Numerical Approximations Using Chebyshev Polynomial Expansions

We present numerical solutions for differential equations by expanding the unknown function in terms of Chebyshev polynomials and solving a system of linear equations directly for the values of the function at the extrema (or zeros) of the Chebyshev polynomial of order N (El-gendi's method). The solutions are exact at these points, apart from round-off computer errors and the convergence of other numerical methods used in connection to solving the linear system of equations. Applications to initial value problems in time-dependent quantum field theory, and second order boundary value problems in fluid dynamics are presented.Comment: minor wording changes, some typos have been eliminate

Water-Soluble Mo3S4 Clusters Bearing Hydroxypropyl Diphosphine Ligands: Synthesis, Crystal Structure, Aqueous Speciation, and Kinetics of Substitution Reactions

The [Mo3S4Cl3(dhprpe)3]+ (1+) cluster cation has been prepared by reaction between Mo3S4Cl4(PPh3)3 (solvent)2 and the watersoluble 1,2-bis(bis(hydroxypropyl)phosphino)ethane (dhprpe, L) ligand. The crystal structure of [1]2[Mo6Cl14] has been determined by X-ray diffraction methods and shows the typical incomplete cuboidal structure with a capping and three bridging sulfides. The octahedral coordination around each metal center is completed with a chlorine and two phosphorus atoms of the diphosphine ligand. Depending on the pH, the hydroxo group of the functionalized diphosphine can substitute the chloride ligands and coordinate to the cluster core to give new clusters with tridentate deprotonated dhprpe ligands of formula [Mo3S4(dhprpe-H)3]+ (2+). A detailed study based on stopped-flow, 31P{1H} NMR, and electrospray ionization mass spectrometry techniques has been carried out to understand the behavior of acid−base equilibria and the kinetics of interconversion between the 1+ and the 2+ forms. Both conversion of 1+ to 2+ and its reverse process occur in a single kinetic step, so that reactions proceed at the three metal centers with statistically controlled kinetics. The values of the rate constants under different conditions are used to discuss on the mechanisms of opening and closing of the chelate rings with coordination or dissociation of chloride

The Drosophila speciation factor HMR localizes to genomic insulator sites

Hybrid incompatibility between Drosophila melanogaster and D. simulans is caused by a lethal interaction of the proteins encoded by the Hmr and Lhr genes. In D. melanogaster the loss of HMR results in mitotic defects, an increase in transcription of transposable elements and a deregulation of heterochromatic genes. To better understand the molecular mechanisms that mediate HMR's function, we measured genome-wide localization of HMR in D. melanogaster tissue culture cells by chromatin immunoprecipitation. Interestingly, we find HMR localizing to genomic insulator sites that can be classified into two groups. One group belongs to gypsy insulators and another one borders HP1a bound regions at active genes. The transcription of the latter group genes is strongly affected in larvae and ovaries of Hmr mutant flies. Our data suggest a novel link between HMR and insulator proteins, a finding that implicates a potential role for genome organization in the formation of species

An overview of the facilities, activities, and developments at the University of North Texas Ion Beam Modification and Analysis Laboratory (IBMAL)

The Ion Beam Modification and Analysis Laboratory (IBMAL) at the University of North Texas includes several accelerator facilities with capabilities of producing a variety of ion beams from tens of keV to several MeV in energy. The four accelerators are used for research, graduate and undergraduate education, and industrial applications. The NEC 3MV Pelletron tandem accelerator has three ion sources for negative ions: He Alphatross and two different SNICS-type sputter ion sources. Presently, the tandem accelerator has four high-energy beam transport lines and one low-energy beam transport line directly taken from the negative ion sources for different research experiments. For the low-energy beam line, the ion energy can be varied from ∼20 to 80 keV for ion implantation/modification of materials. The four post-acceleration beam lines include a heavy-ion nuclear microprobe; multi-purpose PIXE, RBS, ERD, NRA, and broad-beam single-event upset; high-energy ion implantation line; and trace-element accelerator mass spectrometry. The NEC 3MV single-ended Pelletron accelerator has an RF ion source mainly for hydrogen, helium and heavier inert gases. We recently installed a capacitive liner to the terminal potential stabilization system for high terminal voltage stability and high-resolution microprobe analysis. The accelerator serves a beam line for standard RBS and RBS/C. Another beamline for high energy focused ion beam application using a magnetic quadrupole lens system is currently under construction. This beam line will also serve for developmental work on an electrostatic lens system. The third accelerator is a 200 kV Cockcroft-Walton accelerator with an RF ion source. The fourth accelerator is a 2.5 MV Van de Graaff accelerator, which was in operation for last several decades is currently planned to be used mainly for educational purpose. Research projects that will be briefly discussed include materials synthesis/modification for photonic, electronic, and magnetic applications, surface sputtering and micro-fabrication of materials, development of high-energy ion microprobe systems, and educational and outreach activities