We analyze a primal-dual pair of problems generated via a duality theory introduced by Svaiter. We propose a general algorithm and study its convergence properties. The focus is a general primal-dual principle for strong convergence of some classes of algorithms. In particular, we give a different viewpoint for the weak-to-strong principle of Bauschke and Combettes and unify many results concer...

By DIANA GOLDENBERG Election Board will use the campaign rules as a guide, not as binding reo -slrictions, for the remainder 01 the stu· 'dent campaign , lhe Election Board chairman announced Friday. David Miller, A2, Wilmette, Ill" made lhe announcement in response to I statement by Robert Beller, A2, Glencoe, ilL , a presidential candidate, and his vice presidential running mate, Larr, Wood. ...

The Schrödinger operator −∆+V , of a compact Riemannian manifold M , has pure point spectrum. Suppose that V0 is a smooth reference potential. Various criteria are given which guarantee the compactness of all V satisfying spec(−∆+V ) = spec(−∆+V0). In particular, compactness is proved assuming an a priori bound on the Ws,2(M) norm of V , where s > n/2 − 2 and n = dimM . This improves earlier wo...

In this paper, we present a study of various concepts pertaining to compactness properties of a lattice. Special cases include such notions as countably compactness, almost countably compactness, and countably paracompactness. Some investigations in these matters have been done in [2, 7, 14]. We go beyond these results and introduce new subsets of I(L) and their lattices to investigate. This wa...

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An improvement of the author’s result, proved in 1961, concerning necessary and sufficient conditions for the compactness of embedding operators is given. A discussion of the necessity of the compatibility of the norms of the Banach spaces X2 and X3, where X2 ⊂ X3, is given. The injectivity of the embedding operator J : X2 → X3 implies this compatibility.

Much progress has been made in recent years in the area of information retrieval, in particular as embodied in Internet search engine technology. Much progress has also been made in probabilistic, graph-theoretic AI. What are the possibilities for bringing these two lines of research together — for viewing large-scale information retrieval as a core enabling technology for AI systems, and for a...

The controversial attempt to scrap the 24-year-old international moratorium on commercial whaling collapsed last month, to the delight of many anti-whaling campaigners and to the frustration of Japan, Norway and Iceland, the three countries which continue to hunt whales in defiance of world opinion. Delegates from the 88 member states of the International Whaling Commission (IWC) meeting in Aga...