Amenability of Banach algebras of compact operators

In this paper we study conditions on a Banach spaceX that ensure that the Banach algebraК(X) of compact operators is amenable. We give a symmetrized approximation property ofX which is proved to be such a condition. This property is satisfied by a wide range of Banach spaces including all the classical spaces. We then investigate which constructions of new Banach spaces from old ones preserve the property of carrying amenable algebras of compact operators. Roughly speaking, dual spaces, predual spaces and certain tensor products do inherit this property and direct sums do not. For direct sums this question is closely related to factorization of linear operators. In the final section we discuss some open questions, in particular, the converse problem of what properties ofX are implied by the amenability ofК(X). BEJ supported by MSRVP at Australian National University; GAW supported by SERC grant GR-F-74332.     

Transmission induced structure in electron emission spectra

Angle resolved secondary electron emission spectra from tungsten contain fine-structure which to a large extent can be correlated with high density-of-states regions in the bulk band structure. In addition to such structure, strong “extra” peaks have been observed. The “anomalous” peaks, which are particularly dominating in the W{111}-spectra, occur when the “emitting” bulk Bloch state has a group velocity that equals the group velocity of the emitted electron. These particular peaks reflect structure in the transmission probability function and can only be explained by considering the wave-matching at the surface.     

Limits on the production of large transverse momentum direct photons deduced from the measurement of low-mass electron pairs

The hadronic production of electron pairs with masses between 200 and 500 MeV and large transverse momentum has been measured at the CERN Intersecting Storage Rings (ISR). The expected relation between low-mass electron pairs and real photons is used to determine the direct hadronic production of photons. Contrary to indications from some previous experiments, the observed spectrum is consistent with expectations from the decay of known mesons, and leads to a value for the ratio of direct photons to π⁰ of γ/π⁰ = (0.55 ± 0.92)% for 2 < p_T < 3 GeV and 〈√s〉 = 55 GeV.     

Azimuthal correlation of a high pTπ0 and η with a second π0 produced in pp collisions at the ISR

The correlation between a high transverse momentum π⁰and η and a second π⁰ have been measured using an apparatus with large azimuthal acceptance. The angular distribution of α, measuring the deviation from collinearity in azimuth, peaks near zero. The r.m.s. of the distribution is found to have an inverse logarithmic rather than a $\text{1}\text{p}$ fall-off.     

Experimental search for B = 2, T= 0 states in the d + d → d + X reaction

A search for isoscalar dibaryonic resonances by means of missing-mass spectra in the d + d → d + X reaction has been attempted using deuteron beams of T = 2.29,2.00 and 1.65 GeV. The results do not show any evidence for a narrow peak with a limit of $\text{30 nb}\text{GeV}{}^2$ for a 15 MeV width or a broad enhancement which could be unambiguously attributed to a dibaryonic resonance.     

Search for isovector giant monopole resonances via the Pb(3He,tp) reaction

The (nat)Pb(3He,tp) reaction at E(3He) = 177 MeV was studied to identify 2Planck's over 2piomega isovector monopole strength in Bi isotopes. Monopole strength was found in the region -45相似文献   

Thickness-dependent Curie temperatures of ultrathin magnetic films: effect of the range of spin-spin interactions

We present a simple model of spin-spin coupling which provides insight into the nature of the rapid decrease in the Curie temperature with decreasing thin film thickness n (number of monolayers). The shift of Curie temperature t(n) = 1-T(c)(n)/T(c)(infinity) follows the usual power law t(n) approximately n(-lambda) in thin films crossing over to linear behavior t(n) approximately n in the ultrathin film thickness limit. Experimental results for ferromagnetic thin films are compared, and shown to follow curves of t(n) with lambda values dependent on the nature of the spin-spin interactions.     

The Number of Prime Factors of the Scale Function on a Compactly Generated Group is Finite

It is shown that for each compactly generated totally disconnectedlocally compact group G, there is a finite number of prime numbers,p₁, p₂, ..., p_n, such that the scale function s : G N satisfies, where x G.     

Rediscovering Sulfinylamines as Reagents for Organic Synthesis

Sulfinylamines (R−N=S=O), monoaza analogues of sulfur dioxide, have been known for well over a century, and their reactivity as sulfur electrophiles and in Diels-Alder reactions is well-established. However, they have only rarely been used in organic synthesis in recent decades despite the increasing prominence of compounds containing N=S=O functionality, such as sulfoximines and sulfonimidamides. This Minireview aims to bring wider visibility to the unique chemistry enabled by this class of compounds. We focus on advances from the last 10 years, including the first examples of their use in the one-pot syntheses of sulfoximines and sulfonimidamides. Also covered are the reactions of sulfinylamines with carbon-centred radicals, their use for formation of heterocycles through cycloadditions, and catalytic enantioselective allylic oxidation of alkenes via a hetero-ene reaction. These examples highlight the different reactivity modes of sulfinylamines and their underappreciated potential for forming molecules which contain high- or low-valent sulfur, or even no sulfur at all.