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

EVM and Achievable Data Rate Analysis of Clipped OFDM Signals in Visible Light Communication

Orthogonal frequency division multiplexing (OFDM) has been considered for visible light communication (VLC) thanks to its ability to boost data rates as well as its robustness against frequency-selective fading channels. A major disadvantage of OFDM is the large dynamic range of its time-domain waveforms, making OFDM vulnerable to nonlinearity of light emitting diodes (LEDs). DC biased optical OFDM (DCO-OFDM) and asymmetrically clipped optical OFDM (ACO-OFDM) are two popular OFDM techniques developed for the VLC. In this paper, we will analyze the performance of the DCO-OFDM and ACO-OFDM signals in terms of error vector magnitude (EVM), signal-to-distortion ratio (SDR), and achievable data rates under both average optical power and dynamic optical power constraints. EVM is a commonly used metric to characterize distortions. We will describe an approach to numerically calculate the EVM for DCO-OFDM and ACO-OFDM. We will derive the optimum biasing ratio in the sense of minimizing EVM for DCO-OFDM. Additionally, we will formulate the EVM minimization problem as a convex linear optimization problem and obtain an EVM lower bound against which to compare the DCO-OFDM and ACO-OFDM techniques. We will prove that the ACO-OFDM can achieve the lower bound. Average optical power and dynamic optical power are two main constraints in VLC. We will derive the achievable data rates under these two constraints for both additive white Gaussian noise (AWGN) channel and frequency-selective channel. We will compare the performance of DCO-OFDM and ACO-OFDM under different power constraint scenarios

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