Convergent Rates for Solutions of Dirichlet Problems of Quasilinear Equations

The convergent rates for bounded solutions of Dirichlet problemsof quasilinear elliptic (possibly degenerate) equations in slab-likedomains are derived in terms of the convergent rates of theboundary data and the coefficients of the operator. The equationsconsidered include the prescribed mean curvature equation. Theresults are proved by constructing a family of local barrierfunctions based on the structure of the operator and the convergentrate of the boundary data. The construction of local barriersis inspired by early work due to Finn and Serrin that is relatedto the minimal surface equation.     

Problems of control and information theory (Hungary)

The bezoutian matrix, which provides information concerning co-primeness and greatest common divisor of polynomials, has recently been generalized by Heinig to the case of square polynomial matrices. Some of the properties of the bezoutian for the scalar case then carry over directly. In particular, the central result of the paper is an extension of a factorization due to Barnett, which enables the bezoutian to be expressed in terms of a Kronecker matrix polynomial in an appropriate block companion matrix. The most important consequence of this result is a determination of the structure of the kernel of the bezoutian. Thus, the bezoutian is nonsingular if and only if the two polynomial matrices have no common eigenvalues (i.e., their determinants are relatively prime); otherwise, the dimension of the kernel is given in terms of the multiplicities of the common eigenvalues of the polynomial matrices. Finally, an explicit basis is developed for the kernel of the bezoutian, using the concept of Jordan chains.     

Chemical reactions of N 2+ ion beams with group IV elements and their oxides

Ion beam studies of the reactions between nitrogen and surfaces of Group IV elements and their oxides resulting in nitride formation are reported. XPS and UPS are used to examine the products induced by 500 eV N ₂⁺ beams on diamond, graphite and elemental Si, Ge, Sn, Pb and their oxides. Nitrogen adds to the graphite in two positions: at the carbon rings and intersitually between the layers of rings. Reaction with Si, Ge and Sn produces nitrides which are similar to those of the type M ₃N ₄. Reaction with oxides forms nitrides with no evidence of nitrate or nitrite formation. The chemical nature of the reaction is supported by identification of the products through energy level shifts and by the agreement with thermodynamic predictions.     

Compact mid-infrared trace gas sensor based on difference-frequency generation of two diode lasers in periodically poled LiNbO3

3 (PPLN) crystal pumped by two single-frequency diode lasers. A maximum DFG power of 1.6 μW at 3.6 μm was generated with a pump power of 61.4 mW at 832 nm and a signal power of 41.5 mW at 1083 nm incident on a 19-mm-long PPLN crystal, which corresponds to a conversion efficiency of 335 μW W^-2 cm^-1. Received: 16 June 1998     

The synthesis of new weakly coordinating diborate anions: anion stability as a function of linker structure and steric bulk

The successive addition of KCN and Ph3CCl to B(C6F4-C6F5-2)3 (PBB) affords triphenylmethyl salts of the [NC-PBB]- anion. By contrast, the analogous reaction with sodium dicyanamide followed by treatment with Ph(3)CCl leads to the zwitterionic aminoborane H2NB(C12F9)2C12F8, via nucleophilic attack on an o-F atom, together with CPh3[F-PBB]. Whereas treatment of [NC-PBB]- with either PBB or B(C6F5)3 fails to give isolable cyano-bridged diborates, the reaction of Me3SiNC-B(C6F5)3 with PBB in the presence of Ph3CCl affords [Ph3C][PBB-NC-B(C6F5)3]. Due to steric hindrance this anion is prone to borane dissociation. The longer linking group N(CN)2- gives the very voluminous anions [N[CNB(C6F5)3]2]- and [N(CN-PBB)2]-. A comparison of propylene polymerisations with rac-Me2Si(Ind)2ZrMe2 activated with the various boranes or trityl borates gives an anion-dependent activity sequence, in the order [NC-PBB]- < [MeB(C6F5)3]- < [MePBB]- approximately [PBB-NCB(C6F5)3]- approximately [N[CNB(C6F5)3]2]- < [F-PBB]-< [B(C6F5)4]- < [N(CN-PBB)2]-. The anion [N(CN-PBB)2]- gives a catalyst productivity about 2500 times higher than that of [NC-PBB]- and exceeds that of [B(C6F5)4]- based catalysts. The van der Waals volumes and surface areas of the anions have been calculated and provide a rationale for the observed reactivity trends in polymerisation reactions.     

A high power hybrid mid-IR laser source

An efficient hybrid mid-IR laser system comprising a thulium fibre laser, Ho:YAG solid state laser and a zinc germanium phosphide optical parametric oscillator is presented. A 790 nm diode pumped 1908 nm thulium fibre laser operating at 30 W pumps an RTP q-switched Ho:YAG laser emitting 17 W at 40 kHz and 2090 nm. The zinc germanium phosphide optical parametric oscillator efficiently converts this into the 3-5 μm region producing 10.1 W with 59% optical conversion efficiency and an M² = 1.5.     

Collimated multi-MeV ion beams from high-intensity laser interactions with underdense plasma

A beam of multi-MeV helium ions has been observed from the interaction of a short-pulse high-intensity laser pulse with underdense helium plasma. The ion beam was found to have a maximum energy for He2+ of (40(+3)(-8)) MeV and was directional along the laser propagation path, with the highest energy ions being collimated to a cone of less than 10 degrees. 2D particle-in-cell simulations show that the ions are accelerated by a sheath electric field that is produced at the back of the gas target. This electric field is generated by transfer of laser energy to a hot electron beam, which exits the target generating large space-charge fields normal to its boundary.     

Effect of laser intensity on fast-electron-beam divergence in solid-density plasmas

Metal foil targets were irradiated with 1 mum wavelength (lambda) laser pulses of 5 ps duration and focused intensities (I) of up to 4x10;{19} W cm;{-2}, giving values of both Ilambda;{2} and pulse duration comparable to those required for fast ignition inertial fusion. The divergence of the electrons accelerated into the target was determined from spatially resolved measurements of x-ray K_{alpha} emission and from transverse probing of the plasma formed on the back of the foils. Comparison of the divergence with other published data shows that it increases with Ilambda;{2} and is independent of pulse duration. Two-dimensional particle-in-cell simulations reproduce these results, indicating that it is a fundamental property of the laser-plasma interaction.