Generating solutions of Einstein's field equations by typing mistakes

A solution to Einstein's field equations is presented that represents a Petrov type II electromagnetic null field with one Killing vector. This solution generalizes a vacuum solution previously discovered by Hoenselaers. The solution was found by the peculiar method of generalizing a member of this class inadvertently discovered by making a typing error when checking the vacuum solution with the computer algebra system SHEEP.     

Element Pools and Numeric Coprocessors for Linear Programming on Personal Computers

This note discusses the need to use various data-compaction schemes in the implementation of sophisticated large-scale linear programming codes on modest personal computers. It demonstrates a method whereby the overhead of using these schemes is significantly reduced on Intel 80 x 86 processors.     

Measurable,nonleavable gambling problems

The optimal return function for a Borel measurable gambling problem with a bounded utility function was shown by Strauch (1967) to be universally measurable when the problem is leavable in the sense that the gambler may terminate play at any time. The same is shown here for the more general class of nonleavable problems. Research supported by National Science Foundation Grant DMS-8801085.     

A characterization of cardinalsκ such that 2λ = 2κ wheneverκ ≦λ < 2κ

We characterize cardinalsκ such that 2^λ = 2^κ wheneverκ ≦λ < 2^κ using ideals in small algebras of sets satisfying certain completeness and saturation conditions. Research of this author was supported by an NSF Grant.     

Infinitesimale Deformationen von Kegeln über transkanonisch eingebetteten hyperelliptischen Kurven

Abhandlungen aus dem Mathematischen Seminar der Universität Hamburg -     

Influence of SiO2 in SiCp on the microstructure and impact strength of Al/SiCp composites fabricated by pressureless infiltration

The effect of SiO₂ in SiC_p and the following processing parameters on the microstructure and impact strength of Al/SiC_p composites fabricated by pressureless infiltration was investigated: Mg content in the aluminum alloy, SiC particle size, and holding time. Preforms of SiC_p in the form of rectangular bars (10 × 1 × 1 cm) were infiltrated at 1150°C in an argon→nitrogen atmosphere for 45 and 60 min by utilizing two aluminum alloys (Al-6 Mg-11 Si and Al-9 Mg-11 Si, wt.%). The results obtained show that the presence of SiO₂ in SiC affects the microstructure and impact strength of the composites significantly. When Al₄C₃ is formed, the impact strength decreases. However, a high proportion of SiC to SiO₂ limits the formation of the unwanted Al₄C₃ phase in the composites. Also, a higher content of Mg in the Al alloy lowers the residual porosity and, consequently, increases the composite strength. The impact strength grows with decrease in SiC particle size and increases considerably when the residual porosity is less than 1%. Russian translation published in Mekhanika Kompozitnykh Materialov, Vol. 42, No. 3, pp. 401–418, May–June, 2006.     

Ultrasonic evaluation of anisotropic damage in multiaxially textile-reinforced thermoplastic composites made from hybrid yarns

The basic damage and failure models of multiaxially reinforced composites with a thermoplastic matrix are presented and verified. Within the framework of continuum damage mechanics, a phenomenological model is introduced, where the damage is defined as a change in the elasticity tensor. For damage identification, a specific ultrasonic device was developed. A combination of an immersion set-up and a contact coupling device formed a system for an efficient determination of stiffness-tensor components from convenient sets of velocity measurements. Linked to a tensile machine, it allowed us to measure the anisotropic damage of the new materials group caused by tensile loading. Russian translation published in Mekhanika Kompozitnykh Materialov, Vol. 42, No. 2, pp. 221–234, March–April, 2006.