Convergence and spectral analysis of the Frontini-Sormani family of multipoint third order methods from quadrature rule

Point of attraction theory is an important tool to analyze the local convergence of iterative methods for solving systems of nonlinear equations. In this work, we prove a generalized form of Ortega-Rheinbolt result based on point of attraction theory. The new result guarantees that the solution of the nonlinear system is a point of attraction of iterative scheme, especially multipoint iterations. We then apply it to study the attraction theorem of the Frontini-Sormani family of multipoint third order methods from Quadrature Rule. Error estimates are given and compared with existing ones. We also obtain the radius of convergence of the special members of the family. Two numerical examples are provided to illustrate the theory. Further, a spectral analysis of the Discrete Fourier Transform of the numerical errors is conducted in order to find the best method of the family. The convergence and the spectral analysis of a multistep version of one of the special member of the family are studied.     

Synthesis,characterisation and thermal properties of hydrazinium metal oxalate hydrates. crystal and molecular structure of hydrazinium copper oxalate monohydrate

Complexes of the formula (N₂H₅)₂M(C₂O₄)₂·nH₂O where M = Co, Ni, Cu and n = 3, 2, 1 respectively have been prepared and their spectral, magnetic and thermal properties investigated. The copper complex, (N₂H₅)₂Cu(C₂O₄)₂·H₂O has a square planar geometry with no coordination of hydrazinium cations as confirmed by a single crystal X-ray study. Nickel and cobalt form octahedral complexes and X-ray powder patterns reveal that the complexes are not isomorphous.     

Automorphisms and holomorphic differentials in characteristic p

Let G be a group of automorphisms of a function field F of genus g_F over an algebraically closed field K. The space $\text{Ω}{}_{\mathrm{F}}$ of holomorphic differentials of F is a g_F^? dimensional K-space. In response to a query of Hecke, Chevalley and Weil (Abh. Math. Sem. Univ. Hamburg, 10 (1934), 358–361) completely determined the structure of $\text{Ω}{}_{\mathrm{F}}$ as representation space for G in the classical case. They carried out the proof for the special case in which F is unramified over the fixed field of G. The case of cyclic ramified extensions had been previously considered by Hurwitz (Math. Ann., 41 (1893), 37–45). Weil (Abh. Math. Sem. Univ. Hamburg, 11 (1935), 110–115) gave a proof in the general case. The treatment in the last two papers is analytical. In characteristic p, the problem is open. If G is cyclic and F is unramified over the fixed field E of G, Tamagawa (Proc. Japan Acad., 27 (1951), 548–551) proved that the representation is the direct sum of one identity representation of degree 1 and g_E ? 1 regular representations. The principal object of this paper is an extension of Tamagawa's result to arbitrary cyclic extensions of p-power degree. The number of times an indecomposable representation of given degree occurs in the representation of G on $\text{Ω}{}_{\mathrm{F}}$ is explicitly determined in terms of g_E and the Witt vector characterizing the extension $\text{F}\text{E}$. The paper also contains a purely algebraic proof of the result of Chevalley and Weil for arbitrary cyclic extensions of degree relatively prime to p. Using character theory, it can be extended to arbitrary groups of order relatively prime to the characteristic.     

Multimillion Atom Molecular Dynamics Simulations of Nanostructures on Parallel Computers

Scalable space–time multiresolution algorithms implemented on massively parallel computers enable large-scale molecular dynamics (MD) simulations involving up to a billion atoms. Multimillion atom MD simulations are performed to study critical issues in the area of structural and dynamical correlations in nanostructures. Our simulation research is focused on a few semiconductor, ceramic, and metallic nanostructures. These nanostructures systems include: nanometer-scale stress patterns in silicon/silicon nitride nanopixels; self-limiting growth and critical lateral sizes in gallium arsenide/indium arsenide nanomesas; structural transformation in colloidal semiconductor nanocrystals; nanoindentation of crystalline and amorphous silicon nitride films; and dynamics of oxidation of metallic aluminum nanoparticles.     

Diffraction From 1D quasicrystals

Levine and Steinhardt's expression is generalised for the structure factor of a binary quasicrystal with AτB composition. The atomic model used in this generalisation is based on the embedding of quasiperiodic chains of A and B atoms such that there is a B atom within every long interval of the A-chain. For the proposed embedding scheme, the range of interpenetration length as well as the ratio of long and short intervals in the two chains are shown to affect the diffracted intensities drastically. The effect of order-disorder on the motif, average quasilattice constant and diffracted intensities is also considered. Conditions for the composite chain to become self-similar, which for the most general embedding is not necessary, are obtained. The application of present decoration scheme to vacancy ordered phases is discussed.     

Mo-ZrO2 Solid Acid Catalyst For Transesterification of β-Ketoesters

An efficient and mild method for transesterification of β-ketoester catalyzed by Mo-Z1O₂ solid acid catalyst is described.     

Isotope shift measurement of high-lying atomic levels by multi-step photoionization

A new technique has been developed to measure isotope shifts of high-lying atomic levels using multi-step photoionization. This technique has been demonstrated with the measurement of isotope shift between²³⁵U and²³⁸U isotopes in the energy level at 34372.992 cm⁻¹. The value of isotope shift thus measured matches well with the value reported in literature.     

Capillary forces between surfaces with nanoscale roughness

The flow and adhesion behavior of fine powders (approx. less than 10 microm) is significantly affected by the magnitude of attractive interparticle forces. Hence, the relative humidity and magnitude of capillary forces are critical parameters in the processing of these materials. In this investigation, approximate theoretical formulae are developed to predict the magnitude and onset of capillary adhesion between a smooth adhering particle and a surface with roughness on the nanometer scale. Experimental adhesion values between a variety of surfaces are measured via atomic force microscopy and are found to validate theoretical predictions.     

Chemical synthesis of PEDOT nanofibers

A one-step, room-temperature method is described to chemically synthesize bulk quantities of microns long, 100-180 nm diameter nanofibers of electrically conducting poly(3,4-ethylenedioxythiophene)(PEDOT) in the form of powders, or as optically transparent, substrate-supported films using a V2O5 seeding approach.