The Experts below are selected from a list of 33 Experts worldwide ranked by ideXlab platform
Dorfmeister, Josef G. - One of the best experts on this subject based on the ideXlab platform.
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Bounded Negativity and Symplectic 4-Manifolds
2016Co-Authors: Dorfmeister, Josef G.Abstract:Let $(M,\omega)$ be a symplectic 4-manifold of negative Kodaira dimension. Let $C$ be an $\omega$-symplectic curve, $J$-holomorphic for some $J$ tamed by $\omega$. Then $[C]^2$ is bounded below by a constant depending only on $\omega$. Related bounded negativity problems for other structures are also briefly discussed. In particular, the symplectic result implies the bounded negativity conjecture for complex projective surfaces with Kodaira dimension $\kappa=-\infty$.Comment: 21 pages, This paper has been withdrawn. I thank Weiwei Wu for pointing out a crucial gap in the cutting procedure Preceding Theorem 4.
Albert Stralka - One of the best experts on this subject based on the ideXlab platform.
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ON THE DIMENSIONAL CAPACITY OF COMPACT SEMILATTICES
2015Co-Authors: Karl Heinrich Hofmann, Michael Mislove, Albert StralkaAbstract:The question of topological dimension is settled for compact abelian groups with the following classical result [ 7] ß PROPOSITION 0.1 If G is a compact abelian group with character group G and n a natural number, the following statements are equivalent.' (1) The (Lebesgue covering or cohomological) dimension of G is n. (2) The (torsion free) rank of G is n. (3) There is a quotient morphism G->T n (with zero dimensional kernel), where T = R/Z. (4) There is an injectire morphism Z n-> • (with a torsion cokerneD. While in general it is not feasible to assign to a compact space a transfinite cardinal as topological dimension, the Preceding Theorem allows us to do precisely that for compact abelian groups, because statements (2), (3) and (4) remain meaningful for arbitrary cardinals n. Thus, let us make the following definition, denoting with [XI the cardinal of a set X' DEFINITION 0.2. For a compact abelian group G we set #G = sup { IX { ß there is a continuous surmorphism G • T X} and we call this cardinal the (generalized) dimension of G. We then have the following conclusive result' PROPOSITION 0.3. For each compact abelian group G we have #G =rank • =dimQ ©G-, and there isa continuous surmorphism G->T:)pG with zero dimensional kernel. If we now turn to the much larger class of compact abelian monoids, topological dimension becomes much more elusive. This study is a contribution to the question o
Jie Yuan - One of the best experts on this subject based on the ideXlab platform.
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Fuzzy‐Bayesian Approach to Reliability of Existing Structures
Journal of Structural Engineering, 1993Co-Authors: Karen C. Chou, Jie YuanAbstract:Classical reliability has significantly enhanced the ability of engineers to assess the safety of constructed projects. It has been shown that Bayes’ Theorem is an effective tool in updating prior probabilities when the value of a random parameter is known. However, the Preceding Theorem usually fails to adequately address the uncertainties of the subjective parameters (such as “the connections are good”) that are associated with structural evaluation. It has been demonstrated that these parameters can be significant to the overall safety assessment. With the introduction of fuzzy-set theory, it is possible to quantify the qualitative evaluation and incorporate it into the safety assessment. This paper presents an algorithm to compute the posterior probability based on visual inspection of structural components by incorporating fuzzy-set theory into Bayes’ Theorem. The results based on two examples—a reinforced concrete beam and a structural frame—showed that the fuzzy-Bayesian approach is a viable enhancement to the safety assessment of existing structures.
M. Chacron - One of the best experts on this subject based on the ideXlab platform.
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Residually *-Abelian Valuation with Residue Characteristic Not 2
Communications in Algebra, 2014Co-Authors: M. ChacronAbstract:We are given a division ring D with involution (*) and with a *-valuation V such that V(sx − xs) > V(sx), for all nonzero elements x, s of D with s = s*. Let χ denote the characteristic of the residue class division ring associated with V. We reported in Theorem 3.2.5 Part 4 in [3] that, in the case χ = 0, either D is a standard quaternion division algebra or else D contains no algebraic elements other than the scalars. In this article, we carry out a generalization of the Preceding Theorem to the case χ ≠ 2. Our results are fairly complete in the finite dimensional case, and generalize Theorems of, notably, J. Graeter and A. I. Lichtman, in the infinite dimensional case.
Karl Heinrich Hofmann - One of the best experts on this subject based on the ideXlab platform.
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ON THE DIMENSIONAL CAPACITY OF COMPACT SEMILATTICES
2015Co-Authors: Karl Heinrich Hofmann, Michael Mislove, Albert StralkaAbstract:The question of topological dimension is settled for compact abelian groups with the following classical result [ 7] ß PROPOSITION 0.1 If G is a compact abelian group with character group G and n a natural number, the following statements are equivalent.' (1) The (Lebesgue covering or cohomological) dimension of G is n. (2) The (torsion free) rank of G is n. (3) There is a quotient morphism G->T n (with zero dimensional kernel), where T = R/Z. (4) There is an injectire morphism Z n-> • (with a torsion cokerneD. While in general it is not feasible to assign to a compact space a transfinite cardinal as topological dimension, the Preceding Theorem allows us to do precisely that for compact abelian groups, because statements (2), (3) and (4) remain meaningful for arbitrary cardinals n. Thus, let us make the following definition, denoting with [XI the cardinal of a set X' DEFINITION 0.2. For a compact abelian group G we set #G = sup { IX { ß there is a continuous surmorphism G • T X} and we call this cardinal the (generalized) dimension of G. We then have the following conclusive result' PROPOSITION 0.3. For each compact abelian group G we have #G =rank • =dimQ ©G-, and there isa continuous surmorphism G->T:)pG with zero dimensional kernel. If we now turn to the much larger class of compact abelian monoids, topological dimension becomes much more elusive. This study is a contribution to the question o