Uniqueness implies existence for (n,p) boundary value problems

The uniqueness of solutions of certain boundary value problems implies their existence for the nth order nonlinear ordinary differential equation y⁽ⁿ⁾=f(x,y,y^',y^'',....,y^(n-1)) This existence is established by using shooting methods and yields results for (n,p) boundary value problems.     

Existence and multiplicity for positive solutions of a second-order multi-point discrete boundary value problem

We investigate the existence and multiplicity of positive solutions for a system of nonlinear second-order difference equations with multi-point boundary conditions.     

Oxygen nonstoichiometry and transport properties of strontium substituted lanthanum ferrite

This study presents an investigation of the properties of (La_0.6Sr_0.4)_0.99FeO_3-δ (LSF40) covering thermomechanical properties, oxygen nonstoichiometry and electronic and ionic conductivity. Finally, oxygen permeation experiments have been carried out and the oxygen flux has been determined as a function of temperature and driving force.The electrical conductivity was measured using a 4 probe method. It is shown that the electrical conductivity is a function of the charge carrier concentration only. The electron hole mobility is found to decrease with increasing charge carrier concentration in agreement with recent literature.Values of the chemical diffusion coefficient, D_Chem, and the surface exchange coefficient, k_Ex, have been determined using electrical conductivity relaxation. At D_Chem is determined to be with an activation energy of . The surface exchange coefficient is found to decrease with decreasing oxygen partial pressure.Oxygen permeation experiments were carried out. The flux through a membrane placed between air and wet hydrogen/nitrogen was (corresponding to an equivalent electrical current density of ). The oxygen permeation measurements are successfully interpreted based on the oxygen nonstoichiometry data and the determined transport parameters.     

Valuing variable annuity guarantees with the multivariate Esscher transform

Variable annuities are usually sold with a range of guarantees that protect annuity holders from some downside market risk. Although it is common to see variable annuity guarantees written on multiple funds, existing pricing methods are, by and large, based on stochastic processes for one single asset only. In this article, we fill this gap by developing a multivariate valuation framework. First, we consider a multivariate regime-switching model for modeling returns on various assets at the same time. We then identify a risk-neutral probability measure for use with the model under consideration. This is accomplished by a multivariate extension of the regime-switching conditional Esscher transform. We further extend our results to the situation when the guarantee being valued is linked to equity indexes measured in foreign currencies. In particular, we derive a probability measure that is risk-neutral from the perspective of domestic investors. Finally, we illustrate our results with a hypothetical variable annuity guarantee.     

Time-simultaneous prediction bands: A new look at the uncertainty involved in forecasting mortality

Conventionally, isolated (point-wise) prediction intervals are used to quantify the uncertainty in future mortality rates and other demographic quantities such as life expectancy. A pointwise interval reflects uncertainty in a variable at a single time point, but it does not account for any dynamic property of the time-series. As a result, in situations when the path or trajectory of future mortality rates is important, a band of pointwise intervals might lead to an invalid inference. To improve the communication of uncertainty, a simultaneous prediction band can be used. The primary objective of this paper is to demonstrate how simultaneous prediction bands can be created for prevalent stochastic models, including the Cairns-Blake-Dowd and Lee-Carter models. The illustrations in this paper are based on mortality data from the general population of England and Wales.     

Determination of Internal Energy Distributions of Laser Electrospray Mass Spectrometry using Thermometer Ions and Other Biomolecules

The internal energy distributions for dried and liquid samples that were vaporized with femtosecond duration laser pulses centered at 800 nm and postionized by electrospray ionization-mass spectrometry (LEMS) were measured and compared with conventional electrospray ionization mass spectrometry (ESI-MS). The internal energies of the mass spectral techniques were determined by plotting the ratio of the intact parent molecular features to all integrated ion intensities of the fragments as a function of collisional energy using benzylpyridinium salts and peptides. Measurements of dried p-substituted benzylpyridinium salts using LEMS resulted in a greater extent of fragmentation in addition to the benzyl cation. The mean relative internal energies, int> were determined to be 1.62?±?0.06, 2.0?±?0.5, and 1.6?±?0.3 eV for ESI-MS, dried LEMS, and liquid LEMS studies, respectively. Two-photon resonances with the laser pulses likely caused lower survival yields in LEMS analyses of dried samples but not liquid samples. In studies with larger biomolecules, LEMS analyses of dried samples from glass showed a decrease in survival yield compared with conventional ESI-MS for leucine enkephalin and bradykinin of ~15% and 11%, respectively. The survival yields for liquid LEMS analyses were comparable to or better than ESI-MS for benzylpyridinium salts and large biomolecules. Figure

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Scanning tunneling microscopy as a tool to study catalytically relevant model systems

The surface science approach to catalysis, pioneered by 2007 Nobel Laureate in chemistry Gerhard Ertl, has helped revolutionize our understanding of heterogeneous catalysis at the atomic level. In this tutorial review we show how the scanning tunnelling microscope (STM), in combination with this surface science approach, is a very important tool for the study of catalytically relevant model systems. We illustrate how the high spatial and temporal resolution of the STM can be used to obtain quantitative information on elementary processes involved in surface catalyzed reactions. Furthermore, we show that the STM is an outstanding surface science tool to bridge the materials gap and the pressure gap between surface science experiments and real catalysis. Finally, we show that we are approaching an era where the atomic-scale insight gained from fundamental STM surface science studies can be used for the rational design of new catalysts from first principles.     

Vapor pressure and density of thermotropic liquid crystals: MBBA, 5CB, and novel fluorinated mesogens

The vapor pressures and densities of six thermotropic liquid crystal-forming molecules (mesogens) have been determined experimentally as functions of temperature. The ubiquitous mesogenic compounds n-(4-methoxybenzylidene)-4-butylaniline (MBBA) and 4'-cyano-4-n-pentylbiphenyl (5CB), which both exhibit room-temperature nematic phases, are examined in this study, as are a number of trifluorinated bicyclohexyl and cyclohexylbiphenyl derivatives which find modern use in display applications. Although thermotropic mesogens are of prime importance in modern optoelectronic technologies, there is a scarcity of reliable saturation pressure data for such systems. An apparatus suitable for measurements of vapor pressures between 0.1 and 1333 Pa in the temperature range 298-523 K has been constructed. The adequacy of the apparatus has been verified by measurements on n-hexadecane at temperatures between 304 and 372 K, corresponding to vapor pressures between 0.4 and approximately 100 Pa. To our knowledge, our measurements represent the first reliable data for the saturation pressure of the fluid phase of these types of thermotropic compounds; we show that existing data for MBBA is thermodynamically inconsistent. The densities of the fluid phases of these compounds are also measured by means of a glass pycnometer at temperatures between 293 and 368 K.