Boundary interpolation for slice hyperholomorphic Schur functions

A boundary Nevanlinna-Pick interpolation problem is posed and solved in the quaternionic setting. Given nonnegative real numbers $\kappa_1, \ldots, \kappa_N$, quaternions $p_1, \ldots, p_N$ all of modulus $1$, so that the $2$-spheres determined by each point do not intersect and $p_u \neq 1$ for $u = 1,\ldots, N$, and quaternions $s_1, \ldots, s_N$, we wish to find a slice hyperholomorphic Schur function $s$ so that $$\lim_{\substack{r\rightarrow 1\\ r\in(0,1)}} s(r p_u) = s_u\quad {\rm for} \quad u=1,\ldots, N,$$ and $$\lim_{\substack{r\rightarrow 1\\ r\in(0,1)}}\frac{1-s(rp_u)\overline{s_u}}{1-r}\le\kappa_u,\quad {\rm for} \quad u=1,\ldots, N.$$ Our arguments relies on the theory of slice hyperholomorphic functions and reproducing kernel Hilbert spaces

English Language Teaching: Innovative Techniques in Multiple Intelligence Classes

India having a multi-lingual society, gives every language its own privileges and positions. English as an official and second language has also a vital role in making classrooms active in educational institutions and universities as well, by using it as a powerful tool for teaching subjects. The teaching of English language to students from the primary level has become much relevant in India in recent years since it is the medium of instruction in almost esteemed institutions. One reason for this has been the introduction of English as Foreign Language (EFL)/ English as Second Language (ESL) teaching in a number of European countries – but it is also a world-wide phenomenon. The best teaching methods in English class rooms and approaches, which the better understanding of students depends upon, are playing a vital role in making classes effective. One of the recent approaches in English language teaching methods is "the Theory of Multiple Intelligences MI"(1983), which is coined by Howard Gardner, an American psychologist and professor of education at Harvard university. Because since Classes are meant for clashes of the various minds, where students having different strengths and cognitive thinking come together, it is the necessity of classroom activities and teachings to be inclusive and comprehensive as well

A comparative study of density functional and density functional tight binding calculations of defects in graphene

The density functional tight binding approach (DFTB) is well adapted for the study of point and line defects in graphene based systems. After briefly reviewing the use of DFTB in this area, we present a comparative study of defect structures, energies and dynamics between DFTB results obtained using the dftb+ code, and density functional results using the localised Gaussian orbital code, AIMPRO. DFTB accurately reproduces structures and energies for a range of point defect structures such as vacancies and Stone-Wales defects in graphene, as well as various unfunctionalised and hydroxylated graphene sheet edges. Migration barriers for the vacancy and Stone-Wales defect formation barriers are accurately reproduced using a nudged elastic band approach. Finally we explore the potential for dynamic defect simulations using DFTB, taking as an example electron irradiation damage in graphene

Graphene edge structures: Folding, scrolling, tubing, rippling and twisting

Conventional three-dimensional crystal lattices are terminated by surfaces, which can demonstrate complex rebonding and rehybridisation, localised strain and dislocation formation. Two dimensional crystal lattices, of which graphene is the archetype, are terminated by lines. The additional available dimension at such interfaces opens up a range of new topological interface possibilities. We show that graphene sheet edges can adopt a range of topological distortions depending on their nature. Rehybridisation, local bond reordering, chemical functionalisation with bulky, charged, or multi-functional groups can lead to edge buckling to relieve strain, folding, rolling and even tube formation. We discuss the topological possibilities at a 2D graphene edge, and under what circumstances we expect different edge topologies to occur. Density functional calculations are used to explore in more depth different graphene edge types.Comment: Additional figure in published versio

Cerebrospinal Fluid and Blood Neurofilament Light Chain Protein in Prion Disease and Other Rapidly Progressive Dementias: Current State of the Art

Rapidly progressive dementia (RPD) is an umbrella term referring to several conditions causing a rapid neurological deterioration associated with cognitive decline and short disease duration. They comprise Creutzfeldt–Jakob disease (CJD), the archetypal RPD, rapidly progressive variants of the most common neurodegenerative dementias (NDs), and potentially treatable conditions such as infectious or autoimmune encephalitis and cerebrovascular disease. Given the significant clinical and, sometimes, neuroradiological overlap between these different disorders, biofluid markers also contribute significantly to the differential diagnosis. Among them, the neurofilament light chain protein (NfL) has attracted growing attention in recent years as a biofluid marker of neurodegeneration due to its sensitivity to axonal damage and the reliability of its measurement in both cerebrospinal fluid (CSF) and blood. Here, we summarize current knowledge regarding biological and clinical implications of NfL evaluation in biofluids across RPDs, emphasizing CJD, and other prion diseases. In the latter, NfL demonstrated a good diagnostic and prognostic accuracy and a potential value as a marker of proximity to clinical onset in pre-symptomatic PRNP mutation carriers. Similarly, in Alzheimer’s disease and other NDs, higher NfL concentrations seem to predict a faster disease progression. While increasing evidence indicates a potential clinical value of NfL in monitoring cerebrovascular disease, the association between NfL and prediction of outcome and/or disease activity in autoimmune encephalitis and infectious diseases has only been investigated in few cohorts and deserves confirmatory studies. In the era of precision medicine and evolving therapeutic options, CSF and blood NfL might aid the diagnostic and prognostic assessment of RPDs and the stratification and management of patients according to disease progression in clinical trials