Structure of semisimple Hopf algebras of dimension p2q2p^2q^2

Let $p,q$ be prime numbers with $p^4<q$, and $k$ an algebraically closed field of characteristic 0. We show that semisimple Hopf algebras of dimension $p^2q^2$ can be constructed either from group algebras and their duals by means of extensions, or from Radford biproduct R#kG, where $kG$ is the group algebra of group $G$ of order $p^2$, $R$ is a semisimple Yetter-Drinfeld Hopf algebra in ${}^{kG}_{kG}\mathcal{YD}$ of dimension $q^2$. As an application, the special case that the structure of semisimple Hopf algebras of dimension $4q^2$ is given.Comment: 11pages, to appear in Communications in Algebr

The H=xp model revisited and the Riemann zeros

Berry and Keating conjectured that the classical Hamiltonian H = xp is related to the Riemann zeros. A regularization of this model yields semiclassical energies that behave, in average, as the non trivial zeros of the Riemann zeta function. However, the classical trajectories are not closed, rendering the model incomplete. In this paper, we show that the Hamiltonian H = x (p + l_p^2/p) contains closed periodic orbits, and that its spectrum coincides with the average Riemann zeros. This result is generalized to Dirichlet L-functions using different self-adjoint extensions of H. We discuss the relation of our work to Polya's fake zeta function and suggest an experimental realization in terms of the Landau model.Comment: 5 pages, 3 figure

Deformations of Multiparameter Quantum gl(N)

Multiparameter quantum gl(N) is not a rigid structure. This paper defines an essential deformation as one that cannot be interpreted in terms of a similarity transformation, nor as a perturbation of the parameters. All the equivalence classes of first order essential deformations are found, as well as a class of exact deformations. This work provides quantization of all the classical Lie bialgebra structures (constant r-matrices) found by Belavin and Drinfeld for sl(n). A special case, that requires the Hecke parameter to be a cubic root of unity, stands out.Comment: 15 pages. Plain Te

Empirical prediction of peak pressure levels in anthropogenic impulsive noise. Part I: Airgun arrays signals

This paper presents an empirical linear equation to predict peak pressure level of anthropogenic impulsive signals based on its correlation with the sound exposure level. The regression coefficients are shown to be weakly dependent on the environmental characteristics but governed by the source type and parameters. The equation can be applied to values of the sound exposure level predicted with a numerical model, which provides a significant improvement in the prediction of the peak pressure level. Part I presents the analysis for airgun arrays signals, and Part II considers the application of the empirical equation to offshore impact piling noise

Further Improvements in the Understanding of Isotropic Loop Quantum Cosmology

The flat, homogeneous, and isotropic universe with a massless scalar field is a paradigmatic model in Loop Quantum Cosmology. In spite of the prominent role that the model has played in the development of this branch of physics, there still remain some aspects of its quantization which deserve a more detailed discussion. These aspects include the kinematical resolution of the cosmological singularity, the precise relation between the solutions of the densitized and non-densitized versions of the quantum Hamiltonian constraint, the possibility of identifying superselection sectors which are as simple as possible, and a clear comprehension of the Wheeler-DeWitt (WDW) limit associated with the theory in those sectors. We propose an alternative operator to represent the Hamiltonian constraint which is specially suitable to deal with these issues in a satisfactory way. In particular, with our constraint operator, the singularity decouples in the kinematical Hilbert space and can be removed already at this level. Thanks to this fact, we can densitize the quantum Hamiltonian constraint in a rigorous manner. Besides, together with the physical observables, this constraint superselects simple sectors for the universe volume, with a support contained in a single semiaxis of the real line and for which the basic functions that encode the information about the geometry possess optimal physical properties. Namely, they provide a no-boundary description around the cosmological singularity and admit a well-defined WDW limit in terms of standing waves. Both properties explain the presence of a generic quantum bounce replacing the singularity at a fundamental level, in contrast with previous studies where the bounce was proved in concrete regimes and focusing on states with a marked semiclassical behavior.Comment: 13 pages, version accepted for publication in Physical Review

