A Ricci inequality for hypersurfaces in the sphere

Let Mⁿ be a complete Riemannian manifold immersed isometrically in the unity Euclidean sphere In [9], B. Smyth proved that if Mⁿ, n ≧ 3, has sectional curvature K and Ricci curvature Ric, with inf K > −∞, then sup Ric ≧ (n − 2) unless the universal covering of Mⁿ is homeomorphic to Rn or homeomorphic to an odd-dimensional sphere. In this paper, we improve the result of Smyth. Moreover, we obtain the classification of complete hypersurfaces of with nonnegative sectional curvature.Received: 11 November 2003     

Giant enhancement of the Raman scattering by local magnon modes in FeF2:Mn2+

A study of the local magnon mode in FeF₂ crystals with Mn²⁺ impurities by inelastic Raman light scattering is presented. Though the interaction between the radiation and the Mn spins is negligible the scattering by the s₀ local mode is very strong. The data of the frequency and the scattering intensity are analyzed in terms of a magnetization coupled mode approach.     

Examining the design features of a communication-rich,problem-centred mathematics professional development

While there is considerable scholarship describing principles for effective professional development, there have been few attempts to examine these principles in practice. In this paper, we identify and examine the particular design features of a mathematics professional development experience provided for middle grades teachers over 14 weeks. The professional development was grounded in a set of mathematical tasks that each had one right answer, but multiple solution paths. The facilitator engaged participants in problem solving and encouraged participants to work collaboratively to explore different solution paths. Through analysis of this collaborative learning environment, we identified five design features for supporting teacher learning of important mathematics and pedagogy in a problem-solving setting. We discuss these design features in depth and illustrate them by presenting an elaborated example from the professional development. This study extends the existing guidance for the design of professional development by examining and operationalizing the relationships among research-based features of effective professional development and the enacted features of a particular design.     

Study of a finite element method for the time-dependent generalized Stokes system associated with viscoelastic flow

A three-field finite element scheme designed for solving systems of partial differential equations governing time-dependent viscoelastic flows is studied. Once a classical backward Euler time discretization is performed, the resulting three-field system of equations allows for a stable approximation of velocity, pressure and extra stress tensor, by means of continuous piecewise linear finite elements, in both two- and three- dimensional space. This is proved to hold for the linearized form of the system. An advantage of the new formulation is the fact that it provides an algorithm for the explicit iterative resolution of system nonlinearities. Convergence in an appropriate sense applying to these three flow fields is demonstrated.     

On the asymptotic behavior of general projection-pursuit estimators under the common principal components model

The common principal components model for several groups of multivariate observations assumes equal principal axes among the groups. Robust estimators can be defined replacing the sample variance by a robust dispersion measure. This paper studies the asymptotic distribution of robust projection-pursuit estimators under a common principal components model.     

Modular Irreducible Representations of Weyl Groups of Type B n

In this article, we build all the irreducible representations of a Weyl group of type B _n over a field of characteristic p > 2. This construction is based on [2 Aguado , J. , Araujo , J. ( 1998 ). Representations of the symmetric group 𝔖 _n on K[x ₁,…, x _n ] . Revista de la Unión Matemática Argentina 41 . [Google Scholar]], and in fact it extends the results of that article for the modular irreducible representations of the symmetric group.     

Chemical and photochemical reactivity of 6‐hydroxymethyl‐7,8‐dihydropterin in aqueous solutions

6‐Hydroxymethyl‐7,8‐dihydropterin (H₂Hmp) is an intermediate in the biosynthesis of folate, a precursor of coenzymes involved in the metabolism of nucleotides and amino acids. In this work, we have investigated the reactions undergone by H₂Hmp in aqueous solutions at physiological pH, in the absence and in the presence of UV‐A radiation (320–400 nm). In air‐equilibrated solutions, H₂Hmp undergoes slow thermal oxidation (half‐life 37 h) to yield 7,8‐dihydroxanthopterin (H₂Xap) as the main product. The reaction of H₂Hmp with hydrogen peroxide also yields H₂Xap as a main product. In contrast, UV‐A excitation of H₂Hmp leads to the formation of a dimer identified by electrospray ionization mass spectrometry. The corresponding quantum yield of H₂Hmp consumption (Φ_?R) was independent of O₂ and reactant concentration and has a value of 0.10 (±0.02), more than twice higher than that measured for other 6‐subtituted 7,8‐dihydropterins. Copyright © 2012 John Wiley & Sons, Ltd.     

