On the calculation of the James constant of Lorentz sequence spaces

In [M. Kato, L. Maligranda, On James and Jordan-von Neumann constants of Lorentz sequence spaces, J. Math. Anal. Appl. 258 (2001) 457-465], the James constant of the 2-dimensional Lorentz sequence space d(2)(ω,q) is computed in the case where 2?q<∞. It is an open problem to compute it in the case where 1?q<2. In this paper, we completely determine the James constant of d(2)(ω,q) in the case where 1?q<2.     

James orthogonality and orthogonal decompositions of Banach spaces

We establish decompositions of a uniformly convex and uniformly smooth Banach space B and dual space B^∗ in the form B=M?J^∗M^⊥ and B^∗=M^⊥?JM, where M is an arbitrary subspace in B, M^⊥ is its annihilator (subspace) in B^∗, J:B→B^∗ and J^∗:B^∗→B are normalized duality mappings. The sign ? denotes the James orthogonal summation (in fact, it is the direct sums of the corresponding subspaces and manifolds). In a Hilbert space H, these representations coincide with the classical decomposition in a shape of direct sum of the subspace M and its orthogonal complement M^⊥: H=M⊕M^⊥.     

Quenched! The ISABELLE Saga, II

This is the second part of a two-part article about ISABELLE, a colliding-beam accelerator conceived in 1971, officially approved in 1978, partially constructed, and terminated in 1983. I cover here the period from ISABELLE’s groundbreaking in 1978 to its termination in 1983. I treat the problems with ISABELLE’s superconducting magnets, the steps by which the problems became clear within the laboratory and to the outside, the initial failure of the laboratory administration to take forceful steps, conflicts with Fermilab, the alternate magnet projects, the repeated missing of openings that eventually used up the window of opportunity. I cover Robert Palmer’s successful creation of an alternate magnet that used Brookhaven’s existing tooling and techniques and provided (too late) a technical solution to the project’s problems, and the name change to the Colliding Beam Accelerator (CBA). I also discuss the failure of the machine to hold the physics community’s interest, and the project’s termination.     

The rack space

The main result of this paper is a new classification theorem for links (smooth embeddings in codimension 2). The classifying space is the rack space and the classifying bundle is the first James bundle.

We investigate the algebraic topology of this classifying space and report on calculations given elsewhere. Apart from defining many new knot and link invariants (including generalised James-Hopf invariants), the classification theorem has some unexpected applications. We give a combinatorial interpretation for of a complex which can be used for calculations and some new interpretations of the higher homotopy groups of the 3-sphere. We also give a cobordism classification of virtual links.

     

On the tensor algebra of a non-abelian group and applications

We introduce the tensor algebra J() of a crossed complex and give its relations with the James construction for a filtered space. For a group G, we define via multi-derivations the derived algebra I _* G which is isomorphic to the algebra C(JG) of chains on JG We derive from a certain exact sequence for the homology H*JG applications to the homotopy of the suspended classifying space BG.     

On the class of Banach spaces with James constant

In this paper, we study the class of Banach spaces with James constant . It is shown that, for a Banach space of three or more dimensions, the James constant becomes if and only if the norm is induced by an inner product. Moreover, the symmetric absolute norms on with James constant are completely characterized in terms of convex functions on the unit interval, which provides many new examples of such norms other than the Euclidean or regular octagonal norms. However, it is also shown that there exist two‐dimensional normed spaces with James constant outside of the family of symmetric absolute norms.     

On Birkhoff–James orthogonality preservers between real non-isometric Banach spaces

We present a short proof for the fact that if smooth real Banach spaces of dimension three or higher have isomorphic Birkhoff–James orthogonality structures, then they are (linearly) isometric to each other. This generalizes results of Koldobsky and of Wójcik. Moreover, in an arbitrary dimension, we construct examples of non-isometric pairs of non-smooth real Banach spaces that admit norm preserving homogeneous bicontinuous Birkhoff–James orthogonality preservers among them.     

Banach空间有一致正规结构的充分条件

建立了弱收敛序列常数关于R(1,X)和广义von Neumann-Jordan常数(广义James常数)估计式.由此得到了两个Banach空间具有一致正规结构的充分条件,推广和改进了相应的一些结论.     

R. B. Woodward,A Great Physical Organic Chemist

Robert Burns Woodward is considered one of the greatest synthetic organic chemists of our time, if not the greatest. This article presents evidence that Woodward was also one of the greatest physical organic chemists as well. Among Woodward and his collaborators' most important accomplishments in the field of physical organic chemistry are: the Woodward–Hoffmann rules; the derivation and use of structure–mechanism–reactivity relationships in his multifold structure determinations and total syntheses; the Woodward ultraviolet rules and the Octant Rule; and his early demonstration that synthetic organic chemistry can contribute to the synthesis of potential superconductors and thus, to material science. Copyright © 2014 John Wiley & Sons, Ltd.