26 resultados para Maximal Monotone Operators

em University of Queensland eSpace - Australia


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In this paper, we introduce and study a new system of variational inclusions involving (H, eta)-monotone operators in Hilbert space. Using the resolvent operator associated with (H, eta)monotone operators, we prove the existence and uniqueness of solutions for this new system of variational inclusions. We also construct a new algorithm for approximating the solution of this system and discuss the convergence of the sequence of iterates generated by the algorithm. (c) 2005 Elsevier Ltd. All rights reserved.

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In a previous paper R. Mathon gave a new construction method for maximal arcs in finite Desarguesian projective planes via closed sets of conics, as well as giving many new examples of maximal arcs. In the current paper, new classes of maximal arcs are constructed, and it is shown that every maximal arc so constructed gives rise to an infinite class of maximal arcs. Apart from when they are of Denniston type or dual hyperovals, closed sets of conics are shown to give maximal arcs that are not isomorphic to the known constructions. An easy characterisation of when a closed set of conics is of Denniston type is given. Results on the geometric structure of the maximal arcs and their duals are proved, as well as on elements of their collineation stabilisers.

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A central feature in the Hilbert space formulation of classical mechanics is the quantisation of classical Lionville densities, leading to what may be termed Groenewold operators. We investigate the spectra of the Groenewold operators that correspond to Gaussian and to certain uniform Lionville densities. We show that when the classical coordinate-momentum uncertainty product falls below Heisenberg's limit, the Groenewold operators in the Gaussian case develop negative eigenvalues and eigenvalues larger than 1. However, in the uniform case, negative eigenvalues are shown to persist for arbitrarily large values of the classical uncertainty product.

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Sports venues are in a position to potentially influence the safety practices of their patrons. This study examined the knowledge, beliefs and attitudes of venue operators that could influence the use of protective eyewear by squash players. A 50% random sample of all private and public squash venues affiliated with the Victorian Squash Federation in metropolitan Melbourne was selected. Face-to-face interviews were conducted with 15 squash venue operators during August 2001. Interviews were transcribed and content and thematic analyses were performed. The content of the interviews covered five topics: (1) overall injury risk perception, (2) eye injury occurrence, (3) knowledge, behaviors, attitudes and beliefs associated with protective eyewear, (4) compulsory protective eyewear and (5) availability of protective eyewear at venues. Venue operators were mainly concerned with the severe nature of eye injuries, rather than the relatively low incidence of these injuries. Some venue operators believed that players should wear any eyewear, rather than none at all, and believed that more players should use protective eyewear. Generally, they did not believe that players with higher levels of experience and expertise needed to wear protective eyewear when playing. Only six venues had at least one type of eyewear available for players to hire or borrow or to purchase. Operators expressed a desire to be informed about correct protective eyewear. Appropriate protective eyewear is not readily available at squash venues. Better-informed venue operators may be more likely to provide suitable protective eyewear.

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In 1969, Denniston gave a construction of maximal arcs of degree n in Desarguesian projective planes of even order q, for all n dividing q. Recently, Mathon gave a construction method that generalized that of Denniston. In this paper we use that method to give maximal arcs that are not of Dermiston type for all n dividing q, 4 < n < q/2, q even. It is then shown that there are a large number of isomorphism classes of such maximal arcs when n is approximately rootq. (C) 2003 Elsevier Ltd. All rights reserved.

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We develop results for bifurcation from the principal eigenvalue for certain operators based on the p-Laplacian and containing a superlinear nonlinearity with a critical Sobolev exponent. The main result concerns an asymptotic estimate of the rate at which the solution branch departs from the eigenspace. The method can also be applied for nonpotential operators.

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Background and Purpose - A higher plasma concentration of total homocysteine (tHcy) is associated with a greater risk of cardiovascular events. Previous studies, largely in younger individuals, have shown that B vitamins lowered tHcy by substantial amounts and that this effect is greater in people with higher tHcy and lower folate levels. Methods - We undertook a 2-year, double-blind, placebo-controlled, randomized trial in 299 men aged >= 75 years, comparing treatment with a daily tablet containing 2 mg of folate, 25 mg of B-6, and 400 mu g of B-12 or placebo. The study groups were balanced regarding age (mean +/- SD, 78.9 +/- 2.8 years), B vitamins, and tHcy at baseline. Results - Among the 13% with B12 deficiency, the difference in mean changes in treatment and control groups for tHcy was 6.74 mu mol/L (95% CI, 3.94 to 9.55 mu mol/L) compared with 2.88 mu mol/L (95% CI, 0.07 to 5.69 mu mol/L) for all others. Among the 20% with hyperhomocysteinaemia, the difference between mean changes in treatment and control groups for men with high plasma tHcy compared with the rest of the group was 2.8 mu mol/L (95% CI, 0.6 to 4.9 mu mol/L). Baseline vitamin B12, serum folate, and tHcy were significantly associated with changes in plasma tHcy at follow-up (r = 0.252, r = 0.522, and r = -0.903, respectively; P = 0.003, <0.001, and <0.001, respectively) in the vitamin group. Conclusions - The tHcy-lowering effect of B vitamins was maximal in those who had low B12 or high tHcy levels. Community-dwelling older men, who are likely to be deficient in B12 or have hyperhomocysteinemia, may be most likely to benefit from treatment with B vitamins.

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The maximum possible volume of a simple, non-Steiner (v, 3, 2) trade was determined for all v by Xhosrovshahi and Torabi (Ars Combinatoria 51 (1999), 211-223), except that in the-case v equivalent to 5 (mod 6), v >= 23, they were only able to provide an upper, bound on the volume. In this paper we construct trades with volume equal to that bound for all v equivalent to 5 (mod 6), thus completing the problem.