A General SU(2) Formulation for Quantum Searching with Certainty

A general quantum search algorithm with arbitrary unitary transformations and an arbitrary initial state is considered in this work. To serach a marked state with certainty, we have derived, using an SU(2) representation: (1) the matching condition relating the phase rotations in the algorithm, (2) a concise formula for evaluating the required number of iterations for the search, and (3) the final state after the search, with a phase angle in its amplitude of unity modulus. Moreover, the optimal choices and modifications of the phase angles in the Grover kernel is also studied.Comment: 8 pages, 2 figure

Distribution of melanopsin positive neurons in pigmented and albino mice: evidence for melanopsin interneurons in the mouse retina.

Here we have studied the population of intrinsically photosensitive retinal ganglion cells (ipRGCs) in adult pigmented and albino mice. Our data show that although pigmented (C57Bl/6) and albino (Swiss) mice have a similar total number of ipRGCs, their distribution is slightly different: while in pigmented mice ipRGCs are more abundant in the temporal retina, in albinos the ipRGCs are more abundant in superior retina. In both strains, ipRGCs are located in the retinal periphery, in the areas of lower Brn3a(+)RGC density. Both strains also contain displaced ipRGCs (d-ipRGCs) in the inner nuclear layer (INL) that account for 14% of total ipRGCs in pigmented mice and 5% in albinos. Tracing from both superior colliculli shows that 98% (pigmented) and 97% (albino) of the total ipRGCs, become retrogradely labeled, while double immunodetection of melanopsin and Brn3a confirms that few ipRGCs express this transcription factor in mice. Rather surprisingly, application of a retrograde tracer to the optic nerve (ON) labels all ipRGCs, except for a sub-population of the d-ipRGCs (14% in pigmented and 28% in albino, respectively) and melanopsin positive cells residing in the ciliary marginal zone (CMZ) of the retina. In the CMZ, between 20% (pigmented) and 24% (albino) of the melanopsin positive cells are unlabeled by the tracer and we suggest that this may be because they fail to send an axon into the ON. As such, this study provides the first evidence for a population of melanopsin interneurons in the mammalian retina

Lunar and Meteorite Thin Sections for Undergraduate and Graduate Studies

The Johnson Space Center (JSC) has the unique responsibility to curate NASA's extraterrestrial samples from past and future missions. Curation includes documentation, preservation, preparation, and distribution of samples for research, education, and public outreach. Between 1969 and 1972 six Apollo missions brought back 382 kilograms of lunar rocks, core samples, pebbles, sand and dust from the lunar surface. JSC also curates meteorites collected on US expeditions to Antarctica including rocks from Moon, Mars, and many asteroids including Vesta. Studies of rock and soil samples from the Moon and meteorites continue to yield useful information about the early history of the Moon, the Earth, and the inner solar system

Exact solution of the Schrodinger equation with the spin-boson Hamiltonian

We address the problem of obtaining the exact reduced dynamics of the spin-half (qubit) immersed within the bosonic bath (enviroment). An exact solution of the Schrodinger equation with the paradigmatic spin-boson Hamiltonian is obtained. We believe that this result is a major step ahead and may ultimately contribute to the complete resolution of the problem in question. We also construct the constant of motion for the spin-boson system. In contrast to the standard techniques available within the framework of the open quantum systems theory, our analysis is based on the theory of block operator matrices.Comment: 9 pages, LaTeX, to appear in Journal of Physics A: Mathematical and Theoretica

On the effect of Ti on Oxidation Behaviour of a Polycrystalline Nickel-based Superalloy

Titanium is commonly added to nickel superalloys but has a well-documented detrimental effect on oxidation resistance. The present work constitutes the first atomistic-scale quantitative measurements of grain boundary and bulk compositions in the oxide scale of a current generation polycrystalline nickel superalloy performed through atom probe tomography. Titanium was found to be particularly detrimental to oxide scale growth through grain boundary diffusion