Complex differential games of pursuit-evasion type with state constraints,part 1: Necessary conditions for optimal open-loop strategies

Complex pursuit-evasion games with state variable inequality constraints are investigated. Necessary conditions of the first and the second order for optimal trajectories are developed, which enable the calculation of optimal open-loop strategies. The necessary conditions on singular surfaces induced by state constraints and non-smooth data are discussed in detail. These conditions lead to multi-point boundary-value problems which can be solved very efficiently and very accurately by the multiple shooting method. A realistically modelled pursuit-evasion problem for one air-to-air missile versus one high performance aircraft in a vertical plane serves as an example. For this pursuit-evasion game, the barrier surface is investigated, which determines the firing range of the missile. The numerical method for solving this problem and extensive numerical results will be presented and discussed in Part 2 of this paper; see Ref. 1.This paper is dedicated to the memory of Professor John V. Breakwell.The authors would like to express their sincere and grateful appreciation to Professors R. Bulirsch and K. H. Well for their encouraging interest in this work.     

高阶拟线性椭圆型方程奇摄动问题

本文利用微分不等式和多重尺度，研究了一个高阶椭圆型偏微分方程摄动边值问题，并得到了一致有效的渐近展开式。     

Bunched laser cooling of a stored weak 7Li+ ion beam in a pure triplet state

A preparation scheme for a 7Li+ ion beam in a storage ring is presented which provides ions in the metastable triplet states with well controlled longitudinal phase space properties. For both state selective preparation and beam cooling, laser- and electron-cooler forces are applied. The spatial- and momentum distributions of the ions are directly detected by a time resolved measurement of the fluorescence light. At low beam intensities, the remaining heating rate of such a beam is completely determined by residual gas scattering. This revised version was published online in July 2006 with corrections to the Cover Date.     

Photoelectron spectroscopy of methyl,ethyl and isopropyl alcohol adsorbed on the (110) surface of Cu

Methyl, ethyl and isopropyl alcohol were allowed to adsorb on a clean (110) face of a copper crystal at room temperature, and photoelectron spectra were obtained using He(I) (21.2 eV) radiation. The spectra of the adsorbed species differed sufficiently from those of the free molecules to indicate a chemical change on adsorption. In accordance with studies in the literature using flash-desorption and energy-loss spectroscopy, it is suggested that the observed spectra are those of the corresponding alkoxy radicals formed as a result of dehydrogenation. In the case of the methoxy radical, calculations were carried out for a cluster of nine copper atoms and the results shown to be consistent with the experimental data. Results were also obtained on the rates of adsorption and desorption and on the dependence of the spectra on the polar angle between the normal to the surface and the photoelectron direction. Finally, results were obtained on the extent of adsorption by means of X-ray photoelectron spectroscopy.     

Magnetization and magnetic excitations in HoAl2

The magnetization of HoAl₂ single crystals parallel and perpendicular to the applied field for three crystallographic directions has been measured between 4.2 and 300 K in fields up to 8 T. Further the spin wave excitations were investigated by inelastic neutron scattering at 5.2 K along <100>, <110> and <111> directions in reciprocal space. The results are interpreted consistently in terms of a cubic crystal field using a simple molecular field to calculate the magnetization and an isotropic Heisenberg exchange interaction to obtain the magnetic excitations.     

Pt和Pd的超薄覆盖层对Ag膜表面增强喇曼散射的影响

在用化学沉积法制成的银岛膜上,蒸镀上不同厚度的Pt和Pd,测量了吡啶分子在Pt-Ag,Pd-Ag体系的表面增强喇曼散射(SERS)谱,得到SERS谱随覆盖层厚度的增加而衰减的关系曲线,并与电磁衰减理论计算的结果作了比较。此外,在两个体系都发现了新的振动谱线。我们认为它对应于吡啶在Pt和Pd上的吸附态。 关键词：     

离子注入硅的椭圆偏振光谱和光性

为了进一步发展测定离子注入损伤层的椭圆偏光法,我们测量了离子注入硅在4000—7000?波长范围内的椭圆偏振光谱,并由此得到它的色散关系。注入条件为150keV,10¹⁵cm^-2和10¹⁶cm^-2的砷离子注入。由于在硅样品表面处形成无定形层,我们用单层模型,从(ψ,Δ)-λ数据计算出(n,k)-λ关系,并可定出损伤层厚度。在～4800?处,出现折射率n的谱峰,峰值约4.9。本文还比较了离子注入损伤层、溅射无定形硅膜层、蒸发无定形硅膜层和单晶硅的实验结果。 关键词：     

Elastic constants of solid krypton at T = 77 K determined by inelastic neutron scattering

Long-wavelength acoustic phonons have been studied for each of the [ζ00]T, [ζ00]L, [ζζ0]L and [ζζ0]T₁ branches in solid Kr at T = 77 K by means of inelastic neutron scattering utilizing ‘cold neutrons’ as they are available in the long-wave length tail of the pile spectrum. The raw data have been corrected for resolution effects taking into account the curvature of the dispersion surface and variation of mode eigenvectors. It has turned out, that this yields appreciable shifts of the raw data. The results of our experiment give c₁₁ = 4·25 ± 0·10, c₄₄ = 2·04 ± 0·03, c₁₂ = 2·82 ± 0·12 and a value for B = (c₁₁ + 2c₁₂)/3 = 3·30 ± 0·09 × 10¹⁰ dyne/cm². Available thermodynamic data for Kr gives a derived value for B^ad = 2·58 ± 0·06 × 10¹⁰ dyne/cm² indicating a large difference between zero sound and first sound in solid Kr at high temperatures.     

A complete solution of the Bianchi identities in superspace with supergravity constraints

A short discussion of the superspace formulation of supergravity is given and the Bianchi identities are derived. The supergravity constraints are imposed and the identities are solved in terms of superfields and their covariant derivatives.     

Der Zerfall des94Sr

The nuclide⁹⁴Sr was isolated by chemical separation methods after thermal neutron induced fission of²³⁵U. Its decay properties were investigated employing semi-conductor spectrometers and coincidence techniques. A half-life of 74.1±0.3 sec was found. Besides the 1428.3 keV γ-ray we found 4 new γ-rays which could be placed in a decay scheme comprising three excited states of⁹⁴Y. The 1⁺ states in theuu-nuclides^90,92,94Y and^88,90,92Rb are compared.