Absence of high-energy spectral concentration for Dirac systems with divergent potentials
It is known that one-dimensional Dirac systems with potentials q which tend to −∞ (or ∞) at infinity, such that 1/q is of bounded variation, have a purely absolutely continuous spectrum covering the whole real line. We show that, for the system on a half-line, there are no local maxima of the spectral density (points of spectral concentration) above some value of the spectral parameter if q satisfies certain additional regularity conditions. These conditions admit thrice-differentiable potentials of power or exponential growth. The eventual sign of the derivative of the spectral density depends on the boundary condition imposed at the regular end-point.
On the Asymptotics of the Spectral Density of Radial Dirac Operators with Divergent Potential
The radial Dirac operator with a potential tending to infinity at infinity and satisfying a mild regularity condition is known to have a purely absolutely continuous spectrum covering the whole real line. Although having two singular end-points in the limit-point case, the operator has a simple spectrum and a generalised Fourier expansion in terms of a single solution. In the present paper, a simple formula for the corresponding spectral density is derived, and it is shown that, under certain conditions on the potential, the spectral function is convex for large values of the spectral parameter. This settles a question considered in earlier work by M. S. P. Eastham and the author.
Human-Computer User Interface Design for Semiliterate and Illiterate Users
Information and Communication Technology (ICT) has revolutionized the lives of the people. The technology is embedded in daily life of literate or semiliterate/illiterate users. However, the user interface (UI) requirements for semiliterate/illiterate users are different from that of an educated person. The researchers of Human Computer Interaction for Development (HCI4D) face challenges to improve the usability of a UI for the semiliterate users. Therefore, a Systematic Literature Review (SLR) is conducted to provide a set of design factors and guidelines for UI development of semiliterate users. The study is based on extensive research gathered from literature to understand the user-centered design (UCD) approach, enhancing user experience (UX) for semiliterate users. This study analyses fifty two research articles that are published during 2010-2020. The findings shed light on the systematization of UI design guidelines for semiliterate/illiterate users. These guidelines can help in taking advantage of ICT during the COVID-19 pandemic. The analysis shows that seventeen main design factors are indispensable for designing UI of semiliterate users. The most suggested design factors include localization and graphics, which should be incorporated in UI for the target population. Moreover, the lag in the design factors as personalization and consistency open a road for future research.