or signals of scientific interest accurately and even exactly from a number of samples which is far smaller than the desired resolution of the image/signal, e.g., the number of pixels in the image. This new technique draws from results in several fields of mathematics, including algebra, optimization, probability theory, and harmonic analysis. We will discuss some of the key mathematical ideas behind compressive sensing, as well as its implications to other fields: numerical analysis, information theory, theoretical computer science, and engineering.

Abstract:
It is shown that the values of Sylvester type determinants for various orthogonal polynomials considered by Askey in [R.Askey, Evaluation of some determinants, Proceedings of the 4th ISAAC Congress, 200x, xxx-xxx] can be ascertained inductively using simple block-triangularization schemes.

Abstract:
The inverse eigenvalue problem for real symmetric matrices of the form 0 0 0 . 0 0 * 0 0 0 . 0 * * 0 0 0 . * * 0 . . . . . . . 0 0 * . 0 0 0 0 * * . 0 0 0 * * 0 . 0 0 0 is solved. The solution is shown to be unique. The problem is also shown to be equivalent to the inverse eigenvalue problem for a certain subclass of Jacobi matrices.

Abstract:
Hermitian positive definite, totally positive, and nonsingular M-matrices enjoy many common properties, in particular: (A) positivity of all principal minors, (B) weak sign symmetry, (C) eigenvalue monotonicity, (D) positive stability. The class of GKK matrices is defined by properties (A) and (B), whereas the class of nonsingular $\tau$-matrices by (A) and (C). It was conjectured that: (A), (B) implies (D) [D. Carlson, J. Res. Nat. Bur. Standards Sect. B 78 (1974) 1-2], (A), (C) implies (D) [G.M. Engel and H. Schneider, Linear and Multilinear Algebra 4 (1976) 155-176], (A), (B) implies a property stronger than (D) [R. Varga, Numerical Methods in Linear Algebra, 1978, pp. 5-15], (A), (B), (C) implies (D) [D. Hershkowitz, Linear Algebra Appl. 171 (1992) 161-186]. We describe a class of unstable GKK $\tau$-matrices, thus disproving all four conjectures.

Abstract:
A necessary and sufficient condition for the convergence of an infinite right product of matrices of the form | I B | A = | 0 C |, with (uniformly) contracting submatrices $C$, is proven.

Abstract:
The subject of Chapter 1 is GKK $\tau$-matrices and related topics. Chapter 2 is devoted to boundedly invertible collections of matrices, with applications to operator norms and spline approximation. Various structured matrices (Toeplitz, Hessenberg, Hankel, Cauchy, and other) are used extensively throughout the thesis.

Abstract:
Simple proofs of the Hermite-Biehler and Routh-Hurwitz theorems are presented. The total nonnegativity of the Hurwitz matrix of a stable real polynomial follows as an immediate corollary.

Abstract:
Finite dimensional linear spaces (both complex and real) with indefinite scalar product [.,.] are considered. Upper and lower bounds are given for the size of an indecomposable matrix that is normal with respect to this scalar product in terms of specific functions of v = min{v-, v+}, where v-, (v+) is the number of negative (positive) squares of the form [x,x]. All the bounds except for one are proved to be strict.