Uniform Convergence of the Newton Method for Aubin Continuous Maps

* This work was supported by National Science Foundation grant DMS 9404431.

Time-spatial drift of decelerating electromagnetic pulses

A time dependent electromagnetic pulse generated by a current running laterally to the direction of the pulse propagation is considered in paraxial approximation. It is shown that the pulse envelope moves in the time-spatial coordinates on the surface of a parabolic cylinder for the Airy pulse and a hyperbolic cylinder for the Gaussian. These pulses propagate in time with deceleration along the dominant propagation direction and drift uniformly in the lateral direction. The Airy pulse stops at infinity while the asymptotic velocity of the Gaussian is nonzero. © 2013 Optical Society of America.

Approximation of Lipschitz Mappings

2000 Mathematics Subject Classification: 46B03

Highly selective hydrogenation of furfural over supported Pt nanoparticles under mild conditions

The selective liquid phase hydrogenation of furfural to furfuryl alcohol over Pt nanoparticles supported on SiO2, ZnO, γ-Al2O3, CeO2 is reported under extremely mild conditions. Ambient hydrogen pressure, and temperatures as low as 50 °C are shown sufficient to drive furfural hydrogenation with high conversion and >99% selectivity to furfuryl alcohol. Strong support and solvent dependencies are observed, with methanol and n-butanol proving excellent solvents for promoting high furfuryl alcohol yields over uniformly dispersed 4 nm Pt nanoparticles over MgO, CeO2 and γ-Al2O3. In contrast, non-polar solvents conferred poor furfural conversion, while ethanol favored acetal by-product formation. Furfural selective hydrogenation can be tuned through controlling the oxide support, reaction solvent and temperature.

Generation of optical frequency combs in fibres:an optical pulse analysis

The innovation of optical frequency combs (OFCs) generated in passive mode-locked lasers has provided astronomy with unprecedented accuracy for wavelength calibration in high-resolution spectroscopy in research areas such as the discovery of exoplanets or the measurement of fundamental constants. The unique properties of OCFs, namely a highly dense spectrum of uniformly spaced emission lines of nearly equal intensity over the nominal wavelength range, is not only beneficial for high-resolution spectroscopy. Also in the low- to medium-resolution domain, the OFCs hold the promise to revolutionise the calibration techniques. Here, we present a novel method for generation of OFCs. As opposed to the mode-locked laser-based approach that can be complex, costly, and difficult to stabilise, we propose an all optical fibre-based system that is simple, compact, stable, and low-cost. Our system consists of three optical fibres where the first one is a conventional single-mode fibre, the second one is an erbium-doped fibre and the third one is a highly nonlinear low-dispersion fibre. The system is pumped by two equally intense continuous-wave (CW) lasers. To be able to control the quality and the bandwidth of the OFCs, it is crucial to understand how optical solitons arise out of the initial modulated CW field in the first fibre. Here, we numerically investigate the pulse evolution in the first fibre using the technique of the solitons radiation beat analysis. Having applied this technique, we realised that formation of higherorder solitons is supported in the low-energy region, whereas, in the high-energy region, Kuznetsov-Ma solitons appear.

Probabilistic Approach to Design of Large Antenna Arrays

2000 Mathematics Subject Classification: 78A50

An extension of Lorentz's almost convergence and applications in Banach spaces

2000 Mathematics Subject Classification: Primary 40C99, 46B99.

Does Atkinson-Wilcox Expansion Converges for any Convex Domain?

