U

Summary

U, or u, is the twenty-first and sixth-to-last letter and fifth vowel letter of the Latin alphabet, used in the modern English alphabet, the alphabets of other western European languages, and others worldwide. Its name in English is u (pronounced 'juː), plural ues. History U derives from the Semitic waw, as does F, and later, Y, W, and V. Its oldest ancestor goes to Egyptian hieroglyphics, and is probably from a hieroglyph of a mace or fowl, representing the sound v or the sound w. This was borrowed to Phoenician, where it represented the sound w, and seldom the vowel u. In Greek, two letters were adapted from the Phoenician waw. The letter was adapted, but split in two, with Digamma or wau being adapted to represent w, and the second one being Upsilon , which was originally adapted to represent u, later fronted, becoming y. In Latin, a stemless variant shape of the upsilon was borrowed in early times as U, taking the form of modern-day V – either directly from

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Max-stable processes and stationary systems of Levy particles

Sebastian Engelke

We study stationary max-stable processes {n(t): t is an element of R} admitting a representation of the form n(t) = max(i is an element of N) (U-i +Y-i(t)), where Sigma(infinity)(i=1) delta U-i is a Poisson point process on R with intensity e(-u)du, and Y1,Y2 are i.i.d. copies of a process {Y (t) : t is an element of R} obtained by running a Levy process for positive t and a dual Levy process for negative t. We give a general construction of such Levy-Brown-Resnick processes, where the restrictions of Y to the positive and negative half-axes are Levy processes with random birth and killing times. We show that these max-stable processes appear as limits of suitably normalized pointwise maxima of the form Mn(t) = max(i=1),...,n xi i (s(n) + t), where xi 1, xi 2... are i.i.d. Levy processes and sn is a sequence such that s(n) similar to clog n with c > 0. Also, we consider maxima of the form max(i=1),...,n Z(i) (t/log n), where Zi, Z2,... are i.i.d. Ornstein-Uhlenbeck processes driven by an alpha-stable noise with skewness parameter beta = -1. After a linear normalization, we again obtain limiting max-stable processes of the above form. This gives a generalization of the results of Brown and Resnick (1977) to the totally skewed a-stable case. (C) 2015 Elsevier B.V. All rights reserved.

Elsevier2015

Electronic structure of KTi(SO4)(2)center dot H2O: An S=1/2 frustrated chain antiferromagnet

Goran Nilsen, Julian Piatek, Henrik Moodysson Rønnow

The compound KTi(SO4)(2)center dot H2O was recently reported as a quasi-one-dimensional spin-1/2 compound with competing antiferromagnetic nearest-neighbor exchange J(1) and next-nearest-neighbor exchange J(2) along the chain with a frustration ratio alpha = J(2)/J(1) approximate to 0.29 [G. J. Nilsen, H. M. Ronnow, A. M. Lauchli, F. P. A. Fabbiani, J. Sanchez-Benitez, K. V. Kamenev, and A. Harrison, Chem. Mater. 20, 8 (2008)]. Here, we report a microscopically based magnetic model for this compound derived from density functional theory (DFT) based electronic structure calculations along with respective tight-binding models. Our (LSDA+U-d) calculations confirm the quasi-one-dimensional nature of the system with antiferromagnetic J(1) and J(2), but suggest a significantly larger frustration ratio alpha(DFT) approximate to 0.94-1.4, depending on the choice of U-d and structural parameters. Based on transfer matrix renormalization group (TMRG) calculations we find alpha(TMRG) = 1.5. Due to an intrinsic symmetry of the J(1)-J(2) model, our larger frustration ratio alpha is also consistent with the previous thermodynamic data. To identify the frustration ratio alpha unambiguously, we propose performing high-field magnetization and low-temperature susceptibility measurements.

American Physical Society2013

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Improvements in short-circuit currents of micromprph solar cells are investigated, with respect of nano-imprinted textures to glass superstrate. 2-D U-like periodic textures are optimized by means of 3-D rigorous optical simulations. Simulations indicate potential for > 35 % improvements in JSCbot for the optimized U-like textures with high aspect ratio compared to state-of-the-art random textures.

2013