Stationary problem of third-grade fluids in two and three dimensions: existence and uniqueness

This paper is devoted to the stationary problem of third-grade fluids in two and three dimensions. In two dimensions, we show existence of solutions and uniqueness, for a boundary of class C^2,1 and small data, by generalizing the method used by J.M. Bernard for the stationary problem of second-grade fluids (we deal with a polynomial of four degrees instead of two degrees). Contrary to the case of two dimensions, the resolution of the problem of third-grade fluids in three dimensions requires the physical condition |α₁+α₂|<(24νβ)^1/2. From this condition, we derive two “pseudo ellipticities” for the operator ν|A(u)|²+(α₁+α₂)tr(A(u)³)+β|A(u)|⁴, where A(u) is a 3-order symmetric matrix such that tr(A(u))=0. Thus, with, in addition, a sharp estimate of the scalar product (|A(u)|²A(u)-|A(v)|²A(v),A(u)-A(v)), we are able to prove existence of solutions and uniqueness, for a boundary of class C^2,1 and small data, in three dimensions.

Résumé

Cet article est consacré au problème stationnaire des fluides de grade trois en dimension deux et trois. En dimension deux, nous montrons l’existence de solutions et l’unicité, pour une frontière de classe C^2,1 et une donnée petite, en généralisant la méthode utilisée par J.M. Bernard pour le problème stationnaire des fluides de grade deux (nous avons affaire à un polynôme de degré quatre au lieu de deux). Contrairement au cas de la dimension deux, la résolution du problème des fluides de grade trois en dimension trois requière la condition physique |α₁+α₂|<(24νβ)^1/2. De cette condition, nous déduisons deux “pseudo matrice” pour l’opérateur ν|A(u)|²+(α₁+α₂)tr(A(u)³)+β|A(u)|⁴, où A(u) est une matice symétrique d’ordre 3 à trace nulle. De là, avec, en plus, une fine estimation du produit scalaire (|A(u)|²A(u)-|A(v)|²A(v),A(u)-A(v)), nous sommes capables de prouver l’existence de solutions et l’unicité, pour une frontière de classe C^2,1 et une donnée petite, en dimension trois.     

Femtosecond pulse switching in a fiber coupler with third order dispersion and self-steepening effects

A numerical study of femtosecond pulse propagation and switching in a dual-core nonlinear directional coupler with the consideration of third order dispersion and self-steepening effects is reported. The Split Step Fourier Method (SSFM) is used to investigate the switching characteristics of nonlinear directional couplers. It is observed that the energy transfer from core to core is not affected by changing the input pulse shapes except super-Gaussian. While the normalized coupling co-efficient and the input peak power dominate the coupling characteristics, the effects of third order dispersion (TOD) and self-steepening (SS) are also reported.     

Determination of Lanthanide (III) Ions by Using a Flotation - Spectrophotometric Method

Abstract

This paper reports our attempt at determining Ln (III) ions by using a flotation-spectrophotometric method and our findings. When a ternary ion-association complex of Ln (III) coordinated by thiocyanate (SCN^?) and diantipyryl methane (DA[Mdot]) is separated by a mixed solvent containing benzene and chloroform at pH 3.1 – 4.2, a third phase is observed between the aqueous and organic phases. The solid ternary complex can be dissolved in acetone that contains thenoyltrifluoroacetone (TTA). The individual Ln (III) ion can be determined by using the 4th derivative spectra directly. The equilibrium constant of the ternary composition ratio of Ln(II1) to ligand is estimated by the equilibrium shift method. The mole ratio of Ln(II1) to DAM and to SCN^? is 1:3 each. The composition of the tcrnary complex seems to be Ln(III):DAM:SCN^?=1:3:3.     

A Third‐Generation Hydrogen Peroxide Biosensor Based on Horseradish Peroxidase Immobilized in Carbon Nanotubes/ SBA‐15 Film

A new third‐generation biosensor for H₂O₂ assay was developed on the basis of the immobilization of horseradish peroxidase (HRP) in a nanocomposite film of carbon nanotubes (CNTs)‐SBA‐15 modified gold electrode. The biological activity of HRP immobilizing in the composite film was characterized by UV‐vis spectra. The HRP immobilized in the nanocomposite matrix displayed excellent electrocatalytic activity to the reduction of H₂O₂. The effects of the experimental variables such as solution pH and working potential were investigated using steady‐state amperometry. Under the optimal conditions, the resulting biosensor showed a linear range from 1 µM to 7 mM and a detection limit of 0.5 µM (S/N=3). Moreover, the stability and reproducibility of this biosensor were evaluated with satisfactory results.     

