Qualitative analysis of eigenvalues and eigenfunctions of one boundary value-transmission problem

WOS: 000374243400001The aim of this study is to investigate various qualitative properties of eigenvalues and corresponding eigenfunctions of one Sturm-Liouville problem with an interior singular point. We introduce a new Hilbert space and integral operator in it such a way that the problem under consideration can be interpreted as a spectral problem of this operator. By using our own approaches we investigate such properties as uniform convergence of the eigenfunction expansions, the Parseval equality, the Rayleigh-Ritz formula, the minimax principle, and the monotonicity of eigenvalues for the considered boundary value-transmission problem (BVTP)

An observational study of breakthrough SARS-CoV-2 Delta variant infections among vaccinated healthcare workers in Vietnam

Background Data on breakthrough SARS-CoV-2 Delta variant infections in vaccinated individuals are limited. Methods We studied breakthrough infections among Oxford-AstraZeneca vaccinated healthcare workers in an infectious diseases hospital in Vietnam. We collected demographic and clinical data alongside serial PCR testing, measurement of SARS-CoV-2 antibodies, and viral whole-genome sequencing. Findings Between 11th–25th June 2021 (7-8 weeks after the second dose), 69 staff tested positive for SARS-CoV-2. 62 participated in the study. Most were asymptomatic or mildly symptomatic and all recovered. Twenty-two complete-genome sequences were obtained; all were Delta variant and were phylogenetically distinct from contemporary viruses obtained from the community or from hospital patients admitted prior to the outbreak. Viral loads inferred from Ct values were 251 times higher than in cases infected with the original strain in March/April 2020. Median time from diagnosis to negative PCR was 21 days (range 8–33). Neutralizing antibodies (expressed as percentage of inhibition) measured after the second vaccine dose, or at diagnosis, were lower in cases than in uninfected, fully vaccinated controls (median (IQR): 69.4 (50.7-89.1) vs. 91.3 (79.6-94.9), p=0.005 and 59.4 (32.5-73.1) vs. 91.1 (77.3-94.2), p=0.043). There was no correlation between vaccine-induced neutralizing antibody levels and peak viral loads or the development of symptoms. Interpretation Breakthrough Delta variant infections following Oxford-AstraZeneca vaccination may cause asymptomatic or mild disease, but are associated with high viral loads, prolonged PCR positivity and low levels of vaccine-induced neutralizing antibodies. Epidemiological and sequence data suggested ongoing transmission had occurred between fully vaccinated individuals

Achieving Optimal Best: Instructional Efficiency and the Use of Cognitive Load Theory in Mathematical Problem Solving

We recently developed the Framework of Achievement Bests to explain the importance of effective functioning, personal growth, and enrichment of well-being experiences. This framework postulates a concept known as optimal achievement best, which stipulates the idea that individuals may, in general, strive to achieve personal outcomes, reflecting their maximum capabilities. Realistic achievement best, in contrast, indicates personal functioning that may show moderate capability without any aspiration, motivation, and/or effort expenditure. Furthermore, our conceptualization indicates the process of optimization, which involves the optimization of achievement of optimal best from realistic best. In this article, we explore the Framework of Achievement Bests by situating it within the context of student motivation. In our discussion of this theoretical orientation, we explore in detail the impact of instructional designs for effective mathematics learning as an optimizer of optimal achievement best. Our focus of examination of instructional designs is based, to a large extent, on cognitive load paradigm, theorized by Sweller and his colleagues. We contend that, in this case, cognitive load imposition plays a central role in the structure of instructional designs for effective learning, which could in turn influence individuals’ achievements of optimal best. This article, conceptual in nature, explores varying efficiencies of different instructional approaches, taking into consideration the potency of cognitive load imposition. Focusing on mathematical problem solving, we discuss the potentials for instructional approaches to influence individuals’ striving of optimal best from realistic best