Large Deviations Behavior for the Quadratic Error of Density Estimate

For a projection estimator f_n of an unknown density f we investigate the behavior of large deviations probability P{T_n > r_n} when r_n , where T_n is appropriately centered and normed quadratic error f_n-f)².     

Physical application and optimization a shape of core for experience

We present in this work some new theoretical results concerning an influence of the shape of core on the development of magnetization. As a special case the rotary symmetric objects with non-homogeneous magnetization were investigated. The shape of core was optimized on the basis of various practical criteria.     

Linearized augmented plane wave method utilizing the quadratic energy expansion of radial wave functions

Conclusions The developed version of the augmented plane wave method yields eigenvalues and eigenfunctions with higher accuracy than the standard LAPW, preserving its computational efficiency.The approximation of the exact radial solution by the Taylor expansion involving also the second energy derivative of the radial function, except for the first derivative, has two advantages. First, the energy dependence of the logarithmic derivatives atr=R is better described and, therefore, the method is less sensitive to the choice of the centre of expansionE ₀ or, equivalently, acceptably accurate eigenvalues are obtained for the broader energy region aroundE ₀. The other and probably more important advantage is that the approximate radial solutions are remarkably closer to the exact radial functions inside the muffin-tin sphere. This can be of use when evaluating the measurable quantities depending on the wave functions.     

Preparation of a novel HALS polypropylene stabilizer

The radiation induced graft copolymerization of m-isopropenyl-α,α-dimethyl benzyl iso-cyanate (m-TMI) and styrene onto polypropylene was carried out. The extent of grafting increased with increasing amount of styrene and with increased radiation dose. A graft load of 180% was obtained by immersing a 50 kGy pre-irradiated film in a monomer solution containing 25 mol % m-TMI and 75 mol % styrene. The graft copolymer is suitable for covalently binding nonpolymerizable stabilizers with a suitable nucleophilic moiety. In this work the isocyanate moiety of the graft copolymer was allowed to react with 4-amino-2,2,6,6-tetramethyl piperidine, a hindered amine light stabilizer. Fourier trans-formed infrared spectroscopy confirmed the formation of an urea moiety. © 1995 John Wiley & Sons, Inc.     

The inhibited photo-oxidation of polystyrene and styrene/HALS copolymers

The influence of molecular weight and the mode of binding of HALS stabilisers on their efficiency in the inhibited photo-oxidation of polystyrene and styrene/HALS copolymers was investigated. Photo-oxidation was performed with radiation of λ > 310 nm and 366 nm. The following functionalised HALS stabilisers were prepared: 4-methacryloylamino-2,2,6,6-tetramethylpiperidine, 4-methacryloyloxy-2,2,6,6-tetramethylpiperidine, 4-methacryloyloxy-1,2,2,6,6-pentamethylpiperidine and 15-methacryloyl-7,15-diazadispiro [5.1,5.3] hexadecane-14,16-dione. Binding by copolymerisation is substantially less efficient than addition of low molecular weight stabiliser.     

Cosmological Solutions of Bi-metric Theories of Gravitation

The evidence in solar system tests of gravitation theories shows that in cosmological models the propagation velocities of gravitation and light may differ only by action of the local gravitational potential. The condition of approximately equal propagation velocities is shown to be consistent with cosmological models of some bi-metric tetrad theories. The way to analyze the situation is explained. We find a connection between the linear approximation of the theories with those properties of cosmological models, which are responsible for the local propagation of gravitation.     

Carbonaceous phases by IR laser-induced decomposition of 3-butyn-2-one

2 laser radiation in the gas phase results in the deposition of carbonaceous films composed of a graphitic and monohydrogenated carbon, in which H is dominantly bonded to sp³ sites. The films incorporate oxygen in the topmost layers. The technique is suitable for the preparation of thin C-based films at low substrate temperatures. Received: 23 July 1997/Accepted: 18 November 1997