Factorizations of complete graphs into caterpillars of diameter 5

We examine factorizations of complete graphs K_2n into caterpillars of diameter 5. First we present a construction generalizing some previously known methods. Then we use the new method along with some previous partial results to give a complete characterization of caterpillars of diameter 5, which factorize the complete graph K_2n.     

Quantum electrodynamics for vector mesons

Quantum electrodynamics for rho mesons is considered. It is shown that, at the tree level, the value of the gyromagnetic ratio of the rho+ is fixed to 2 in a self-consistent effective quantum field theory. Further, the mixing parameter of the photon and the neutral vector meson is equal to the ratio of electromagnetic and strong couplings, leading to the mass difference M(rho0)-M(rho+/-) approximately 1 MeV at tree order.     

Lagrangian and Hamiltonian formalisms for coupled higher-order elements: theory,modeling, simulation

Nonlinear Dynamics - In this work, the definition of the constitutive relation of a classical higher-order two-terminal element from Chua’s table is extended to the coupled element. The way...     

On the Weak Invariance Principle for Non-Adapted Sequences under Projective Criteria

In this paper we study the central limit theorem and its weak invariance principle for sums of non-adapted stationary sequences, under different normalizations. Our conditions involve the conditional expectation of the variables with respect to a given σ-algebra, as done in Gordin (Dokl. Akad. Nauk SSSR 188, 739–741, 1969) and Heyde (Z. Wahrsch. verw. Gebiete 30, 315–320, 1974). These conditions are well adapted to a large variety of examples, including linear processes with dependent innovations or regular functions of linear processes.     

Orthogonal Double Covers of Complete Graphs by Caterpillars of Diameter 5

An orthogonal double cover (ODC) of the complete graph K_n by a graph G is a collection = {G_i|i = 1,2, . . . ,n} of spanning subgraphs of K_n, all isomorphic to G, with the property that every edge of K_n belongs to exactly two members of and any two distinct members of share exactly one edge. A caterpillar of diameter five is a tree arising from a path with six vertices by attaching pendant vertices to some or each of its vertices of degree two. We show that for any caterpillar of diameter five there exists an ODC of the complete graph K_n.     

Simple,Rapid and Sensitive Electrochemical Method for the Determination of the Triketone Herbicide Sulcotrione in River Water Using a Glassy Carbon Electrode

We report a novel, simple, rapid and sensitive electrochemical method for the determination of sulcotrione, a member of the relatively new class of triketone herbicides, using differential pulse voltammetry on a glassy carbon electrode. Its electrochemical behavior including influences of electrolyte composition, pH and scan rate was studied to select optimal experimental parameters for its determination. In Britton? Robinson buffer at pH 3 sulcotrione provided a well‐defined reduction peak at ?0.84 V (vs. Ag/AgCl electrode), with good repeatability (relative standard deviation of 2.3 % for 8 measurements at 10 µM concentration level). With optimized parameters differential pulse voltammetry rendered two linear concentration ranges from 0.2 to 2 µM and from 2 to 50 µM with a detection limit of 0.05 µM. The proposed procedure was successfully applied to the determination of sulcotrione in spiked river water samples with satisfactory recoveries (93–109 %). The developed method may represent a simple, rapid and sensitive alternative to highly toxic mercury electrodes and chromatographic methods.     

Two-photon induced uncaging of a reactive intermediate. Multiphoton in situ detection of a potentially valuable label for biological applications

[reaction: see text] Two-photon induced Wolff rearrangement of a terphenyl diazoketone 1 was achieved by using focused laser pulses of 532 nm from a Q-switched Nd:YAG laser. The nonfluorescent terphenyl diazoketone 1 was transformed into a fluorescent ester derivative 4, which can be detected in situ using the focused laser pulses at 532 nm. Laser power dependence studies show that the Wolff rearrangement is induced by two-photon absorption of the terphenyl diazoketone 1, but suggests that more than two photons of 532 nm are involved (a multiphoton process) in excitation of the ester derivative 4.     

A boundary element method for homogenization of periodic structures

Homogenized coefficients of periodic structures are calculated via an auxiliary partial differential equation in the periodic cell. Typically, a volume finite element discretization is employed for the numerical solution. In this paper, we reformulate the problem as a boundary integral equation using Steklov–Poincaré operators. The resulting boundary element method only discretizes the boundary of the periodic cell and the interface between the materials within the cell. We prove that the homogenized coefficients converge super-linearly with the mesh size, and we support the theory with examples in two and three dimensions.