An algebraic approach for obtaining nilpotent normal forms in dimension 4

In this paper, an algebraic approach is presented for determiningthe normal forms of four-dimensional systems with a nilpotentlinear part. Certain transformations introduced in this caseresult in a simplified procedure for the calculation of normalforms. Thus, one does not need to solve a series of partialdifferential equations as usually required by the normal-formtheory; indeed, algebraic calculations are sufficient. The approachcan be applied to higher-order systems with a nilpotent linearpart as well. To illustrate the new approach, five examplesare presented. Normal forms and the associated coefficientsof two physical systems, an electric network and a mechanicalsystem, are fully analyzed.     

Electrochemical evaluation of different graphene/sulfur composite synthesis routes in all-solid-state lithium-sulfur batteries

Journal of Solid State Electrochemistry - The preparation of different cathode composites with intimate contact between the components is of great importance to obtain batteries with better...     

On an isotropic property of anti-Kähler–Codazzi manifolds

We give a proof of the fact that an anti-Kähler–Codazzi manifold reduces to an isotropic anti-Kähler manifold if and only if the Ricci tensor field coincides with the Ricci* tensor field.     

Approximate Analytical Solutions of Dirac Equation with Spin and Pseudo Spin Symmetries for the Diatomic Molecular Potentials Plus a Tensor Term with Any Angular Momentum

Approximate analytical solutions of the Dirac equation are obtained for some diatomic molecular potentials plus a tensor interaction with spin and pseudospin symmetries with any angular momentum. We find the energy eigenvalue equations in the closed form and the spinor wave functions by using an algebraic method. We also perform numerical calculations for the Pöschl-Teller potential to show the effect of the tensor interaction. Our results are consistent with ones obtained before.     

Spectral approximation for a nonlinear partial differential equation arising in thin film flow of a non-Newtonian fluid

Start-up thin film flow of fluids of grade three over a vertical longitudinally oscillating solid wall in a porous medium is investigated. The governing non-linear partial differential equation representing the momentum balance is solved by the Fourier-Galerkin approximation. The effect of the porosity, material constants as well as oscillations on the drainage rate and flow enhancement is explored and clarified.     

Spectroscopic characterization of Tm3+:TeO2–K2O–Nb2O5 glasses for 2-μm lasing applications

We have performed detailed experiments to investigate the spectroscopic properties of a new type of tellurite based host doped with thulium: Tm₂O₃:(0.70)TeO₂–(0.15)K₂O–(0.15)Nb₂O₅ having Tm₂O₃ concentrations of 0.125, 0.25, 0.5, and 1.0 mol%. By performing a Judd–Ofelt analysis of the absorption bands, we obtained average radiative lifetimes of 2.57±0.20 and 0.35±0.01 ms for the ³H₄ and ³F₄ levels, respectively. Furthermore, we also observed that an increase in the Tm₂O₃ concentration from 0.125 to 1.0 mol% results in a decrease of the measured fluorescence lifetime from 814 to 439 μs and from 258 to 47 μs for the ³H₄ and ³F₄ levels, respectively, due to efficient non-radiative decay. The highest quantum efficiency of 32% was obtained for the sample doped with 0.125 mol% Tm₂O₃ for the ³H₄ level. Results show that cross relaxation becomes important as the ion concentration is increased, leading to the quenching of the 1460-nm band and enhancement of the 1860-nm emission. The highest emission cross section of 6.85×10^?21 cm² measured for the 1860-nm band reveals the potential of this host for the development of 2-μm lasers in bulk glass as well as fiber media.     

Markovian analysis for automatic new topic identification in search engine transaction logs

Topic analysis of search engine user queries is an important task, since successful exploitation of the topic of queries can result in the design of new information retrieval algorithms for more efficient search engines. Identification of topic changes within a user search session is a key issue in analysis of search engine user queries. This study presents an application of Markov chains in the area of search engine research to automatically identify topic changes in a user session by using statistical characteristics of queries, such as time intervals, query reformulation patterns and the continuation/shift status of the previous query. The findings show that Markov chains provide fairly successful results for automatic new topic identification with a high level of estimation for topic continuations and shifts. Copyright © 2009 John Wiley & Sons, Ltd.     

Controlled viable release of selectively captured label-free cells in microchannels

Selective capture of cells from bodily fluids in microchannels has broadly transformed medicine enabling circulating tumor cell isolation, rapid CD4(+) cell counting for HIV monitoring, and diagnosis of infectious diseases. Although cell capture methods have been demonstrated in microfluidic systems, the release of captured cells remains a significant challenge. Viable retrieval of captured label-free cells in microchannels will enable a new era in biological sciences by allowing cultivation and post-processing. The significant challenge in release comes from the fact that the cells adhere strongly to the microchannel surface, especially when immuno-based immobilization methods are used. Even though fluid shear and enzymes have been used to detach captured cells in microchannels, these methods are known to harm cells and affect cellular characteristics. This paper describes a new technology to release the selectively captured label-free cells in microchannels without the use of fluid shear or enzymes. We have successfully released the captured CD4(+) cells (3.6% of the mononuclear blood cells) from blood in microfluidic channels with high specificity (89% ± 8%), viability (94% ± 4%), and release efficiency (59% ± 4%). We have further validated our system by specifically capturing and controllably releasing the CD34(+) stem cells from whole blood, which were quantified to be 19 cells per million blood cells in the blood samples used in this study. Our results also indicated that both CD4(+) and CD34(+) cells released from the microchannels were healthy and amenable for in vitro culture. Manual flow based microfluidic method utilizes inexpensive, easy to fabricate microchannels allowing selective label-free cell capture and release in less than 10 minutes, which can also be used at the point-of-care. The presented technology can be used to isolate and purify a broad spectrum of cells from mixed populations offering widespread applications in applied biological sciences, such as tissue engineering, regenerative medicine, rare cell and stem cell isolation, proteomic/genomic research, and clonal/population analyses.     

Understanding rigid geometric transformations: Jeff's learning path for translation

This article describes the development of knowledge and understanding of translations of Jeff, a prospective elementary teacher, during a teaching experiment that also included other rigid transformations. His initial conceptions of translations and other rigid transformations were characterized as undefined motions of a single object. He conceived of transformations as movement and showed no indication about what defines a transformation. The results of the study indicate that the development of his thinking about translations and other rigid transformations followed an order of (1) transformations as undefined motions of a single object, (2) transformations as defined motions of a single object, and (3) transformations as defined motions of all points on the plane. The case of Jeff is part of a bigger study that included four prospective teachers and analyzed their development in understanding of rigid transformations. The other participants also showed a similar evolution.     

A tighter variant of Jensen’s lower bound for stochastic programs and separable approximations to recourse functions

In this paper, we propose a new method to compute lower bounds on the optimal objective value of a stochastic program and show how this method can be used to construct separable approximations to the recourse functions. We show that our method yields tighter lower bounds than Jensen’s lower bound and it requires a reasonable amount of computational effort even for large problems. The fundamental idea behind our method is to relax certain constraints by associating dual multipliers with them. This yields a smaller stochastic program that is easier to solve. We particularly focus on the special case where we relax all but one of the constraints. In this case, the recourse functions of the smaller stochastic program are one dimensional functions. We use these one dimensional recourse functions to construct separable approximations to the original recourse functions. Computational experiments indicate that our lower bounds can significantly improve Jensen’s lower bound and our recourse function approximations can provide good solutions.