Cryogenic/high temperature structural adhesives

Results are described of the work performed to develop a structural adhesive system which possesses useful properties over a 20K (-423 F) to 589 K (600 F) temperature range. Adhesives systems based on polyimide, polyphenylquinoxaline polyquinoxaline, polybenzothiazole and polybenzimidazole polymers first were screened for suitability. Detailed evaluation of two polyimide adhesive sytems, Br34/FM34 and P4/A5F or P4A/A5FA, and one polyphenylquinoxaline adhesive system, PPQ II (IMW), then was performed. Property information was generated over the full temperature range for shear strength, stressed and unstressed thermal aging, thermal shock and coefficient of thermal expansion. Both polyimide adhesive systems were identified as being capable of providing structural adhesive joints for cryogenic/high temperature service

A Note on Šnirel’man’s Approach to Goldbach’s Problem

Peer Reviewedhttp://deepblue.lib.umich.edu/bitstream/2027.42/135250/1/blms0245.pd

Diophantine Approximation by Prime Numbers, III

Peer Reviewedhttp://deepblue.lib.umich.edu/bitstream/2027.42/135627/1/plms0177.pd

Development of autoclavable addition type polyimides

Two highly promising approaches to yield autoclavable addition-type polyimides were identified and evaluated in the program. Conditions were established for autoclave preparation of Hercules HMS graphite fiber reinforced composites in the temperature range of 473 K to 505 K under an applied pressure of 0.7 MN/m2 (100 psi) for time durations up to four hours. Upon oven postcure in air at 589 K, composite samples demonstrated high mechanical property retention at 561 K after isothermal aging in air for 1000 hours. Promise was shown for shorter term mechanical property retention at 589 K upon exposure in air at this temperature

Development of autoclavable polyimides

A poly(Diels-Alder) (PDA) resin approach was investigated as a means to achieve autoclavability of high temperature resistant resin/fiber composites under mild fabrication procedures. Low void content Type A-S graphite reinforced composites were autoclave fabricated from a PDA resin/fiber prepared from an acetone:methanol:dioxane varnish. Autoclave conditions were 477K (400F) and 0.7 MN/sq m (100 psi) for up to two hours duration. After postcure at temperatures up to 589K (600F), the composites demonstrated high initial mechanical properties at temperatures up to 561K (550F). The results from isothermal aging studies in air for 1000 hours indicated potential for long-term ( 1000 hours) use at 533K (500F) and shorter-term (up to 1000 hours) at 561K (550F)

Nighttime observations of thunderstorm electrical activity from a high altitude airplane

Nocturnal thunderstorms were observed from above and features of cloud structure and lightning which are not generally visible from the ground are discussed. Most, lightning activity seems to be associated with clouds with strong convective cauliflower tops. In both of the storms lightning channels were visible in the clear air above the cloud. It is shown that substances produced by thunderstorm electrical discharges can be introduced directly into the stratosphere. The cause and nature of the discharges above the cloud are not clear. They may be produced by accumulations of space charge in the clear air above the cloud. The discharges may arise solely because of the intense electric fields produced by charges within the cloud. In the latter case the ions introduced by these discharges will increase the electrical conductivity of the air above the cloud and increase the conduction current that flows from the cloud to the electrosphere. More quantitative data at higher resolution may show significant spectral differences between cloud to ground and intracloud strokes. It is shown that electric field change data taken with an electric field change meter mounted in an airplane provide data on lightning discharges from above that are quite similar to those obtained from the ground in the past. The optical signals from dart leaders, from return strokes, and from continuing currents are recognizable, can be used to provide information on the fine structure of lightning, and can be used to distinguish between cloud to ground and intracloud flashes

Sums of two squares and a power

We extend results of Jagy and Kaplansky and the present authors and show that for all $k\geq 3$ there are infinitely many positive integers $n$, which cannot be written as $x^2+y^2+z^k=n$ for positive integers $x,y,z$, where for $k\not\equiv 0 \bmod 4$ a congruence condition is imposed on $z$. These examples are of interest as there is no congruence obstruction itself for the representation of these $n$. This way we provide a new family of counterexamples to the Hasse principle or strong approximation.Comment: 6 pages, to appear in the memorial volume "From Arithmetic to Zeta-Functions - Number Theory in Memory of Wolfgang Schwarz