Boundaries of Asplund spaces

We study the relationship between the classical combinatorial inequalities of Simons and the more recent (I)-property of Fonf and Lindenstrauss. We obtain a characterization of strong boundaries for Asplund spaces using the new concept of finitely self-predictable set. Strong properties for w^∗-K-analytic boundaries are established as well as a sup-lim sup theorem for Baire maps.     

赫兹对经典电磁场理论发展的贡献及其影响

文章根据赫兹的日记、书信和论文集，对赫兹在电磁场理论研究方面的主要论著进行了深入分析，对他在经典电磁场理论发展过程中所起到的重要作用和历史地位给予了更为客观的评价．文章指出，赫兹所发表的电磁学理论研究论文不仅促进了麦克斯韦理论在德国的传播和认同，而且对麦克斯韦方程组的理论基础进行了合理的重建和拓展，并给予更为清晰的逻辑论证，从而对经典电磁场理论的发展和最终完善起到了重要作用．文章还指出，赫兹在电磁场理论研究方面的成就对洛伦兹电子论的建立起到了一定的启发作用，对爱因斯坦早期物理学研究也产生了直接的影响。     

Enrico Fermi’s Discovery of Neutron-Induced Artificial Radioactivity: Neutrons and Neutron Sources

We reconstruct and analyze the path leading from James Chadwick’s discovery of the neutron in February 1932 through Frédéric Joliot and Irène Curie’s discovery of artificial radioactivity in January 1934 to Enrico Fermi’s discovery of neutron-induced artificial radioactivity in March 1934. We show, in particular, that Fermi’s innovative construction and use of radon-beryllium neutron sources permitted him to make his discovery.     

也论电磁波的预言及其发现过程

文章根据麦克斯韦的著作和赫兹的《综合文集》、《电波》和《回忆、书信和日记》以及相关文献，对麦克斯韦预言电磁波的问题和赫兹实验发现电磁波的过程进行了仔细考察，指出麦克斯韦没有明确预言电磁波的存在，麦克斯韦的理论不是赫兹电磁学实验研究的直接指导思想．文章认为亥姆霍兹为普鲁士科学院所提出的1879年悬赏课题对赫兹发现电磁波起到了直接的引导作用，而电磁波的发现则主要归因于赫兹精湛的实验技能和敏锐的观察力．     

An Extension of a Simply Inequality Between von Neumann–Jordan and James Constants in Banach Spaces

For a non-trivial Banach space X, let J(X), CNJ(X), C_(NJ)~(p)(X) respectively stand for the James constant, the von Neumann–Jordan constant and the generalized von Neumann–Jordan constant recently inroduced by Cui et al. In this paper, we discuss the relation between the James and the generalized von Neumann–Jordan constants, and establish an inequality between them: C_(NJ)~(p)(X) ≤J(X) with p ≥ 2, which covers the well-known inequality CNJ(X) ≤ J(X). We also introduce a new constant, from which we establish another inequality that extends a result of Alonso et al.     

Computational Methods for Semiparametric Linear Regression with Censored Data

Abstract

Semiparametric linear regression with censored data assumes a linear relationship between failure time and covariates without specifying the distributional form of the error term. This approach has attracted considerable attention recently. Most notably, rank regression methods have been derived for parameter estimation, hypothesis testing, and goodness-of-fit analysis. The implementation of these methods requires minimizing discrete objective functions with multiple local minima. Conventional optimization algorithms cannot be used to solve such minimization problems. We develop computational methods to implement rank regression procedures using simulated annealing. Two real data sets are used for illustration. Applications of the new algorithms to the modified least squares estimator of Buckley and James and several other related problems are also described.     

Maximal Monotone Multifunctions of Br?ndsted–Rockafellar Type

We consider whether the inequality-splitting property established in the Brøndsted–Rockafellar theorem for the subdifferential of a proper convex lower semicontinuous function on a Banach space has an analog for arbitrary maximal monotone multifunctions. We introduce the maximal monotone multifunctions of type (ED), for which an inequality-splitting property does hold. These multifunctions form a subclass of Gossez"s maximal monotone multifunctions of type (D); however, in every case where it has been proved that a multifunction is maximal monotone of type (D) then it is also of type (ED). Specifically, the following maximal monotone multifunctions are of type (ED): ultramaximal monotone multifunctions, which occur in the study of certain nonlinear elliptic functional equations; single-valued linear operators that are maximal monotone of type (D); subdifferentials of proper convex lower semicontinuous functions; subdifferentials of certain saddle-functions. We discuss the negative alignment set of a maximal monotone multifunction of type (ED) with respect to a point not in its graph – a mysterious continuous curve without end-points lying in the interior of the first quadrant of the plane. We deduce new inequality-splitting properties of subdifferentials, almost giving a substantial generalization of the original Brøndsted–Rockafellar theorem. We develop some mathematical infrastructure, some specific to multifunctions, some with possible applications to other areas of nonlinear analysis: the formula for the biconjugate of the pointwise maximum of a finite set of convex functions – in a situation where the obvious formula for the conjugate fails; a new topology on the bidual of a Banach space – in some respects, quite well behaved, but in other respects, quite pathological; an existence theorem for bounded linear functionals – unusual in that it does not assume the existence of any a priori bound; the 'big convexification" of a multifunction.     

The Dunkl-Williams constant, convexity, smoothness and normal structure

In this paper we exhibit some connections between the Dunkl-Williams constant and some other well-known constants and notions. We establish bounds for the Dunkl-Williams constant that explain and quantify a characterization of uniformly nonsquare Banach spaces in terms of the Dunkl-Williams constant given by M. Baronti and P.L. Papini. We also study the relationship between Dunkl-Williams constant, the fixed point property for nonexpansive mappings and normal structure.     

Renorming James tree space

We show that the James tree space can be renormed to be Lipschitz separated. This negatively answers the question of J. Borwein, J. Giles and J. Vanderwerff as to whether every Lipschitz separated Banach space is an Asplund space.