Hydrothermal synthesis and electrochemical performance of Fe-doped Co hydroxide electrode materials

Journal of Solid State Electrochemistry - In order to meet the growing energy demand, it is of great significance to develop high-performance electrochemical energy storage materials. In this...     

New convergence results on functional iteration techniques for the numerical solution of M/G/1 type Markov chains

Summary. By performing an accurate analysis of the convergence, we give a complete theoretical explanation of the experimental behaviour of functional iteration techniques for the computation of the minimal nonnegative solution of the matrix equation , arising in the numerical solution of M/G/1 type Markov chains (here the 's are nonnegative matrices such that the matrix is column stochastic). Moreover, we introduce a general class of functional iteration methods, which includes the standard methods, and we give an optimality convergence result in this class. Received September 1, 1995 / Revised version received September 9, 1996     

Factorization of analytic functions by means of Koenig's theorem and Toeplitz computations

Summary. By providing a matrix version of Koenig's theorem we reduce the problem of evaluating the coefficients of a monic factor r(z) of degree h of a power series f(z) to that of approximating the first h entries in the first column of the inverse of an Toeplitz matrix in block Hessenberg form for sufficiently large values of n. This matrix is reduced to a band matrix if f(z) is a polynomial. We prove that the factorization problem can be also reduced to solving a matrix equation for an matrix X, where is a matrix power series whose coefficients are Toeplitz matrices. The function is reduced to a matrix polynomial of degree 2 if f(z) is a polynomial of degreeN and . These reductions allow us to devise a suitable algorithm, based on cyclic reduction and on the concept of displacement rank, for generating a sequence of vectors that quadratically converges to the vector having as components the coefficients of the factor r(z). In the case of a polynomial f(z) of degree N, the cost of computing the entries of given is arithmetic operations, where is the cost of solving an Toeplitz-like system. In the case of analytic functions the cost depends on the numerical degree of the power series involved in the computation. From the numerical experiments performed with several test polynomials and power series, the algorithm has shown good numerical properties and promises to be a good candidate for implementing polynomial root-finders based on recursive splitting strategies. Applications to solving spectral factorization problems and Markov chains are also shown. Received September 9, 1998 / Revised version received November 14, 1999 / Published online February 5, 2001     

Effective Fast Algorithms for Polynomial Spectral Factorization

Let p(z) be a polynomial of degree n having zeros |ξ₁|≤???≤|ξ _m |<1<|ξ _m+1|≤???≤|ξ _n |. This paper is concerned with the problem of efficiently computing the coefficients of the factors u(z)=∏ _i=1 ^m (z?ξ _i ) and l(z)=∏ _i=m+1 ⁿ (z?ξ _i ) of p(z) such that a(z)=z ^?m p(z)=(z ^?m u(z))l(z) is the spectral factorization of a(z). To perform this task the following two-stage approach is considered: first we approximate the central coefficients x _?n+1,. . .x _n?1 of the Laurent series x(z)=∑ _i=?∞ ^+∞ x _i z ⁱ satisfying x(z)a(z)=1; then we determine the entries in the first column and in the first row of the inverse of the Toeplitz matrix T=(x _i?j ) _i,j=?n+1,n?1 which provide the sought coefficients of u(z) and l(z). Two different algorithms are analyzed for the reciprocation of Laurent polynomials. One algorithm makes use of Graeffe's iteration which is quadratically convergent. Differently, the second algorithm directly employs evaluation/interpolation techniques at the roots of 1 and it is linearly convergent only. Algorithmic issues and numerical experiments are discussed.     

Solving matrix polynomial equations arising in queueing problems

The matrix equation ∑_i=0ⁿA_iXⁱ=0, where the A_i's are m×m matrices, is encountered in the numerical solution of Markov chains which model queueing problems. We provide here a unifying framework in terms of Möbius' mapping to relate different resolution algorithms having a quadratic convergence. This allows us to compare algorithms like logarithmic reduction (LR) and cyclic reduction (CR), which extend Graeffe's iteration to matrix polynomials, and the invariant subspace (IS) approach, which extends Cardinal's algorithm. We devise new iterative techniques having quadratic convergence and present numerical experiments.     

