CFD modeling of hydrodynamic characteristics of a gas–liquid two-phase stirred tank

A three-dimensional CFD model was developed in this work to simulate hydrodynamic characteristics of a gas–liquid two-phase stirred tank with two six-bladed turbines and four baffles, coupling of the Multiple Size Group model to determine bubble size distribution. Important hydrodynamic parameters of the multi-phase system such as volume-averaged overall and time-averaged local gas holdups and axial liquid velocities along time and transversal courses were simulated and analyzed in detail, under varied operating conditions (inlet air flow rate and impeller rotation speed). Model predictions of local transient gas holdup and liquid velocity distributions on vertical and horizontal sections of the tank were also carried out. The overall flow patterns were discussed in detail to assess the mixing. Bubble size distributions were further predicted to reveal the unique properties of gas phase. Experimental measurements of overall gas holdups and local axial liquid velocities were used to validate the developed model.     

Matrix Pearson Equations Satisfied by Koornwinder Weights in Two Variables

We consider Koornwinder’s method for constructing orthogonal polynomials in two variables from orthogonal polynomials in one variable. If semiclassical orthogonal polynomials in one variable are used, then Koornwinder’s construction generates semiclassical orthogonal polynomials in two variables. We consider two methods for deducing matrix Pearson equations for weight functions associated with these polynomials, and consequently, we deduce the second order linear partial differential operators for classical Koornwinder polynomials.     

Facile synthesis of α-MnO2 nanorods for high-performance alkaline batteries

Single-crystalline α-MnO₂ nanorods have been successfully synthesized by a novel hydrothermal method based on the redox reactions between the permanganate anion MnO₄^- and H₂O in mixture containing KMnO₄ and HNO₃. The products have been characterized by powder X-ray diffraction (XRD), scanning electron microscopy (SEM), energy-dispersive X-ray spectroscopy (EDX), transmission electron microscopy (TEM), Fourier transform infrared spectrum (FT-IR) and Brunauer-Emmett-Teller (BET). The results prove that the grain size of α-MnO₂ nanorods with the surface area ∼95.2 m² g⁻¹ is homogeneous with diameters ranging from 10 to 20 nm. The electrochemical property of the material shows that compared with the commercial electrolytic manganese dioxide (EMD), the discharge capacity of the as-prepared α-MnO₂ nanorods is increased by 70.4%, 104.1% and 135.7% at different constant currents of 50, 250 and 500 mA g⁻¹, respectively.     

On the subfield subcodes of Hermitian codes

We present a fast algorithm using Gröbner basis to compute the dimensions of subfield subcodes of Hermitian codes. With these algorithms we are able to compute the exact values of the dimension of all subfield subcodes up to q ≤  32 and length up to 2¹⁵. We show that some of the subfield subcodes of Hermitian codes are at least as good as the previously known codes, and we show the existence of good long codes.     

On multiple ergodicity of affine cocycles over irrational rotations

Let \({T_\alpha }\) denote the rotation \({T_\alpha }x = x + \alpha \) (mod 1) by an irrational number α on the additive circle T = [0, 1). Let β ₁, …, β _d be d ≥ 1 parameters in [0, 1). One of the goals of this paper is to describe the ergodic properties of the cocycle (taking values in ? ^d+1) generated over \({T_\alpha }\) by the vectorial function Ψ _d+1(x):= (φ(x), φ(x+β ₁), …, φ(x+β _d )), with φ(x) = {x}?½. It was already proved in [LeMeNa03] that Ψ₂ is regular for α with bounded partial quotients. In the present paper we show that Ψ₂ is regular for any irrational α. For higher dimensions, we give sufficient conditions for regularity. While the case d = 2 remains unsolved, for d = 3 we provide examples of non-regular cocycles Ψ₄ for certain values of the parameters β ₁, β ₂, β ₃. We also show that the problem of regularity for the cocycle Ψ _d+1 reduces to the regularity of the cocycles of the form \({\Phi _d} = {({1_{[0,{\beta _j}]}} - {\beta _j})_{j = 1, \ldots ,d}}\) (taking values in ? ^d ). Therefore, a large part of the paper is devoted to the classification problems of step functions with values in ? ^d .     

Para-CR Structures of Codimension 2 on Tangent Bundles in Riemann–Finsler Geometry

We determine a 2-codimensional para-CR structure on the slit tangent bundle T0 M of a Finsler manifold（M,F） by imposing a condition regarding the almost paracomplex structure P associated to F when restricted to the structural distribution of a framed para-f-structure.This condition is satisfied when（M,F） is of scalar flag curvature（particularly constant） or if the Riemannian manifold（M,g） is of constant curvature.     

Charge order melting and magnetic transition in Nd0.5(1+x)Ca0.5(1−x)Mn(1−x)CrxO3 system

The magnetic property of double doped manganite Nd_0.5(1+x)Ca_0.5(1−x)Mn_(1−x)Cr_xO₃ with a fixed ratio of Mn³⁺:Mn⁴⁺=1:1 has been investigated. For the undoped sample, it undergoes one transition from charge disordering to charge ordering (CO) associated with paramagnetic (PM)-antiferromagnetic (AFM) phase transition at T<250 K. The long range AFM ordering seems to form at 35 K, rather than previously reported 150 K. At low temperature, an asymmetrical M-H hysteresis loop occurs due to weak AFM coupling. For the doped samples, the substitution of Cr³⁺ for Mn³⁺ ions causes the increase of magnetization and the rise of T_c. As the Cr³⁺ concentration increases, the CO domain gradually becomes smaller and the CO melting process emerges. At low temperature, the FM superexchange interaction between Mn³⁺ and Cr³⁺ ions causes a magnetic upturn, namely, the second FM phase transition.     

在瞬态自动测量仪上用脉冲法测量材料的热物理系数

简述了热物理性质瞬态自动测量仪的结构和原理，应用该仪器采用脉冲法测量了材料的热扩散系数和热导率。     

四元数分析中T_Gf算子的Hlder连续性和Riemann-Hilbert边值问题

本文证明了四元数分析中的有界区域G上的非齐次Dirac方程u=f的分布解T_Gf,当f∈L_P(G),P>4时,在G上具有Holder连续性,讨论了超球和双圆柱上的方程u=f的Riemann-Hilbert边值问题,给出了可解条件和通解的积分表示,并且还证明了通解的Holder连续性。     

A generating function for nonstandard orthogonal polynomials involving differences: the Meixner case

In this paper we deal with a family of nonstandard polynomials orthogonal with respect to an inner product involving differences. This type of inner product is the so-called Δ-Sobolev inner product. Concretely, we consider the case in which both measures appearing in the inner product correspond to the Pascal distribution (the orthogonal polynomials associated to this distribution are known as Meixner polynomials). The aim of this work is to obtain a generating function for the Δ-Meixner–Sobolev orthogonal polynomials and, by using a limit process, recover a generating function for Laguerre–Sobolev orthogonal polynomials.