2000 Mathematics Subject Classification: 35C10, 35C20, 35P25, 47A40, 58D30, 81U40.

Sobolev Type Decomposition of Paley-Wiener-Schwartz Space with Application to Sampling Theory

2000 Mathematics Subject Classification: 94A12, 94A20, 30D20, 41A05.

Relationship between Extremal and Sum Processes Generated by the same Point Process

2000 Mathematics Subject Classification: Primary 60G51, secondary 60G70, 60F17.

Subclasses of Starlike Functions of Complex Order Involving Generalized Hypergeometric Functions

MSC2010: 30C45, 33C45

The Lindelöf number greater than continuum is u-invariant

2000 Mathematics Subject Classification: 54C35, 54D20, 54C60.

Numerical modelling of spectral, temporal and statistical properties of Raman fiber lasers

Efficient numerical modelling of the power, spectral and statistical properties of partially coherent quasi-CW Raman fiber laser radiation is presented. XPM between pump wave and generated Stokes wave is not important in the generation spectrum broadening and XPM term can be omitted in propagation equation what sufficiently speeds-up simulations. The time dynamics of Raman fiber laser (RFL) is stochastic exhibiting events several times more intense that the mean value on the ps timescale. However, the RFL has different statistical properties on different time scales. The probability density function of spectral power density is exponential for the generation modes located either in the spectrum centre or spectral wings while the phases are distributed uniformly. The pump wave preserves the initial Gaussian statistics during propagation in the laser cavity. Intense pulses in the pump wave are evolved under the SPM influence and are not disturbed by the dispersion. Contrarily, in the generated wave the dispersion plays a significant role that results in stochastic behavior. © 2012 Elsevier B.V. All rights reserved.

A template model predicts detection of sparse stimul

Contemporary models of contrast integration across space assume that pooling operates uniformly over the target region. For sparse stimuli, where high contrast regions are separated by areas containing no signal, this strategy may be sub-optimal because it pools more noise than signal as area increases. Little is known about the behaviour of human observers for detecting such stimuli. We performed an experiment in which three observers detected regular textures of various areas, and six levels of sparseness. Stimuli were regular grids of horizontal grating micropatches, each 1 cycle wide. We varied the ratio of signals (marks) to gaps (spaces), with mark:space ratios ranging from 1 : 0 (a dense texture with no spaces) to 1 : 24. To compensate for the decline in sensitivity with increasing distance from fixation, we adjusted the stimulus contrast as a function of eccentricity based on previous measurements [Baldwin, Meese & Baker, 2012, J Vis, 12(11):23]. We used the resulting area summation functions and psychometric slopes to test several filter-based models of signal combination. A MAX model failed to predict the thresholds, but did a good job on the slopes. Blanket summation of stimulus energy improved the threshold fit, but did not predict an observed slope increase with mark:space ratio. Our best model used a template matched to the sparseness of the stimulus, and pooled the squared contrast signal over space. Templates for regular patterns have also recently been proposed to explain the regular appearance of slightly irregular textures (Morgan et al, 2012, Proc R Soc B, 279, 2754–2760)

Synthesis of magnetically separable and recyclable g‑C3N4−Fe3O4 hybrid nanocomposites with enhanced photocatalytic performance under visible-light irradiation

Herein we demonstrate a facile, reproducible, and template-free strategy to prepare g-C3N4–Fe3O4 nanocomposites by an in situ growth mechanism. The results indicate that monodisperse Fe3O4 nanoparticles with diameters as small as 8 nm are uniformly deposited on g-C3N4 sheets, and as a result, aggregation of the Fe3O4 nanoparticles is effectively prevented. The as-prepared g-C3N4–Fe3O4 nanocomposites exhibit significantly enhanced photocatalytic activity for the degradation of rhodamine B under visible-light irradiation. Interestingly, the g-C3N4–Fe3O4 nanocomposites showed good recyclability without loss of apparent photocatalytic activity even after six cycles, and more importantly, g-C3N4–Fe3O4 could be recovered magnetically. The high performance of the g-C3N4–Fe3O4 photocatalysts is due to a synergistic effect including the large surface-exposure area, high visible-light-absorption efficiency, and enhanced charge-separation properties. In addition, the superparamagnetic behavior of the as-prepared g-C3N4–Fe3O4 nanocomposites also makes them promising candidates for applications in the fields of lithium storage capacity and bionanotechnology.