Evaluating the Frechet derivative of the matrix exponential

LetM _n denote the space ofn×n matrices. GivenX, ZM _n define

Existence of generic homoclinic tangencies for henon mappings

It is an open question whether there is a strange attractor for the Henon mapping. We show that for certain maps close to the Henon map there are strange attractors.     

The tame kernel of imaginary quadratic fields with class number 2 or 3

This paper presents improved bounds for the norms of exceptional finite places of the group , where is an imaginary quadratic field of class number 2 or 3. As an application we show that .

     

Transfinite sequences of continuous and Baire class 1 functions

The set of continuous or Baire class 1 functions defined on a metric space is endowed with the natural pointwise partial order. We investigate how the possible lengths of well-ordered monotone sequences (with respect to this order) depend on the space .

     

Hyperbolic mean growth of bounded holomorphic functions in the ball

We consider the hyperbolic Hardy class , . It consists of holomorphic in the unit complex ball for which and

where denotes the hyperbolic distance of the unit disc. The hyperbolic version of the Littlewood-Paley type -function and the area function are defined in terms of the invariant gradient of , and membership of is expressed by the property of the functions. As an application, we can characterize the boundedness and the compactness of the composition operator , defined by , from the Bloch space into the Hardy space .

     

Local field enhancements on gold and silver nanostructures for aperture near field spectroscopy

Optical properties of silver and gold semi-continuous films near the percolation threshold are investigated by scanning near field optical microscopy (SNOM) operating in the collection/transmission mode. The electromagnetic enhanced fields, due to plasmon-polariton localizations, are observed and the intensity distribution is shown to present high intensity variations that increase with the wavelength. The local fields are also demonstrated to be polarization dependent. The intensity distribution is investigated as function of the incident wavelength both for gold and silver films. The calculated probability distribution function (PDF) exhibits an exponential decay for large enhancement factors and is proved to be wavelength dependent.     

High-power continuous-wave operation of a diode-pumped laser at

The continuous-wave laser properties of an efficient diode-pumped Nd:GdVO₄ crystal operating at formed with a simple plane-concave cavity have been studied. With the incident pump power of 21 W, an output power of 6.9 W was obtained, giving an optical conversion efficiency of 32.8% and a slope efficiency of 35.3%. The laser characterization of two different Nd³⁺-doped concentration of Nd:GdVO₄ crystals were studied.     

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Influence of Thermal Treatment on the Thermal Behavior of Poly‐L‐lactide

The influences of thermal treatment on cold crystallization and the thermal behavior of poly‐L‐lactide (PLLA) were investigated by DSC and polarizing microscopy. Both the cooling and heating rates had effects on cold crystallization. Double peaks were observed for the samples on subsequently heating at 10°C min^?1 after cooling between 5 and 20°C min^?1. The degrees of crystallinity dramatically increased with decreasing cooling rate, and the size of PLLA spherulites increased with a decrease in the cooling rate. Double cold crystallization peaks were also observed during heating traces at higher rates for this material after fast cooling (20°C min^?1) from the melt. The competition between the crystallization from the nuclei formed during cooling, and that from spontaneous nucleation might be responsible for the appearance of double peaks.