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.     

Bidual renormings of Banach spaces

Given a separable Banach space X with no isomorphic copies of ℓ₁ and a separable subspace Y of its bidual, we provide a sufficient condition on Y to ensure that X admits an equivalent norm such that the restriction to Y of the corresponding bidual norm is midpoint locally uniformly rotund. This result applies to the separable subspaces of the bidual of a Banach space with a shrinking unconditional Schauder basis and to the bidual of the James space.     

On the norm attainment set of a bounded linear operator

In this paper we explore the properties of a bounded linear operator defined on a Banach space, in light of operator norm attainment. Using Birkhoff–James orthogonality techniques, we give a necessary condition for a nonzero bounded linear operator to attain norm at a particular point of the unit sphere. We prove four corollaries to establish the importance of our study. As part of our exploration, we also obtain a characterization of smooth Banach spaces in terms of operator norm attainment and Birkhoff–James orthogonality. Restricting our attention to $l_p^2(p\in \mathbb{N}?\{1\})$ spaces, we obtain an upper bound for the number of points at which any linear operator, which is not a scalar multiple of an isometry, may attain norm.     

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.     

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.     

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。