Asplund Functions and Projectional Resolutions of the Identity

*Supported by the Grants AV ˇCR 101-97-02, 101-90-03, GA ˇCR 201-98-1449, and by the Grant of the Faculty of Civil Engineering of the Czech Technical University No. 2003.

Alternative Characterization of the Class k-UCV and Related Classes of Univalent Functions

In this paper an alternative characterization of the class of functions called k -uniformly convex is found. Various relations concerning connections with other classes of univalent functions are given. Moreover a new class of univalent functions, analogous to the ’Mocanu class’ of functions, is introduced. Some results concerning this class are derived.

Equisummability Theorems for Laguerre Series

Here we prove results about Riesz summability of classical Laguerre series, locally uniformly or on the Lebesgue set of the function f such that (∫(1 + x)^(mp) |f(x)|^p dx )^(1/p) < ∞, for some p and m satisfying 1 ≤ p ≤ ∞, −∞ < m < ∞.

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.