Some estimates for the weakly convergent sequence coefficient in Banach spaces

We present relations between the weakly convergent sequence coefficient of a Banach space and other coefficients. Some estimates are sharp.     

On James and von Neumann-Jordan constants and sufficient conditions for the fixed point property

In this paper, we prove that a Banach space X and its dual space X^∗ have uniform normal structure if . The García-Falset coefficient R(X) is estimated by the CNJ(X)-constant and the weak orthogonality coefficient introduced by B. Sims. Finally, we present an affirmative answer to a conjecture by L. Maligranda concerning the relation between the James and CNJ(X)-constants for a Banach space.     

Heike Kamerlingh Onnes: Master of Experimental Technique and Quantitative Research

Heike Kamerlingh Onnes (1853-1926), born a century and a half ago, was a major protagonist in the so-called Second Golden Age of Dutch Science. He devoted his career to the emerging field of low-temperature physics. His particular concern was to test the theories of his older compatriot Johannes Diderik van der Waals (1837-1923) by creating a style of research that was characterized by meticulous planning, precise measurement, and constant improvement of techniques and instruments. He made numerous contributions to low-temperature physics, but I focus on his liquefaction of helium, for which he received the Nobel Prize in Physics for 1913, and on his discovery of superconductivity. He became known internationally as le gentleman du zéro absolu.     

Counterexample to a problem of Geoghegan-West

Let be a Banach space and its general linear group. Let denote the operator norm and ``' the pointwise convergence topology on . Is the identity map a homotopy equivalence? The answer is negative. One of the possible counterexamples is a well-known James space ---the ``space of counterexamples in Banach spaces theory'.

     

Once Upon a Time in Physics When Both Mathematics and Experiment Were Helpless: A Strange Life of Voltaic Contact Potential

This paper aims to answer the question of why the debate over the voltaic contact effect was so prolonged without a consensus during the nineteenth century. I propose that both experiment and mathematics were helpless to decide who was right. To demonstrate this, I will focus on the voltaic debates between James Clerk Maxwell and the Maxwellians, on the one hand, and William Thomson and the Thomsonians, on the other, and examine ten points: (1) the fundamental assumption, (2) the seat of the voltaic potential difference, (3) the role of the contact, (4) the magnitude of the potentials of two contacted metals, (5) the definition of potential, (6) the electrostatic measurement, (7) the thermoelectric measurement, (8) the physical interpretation of the same mathematical formula, (9) experiments in different media, and (10) experiments in the vacuum – all of which were in dispute between the Thomsonian and Maxwellian parties. I show that the two parties differed in theory, in the interpretation of measured data, in the physical interpretation of mathematical relationship, and in what they believed would constitute a crucial experiment. I assert that the Maxwellian and Thomsonian voltaic theories were incommensurable, but that this incommensurability was not exactly symmetrical because it mainly resided on the side of William Thomson.     

《计算统计学基础》简介及简评

A brief introduction and review of new book about the Elements of Computational Statistics is given.     

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.     

维特根斯坦是实用主义者吗—一项学术史的考察

维特根斯坦与实用主义的关系问题长期以来一直是研究者们讨论的热门话题,如何理解这种关系构成了当前国际维特根斯坦研究中的重要内容。维特根斯坦思想与实用主义哲学之间的某些相似之处,使得研究者们坚信两者之间存在思想上的一致性。然而,通过对维特根斯坦提及实用主义的语境分析,我们会发现,维特根斯坦对实用主义的理解远比研究者们所想象的更为疏远,维特根斯坦的思想完全不能被解释为一种实用主义,无论是在何种意义上的实用主义。维特根斯坦与詹姆斯思想之间被看作共享一系列承诺,包括反基础主义、对人类生活具体细节的描述、实践对思想的优先性以及宗教在理解人类生活中的重要作用等。然而,这些承诺包含了许多尚未确认的假设前提。对这些前提的细致分析揭示了维特根斯坦与詹姆斯思想之间的明显不同。对维特根斯坦与实用主义关系的讨论应被看作当代实用主义接受维特根斯坦思想的学术效果史,而不是实用主义对维特根斯坦思想的影响史。     

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．