An elementary proof of the theorem that absolute gauge integrability implies Lebesgue integrability

It is commonly known that absolute gauge integrability, or Henstock-Kurzweil (H-K) integrability implies Lebesgue integrability. In this article, we are going to present another proof of that fact which utilizes the basic definitions and properties of the Lebesgue and H-K integrals.     

Photoluminescent carbon nitride films grown by vapor transport of carbon nitride powders

The thermal vapor transport of nitrogen-rich carbon nitride powders produces carbon nitride films on substrates that retain significant nitrogen content, have conjugated bond character, and show blue photoluminescent emission near 450 nm.     

Amphipols can support the activity of a membrane enzyme

Amphipathic polymers ("amphipols") were introduced several years ago (Tribet, C.; Audebert, R.; Popot, J.-L. Proc. Natl. Acad. Sci. U.S.A. 1996, 93, 15047-15050) as an alternative method for solubilizing integral membrane proteins in stable, nativelike conformations. However, direct maintenance of full membrane protein functionality in amphipol solutions has not previously been demonstrated in the absence of added lipid or detergent. In this contribution, the first zwitterionic amphipol "PMAL-B-100" is introduced. PMAL-B-100 not only maintains membrane protein structure and solubility, but also supports the full catalytic activity of an integral membrane enzyme, diacylglycerol kinase, in the complete absence of additional lipid or detergent. All of the roles which a lipid bilayer normally plays in maintaining diacylglycerol kinase's structure and in facilitating catalysis are satisfied by the environment and interactions supplied by PMAL-B-100.     

Laser beacon wave-front sensing without focal anisoplanatism

Wave-front sensing from artificial beacons is normally performed by formation of a focused spot in the atmosphere and sensing of the wave-front distortions produced during the beam's return passage. We propose an alternative method that senses the distortions produced during the outgoing path by forming an intensity pattern in the atmosphere that is then viewed from the ground. A key advantage of this method is that a parallel beam is used, and therefore the wave-front measurements will not suffer from the effects of focal anisoplanatism. We also envisage other geometries, all based on the concept of projecting a pupil pattern onto the atmosphere.     

The Boolean algebra of the theory of linear orders

We characterize the isomorphism type of the Boolean algebra of sentences of the theory of linear orders. It is isomorphic to the sentence algebras of the theory of equivalence relations, the theory of permutations and the theory of well-orderings. This work was partially supported by the National Science Foundation under research grant MCS 76-07249.