Operator preconditioning with efficient applications for nonlinear elliptic problems

This paper is devoted to the numerical solution of nonlinear elliptic partial differential equations. Such problems describe various phenomena in science. An approach that exploits Hilbert space theory in the numerical study of elliptic PDEs is the idea of preconditioning operators. In this survey paper we briefly summarize the main lines of this theory with various applications.     

Vanadium(IV)-oxo Corrole Catalyzed Selective Oxidative Cleavage of Alkenes to Aldehydes

A practical and efficient protocol for oxidative cleavage of olefinic bonds especially in arylated olefins has been demonstrated. Herein, an oxo[5,10,15-tris(4-nitrophenyl)corrolato]vanadium (IV) complex (cat.), has been successfully synthesized and the existence of two tautomeric forms of this complex in solution has been established. Oxo[5,10,15-tris(4-nitrophenyl)corrolato]vanadium (IV) (cat.) in the presence of H₂O₂ cleaves olefinic bonds to yield the corresponding aldehyde compounds. In general, a high valent, oxo-(porphyrinoid)-metal complex catalyzes the epoxide formation reactions, however, in the present case, we have observed the exclusive formation of aldehydes. The reaction offered aryl aldehydes with good yields and excellent selectivity. A mechanism was also proposed for these catalysis reactions.     

Electrochemical coupling of mono and dihalopyridines catalyzed by nickel complex in undivided cell

One step nickel-catalyzed electroreductive homocoupling among 2-bromopicolines and 2-bromopyridine has been investigated by our group in an undivided cell and using zinc or iron as sacrificial anode. In this work, it was developed mono and dihalopyridines coupling to obtain possible products from heterocoupling. A series of reactions were carried out in order to develop a synthetic method for the preparation of unsymmetrical 2,2′-bipyridines and 2,2′:6′,2″-terpyridines. Statistical yields (50%) were observed for 2-bromopyridines/2-bromo-6-methylpyridine heterocoupling. In a preliminary study devoted to terpyridines preparation, good results were obtained for 2,6-dihalopyridines homocoupling, affording 2,6-dichloro-2,2′-bipyridine (46%) and 2,6-dibromo-2,2′-bipyridine (56%), at controlled reaction time. At major reaction time, it was observed that the direct electroreduction of the 2,6′-dihalo-2,2′-bipyridines intermediates and 2,6″-dihalo-2,2′:6′,2″-terpyridines products on the cathode surface. A reasonable isolated product yield of 6,6″-dimethyl-2,2′:6′,2″-terpyridine (10%) was only observed in the reaction between 2,6-dichloropyridine and 2-bromo-6-methylpyridine (1:2).     

Robust tracking control of nonlinear unmatched uncertain systems via event-based adaptive dynamic programming

Nonlinear Dynamics - In this paper, a novel robust tracking control strategy for nonlinear unmatched uncertain systems is formulated using the event-based adaptive dynamic programming (ADP)...     

Almost global attitude consensus of multi-agent rigid bodies on $$mathrm{TSO}(3)^N$$ TSO ( 3 ) N in the presence of disturbances and directed topology

Nonlinear Dynamics - The article proposes a distributed attitude consensus algorithm for multi-agent rigid bodies on the tangent bundle $$mathrm{TSO}(3)^N$$ . It is assumed that a directed fixed...     

Photoinduced intramolecular charge transfer reaction in (E)-3-(4-Methylamino-phenyl)-acrylic acid methyl ester: A fluorescence study in combination with TDDFT calculation

A donor-acceptor substituted aromatic system (E)-3-(4-Methylamino-phenyl)-acrylic acid methyl ester (MAPAME) has been synthesized, and its photophysical behavior obtained spectroscopically has been compared with the theoretical results. The observed dual fluorescence from MAPAME has been assigned to emission from locally excited and twisted intramolecular charge transfer states. The donor and acceptor angular dependency on the ground and excited states potential energy surfaces have been calculated both in vacuo and in acetonitrile solvent using time dependent density functional theory (TDDFT) and TDDFT polarized continuum model (TDDFT-PCM), respectively. Calculation predicts that a stabilized twisted excited state is responsible for red shifted charge transfer emission.     

Positron annihilation spectroscopic studies of solvothermally synthesized ZnO nanobipyramids and nanoparticles

Zinc oxide (ZnO) samples in the form of hexagonal-based bipyramids and particles of nanometer dimensions were synthesized through solvothermal route and characterized by x-ray diffraction and transmission electron microscopy. Positron annihilation experiments were performed to study the structural defects such as vacancies and surfaces in these nanosystems. From coincidence Doppler broadening measurements, the positron trapping sites were identified as Zn vacancies or Zn-O-Zn trivacancy clusters. The positron lifetimes, their relative intensities, and the Doppler broadened lineshape parameter S all showed characteristic changes across the nanobipyramid size corresponding to the thermal diffusion length of positrons. In large nanobipyramids, vacancies within the crystallites also trapped positrons and the effects of agglomeration of such vacancies due to increased temperatures of synthesis were reflected in the variation of the annihilation parameters with their base diameters. The sizes of the nanoparticles used were all in the limit of thermal diffusion length of positrons and the annihilation characteristics were in accordance with the decreasing contribution from surfaces with increasing particle size.     

Recovery of plutonium and cerium from alumina crucible

Journal of Radioanalytical and Nuclear Chemistry - Plutonium recovery is inevitable from plutonium bearing alumina crucibles generated over the years as part of carbon analysis during chemical...     

Nonlinear Dynamics of a Cantilever Beam Carrying an Attached Mass with 1:3:9 Internal Resonances

In this paper the nonlinear response of a base-excited slender beam carrying an attached mass is investigated with 1:3:9 internal resonances for principal and combinationparametric resonances. Here the method of normal forms is used to reduce the second order nonlinear temporal differential equation of motion of the system to a set offirst order nonlinear differential equations which are used to find the fixed-point, periodic, quasi-periodic and chaotic responses of the system.Stability and bifurcation analysis of the responses are carried out and bifurcation sets are plotted. Many chaotic phenomena are reported in this paper.