James constant for interpolation spaces

Estimates for the James constant for various norms in real interpolation spaces for finite families of Banach spaces are given. As a corollary it is shown that if a family contains at least one space which is uniformly nonsquare, then the interpolation space is uniformly nonsquare.     

Storming a Citadel: Mathematical Theory and Experimental Practice

Based upon a comparison of the viscosity experiments of James Clerk Maxwell (1831–1879) and Oskar Emil Meyer (1834–1909) in the 1860s, I argue that mathematical theory plays a significant role in both aspects of experimental practice, the design and construction of an experimental apparatus and the transformation of the observed experimental data into the value of a physical quantity. I argue further that Maxwell’s and Meyer’s evaluation of each other’s theoretical and experimental work depended significantly on the mathematical tools they employed in their theories.     

American Physicists, Nuclear Weapons in World War II, and Social Responsibility

Social responsibility in science has a centuries-long history, but it was such a minor thread that most scientists were unaware of the concept. Even toward the conclusion of the Manhattan Project, which produced the first nuclear weapons, only a handful of its participants had some reservations about use of a weapon of mass destruction. But the explosions over Hiroshima and Nagasaki not only made society more aware of the importance of science, they made scientists more aware of their responsibility to society. I describe the development of the concept of social responsibility and its appearance among American scientists both before and after the end of World War II.Expanded version of a talk in Hiroshima, Japan,August 10, 2003.Lawrence Badash is Professor Emeritus of History of Science at the University of California, Santa Barbara.     

When Does the Equality J(X~*) = J(X) Hold for a Two-dimensional Banach Space X ?

In this paper, we consider the following problem about the James constant: When does the equality J(X*) = J(X) hold for a Banach space X ? It is known that the James constant of a Banach space does not coincide with that of its dual space in general. In fact, we already have counterexamples of two-dimensional normed spaces that are equipped with either symmetric or absolute norms. However,we show that if the norm on a two-dimensional space X is both symmetric and absolute, then the equality J(X*) = J(X) holds. This provides a global answer to the problem in the two-dimensional case.     

The Physical Tourist Physics in Glasgow: A Heritage Tour

I trace the history of the physical and applied sciences, and particularly physics, in Glasgow. Among the notable individuals I discuss are Joseph Black (1728–1799), James Watt (1736–1819), William John Macquorn Rankine (1820–1872), William Thomson, Lord Kelvin (1824–1907), John Kerr (1824–1907), Frederick Soddy (1877–1956), John Logie Baird (1888–1946), and Ian Donald (1910–1987), as well as physics-related businesses.The locations, centering on the city center and University of Glasgow, include sites both recognizable today and transformed from past usage, as well as museums and archives related to the history and interpretation of physics.     

Early Attempts to Detect the Neutrino at the Cavendish Laboratory

In the 1920s and early 1930s the Cavendish Laboratory in Cambridge was preeminent in experimental research on radioactivity and nuclear physics, with theoretical physics playing a subsidiary role in guiding, but not determining the course of experimental research. Soon after Wolfgang Pauli (1900–1958) proposed his neutrino hypothesis in 1930 to preserve conservation of energy and momentum in beta decay, experiments – the first of their kind – were carried out in the Cavendish Laboratory to detect Pauli’s elusive particle, but they were abandoned in 1936. I trace these early attempts and suggest reasons for their abandonment, which may contribute to an understanding of the complex way in which theoretical entities are accepted by physicists.     

Some geometric conditions which imply the fixed point property for multivalued nonexpansive mappings

We show some geometric conditions on a Banach space X concerning the modulus of smoothness, the coefficient of weak orthogonality, the coefficient R(a,X), the James constant and the Jordan-von Neumann constant, which imply the existence of fixed points for multivalued nonexpansive mappings. These fixed point theorems improve some previous results and give affirmative answers to some open questions.     

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.