Synthesis and characterization of sulfone containing main chain oligobenzoxazine precursors

The preparation of soluble and processable polybenzoxazine precursors capable of forming high performance networks is an important field of research with a broad spectrum of application. This study demonstrates an approach that utilizes aromatic sulfonediamine, bisphenol‐A, and formaldehyde in Mannich‐type polycondesation to prepare polybenzoxazine precursor. The structure of the oligomeric precursor (M_n = 2600) was confirmed by FTIR and ¹H NMR spectral analysis. The precursor contained both sulfone and benzoxazine ring structures in the backbone. It was shown that small amount of ring‐opened phenolic groups were also present. Thermally activated self‐curing behavior of precursor in the absence of catalyst was studied by differential scanning calorimetry. Thermal properties of the cured polymers were also investigated by thermo gravimetric analysis. © 2011 Wiley Periodicals, Inc. J Polym Sci Part A: Polym Chem, 2011     

Operator splitting for numerical solution of the modified Burgers' equation using finite element method

The aim of this study is to obtain numerical behavior of a one‐dimensional modified Burgers' equation using cubic B‐spline collocation finite element method after splitting the equation with Strang splitting technique. Moreover, the Ext4 and Ext6 methods based on Strang splitting and derived from extrapolation have also been applied to the equation. To observe how good and effective this technique is, we have used the well‐known the error norms L₂ and L_∞ in the literature and compared them with previous studies. In addition, the von Neumann (Fourier series) method has been applied after the nonlinear term has been linearized to investigate the stability of the method.     

The Fermi-Walker Derivative on the Spherical Indicatrix of a Space Curve

In this paper Fermi-Walker derivative and Fermi-Walker parallelism and non-rotating frame concepts are given along the spherical indicatrix of a curve in E ³. First, we consider a curve in Euclid space and investigate the Fermi-Walker derivative along the tangent. The concepts which Fermi-Walker derivative are analyzed along its tangent. Then, the Fermi-Walker derivative and its theorems are analyzed along the principal normal indicatrix and the binormal indicatrix of any curve in E ³.     

On the solvability of initial boundary value problems for nonlinear time-dependent Schrödinger equations

In this paper, we study the initial boundary value problems for a nonlinear time-dependent Schrödinger equation with Dirichlet and Neumann boundary conditions, respectively. We prove the existence and uniqueness of solutions of the initial boundary value problems by using Galerkin’s method.     

Upper Maximal Graphs of Posets

We introduce and study a class of simple graphs, the upper-maximal graphs (UM-graphs), associated to finite posets. The vertices of the UM-graph of a given poset P are the elements of P, and edges are formed by those vertices x and y whenever any maximal element of P that is greater than x is also greater than y or vise versa. We show that the class of UM-graphs constitutes a subclass of comparability graphs. We further provide a characterization of chordal UM-graphs, and compare UM-graphs with known bound graphs of posets.     

Gold nanoparticles produced in a microalga

An efficient biological route to production of gold nanoparticles which allows the nanoparticles to be easily recovered remains elusive. Live cells of the green microalga Chlorella vulgaris were incubated with a solution of gold chloride and harvested by centrifugation. Nanoparticles inside intact cells were identified by transmission electron microscopy and confirmed to be metallic gold by synchrotron based X-ray powder diffraction and X-ray absorption spectroscopy. These intracellular gold nanoparticles were 40–60 nm in diameter. At a concentration of 1.4% Au in the alga, a better than 97% recovery of the gold from solution was achieved. A maximum of 4.2% Au in the alga was obtained. Exposure of C. vulgaris to solutions containing dissolved salts of palladium, ruthenium, and rhodium also resulted in the production of the corresponding nanoparticles within the cells. These were surmised to be also metallic, but were produced at a much lower intracellular concentration than achieved with gold. Iridium was apparently toxic to the alga. No nanoparticles were observed using platinum solutions. C. vulgaris provides a possible route to large scale production of gold nanoparticles.     

Emission of matter waves by photons

A new hypothesis, based on the dualistic nature of matter and light, is proposed. The frequency shift of a photon creates an electron. The phenomenon is investigated according to the conservation laws of energy and momentum. The concept of particle velocity and wavelength of a photon, based on a relation between the energy and momentum conservation laws, is also introduced. The proposal is also supported by some experiments on matter–antimatter creation by the collision of photons.