Banach spaces of distributions having two module structures

After a discussion of a space of test functions and the corresponding space of distributions, a family of Banach spaces (B, ∥ ∥_B) in standard situation is described. These are spaces of distributions having a pointwise module structure and also a module structure with respect to convolution. The main results concern relations between the different spaces associated to B established by means of well-known methods from the theory of Banach modules, among them B₀ and $\text{B}\text{?}$, the closure of the test functions in B and the weak relative completion of B, respectively. The latter is shown to be always a dual Banach space. The main diagram, given in Theorem 4.7, gives full information concerning inclusions between these spaces, showing also a complete symmetry. A great number of corresponding formulas is established. How they can be applied is indicated by selected examples, in particular by certain Segal algebras and the A_p-algebras of Herz. Various further applications are to be given elsewhere.     

Cross sections of the interactions of He nuclei with protons

⁴He-p collisions at two values of⁴He momenta 8.6 GeV/c and 13.6 GeV/c as well as the³He-p collisions at 13.5 GeV/c have been studies using the one-meter JINR hydrogen bubble chamber. Total, elastic, topological and reaction cross sections have been measured. The cross sections have been determined on a sample of minimum biased events.     

Worldsheet instantons,torsion curves and non-perturbative superpotentials

As a first step towards computing instanton-generated superpotentials in heterotic standard model vacua, we determine the Gromov–Witten invariants for a Calabi–Yau threefold with fundamental group π₁(X)=Z₃×Z₃${\pi }_1(X)={\mathbb{Z}}_3\times {\mathbb{Z}}_3$. We find that the curves fall into homology classes in H₂(X,Z)=Z³⊕(Z₃⊕Z₃)$H_2(X,\mathbb{Z})={\mathbb{Z}}^3\oplus ({\mathbb{Z}}_3\oplus {\mathbb{Z}}_3)$. The unexpected appearance of the finite torsion subgroup in the homology group complicates our analysis. However, we succeed in computing the complete genus-0 prepotential. Expanding it as a power series, the number of instantons in any integral homology class can be read off. This is the first explicit calculation of the Gromov–Witten invariants of homology classes with torsion. We find that some curve classes contain only a single instanton. This ensures that the contribution to the superpotential from each such instanton cannot cancel.     

Observation of geometric phases for mixed states using NMR interferometry

Examples of geometric phases abound in many areas of physics. They offer both fundamental insights into many physical phenomena and lead to interesting practical implementations. One of them, as indicated recently, might be an inherently fault-tolerant quantum computation. This, however, requires one to deal with geometric phases in the presence of noise and interactions between different physical subsystems. Despite the wealth of literature on the subject of geometric phases very little is known about this very important case. Here we report the first experimental study of geometric phases for mixed quantum states. We show how different they are from the well-understood, noiseless, pure-state case.     

Configuration-Space Faddeev Calculation for Proton�CDeuteron Elastic Scattering Observables

A new computational method for solving the nucleon?Cdeuteron breakup scattering problem has been applied to study the elastic nucleon?Cdeuteron scattering on the basis of the configuration-space Faddeev?CNoyes?CNoble?CMerkuriev equations. The Merkuriev?CGignoux?CLaverne approach has been generalized for arbitrary nucleon?Cnucleon potentials and with an arbitrary number of partial waves. The nucleon?Cdeuteron observables at the incident nucleon energy 3?MeV have been calculated using the charge-independent AV14 nucleon?Cnucleon potential including the Coulomb force for the proton?Cdeuteron scattering. Results have been compared with those of other authors and with experimental proton?Cdeuteron scattering data.     

Soft X‐ray absorption spectroscopy and resonant inelastic X‐ray scattering spectroscopy below 100 eV: probing first‐row transition‐metal M‐edges in chemical complexes

X‐ray absorption and scattering spectroscopies involving the 3d transition‐metal K‐ and L‐edges have a long history in studying inorganic and bioinorganic molecules. However, there have been very few studies using the M‐edges, which are below 100 eV. Synchrotron‐based X‐ray sources can have higher energy resolution at M‐edges. M‐edge X‐ray absorption spectroscopy (XAS) and resonant inelastic X‐ray scattering (RIXS) could therefore provide complementary information to K‐ and L‐edge spectroscopies. In this study, M_2,3‐edge XAS on several Co, Ni and Cu complexes are measured and their spectral information, such as chemical shifts and covalency effects, are analyzed and discussed. In addition, M_2,3‐edge RIXS on NiO, NiF₂ and two other covalent complexes have been performed and different d–d transition patterns have been observed. Although still preliminary, this work on 3d metal complexes demonstrates the potential to use M‐edge XAS and RIXS on more complicated 3d metal complexes in the future. The potential for using high‐sensitivity and high‐resolution superconducting tunnel junction X‐ray detectors below 100 eV is also illustrated and discussed.