Statistical modelling of higher-order correlations in pools of neural activity

Simultaneous recordings from multiple neural units allow us to investigate the activity of very large neural ensembles. To understand how large ensembles of neurons process sensory information, it is necessary to develop suitable statistical models to describe the response variability of the recorded spike trains. Using the information geometry framework, it is possible to estimate higher-order correlations by assigning one interaction parameter to each degree of correlation, leading to a (2^N−1)$(2^N-1)$-dimensional model for a population with N$N$ neurons. However, this model suffers greatly from a combinatorial explosion, and the number of parameters to be estimated from the available sample size constitutes the main intractability reason of this approach. To quantify the extent of higher than pairwise spike correlations in pools of multiunit activity, we use an information-geometric approach within the framework of the extended central limit theorem considering all possible contributions from higher-order spike correlations. The identification of a deformation parameter allows us to provide a statistical characterisation of the amount of higher-order correlations in the case of a very large neural ensemble, significantly reducing the number of parameters, avoiding the sampling problem, and inferring the underlying dynamical properties of the network within pools of multiunit neural activity.     

Structural characterization of MnNi and MnPt antiferromagnetic materials for spintronic applications

MnNi and MnPt become antiferromagnetic (AFM) when annealed at high enough temperatures, for which a face-centered cubic (fcc) to face-centered tetragonal (fct) structural transition occurs. Thus, structural information is essential when optimizing exchange bias in these materials. We performed structural (X-ray diffraction), magnetic (Magneto-Optical Kerr effect) and magneto-transport (magnetoresistance) measurements on MnNi based spin valves subjected to different annealing procedures and MnPt/CoFe bilayers with different MnPt thicknesses. We show that high annealing temperatures can in fact lead to the fct antiferromagnetic phase in both materials, but the annealing procedure is also an important factor on the obtained exchange field values. Also, MnPt/CoFe bilayers allowed us to probe the influence of average AFM-grain size on exchange bias.     

WavePacket: A Matlab package for numerical quantum dynamics. III. Quantum-classical simulations and surface hopping trajectories

WavePacket is an open-source program package for numerical simulations in quantum dynamics. Building on the previous Part I (Schmidt and Lorenz, Comput. Phys. Commun. 2017, 213, 223] and Part II (Schmidt and Hartmann, Comput. Phys. Commun. 2018, 228, 229] which dealt with quantum dynamics of closed and open systems, respectively, the present Part III adds fully classical and mixed quantum-classical propagation techniques to WavePacket. There classical phase-space densities are sampled by trajectories which follow (diabatic or adiabatic) potential energy surfaces. In the vicinity of (genuine or avoided) intersections of those surfaces, trajectories may switch between them. To model these transitions, two classes of stochastic algorithms have been implemented: (1) Tully's fewest switches surface hopping and (2) Landau–Zener-based single switch surface hopping. The latter one offers the advantage of being based on adiabatic energy gaps only, thus not requiring nonadiabatic coupling information any more. The present work describes the MATLAB version of WavePacket 6.1.0, which is essentially an object-oriented rewrite of previous versions, allowing to perform fully classical, quantum-classical and quantum-mechanical simulations on an equal footing, that is, for the same physical system described by the same WavePacket input. The software package is hosted and further developed at the Sourceforge platform, where also extensive Wiki-documentation as well as numerous worked-out demonstration examples with animated graphics are available. © 2019 Wiley Periodicals, Inc.