Volatile chemical composition and bioactivity of six essential oils against the stored food insect Sitophilus zeamais Motsch. (Coleoptera Dryophthoridae)

Essential oils (EOs) of Achillea millefolium, Myrtus communis, Rosmarinus officinalis, Helichrysum italicum, Foeniculum vulgare and Lavandula angustifolia were analysed with GC-FID and GC-MS in order to define their aromatic profiles and then their toxicity and repellent activity against Sitophilus zeamais Motsch. (Coleoptera Dryophthoridae) with specific bioassays were evaluated. Results from topical applications on insects showed that all EOs had variable and significant insecticidal activity. Mortality rate never exceeded 76%. Results of repellency tests are indicated for M. communis and L. angustifolia EOs, displaying high repellent activity to S. zeamais adults.     

酸处理石墨化碳载体对燃料电池催化剂性能的影响

通过1700 ℃高温处理XC-72CB得到石墨化碳黑(GCB), 并采用酸处理对GCB碳载体进行官能团修饰. 透射电子显微镜(TEM)、 X射线粉末衍射(XRD)和拉曼光谱的结果显示, 酸处理后GCB的石墨化程度增加; N₂吸附-脱附结果证明GCB比表面积减小, 微孔数量减少; 热重分析结果表明, GCB热稳定性增强; 红外光谱和拉曼光谱结果显示, GCB表面引入了含氧官能团, 并同时保持了GCB的有序化结构. 采用循环伏安(CV)法和线性扫描伏安(LSV)法测试了不同预处理后催化剂的电化学性能, 表明其电化学活性表面积(ECSA, 75.25 m²/g)和质量比活性(MA, 0.093 A/mg)均高于商业Pt/C(JM)催化剂. TEM结果表明, 使用经过浓硫酸和浓硝酸混合酸处理的GCB(简称OGCB)作为载体得到的Pt/OGCB平均粒径为2.28 nm, 略小于商业Pt/C(JM)催化剂(约2.5 nm); 经5000周电化学循环伏安测试后, Pt/OGCB的电化学活性表面积衰减17.3%, 质量比活性衰减29.5%, 而Pt/C(JM)的ECSA衰减达到25.1%, MA衰减达到42.5%.     

Monolayer Assembly of Pyrene on Glass Plate Surface and Its Selective Sensing Performances to Organic Copper (II) Salts

A novel fluorescent sensing film was developed by covalently attaching pyrene moieties onto a glass plate surface via triethylenetetramine in a self-assembled monolayer manner. Fluorescence measurements demonstrated that the emission of the film could be quenched by organic copper (II) salts, including copper acetate, copper tartrate, and copper citrate, with high selectivity and sensitivity, and the response of the film to Cu(Ac)₂ is fully reversible. In contrast, the presence of inorganic copper salts, such as Cu(NO₃)₂, CuSO₄, and CuCl₂, showed lower quenching efficiency. The sensing performance of the film to Cu(Ac)₂ is slightly influenced by other divalent metal acetates, including Zn(Ac)₂,Pb(Ac)₂, Co(Ac)₂,andNi(Ac)₂.Furthermore,thequenchingof Cu(Ac)₂ to the emission of the film is static in nature.     

Transforming algebraic Riccati equations into unilateral quadratic matrix equations

The problem of reducing an algebraic Riccati equation XCX − AX − XD + B = 0 to a unilateral quadratic matrix equation (UQME) of the kind PX ² + QX + R = 0 is analyzed. New transformations are introduced which enable one to prove some theoretical and computational properties. In particular we show that the structure preserving doubling algorithm (SDA) of Anderson (Int J Control 28(2):295–306, 1978) is in fact the cyclic reduction algorithm of Hockney (J Assoc Comput Mach 12:95–113, 1965) and Buzbee et al. (SIAM J Numer Anal 7:627–656, 1970), applied to a suitable UQME. A new algorithm obtained by complementing our transformations with the shrink-and-shift technique of Ramaswami is presented. The new algorithm is accurate and much faster than SDA when applied to some examples concerning fluid queue models.     

The cyclic reduction algorithm: from Poisson equation to stochastic processes and beyond

Cyclic reduction is an algorithm invented by G. H. Golub and R. W. Hockney in the mid 1960s for solving linear systems related to the finite differences discretization of the Poisson equation over a rectangle. Among the algorithms of Gene Golub, it is one of the most versatile and powerful ever created. Recently, it has been applied to solve different problems from different applicative areas. In this paper we survey the main features of cyclic reduction, relate it to properties of analytic functions, recall its extension to solving more general finite and infinite linear systems, and different kinds of nonlinear matrix equations, including algebraic Riccati equations, with applications to Markov chains, queueing models and transport theory. Some new results concerning the convergence properties of cyclic reduction and its applicability are proved under very weak assumptions. New formulae for overcoming breakdown are provided.