Operator–valued Fourier multiplier theorems on Besov spaces

We investigate analytical properties of a measure geometric Laplacian which is given as the second derivative w.r.t. two atomless finite Borel measures μ and ν with compact supports supp μ ? supp ν on the real line. This class of operators includes a generalization of the well‐known Sturm‐Liouville operator as well as of the measure geometric Laplacian given by . We obtain for this differential operator under both Dirichlet and Neumann boundary conditions similar properties as known in the classical Lebesgue case for the euclidean Laplacian like Gauß‐Green‐formula, inversion formula, compactness of the resolvent and its kernel representation w.r.t. the corresponding Green function. Finally we prove nuclearity of the resolvent and give two representations of its trace.     

Determination of calcium,strontium and barium in single crystals of alkali halides by neutron activation

The determination by neutron activation of trace quantities of calcium, strontium and barium in single crystals of alkali halides has been studied. The matrix is eliminated before the irradiation by an ion-exchange procedure. Gamma spectroscopy after radiochemical separation is used to determine strontium and barium. Calcium is determined by measuring the β-activity of ⁴⁹Sc formed by the decay of ⁴⁹Ca. Long-lived radioactive tracers are used to determine the chemical yields.     

On the goethite to hematite phase transformation

This study deals with some microstructural and crystallographic aspects of the thermally induced transformation of goethite (α-FeOOH) into hematite (α-Fe₂O₃), occurring at about 300 °C. Powder specimens of goethite have been annealed in air at different temperatures, ranging from 200 °C up to 1,000 °C. The resulting products have been analyzed for a complete characterization of the changes brought about by the thermal treatments, using a multianalytical approach, based on: thermogravimetry, differential thermal analysis, transmission electron microscopy, Raman spectroscopy, and X-ray diffraction. At lower temperatures, the transition to hematite produces no important changes in size and shape of the original goethite grains. Recrystallization, and partial sintering, occurs only at temperatures in excess of 800 °C. The relevant evolution of pores present in both phases has been also considered, as it may provide important indications on the actual formation mechanism of hematite.     

Operator-valued Fourier multiplier theorems on Lp(X) and geometry of Banach spaces

This paper gives the optimal order l of smoothness in the Mihlin and Hörmander conditions for operator-valued Fourier multiplier theorems. This optimal order l is determined by the geometry of the underlying Banach spaces (e.g. Fourier type). This requires a new approach to such multiplier theorems, which in turn leads to rather weak assumptions formulated in terms of Besov norms.     

Universal non-completely-continuous operators

A bounded linear operator between Banach spaces is calledcompletely continuous if it carries weakly convergent sequences into norm convergent sequences. Isolated is a universal operator for the class of non-completely-continuous operators fromL ₁ into an arbitrary Banach space, namely, the operator fromL ₁ into ⊆_∞ defined byT ₀(f) = (∫r _n f d μ) _n>-0, wherer _n is thenth Rademacher function. It is also shown that there does not exist a universal operator for the class of non-completely-continuous operators between two arbitrary Banach spaces. The proof uses the factorization theorem for weakly compact operators and a Tsirelson-like space. Supported in part by NSF grant DMS-9306460. Participant, NSF Workshop in Linear Analysis & Probability, Texas A&M University (supported in part by NSF grant DMS-9311902). Supported in part by NSF grant DMS-9003550.     

Application of neutron activation analysis to metallobiochemistry

Some typical applications of long-term/low-level exposure (LLE) is presented including in vivo LLE study on rats and in vitro experiments on some metal binding components as well as on cadimium binding protein.     

Radiochemical separations by retention on ionic precipitate adsorption tests on 11 materials

The retention of different radio-ions on columns of eleven ionic precipitates from different acid media was studied, in view of possible applications for radiochemical separations. The results of about 2,000 adsorption experiments, carried out in a standardized way, are presented schematically in periodic tables.     

The needle in the large pT haystack: Higgs versus quark or gluon jets together with Z0 in hadronic reactions

The possibility of observing a Higgs particle via high p_T bremsstrahlung from a weak Z₀ in p$\text{p}$ and pp collisions is examined. It appears that, although very weak, some signal might be observed in the future p$\text{p}$ collision experiments.