Manuals in orthogonal categories

The notion of a manual, introduced and investigated in detail by Foulis, Randall, and their followers, has turned out to be further reaching than its originators had envisaged. Its omnipresence is comparable with the notion of a sheaf, whose significance is well recognized by every pure and applied mathematician. The principal concern of this paper is to give an appropriate vehicle, as general as possible, by which the theory of manuals can be developed. The vehicle is called an orthogonal category, which is akin to the notion of a category with coproducts. Orthogonal categories provide also a new perspective on the notion of a sheaf over a complete Boolean algebra, deepening our comprehension of Boolean mathematics and paving the way to quantum mathematics.     

Study of Proton Resonances in ~(22)Mg by Resonant Elastic Scattering of ~(21)Na+p and Its Astrophysical Implication in ~(18)Ne(α,p)~(21)Na Reaction Rate

Proton resonant states in ~(22)Mg have been investigated by the resonant elastic scattering of ~(21)Na+p.The ~(21)Na beam with a mean energy of 4.00 MeV/u was separated by the CNS radioactive ion beam separator(CRIB) and bombarded a thick(CH_2)_n target.The energy spectra of recoiled protons were measured at scattering angles of θ_(cm)～172° and 146°,respectively.A new state at 7.06 MeV has been observed clearly and another new one at 7.28 MeV is tentatively identified due to its low statistics.The proton resonant parameters were deduced from an R-matrix analysis of the differential cross section data.The astrophysical resonant reaction rate for the ~(18)Ne(α,p) ~(21)Na reaction has been estimated,and it is about five times larger than that assumed before.     

Voltammetric studies of antimony ions in soda-lime-silica glass melts up to 1873 K.

The half wave potential of reduction of Sb5+ in 16Na2O x 10CaO x 74SiO2 glass melts was examined by differential pulse voltammetry up to 1873 K. The half wave potential shifted to the positive direction with an increase in temperature. The results indicate that the equilibrium of Sb5+/Sb3+ shifted to negative direction with an increase in temperature. The half wave potential shifted to positive direction (48 mV at 1473 K) when the atmosphere over the melts changed from pure oxygen gas to air, in agreement with the theoretical prediction. The reversibility of Pt:O2 reference electrode is confirmed.     

Load-absorption by a discontinuous filament in a fiber-reinforced composite

Zusammenfassung Diese Arbeit befasst sich analytisch mit der statischen Kraftübertragung auf eine einzelne unendliche, elastische Faser, die an einem Querschnitt unterbroche ist. Die Faser ist vollständig in einem unendlich ausgedehnten Körper von anderen elastischen Eigenschaften eingebettet. Der Körper selbst ist im Unendlichen einer einachsigen Zugspannung parallel zur Faser ausgesetzt. Die Charakterisierung der gesuchten Faserkraft wird durch eine schon früher erprobte Annäherungsmethode auf eine Fredholmsche Integralgleichung zweiter Art zurückgeführt und die letztere wird auf numerischem Wege gelöst. Die Verteilung der Faserkraft ist für verschiedene Werte des Verhältnisses der beiden Elastizitätsmodulen dargestellt.

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The results communicated in this paper were obtained in the course of an investigation conducted under Contract N00014-67-A-0094-0020 with the Office of Naval Research in Washington, D.C.     

Temperature-induced gelation of concentrated silicon carbide suspensions

Due to the steric barrier provided by the adsorption of the dispersant hypermer KD1 (a polyester/polyamine condensation polymer), stable and low-viscosity suspensions of SiC, Y(2)O(3), and Al(2)O(3) powder mixtures could be prepared in methyl ethyl ketone (MEK)/ethanol (E) solvent with solids loading as high as 60 vol%. The solvency of the dispersant in MEK/E decreased dramatically on cooling. Steady shear viscosity and oscillatory measurements were performed as a function of temperature for suspensions with different solids loading. The viscosity and elastic modulus of suspension increased with decreasing temperature and became more sensitive with the increase of solids loading. The suspensions with solids loading higher than 40 vol% could be solidified with decreasing temperature, but gelation temperature and gelation stiffness decreased with decreasing solids loading. The 60 vol% solid-loaded suspension was a stable and free-flowing fluid at 20 degrees C and gradually transformed to a very highly viscous and elastic system upon cooling to about 13 degrees C. Complete solidification occurred when the temperature was decreased to 5 degrees C. The gelation mechanism was mainly based on the collapse of the adsorbed layer as the temperature decreases, which induced incipient flocculation and formed a stiff network. The gelled body was further strengthened by separation of the dispersant from the suspension.     

Versatile diastereoselectivity in formal [3,3]-sigmatropic shifts of substituted 1-alkenyl-3-alkylidenecyclobutanols and their silyl ethers

A new method for the preparation of highly substituted cyclohexenones is reported. [2 + 2] Cycloaddition of 2-silyloxydienes with allenecarboxylate affords the 1-alkenyl-3-alkylidenecyclobutanol silyl ethers. Thermolysis of these compounds affords the methylene cyclohexenyl silyl ethers with excellent exo selectivity (>95:5) when monosubstituted alkenyl groups are used, while the use of disubstituted alkenyl groups gives generally low selectivity ( approximately 2:1). However, rearrangement of the anion of the cyclobutanol (prepared by acidic hydrolysis of the TMS silyl ether) at low temperature gives the endo product with good to excellent diastereoselectivity (5-23:1). Two different mechanistic rationales are given for the two different processes: the first via a diradical and the second via a cleavage intramolecular Michael addition. Thus, the same starting material (e.g., 20) can be converted into either the exo or endo product, 22x or 22n, with good diastereocontrol by just changing the rearrangement conditions.