Electronic structure and optical properties of ZnX (X=O, S, Se, Te)

Electronic band structure and optical properties of zinc monochalcogenides with zinc-blende- and wurtzite-type structures were studied using the ab initio density functional method within the LDA, GGA, and LDA+U approaches. Calculations of the optical spectra have been performed for the energy range 0-20 eV, with and without including spin-orbit coupling. Reflectivity, absorption and extinction coefficients, and refractive index have been computed from the imaginary part of the dielectric function using the Kramers--Kronig transformations. A rigid shift of the calculated optical spectra is found to provide a good first approximation to reproduce experimental observations for almost all the zinc monochalcogenide phases considered. By inspection of the calculated and experimentally determined band-gap values for the zinc monochalcogenide series, the band gap of ZnO with zinc-blende structure has been estimated.Comment: 17 pages, 10 figure

The structures of Hausdorff metric in non-Archimedean spaces

For non-Archimedean spaces $X$ and $Y,$ let $\mathcal{M}_{\flat } (X), \mathfrak{M}(V \rightarrow W)$ and $\mathfrak{D}_{\flat }(X, Y)$ be the ballean of $X$ (the family of the balls in $X$), the space of mappings from $X$ to $Y,$ and the space of mappings from the ballen of $X$ to $Y,$ respectively. By studying explicitly the Hausdorff metric structures related to these spaces, we construct several families of new metric structures (e.g., $\widehat{\rho } _{u}, \widehat{\beta }_{X, Y}^{\lambda }, \widehat{\beta }_{X, Y}^{\ast \lambda }$) on the corresponding spaces, and study their convergence, structural relation, law of variation in the variable $\lambda,$ including some normed algebra structure. To some extent, the class $\widehat{\beta }_{X, Y}^{\lambda }$ is a counterpart of the usual Levy-Prohorov metric in the probability measure spaces, but it behaves very differently, and is interesting in itself. Moreover, when $X$ is compact and $Y = K$ is a complete non-Archimedean field, we construct and study a Dudly type metric of the space of $K-$valued measures on $X.$Comment: 43 pages; this is the final version. Thanks to the anonymous referee's helpful comments, the original Theorem 2.10 is removed, Proposition 2.10 is stated now in a stronger form, the abstact is rewritten, the Monna-Springer is used in Section 5, and Theorem 5.2 is written in a more general for

Exceptional elliptic curves over quartic fields

We study the number of elliptic curves, up to isomorphism, over a fixed quartic field $K$ having a prescribed torsion group $T$ as a subgroup. Let $T=\Z/m\Z \oplus \Z/n\Z$, where $m|n$, be a torsion group such that the modular curve $X_1(m,n)$ is an elliptic curve. Let $K$ be a number field such that there is a positive and finite number of elliptic curves $E_T$ over $K$ having $T$ as a subgroup. We call such pairs $(E_T, K)$ \emph{exceptional}. It is known that there are only finitely many exceptional pairs when $K$ varies through all quadratic or cubic fields. We prove that when $K$ varies through all quartic fields, there exist infinitely many exceptional pairs when $T=\Z/14\Z$ or $\Z/15\Z$ and finitely many otherwise

On Haagerup's list of potential principal graphs of subfactors

We show that any graph, in the sequence given by Haagerup in 1991 as that of candidates of principal graphs of subfactors, is not realized as a principal graph except for the smallest two. This settles the remaining case of a previous work of the first author.Comment: 19 page

Boundary fields and renormalization group flow in the two-matrix model

We analyze the Ising model on a random surface with a boundary magnetic field using matrix model techniques. We are able to exactly calculate the disk amplitude, boundary magnetization and bulk magnetization in the presence of a boundary field. The results of these calculations can be interpreted in terms of renormalization group flow induced by the boundary operator. In the continuum limit this RG flow corresponds to the flow from non-conformal to conformal boundary conditions which has recently been studied in flat space theories.Comment: 31 pages, Late

Scholarship in Review 84(2)

Scholarship in Review was a magazine highlighting research and scholarly activities at Central Washington University, published by the Office of Graduate Studies and Research.https://digitalcommons.cwu.edu/scholarship_in_review/1000/thumbnail.jp

