Sequences of related linear PDEs

AbstractWe introduce a transformation theory to generate chains of linear PDEs and related solution sequences. Our procedure depends on representing a given linear PDE in terms of a special equivalent system of two coupled linear PDEs where the auxiliary dependent variable satisfies the next PDE of a sequence. The solution of a PDE with variable coefficient depending on n + 1 constants α1, α2, …, αn + 1} is obtained from any solution of a PDE of the same type with variable coefficient depending on n constants {;α1, α2…, αn} by a simple Bäcklund transformation. Each sequence contains two inclusive chains since the PDE with n constants is a special case of the PDE with n + 2 constants. We generate solutions of wave equations with wave speeds C(x; α1, α2, …, αn), Fokker-Planck equations with drifts F(x; α1, α2, … αn), and diffusion equations with diffusivities K(x; α1 α2, …, αn), where {α1, α2, …, αn} are arbitrary constants, n = 1, 2, … New explicit general solutions are obtained for a class of wave equations with wave speeds depending on three parameters

JARDÍN BOTÁNICO [Material gráfico]

ADQUIRIDA POR EL COLECCIONISTA EN LAS PALMAS G.C.FOTO POSTAL DE JARDIN EN LA VILLA OROTAVACopia digital. Madrid : Ministerio de Educación, Cultura y Deporte. Subdirección General de Coordinación Bibliotecaria, 201

Can we improve the prediction of hip fracture by assessing bone structure using shape and appearance modelling?

Copyright 2013 Elsevier B.V., All rights reserved.Peer reviewedPreprin

Electrochemical behavior and morphological evolution in carbonaceous and metal anodes for Li-ion and Zn-ion batteries

Li-ion batteries are ubiquitous in modern society with widespread applications in electric vehicles, personal electronics, and renewable energy storage. However, the practical energy density of the graphite anode commonly used in commercially available Li-ion batteries is approaching its theoretical limits. One potential solution to overcome this limitation is to replace graphite anodes with metallic anodes which have much higher theoretical charge storage capacities (3860, 1165, 860 mAh/g for Li, Na, Zn metal anodes respectively vs. 372 mAh/g for graphite). Unfortunately, problems arise during charging of metal anodes when metal ions are plated onto the electrode. These ions tend to deposit unevenly over the surface producing rough morphologies called dendrites which can grow through the separator and contact the counter electrode causing a short circuit, thermal runaway, and potential ignition of the flammable electrolyte and explosion.My master's project investigated how electrode surface layers impact dendrite growth on Zn metal electrodes. Zn metal provides the opportunity to elucidate the effect of organic surface layers on metal deposition since Zn is stable in both organic and aqueous electrolytes. Symmetric cells were assembled using Li, Na, or Zn metal in an analogous organic electrolyte (1 M M(ClO4)x in EC:DMC where M is Li, Na, or Zn) and compared to a Zn cell with aqueous electrolyte (1 M Zn(ClO4)2). Further investigations were done to determine the surface layer effects by forming an organic surface layer on Zn metal electrodes and cycling them in aqueous electrolyte and comparing this to the performance of Zn metal anodes with an inorganic layer cycled in organic electrolytes.My master's studies included another project about utilization of industrial waste as potential Li-ion battery electrodes. The effectiveness of collected diesel engine exhaust soot as a potential anode material for Li-ion batteries was evaluated through a series of electrochemical characterization tests including rate performance testing, long-term cycling stability, and charge storage kinetics analysis. Material properties were determined using XRD, XPS, and Raman spectroscopy. The annealed soot electrodes displayed excellent rate capability and capacity retention along with a pseudocapacitive contribution to charge storage making them an inexpensive alternative to the graphite anode

PUERTO DE LA CRUZ Y HOTEL TAORO [Material gráfico]

ADQUIRIDA POR EL COLECCIONISTA EN LAS PALMAS G.C.FOTO POSTAL DE OROTAVA- CON GRAN HOTEL"Copia digital. Madrid : Ministerio de Educación, Cultura y Deporte. Subdirección General de Coordinación Bibliotecaria, 201