qq-enumeration of type B and D Eulerian polynomials based on parity of descents

Carlitz and Scoville in 1973 considered four-variable polynomials enumerating the permutations according to the parity of both descents and ascents. In a recent work, Pan and Zeng proved a $q$-analogue of Carlitz-Scoville's generating function by counting the inversion number. Moreover, they also proved a type B analogue by enumerating the signed permutations with respect to the parity of descent and ascent position. In this work we prove a $q$-analogue of the type B result of Pan and Zeng by counting the type B inversion number. We also obtain a $q$-analogue of the generating functions for the bivariate alternating descent polynomials. Similar results are also obtained for type D Coxeter groups. As a by-product of our proofs, we get $q$-analogues of Hyatt's recurrences for the type B and type D Eulerian polynomials.Comment: 23 pages. Comments are welcom

Biography and Homoeopathy in Bengal: Colonial lives of a European heterodoxy

AbstractDespite being recognized as a significant literary mode in understanding the advent of the modern self, biographies as agenrehave received relatively little attention from South Asian historians. Likewise, histories of science and healing in British India have largely ignored the colonial trajectories of those sectarian, dissenting, supposedly pseudo-sciences and medical heterodoxies that have flourished in Europe since the late eighteenth century. This article addresses these gaps in the historiography to identify biographies as a principal mode through which an incipient, ‘heterodox’ Western science like homoeopathy could consolidate and sustain itself in Bengal. In recovering the cultural history of a category that the state archives render largely invisible, this article argues that biographies are more than a mere repository of individual lives, and in fact are a veritable site of power. In bringing histories of print and publishing, histories of medicine, and histories of life writing practices together, it pursues two broad themes: first, it analyses the sociocultural strategies and networks by which scientific doctrines and concepts are translated across cultural borders. It explores the relation between medical commerce, print capital, and therapeutic knowledge to illustrate that acculturation of medical science necessarily drew upon and reinforced local constellations of class, kinship, and religion. Second, it simultaneously reflects upon the expanding genre of homoeopathic biographies published since the mid-nineteenth century: on their features, relevance, and functions, examining in particular the contemporary status of biography vis-à-vis ‘history’ in writing objective pasts.This is the accepted manuscript. The final version is available from CUP at http://dx.doi.org/10.1017/S0026749X1400057

Interfacial properties of epitaxial gold nanocrystals supported on rutile titanium dioxide

Interfacial science is a fascinating field in materials science. From grain boundaries in bulk materials to interfaces in thin films, the properties of interfaces can lead to novel functionality in materials. The effect of interfaces on a material???s properties becomes amplified as the proportion of interfaces increases in relation to the volume of the material, for example in supported nanocrystals (NCs). While interfaces in bulk materials and thin films have been well characterized, atomic level characterization of NC interfaces is limited. The aim of this thesis is to develop a general set of methods to comprehensively study NC interfaces including interfacial atomic structure, interfacial energy and interfacial line tension. We have selected Au-TiO2 interface that has significant attention for its role in the remarkably low temperature catalytic oxidation of carbon monoxide to carbon dioxide. One of the best methods to study interfaces in bulk materials and thin films is cross sectional Transmission Electron Microscopy (TEM). Particularly with the advent of aberration corrected electron microscopy the experimental power to probe interfaces has increased manifold. However it is difficult to prepare NCs in the cross sectional viewing geometry for TEM without damaging the NCs using conventional specimen preparation methods. To enable this work, firstly a specimen preparation method was developed to support epitaxial Au NCs in the cross sectional geometry for TEM investigations without damaging the NCs. The interfacial atomic structure was investigated using aberration corrected Scanning Transmission Electron Microscopy (STEM) with a spatial resolution of ~1??. Interfacial energy of the NCs has been measured from cross sectional STEM images of NCs. It is found that Au NCs with the epitaxial relationship Au(111)[-110] || TiO2 (110)[001] have the largest adhesion to TiO2 (110) with an interfacial energy of 0.61??0.05 J/m2 (assuming ??TiO2(110) = 0.33 J/m2 and ??Au(111) = 1.283 J/m2). The stability of this epitaxy is attributed to the nucleation of Au atoms in the missing titanium row of a (1x2) TiO2 (110) reconstruction ??? resulting in an interfacial reconstruction of Au, Ti and O atoms which lowers the interfacial energy and enhances the adhesion of Au NCs to TiO2 (110). It has been found that smaller Au NCs dewet more than bigger Au NCs on TiO2 (110). The dewetting is attributed to the effect of interfacial line tension. In order to measure interfacial line tension, the Wulff-Kaishew was modified to incorporate the effect of interfacial line tension on NC shapes. The lower limit of interfacial line tension was measured to be 0.85??0.24 eV/?? (1.36??0.38 x 10-9 N) (assuming ??TiO2(110) = 0.33 J/m2 and ??Au(111) = 1.283 J/m2) for NCs with the epitaxial relationship of Au(111)[-110] || TiO2 (110)[001]. Since TEM/STEM studies are limited to individual NCs, the formation of epitaxial Au NCs was also probed using Reflection High Energy Electron Diffraction (RHEED) of Au NCs on flat TiO2 (110) supports in order to obtain structural information averaged from a larger number of NCs. The RHEED study confirms the epitaxial relationship of Au NCs as Au(111)[-110] || TiO2 (110)[001], irrespective of the details of the starting TiO2 (110) surface structure and the annealing atmosphere. On reconstructed (1x2) TiO2 (110) surfaces, the onset and completion of epitaxy formation occurred at much lower temperatures than unreconstructed TiO2 (110) surfaces. This shows that Au prefers to nucleate and grow as epitaxial NCs over (1x2) reconstructed TiO2 (110) in agreement with TEM/STEM images of NCs

Transcranial direct current stimulation (tDCS) for improving fatigue, motor function, and pain in people with multiple sclerosis

This is a protocol for a Cochrane Review (Intervention). The objectives are as follows: To assess the effects of transcranial direct current stimulation (tDCS) on fatigue, motor function, and pain in people with MS. © 2019 John Wiley and Sons Ltd. All rights reserved