Mapping 6D N = 1 supergravities to F-theory

We develop a systematic framework for realizing general anomaly-free chiral 6D supergravity theories in F-theory. We focus on 6D (1, 0) models with one tensor multiplet whose gauge group is a product of simple factors (modulo a finite abelian group) with matter in arbitrary representations. Such theories can be decomposed into blocks associated with the simple factors in the gauge group; each block depends only on the group factor and the matter charged under it. All 6D chiral supergravity models can be constructed by gluing such blocks together in accordance with constraints from anomalies. Associating a geometric structure to each block gives a dictionary for translating a supergravity model into a set of topological data for an F-theory construction. We construct the dictionary of F-theory divisors explicitly for some simple gauge group factors and associated matter representations. Using these building blocks we analyze a variety of models. We identify some 6D supergravity models which do not map to integral F-theory divisors, possibly indicating quantum inconsistency of these 6D theories.Comment: 37 pages, no figures; v2: references added, minor typos corrected; v3: minor corrections to DOF counting in section

Symmetries and reversing symmetries of toral automorphisms

Toral automorphisms, represented by unimodular integer matrices, are investigated with respect to their symmetries and reversing symmetries. We characterize the symmetry groups of GL(n,Z) matrices with simple spectrum through their connection with unit groups in orders of algebraic number fields. For the question of reversibility, we derive necessary conditions in terms of the characteristic polynomial and the polynomial invariants. We also briefly discuss extensions to (reversing) symmetries within affine transformations, to PGL(n,Z) matrices, and to the more general setting of integer matrices beyond the unimodular ones.Comment: 34 page

Decreased mental time travel to the past correlates with default-mode network disintegration under lysergic acid diethylamide

This paper reports on the effects of LSD on mental time travel during spontaneous mentation. Twenty healthy volunteers participated in a placebo-controlled crossover study, incorporating intravenous administration of LSD (75 μg) and placebo (saline) prior to functional magnetic resonance imaging (fMRI). Six independent, blind judges analysed mentation reports acquired during structured interviews performed shortly after the functional magnetic resonance imaging (fMRI) scans (approximately 2.5 h post-administration). Within each report, specific linguistic references to mental spaces for the past, present and future were identified. Results revealed significantly fewer mental spaces for the past under LSD and this effect correlated with the general intensity of the drug’s subjective effects. No differences in the number of mental spaces for the present or future were observed. Consistent with the previously proposed role of the default-mode network (DMN) in autobiographical memory recollection and ruminative thought, decreased resting-state functional connectivity (RSFC) within the DMN correlated with decreased mental time travel to the past. These results are discussed in relation to potential therapeutic applications of LSD and related psychedelics, e.g. in the treatment of depression, for which excessive reflection on one’s past, likely mediated by DMN functioning, is symptomatic

Physico-Chemical Characteristics of Shungite Rock of Kazakhstan

Physico-chemical characteristics of shugite rocks of Kazakhstan (Bakyrchik deposit) were studied using the methods of elementary analysis, IR-spectroscopy, scanning electron microscopy, Raman spectroscopy and X-ray phase analysis. The content of carbon in shungite rock was determined to be from 3% to 19 %. The flotation technology for shungite rocks of Kazakhstan was developed, the content of carbon in the concentrate reaching 40.0%. When studying the elemental composition, the mineral part of shungite rocks was stated to be presented, mainly, by silicon, aluminium, calcium, magnesium, potassium, sodium, iron and titanium oxides. IR-spectroscopic investigations showed that in the concentrate, apart from polycyclic hydrocarbons containing methylene groups, there appeared carboxyl groups. The results of scanning electron microscopy (SEM) showed that flotation and thermal activation of shungite rocks on carbon allow obtaining a more developed surface structure and porosity. The structure of shungite carbon was shown by the method of Raman scattering to be close to that of glassy carbon. The results of X-ray diffraction analysis (XRD) of natural shungite rocks showed that the samples under study contained a carbonaceous substance and a number of mineral components: quartz, illite, bassanite, burgerite, muscovite. It is shown that shungite carbon of “Bakyrchik” deposit is identical to shungite of Zazhogino deposit in Russia. The stated physicochemical characteristics allow to determine the directions of the use of carbon concentrate for solution of ecological and technological problems