Theory of a FIR optical digital differentiator

An optical realization of a proposed family of the finite impulse response (FIR) qth-order mth-derivative digital differentiators (under coherent operation), whose transfer functions are derived from the well-known numerical differentiation scheme (namely, the backward Taylor series expansion), using the amplified fiber optic transversal filters is presented. Several input pulse shapes, such as polynomials of various orders and the Gaussian and exponential pulses, are chosen as examples for illustration of the accuracy of the proposed optically realized differentiators. A mathematical model describing the dynamic (or transient) response of any optical discrete-time systems using the z-transform technique is proposed. The real-time performances of the proposed differentiators have been analyzed using both the steady-state and the dynamic analyses, Although the analysis is directed at fiber optic systems, the methodology and the results are applicable to other physical systems.     

Muon anomalous magnetic moment in the supersymmetric economical 3-3-1 model

We investigate the muon anomalous magnetic moment in the context of a supersymmetric version of the economical 3-3-1 model. We compute the 1-loop contribution of superpartner particles. We show that the contribution of superparticle loops become significant when tanγ is large. We investigate the cases of both small and large values of tanγ. We find the region of the parameter space where the slepton masses of a few hundred GeV are favored by the muon g–2 for small tanγ (tanγ ≈ 5). Numerical estimation gives the mass of supersymmetric particles, the mass of gauginos m _G ≈ 700 GeV, and the light slepton mass \(m_{\tilde L} \) of the order of O (100) GeV. When tanγ is large (tanγ ≈ 60), the charged slepton mass \(m_{\tilde L} \) and the gaugino mass m _G are O(1) TeV, while the sneutrino mass ≈450 GeV is in the reach of the LHC.     

Selective Semihydrogenation of Alkynes on Shape‐Controlled Palladium Nanocrystals

A systematic study on the selective semihydrogenation of alkynes to alkenes on shape‐controlled palladium (Pd) nanocrystals was performed. Pd nanocrystals with a cubic shape and thus exposed {100} facets were synthesized in an aqueous solution through the reduction of Na₂PdCl₄ with L ‐ascorbic acid in the presence of bromide ions. The Pd nanocubes were tested as catalysts for the semihydrogenation of various alkynes such as 5‐decyne, 2‐butyne‐1,4‐diol, and phenylacetylene. For all substrates, the Pd nanocubes exhibited higher alkene selectivity (>90 %) than a commercial Pd/C catalyst (75–90 %), which was attributed to a large adsorption energy of the carbon–carbon triple bond on the {100} facets of the Pd nanocubes. Our approach based on the shape control of Pd nanocrystals offers a simple and effective route to the development of a highly selective catalyst for alkyne semihydrogenation.     

Theoretical and experimental studies of the diketene system: Product branching decomposition rate constants and energetics of isomers

The kinetics and mechanism for the thermal decomposition of diketene have been studied in the temperature range 510–603 K using highly diluted mixtures with Ar as a diluent. The concentrations of diketene, ketene, and CO₂ were measured by FTIR spectrometry using calibrated standard mixtures. Two reaction channels were identified. The rate constants for the formation of ketene (k₁) and CO₂ (k₂) have been determined and compared with the values predicted by the Rice–Ramsperger–Kassel–Marcus (RRKM) theory for the branching reaction. The first-order rate constants, k₁ (s⁻¹) = 10^{15.74 ± 0.72} exp(−49.29 (kcal mol⁻¹) (±1.84)/RT) and k₂ (s⁻¹) = 10^{14.65 ± 0.87} exp(−49.01 (kcal mol⁻¹) (±2.22)/RT); the bulk of experimental data agree well with predicted results. The heats of formation of ketene, diketene, cyclobuta-1,3-dione, and cyclobuta-1,2-dione at 298 K computed from the G2M scheme are −11.1, −45.3, −43.6, and −40.3 kcal mol⁻¹, respectively. © 2007 Wiley Periodicals, Inc. Int J Chem Kinet 39: 580–590, 2007     

Oxidized Xanthan Gum Crosslinked NOCC: Hydrogel System and Their Biological Stability from Oxidation Levels of the Polymer

Dynamic hydrogel systems from N,O-carboxymethyl chitosan (NOCC) are investigated in the past years, which has facilitated their widespread use in many biomedical engineering applications. However, the influence of the polymer's oxidation levels on the hydrogel biological properties is not fully investigated. In this study, chitosan is converted into NOCC and introduced to react spontaneously with oxidized xanthan gum (OXG) to form several injectable hydrogels with controlled degradability. Different oxidation levels of xanthan gum, as well as NOCC/OXG volume ratios, are trialed. The infrared spectroscopy spectra verify chemical modification on OXG and successful crosslinking. With increasing oxidation levels, more dialdehyde groups are introduced into the OXG, resulting in changes in physical properties including gelation, swelling, and self-healing efficiency. Under different volume ratios, the hydrogel shows a stable structure and rigidity with higher mechanical properties, and a slower degradation rate. The shear-thinning and self-healing properties of the hydrogels are confirmed. In vitro assays with L929 cells show the biocompatibility of all formulations although the use of a high amount of OXG15 and OXG25 limited the cell proliferation capacity. Findings in this study suggested a suitable amount of OXG at different oxidation levels in NOCC hydrogel systems for tissue engineering applications.     

Fine structures for the solutions of the two-dimensional Riemann problems by high-order WENO schemes

The two-dimensional Riemann problem with polytropic gas is considered. By a restriction on the constant states of each quadrant of the computational domain such that there is only one planar centered wave connecting two adjacent quadrants, there are nineteen genuinely different initial configurations of the problem. The configurations are numerically simulated on a fine grid and compared by the 5th-order WENO-Z5, 6th-order WENO-??6, and 7th-order WENO-Z7 schemes. The solutions are very well approximated with high resolution of waves interactions phenomena and different types of Mach shock reflections. Kelvin-Helmholtz instability-like secondary-scaled vortices along contact continuities are well resolved and visualized. Numerical solutions show that WENO-??6 outperforms the comparing WENO-Z5 and WENO-Z7 in terms of shock capturing and small-scaled vortices resolution. A catalog of the numerical solutions of all nineteen configurations obtained from the WENO-??6 scheme is listed. Thanks to their excellent resolution and sharp shock capturing, the numerical solutions presented in this work can be served as reference solutions for both future numerical and theoretical analyses of the 2D Riemann problem.