Sheaves on Involutive Quantaloids

We extend the well-known notions of a singleton, complete -set, presheaf and sheaf over a complete Heyting algebra or a right-sided idempotent quantale to arbitrary involutive quantaloids. We show that sheaves on and complete -sets come to the same thing. This paper can be considered as a symmetric version of an earlier work of the author.     

On quantaloids and quantal categories

Institute of Mathematics and Informatics, Akademijos 4, 2600 Vilnius, Lithuania. Published in Lietuvos Matematikos Rinkinys, Vol. 35, No. 3, pp. 266–296, July–September, 1995.     

Influence of Vertical Foam Flow Liquid Drainage on Tube Bundle Heat Transfer Intensity

The results of an experimental investigation of staggered tube bundle heat transfer to upward and downward moving vertical foam flow are presented in this article. It was determined that a dependency exists between tube bundle heat transfer intensity on foam volumetric void fraction, foam flow velocity and direction, and liquid drainage from foam. In addition to this, the influence of tube position of the bundle on heat transfer was investigated. Experimental results were summarized by criterion equations, which can be applied in the design of foam type heat exchangers.     

Involutive and relational quantaloids

We present a discussion of involutive and relational quantaloids in a fashion similar to the one for quantales developed by C. J. Mulvey and J. W. Pelletier, C. Brown and D. Gurr, and S. Valentini. We introduce two classes of involutive quantaloids and prove that every quantaloid is isomorphic to a relational quantaloid. Institute of Mathematics and Informatics, Akademijos 4, 2600 Vilnius, Lithuania. Published in Lietuvos Matematikos Rinkinys, Vol. 39, No. 4, pp. 475–492, October–December, 1999.     

Measurement of the Raman cross section of O(2)(a(1)D(g))

Two different measurement methods are described that indicate that the Raman cross section of O(2)(a(1)D(g)), sigma(a)= (0.45+/-0.02) sigma(X), where sigma(X) is the Raman cross section of O(2)(X(3)?(g)(-)). Spontaneous Raman scattering is a potentially useful technique for measuring the singlet O(2)yield in high-power oxygen iodine lasers. For the full potential of this method to be realized, one must determine sigma(O)(2(a)) to measure the yield directly.     

Sheaves on quantaloids

We generalize the well-known notions of a singleton, completeQ-set, presheaf, and sheaf over a complete Heyting algebra or a right-sided idempotent quantale to arbitrary quantaloids. We show that every completeQ-set can be viewed as a sheaf and vice versa. Published in Lietuvos Matematikos Rinkinys, Vol. 40, No. 2, pp. 133–171, April–June, 2000.