Layered Zirconium(IV) Aminoethylphosphonate Intercalated with Horseradish Peroxidase for an Amperometric Biosensor

Layered zirconium(IV) aminoethylphosphonate (ZrAEP) have been used as matrices for immobilization of horseradish peroxidase (HRP) to fabricate enzyme electrode for an amperometric biosensor. The biocompatible HRP–ZrAEP films were fabricated on gold electrode surface by electro‐co‐deposition method. The morphology of the HRP–ZrAEP composite was characterized by scanning electron microscopy (SEM). UV–vis spectroscopy indicated that the intercalated HRP retained its native structure after incorporation in the ZrAEP. The immobilized HRP at the HRP–ZrAEP films exhibited good electro catalytic responses to the reduction of hydrogen peroxide. The response time of the biosensor was less than 3 s, and the linear range is from 2.5 × 10^?6 to 3.22 × 10^?3 M, with a detection limit of 7.0 × 10^?7 M (S/N = 3). The Michaelis–Menten constant (K^app_M) value is estimated to be 2.21 mM. In addition, the obtained biosensor possesses high sensitivity, good stability and reproducibility.     

Third Generation ATP Sensor with Enzymatic Analyte Recycling

For the first time the direct electron transfer of an enzyme ‐ cellobiose dehydrogenase, CDH ‐ has been coupled with the hexokinase catalyzed competition for glucose in a sensor for ATP. To enhance the signal output for ATP, pyruvate kinase was coimmobilized to recycle ADP by the phosphoenolpyruvate driven reaction. The new sensor overcomes the limit of 1 : 1 stoichiometry of the sequential or competitive conversion of ATP by effective enzymatic recycling of the analyte. The anodic oxidation of the glucose converting CDH proceeds at electrode potentials below 0 mV vs. Ag|AgCl thus potentially interfering substances like ascorbic acid or catecholamines do not influence the measuring signal. The combination of direct electron transfer of CDH with the enzymatic recycling results in an interference‐free and oxygen‐independent measurement of ATP in the lower µmolar concentration range with a lower limit of detection of 63.3 nM (S/N=3).     

Theory of third-harmonic generation using double half-Gaussian hollow beams and self-phase-matching

We first (to best of out knowledge) use the slowly varying envelope approximation (SVEA) to obtain the equation of third harmonic (TH) generated by focusing the double half-Gaussian hollow beams into an atomic medium. The two-dimension intensity distribution is achieved by simulating, and it is similar to that generated by the 0th order Bessel beams. In addition to the similarities between the experimental setups, we demonstrate the accuracy of the equation. Compared with that generated by the Bessel beams, the pattern of the TH intensity generated by the double half-Gaussian hollow beams has salient features.     

Successive approximation-like 4-bit full-optical analog-to-digital converter based on Kerr-like nonlinear photonic crystal ring resonators

Implementing of photonic sampling and quantizing analog-to-digital converters (ADCs) enable us to extract a single binary word from optical signals without need for extra electronic assisting parts. This would enormously increase the sampling and quantizing time as well as decreasing the consumed power. To this end, based on the concept of successive approximation method, a 4-bit full-optical ADC that operates using the intensity-dependent Kerr-like nonlinearity in a two dimensional photonic crystal (2DPhC) platform is proposed. The Silicon (Si) nanocrystal is chosen because of the suitable nonlinear material characteristic. An optical limiter is used for the clamping and quantization of each successive levels that represent the ADC bits. In the proposal, an energy efficient optical ADC circuit is implemented by controlling the system parameters such as ring-to-waveguide coupling coefficients, the ring’s nonlinear refractive index, and the ring’s length. The performance of the ADC structure is verified by the simulation using finite difference time domain (FDTD) method.     

基础化学实验教学的新理念——再议实验教学之本质

最近20年以来,国内高校的本科基础化学实验教学从理念、内容、标准,到组织机构和评价方法,都经历了一系列变化和改革。立足于新的历史机遇和时代,有必要深刻理解和厘清本科阶段基础化学实验教学的本质和角色,既不轻视和简慢其地位、也不夸大和拔高其效用;须还基础实验教学以其本来面目,着重深挖其在传播"第三类知识"(Knowhow)以及培养"元认知"能力当中的不可替代作用,才能在化学实验教学改革大潮中不懈怠、不迷惘。     

Third-order extensions of Lo’s semiparametric bound for European call options

Computing semiparametric bounds for option prices is a widely studied pricing technique. In contrast to parametric pricing techniques, such as Monte-Carlo simulations, semiparametric pricing techniques do not require strong assumptions about the underlying asset price distribution. We extend classical results in this area. Specifically, we derive closed-form semiparametric bounds for the payoff of a European call option, given up to third-order moment (i.e., mean, variance, and skewness) information on the underlying asset price. We analyze how these bounds tighten the corresponding bounds, when only second-order moment (i.e., mean and variance) information is provided. We describe applications of these results in the context of option pricing; as well as in other areas such as inventory management, and actuarial science.