Approximate Solutions by Truncated Taylor Series Expansions of Nonlinear Differential Equations and Related Shadowing Property with Applications

This paper investigates the errors of the solutions as well as the shadowing property of a class of nonlinear differential equations which possess unique solutions on a certain interval for any admissible initial condition. The class of differential equations is assumed to be approximated by well-posed truncated Taylor series expansions up to a certain order obtained about certain, in general nonperiodic, sampling points t(i) is an element of [t(0), t(J)] for i = 0, 1, . . . , J of the solution. Two examples are provided.

Pluralismo, política e julgamento: para um projeto crítico à luz da filosofia de Charles Taylor

O objetivo da tese de doutorado consistirá na defesa de uma alternativa para os dilemas políticos concernentes à incomparabilidade no interior de uma comunidade específica ou entre comunidades distintas, presente nas discussões em torno do pluralismo contemporâneo. Esta via é inspirada nos conceitos de bens constitutivos, avaliações fortes e articulação, desenvolvidos pelo filósofo canadense Charles Taylor, e é também uma tentativa de se pensar acerca de um projeto de crítica política que leve em consideração a motivação como elemento incontornável para a filosofia prática. A incomparabilidade, isto é, impossibilidade de critérios no julgamento entre práticas específicas, mas com repercussões públicas, levanta a questão de até que ponto é possível avaliar e deliberar racionalmente sobre modos de vida distintos e, às vezes, auto-excludentes. Tal problemática pode ser vista fortemente no chamado debate liberal-comunitarista, na década de 1980, bem como em seus desdobramentos nas discussões acerca do multiculturalismo, na década seguinte. E ainda, mais recentemente, nos impasses em torno do papel da religião na esfera pública. Mais do que pontos divergentes acerca da questão do julgamento, os que essas discussões também evidenciam é um debate mais central acerca do lugar que pode ocupar a política diante de nossa situação bem como as categorias pelas quais compreendemos o fenômeno do pluralismo. Sob a alcunha de comunitarista, o pensamento de Taylor aparece como uma forma atrativa por não se submeter ao relativismo (a impossibilidade de critério) e tampouco a um universalismo forte (baseado em critérios gerais e anteriores às práticas), ao desenvolver uma ontologia fundada em um conflito de bens constitutivos em disputa, sem desconsiderar o fenômeno do pluralismo. Com efeito, isto se dá na medida em que diante de práticas divergentes e concorrentes há implícita ou explicitamente uma posição acerca de como e a partir de onde podemos nos posicionar criticamente frente ao pluralismo vigente, uma vez que movimentos, discursos e relações são construídos em nome daquilo que se apresenta efetivamente como valioso ou digno de respeito e admiração. Neste sentido, qualquer tentativa de avaliação já diz respeito a nossa compreensão: de nós, do mundo e de nossa relação com o mundo. Um projeto crítico, levando em consideração nossas fontes que impulsionam a ação, requer um olhar detalhado que o pensamento de Taylor pode oferecer, especialmente a partir da relação entre os conceitos supracitados.

Small-scale turbulent fluctuations beyond Taylor's frozen-flow hypothesis

The space-time cross-correlation function C-T(r, tau) of local temperature fluctuations in turbulent Rayleigh-Benard convection is obtained from simultaneous two-point time series measurements. The obtained C-T(r, tau) is found to have the scaling form C-T(r(E), 0) with r(E)=[(r-U tau)(2)+ V-2 tau(2)](1/2), where U and V are two characteristic velocities associated with the mean and rms velocities of the flow. The experiment verifies the theory and demonstrates its applications to a class of turbulent flows in which the requirement of Taylor's frozen flow hypothesis is not met.

Molecular weight effects on the phase morphology of PS/P4VP blend films on homogeneous SAM and heterogeneous SAM/Au substrates

The effects of the molecular weight of polystyrene (PS) component on the phase separation of PS/poly(4-vinylpyridine) (PS/P4VP) blend films on homogeneous alkanethiol self-assembled monolayer (SAM) and heterogeneous SAM/Au substrates have been investigated by means of atomic force microscopy (AFM). For the PS (22.4k)/P4VP (60k) system, owing to the molecular weight of PS component is relatively small, the well-aligned PS and P4VP stripes with good thermal stability are directed by the patterned SAM/Au surfaces. With the increase of the molecular weight of PS component (for the PS (582k)/P4VP (60k) system), the diffusion of P4VP is hindered by the high viscosity of PS during the fast spin-coating process. The phase separation behavior of PS/P4VP on the SAM/Au patterned substrates is similar to that on the homoueneous SAM and cannot be easily directed by the patterned SAM surfaces even though the characteristic length of the lateral domain morphology is commensurate with the stripe width.

Selective penetration of liquid-phase organic probe molecules into SAM of 2-mercapto-3-n-octylthiophene

An inherently disorganized self-assembled monolayer (SAM) of 2-mercapto-3-n-octylthiophene (MOT) has been formed on a gold bead electrode from its dilute ethanolic solution. The disorganization of the monolayer is attributed to the loose packing of the aliphatic chains of the MOT adsorbates, which results from a large difference in dimension/or cross-sectional area between the head (thiophene thiolate) and the tail (alkane chain) groups. Electrochemical measurements including ac impedance spectroscopy and metal underpotential deposition have shown that the monolayer is almost pinhole free. However, the MOT SAM can be penetrated by an organic probe molecule with affinity for the alkane chain part of the monolayer. Some typical probe molecules with different size and hydrophilicity have been employed to assess the permselectivity of the monolayer. Measurement results demonstrate that the ability of the employed probe molecules to penetrate into the monoalyer is mainly dominated by their hydrophilicity/or hydrophobicity. The results presented here suggest the potential application of MOT monoalyer to effectively modify the electrode surface for several research areas such as electrochemical sensors, electrocatalysis, electroanalysis, and supported hybrid bilayer membranes.

Determination of surface pK(a) of SAM using an electrochemical titration method

A self-assembled monolayer (SAM) of 3-mercaptopropionic acid (HSCH2CH2COOH) was formed on a gold electrode. The effect of the charge of the end group on the electrochemical response of Fe(CN)(6)(3-) at the SAM modified electrode was studied by using cyclic voltammetry. At high pH, when the -COOH groups are dissociated, Fe(CN)(6)(3-) current is suppressed; as the solution pH is lowered, Fe(CN)(6)(3-) current increases. The electrochemical titration curve was obtained by correlating the currents to the different electrolyte pH values, from which the surface pK(a) was obtained to be 5.2+/-0.1. Furthermore, a calculation equation was presented to simulate the electrochemical titration. As comparison, the surface pK(a) was also measured by contact angle titration as 5.6+/-0.1. The surface pK(a) values determined by the two methods in our work are consistent and accurate.

Some by-products of missions, by Isaac Taylor Headland.

http://www.archive.org/details/somebyproductsof013993mbp

China's new day; a study of events that have led to its coming, by Isaac Taylor Headland.

$u http://books.google.com/books?vid=OCLC02623863&id=mQz8gPn0et8C&a_sbrr=1 View book via Google

A retrospect / by J. Hudson Taylor.

http://www.archive.org/details/aretrospect00tayluoft

California life illustrated / by William Taylor, of the California Conference.

http://www.archive.org/details/calilifeillustrated00taylrich

The missionary interpretation of history by Richard Taylor Stevenson

Boston University Theology Library