Determinant of a matrix that commutes with a Jordan matrix

Given a Jordan matrix J, we obtain an explicit formula for the determinant of any matrix T that commutes with it.     

Bassianolone: an antimicrobial precursor of cephalosporolides E and F from the entomoparasitic fungus Beauveria bassiana

We have established the chemical structure of (+)-bassianolone (3), the antimicrobial compound precursor of cephalosporolides E and F, and that of the furan metabolite 4 from the entomopathogenic fungus Beauveria bassiana.     

A system of grabbing particles related to Galton‐Watson trees

We consider a system of particles with arms that are activated randomly to grab other particles as a toy model for polymerization. We assume that the following two rules are fulfilled: once a particle has been grabbed then it cannot be grabbed again, and an arm cannot grab a particle that belongs to its own cluster. We are interested in the shape of a typical polymer in the situation when the initial number of monomers is large and the numbers of arms of monomers are given by i.i.d. random variables. Our main result is a limit theorem for the empirical distribution of polymers, where limit is expressed in terms of a Galton‐Watson tree. © 2010 Wiley Periodicals, Inc. Random Struct. Alg., 2010     

Efficient three-step iterative methods with sixth order convergence for nonlinear equations

In this paper, we present two new three-step iterative methods for solving nonlinear equations with sixth convergence order. The new methods are obtained by composing known methods of third order of convergence with Newton’s method and using an adequate approximation for the derivative, that provides high order of convergence and reduces the required number of functional evaluations per step. The first method is obtained from Potra-Pták’s method and the second one, from Homeier’s method, both reaching an efficiency index of 1.5651. Our methods are comparable with the method of Parhi and Gupta (Appl Math Comput 203:50–55, 2008). Methods proposed by Kou and Li (Appl Math Comput 189:1816–1821, 2007), Wang et al. (Appl Math Comput 204:14–19, 2008) and Chun (Appl Math Comput 190:1432–1437, 2007) reach the same efficiency index, although they start from a fourth order method while we use third order methods and simpler arithmetics. We prove the convergence results and check them with several numerical tests that allow us to compare the convergence order, the computational cost and the efficiency order of our methods with those of the original methods.     

A modified Newton-Jarratt’s composition

A reduced composition technique has been used on Newton and Jarratt’s methods in order to obtain an optimal relation between convergence order, functional evaluations and number of operations. Following this aim, a family of methods is obtained whose efficiency indices are proved to be better for systems of nonlinear equations.     

Functionalization of linear and cyclic siloxanes and a dendritic carbosilane with (η-C5H5)Fe(CO)2Si(CH3)2CHCH2 via hydrosilylation reaction

A series of multimetallic systems containing silicon-linked cyclopentadienyl dicarbonyl iron moieties including carbosilane dendrimers and cyclic and polymeric siloxanes have been prepared using hydrosilylation reactions. For this purpose the vinyl-substituted silyliron complex (η⁵-C₅H₅)Fe(CO)₂Si(CH₃)₂ CHCH₂ (1) was prepared by salt elimination reaction between Na[(η⁵-C₅H₅)Fe(CO)₂] and ClSi(CH₃)₂CHCH₂ and fully characterized. Hydrosilylation reaction of 1 with the appropriate Si-H functionalized molecules in the presence of Karstedt catalyst afforded the novel silyl carbonyl iron-functionalized cyclotetrasiloxane 2, dendrimer 3 and copolymer 4, in which the organometallic units are attached to the silicon-based frameworks through a two-methylene flexible spacer. The electrochemical behaviour of compounds 1-4 has been examined in dichloromethane, tetrahydrofuran and acetonitrile solutions using cyclic voltammetry.     

Exponential divergence estimates and heat kernel tail

We obtain a lower bound for the density of a real random variable on the Wiener space under an exponential moment condition of the divergence. We apply this result to the solution of a non-linear SDE. To cite this article: E. Nualart, C. R. Acad. Sci. Paris, Ser. I 338 (2004).     

Effective sorbents for solid-phase extraction in the analysis of quinolones in animal tissues by capillary electrophoresis

In this work, several commercial sorbents (Zorbax C18, Bond Elut C18, Isolute ENV+, Oasis HLB, Oasis MAX, SDB-RPS, and MPC-SD) were compared for the solid-phase extraction of the series of quinolones regulated by the European Community in chicken tissues in order to establish a method for the determination of this series of quinolones by capillary electrophoresis and diode array detection. Sorbents were chosen in order to achieve maximum recoveries and optimal clean-up efficiency. Better results were obtained using SDB-RPS and Oasis MAX which would provide suitable limits of detection, below of the maximum residue limits (MRLs) regulated.     

Randomized polynuclear growth with a columnar defect

We study a variant of poly-nuclear growth where the level boundaries perform continuous-time, discrete-space random walks, and study how its asymptotic behavior is affected by the presence of a columnar defect on the line. We prove that there is a non-trivial phase transition in the strength of the perturbation, above which the law of large numbers for the height function is modified.     

Controlled synthesis of 2-D and 3-D dendritic platinum nanostructures

Seeding and autocatalytic reduction of platinum salts in aqueous surfactant solution using ascorbic acid as the reductant leads to remarkable dendritic metal nanostructures. In micellar surfactant solutions, spherical dendritic metal nanostructures are obtained, and the smallest of these nanodendrites resemble assemblies of joined nanoparticles and the nanodendrites are single crystals. With liposomes as the template, dendritic platinum sheets in the form of thin circular disks or solid foamlike nanomaterials can be made. Synthetic control over the morphology of these nanodendrites, nanosheets, and nanostructured foams is realized by using a tin-porphyrin photocatalyst to conveniently and effectively produce a large initial population of catalytic growth centers. The concentration of seed particles determines the ultimate average size and uniformity of these novel two- and three-dimensional platinum nanostructures.