New and clean synthesis of N-substituted pyrroles under microwave irradiation

N-Substituted homochiral pyrrole derivatives were synthesized by the ring-closure reaction of cis-1,4-dichloro-2-butene with various amine compounds on a silica surface under microwave irradiation.     

Curvature and closed trapped surfaces in 4-dimensional space-times

The way a spacelike surfaceH sits in a 4-dimensional space-timeM may be measured by the average null curvature function _H and the shape function _H ofH. Relations between the shape function _H of a spaceiike surfaceH and curvature of a 4-dimensional space-time obeying the Einstein equation are investigated. Some relations between the shape functions of compact spacelike surfaces and infinite curvature are obtained and discussed. Assuming some curvature conditions, some results concerning the evolution of closed trapped surfaces from a restricted type of marginally trapped surfaces diffeomorphic toS ² are obtained.Based on Chapter 4 of the author's Ph.D. thesis.     

Pseudo-steady-state solutions for solidification in a wedge

Polubarinova-Kochina's analytical differential equation methodis used to determine the pseudo-steady-state solution to problemsinvolving the freezing (solidification) of wedges of liquidwhich are initially at their fusion temperature. In particular,we consider four distinct problems for wedges which are: freezingwith the same constant boundary temperature, freezing with thesame constant boundary heat fluxes, freezing with distinct constantboundary temperatures and freezing with distinct constant fluxesat the boundaries. For the last two problems, a Heun's differentialequation with an unknown singularity is derived, which in bothcases admits a particularly elegant simple solution for thespecial case when the wedge angle is . The moving boundariesobtained are shown pictorially.     

Measurement of angular dependencies of M X-ray differential cross sections and production cross sections using 5.96 keV photons

The differential cross sections of the emission of M-shell fluorescence X-rays from Tl and Pb have been measured by 5.96 keV photons at seven angles ranging from 50° to 110°. The differential cross section is found to decrease with the increasing emission angle, showing an anisotropic spatial distribution of M-shell fluorescence X-rays. Furthermore, M-shell fluorescence cross sections and the average fluorescence yields were measured for Pt, Au, Hg, Tl, Pb, Bi, Th, and U at an excitation energy of 5.96 keV using a Si(Li) detector. The experimental results of the total M X-ray fluorescence cross sections and M-shell fluorescence yields were compared with the theoretical values.This revised version was published online in November 2005 with corrections to the Cover Date.     

Delay equations with fluctuating delay related to the regenerative chatter II: analysis of reduced bifurcation equation

In this article, we study the reduced bifurcation equations of the nonlinear delay differential equations with periodic delays, which models the machine tool chatter with continuously modulated spindle speed to determine the periodic solutions and analyze the tool motion. Analytical results show both modest increase of stability and existence of periodic solutions close to the new stability boundary.     

Delay equations with fluctuating delay related to the regenerative chatter I: reduced bifurcation equation

The mathematical models representing machine tool chatter dynamics have been cast as differential equations with delay. The suppression of regenerative chatter by spindle speed variation is attracting increasing attention. In this paper, we study nonlinear delay differential equations with periodic delays which models the machine tool chatter with continuously modulated spindle speed. The explicit time-dependent delay terms, due to spindle speed modulation, are replaced by state dependent delay terms by augmenting the original equations. The augmented system of equations is autonomous and has two pairs of pure imaginary eigenvalues without resonance. The reduced bifurcation equation is obtained by making use of Lyapunov–Schmidt Reduction method.     

Preparation and characterization of surface modified γ-Fe2O3 (maghemite)-silica nanocomposites used for the purification of benzaldehyde lyase

γ-Fe₂O₃ (maghemite)-silica nanocomposite particles were synthesized using a sol-gel method. The condensation products of 3-glycidoxy propyltrimethoxy silane (GPTMS) and nitrilotriacetic acid (NTA) were introduced onto the surfaces of the γ-Fe₂O₃-silica nanocomposite particles and subsequently, these modified surfaces were complexed with cobalt (Co⁺²) metal ions. A possibility of using these surface modified γ-Fe₂O₃-silica particles for the purification of 6×histidine tagged recombinant benzaldehyde lyase (BAL, EC 4.1.2.38) based on magnetic separation was investigated. X-ray diffraction (XRD), thermal analysis, and vibrating sample magnetometry (VSM) methods were used to characterize the surface modified superparamagnetic γ-Fe₂O₃ (maghemite)-silica nanoparticles. XRD (Scherer's equation) results indicate that the primary particle size of maghemite was around 11 nm. Magnetic characterization results confirmed that the γ-Fe₂O₃ (maghemite)-silica nanoparticles were superparamagnetic. According to sodium dodecyl sulfate-polyacrylamide gel electrophoresis (SDS-PAGE) results, these superparamagnetic nanoparticles specifically capture 6×His-tagged BAL from crude extract of Escherichia coli (E. coli) BL21(DE3)pLysS/BAL_HIS. This study shows that the surface modified γ-Fe₂O₃ (maghemite)-silica nanoparticles are eligible for immobilized metal-ion affinity adsorption for histidine tagged recombinant proteins with its high capacity (3.16±0.4 mg/g) and selectivity.     

Comparative study of large-solid-core photonic crystal fibers: Dispersion and effective mode area

In this study, large-solid-core photonic crystal fibers with fixed air-hole diameter d = 0.84 μm and with fixed pitch length Λ = 4.2 μm are investigated for different d/Λ ratios. The dispersions and the effective mode-areas are obtained and compared for both the structures. It is seen that the dispersion management is easier by using the fixed d structures, but for working around the same zero dispersion points in a large interval of d/Λ the fixed Λ structures are more available. The A_eff values larger than 100 μm² are obtained with d/Λ smaller than 0.2 for both the two structures. A_eff increases rapidly with decreasing d/Λ to 0.1 and then reaches to A_eff value of 500 μm² at the d/Λ = 0.1 for the fixed d structures. The single-mode regime for the two structures is also discussed.