Numerical solution of fractional Sturm-Liouville equation in integral form

In this paper a fractional differential equation of the Euler-Lagrange / Sturm-Liouville type is considered. The fractional equation with derivatives of order $\alpha \in \left( 0,1 \right]$ in the finite time interval is transformed to the integral form. Next the numerical scheme is presented. In the final part of this paper examples of numerical solutions of this equation are shown. The convergence of the proposed method on the basis of numerical results is also discussed.Comment: 14 pages, 3 figures, 2 table

Generation Z And Their Use Of Learning Management System In Programming Courses

Generation Z students have grown up with ICT (information and communication technology) and are therefore used to being online more or less simultaneously on different types of media. Universities have different kinds of Learning Management Systems (LMS) with different possibilities for engagement. In the Electrical Engineering B. Eng. program at the Technical University of Denmark (DTU) we use a system called Learn. It has features for setting up individual study plans as well as common plans. Features such as surveys, quizzes, peer reviews are built in. We are interested in the students\u27 use of the LMS, their engagement and the relation to their achievement in the examination. The research questions we would like to answer are: How much do the students use Learn? What kind of materials do the students prefer? Is there any correlation between the use of materials on Learn and the grade? Is there any correlation between the score in quizzes and the grade? In this paper, we would like to describe and compare how much students use the materials in two different courses on the 2nd semester Digital Electronics and Programming (id 62734) and on the 4th semester Digital Design (id 62711). To answer these questions, we use data from Learn. And we conduct two qualitative surveys, one about students\u27 motivation, (Sekala, A et. al, 2023) and the other one as a part of the final course-evaluations in spring 2023

The Long-Baseline Neutrino Experiment: Exploring Fundamental Symmetries of the Universe

The preponderance of matter over antimatter in the early Universe, the dynamics of the supernova bursts that produced the heavy elements necessary for life and whether protons eventually decay --- these mysteries at the forefront of particle physics and astrophysics are key to understanding the early evolution of our Universe, its current state and its eventual fate. The Long-Baseline Neutrino Experiment (LBNE) represents an extensively developed plan for a world-class experiment dedicated to addressing these questions. LBNE is conceived around three central components: (1) a new, high-intensity neutrino source generated from a megawatt-class proton accelerator at Fermi National Accelerator Laboratory, (2) a near neutrino detector just downstream of the source, and (3) a massive liquid argon time-projection chamber deployed as a far detector deep underground at the Sanford Underground Research Facility. This facility, located at the site of the former Homestake Mine in Lead, South Dakota, is approximately 1,300 km from the neutrino source at Fermilab -- a distance (baseline) that delivers optimal sensitivity to neutrino charge-parity symmetry violation and mass ordering effects. This ambitious yet cost-effective design incorporates scalability and flexibility and can accommodate a variety of upgrades and contributions. With its exceptional combination of experimental configuration, technical capabilities, and potential for transformative discoveries, LBNE promises to be a vital facility for the field of particle physics worldwide, providing physicists from around the globe with opportunities to collaborate in a twenty to thirty year program of exciting science. In this document we provide a comprehensive overview of LBNE's scientific objectives, its place in the landscape of neutrino physics worldwide, the technologies it will incorporate and the capabilities it will possess.Comment: Major update of previous version. This is the reference document for LBNE science program and current status. Chapters 1, 3, and 9 provide a comprehensive overview of LBNE's scientific objectives, its place in the landscape of neutrino physics worldwide, the technologies it will incorporate and the capabilities it will possess. 288 pages, 116 figure

An Exact Solution of the Second-Order Differential Equation with the Fractional/Generalised Boundary Conditions

We analysed the initial/boundary value problem for the second-order homogeneous differential equation with constant coefficients in this paper. The second-order differential equation with respect to the fractional/generalised boundary conditions is studied. We presented particular solutions to the considered problem. Finally, a few illustrative examples are shown