Non-linear operators on sets of measures

Summary If M[ℬ, U(C, C)] is the collection of U(C, C)-valued (non-linear) set functions defined on the Borel subsetsℬ of the compact Hausdorff space S, one may define operators on M[ℬ, U(C, C)] which are ? of the Hammerstein type ?. We initiate a study of a concept analogous to the second dual of a space of continuous functions by inquiring as to what representation theorems one may obtain for these operators. A ? Lebesgue type ? decomposition theorem for elements of M[ℬ, U(C, C)] is obtained. A ? density ? theorem is also obtained for the space M[ℬ, U(C, C)]. Entrata in Redazione il 6 marzo 1974.     

Averaging operators on normed köthe spaces

Summary Under study is the existence of averaging operators determined by measurable maps φ from a measure space (S, Σ, μ) into an arbitrary Hausdorff topological space T. The map φ induces a continuous map φ^e from the space C_b(T) into the normed (Banach) function space L_ϱ = L_ϱ(S, Σ, μ) defined by φ^e(f)=foφ for all f ε C_b(T). An integral representation for such operators is first studied. The existence is then determined by the existence of an averaging operator U₁ for the restriction of φ to a certain measurable subset B₁ of S. Utilizing a representation of L_ϱ(S, Σ, μ) as a Banach function space over a compact extremally disconnected Hausdorff space Ŝ, we are able to give a definition for the concept of plural points and irreducible map. A significant upper bound is given for the operator U₁. Finally conditions are considered under which no bounded projection from L_ϱ onto the range of φ^e may exist. From a topological point of view the development is pursued in a general setting. Averaging operators have recently been used for the study of injective Banach spaces of the type C_b(T) and in non-linear prediction and approximation theory relative to Tshebyshev subspaces of L_ϱ. Entrata in Redazione l’ll settembre 1975.     

On the possible coexistence of itinerant-electron antiferromagnetism with the itinerant-electron ferromagnetism

It is shown that in an electron gas with coexisting charge density wave and spin density wave a spontaneous magnetization can occur. In the first paramagnetic region (T,T_t;Δ_s = Δ_t = 0) the spin susceptibility is independent of temperature (Pauli paramagnetism). In the second paramagnetic region (T_K<T<T_t,Δ_t≠0;Δ_s=0) the total susceptibility of the spin density wave is enhanced by a temperature dependent paramagnetic susceptibility with a Curie type law. This reflects the instability of the system to the formation of a charge density wave or to ferromagnetism. At sufficiently low temperatures (T～T_K) the spin susceptibility is anomalous great a fact which cannot be explained with the standard Fedders-Martin theory. Experimental results for pure chromium are in good agreement with our predictions.     

New results on the superdeformed 196Pb nucleus: decay of the excited bands to the yrast band

The study of the superdeformed ¹⁹⁶Pb nucleus has been revisited using the EUROGAMphase 2 array. In addition to the known yrast and two excited SD bands, a third excited SD band has been found. All of the three excited bands were found to decay to the yrast SD band through presumably E1 transitions. Comparisons with calculations using RPAapproximation indicate that the excited bands can be interpreted as octupole-vibrational structures.     

Uniqueness of complete spacelike hypersurfaces of constant mean curvature in generalized Robertson-Walker spacetimes

A new technique is introduced in order to solve the following question:When is a complete spacelike hypersurface of constant mean curvature in a generalized Robertson-Walker spacetime totally umbilical and a slice? (Generalized Robertson-Walker spacetimes extend classical Robertson-Walker ones to include the cases in which the fiber has not constant sectional curvature.) First, we determine when this hypersurface must be compact. Then, all these compact hypersurfaces in (necessarily spatially closed) spacetimes are shown to be totally umbilical and, except in very exceptional cases, slices. This leads to proof of a new Bernstein-type result. The power of the introduced tools is also shown by reproving and extending several known results.     

A maximum principle for hypersurfaces with constant scalar curvature and applications

In this article, we establish a weak maximum principle for complete hypersurfaces with constant scalar curvature into Riemannian space forms, and give some applications to estimate the norm of the traceless part of its second fundamental form.     

Evaluation of temperature effect on growth rate of Lactobacillus rhamnosus GG in milk using secondary models

The application of secondary temperature models on growth rates of Lactobacillus rhamnosus GG, the much studied probiotic bacterium, is investigated. Growth parameters resulting from a primary fitting were modelled against temperature using the following models: Hinshelwood model (H), Ratkowsky extended model (RTK2), Zwietering model (ZWT), and cardinal temperature model with inflection (CTMI). As experienced by other authors, the RTK2, ZWT, and CTMI models provided the best statistical indices related to fitting the experimental data. Moreover, with the biological background, the following cardinal temperatures of L. rhamnosus GG resulted from the study by the model application: t _min = 2.7°C, t _opt = 44.4°C, t _max = 52.0°C. The growth rate of the strain under study at optimal temperature was 0.88 log₁₀(CFU mL^?1 h^?1).     

Synthesis of Novel Polyfunctionally Substituted Thieno[2,3‐c]pyridazines

4‐Cyano‐5,6‐dimethylpyridazin‐3‐(2H)‐thione 3b was used as a key intermediate for the synthesis of novel polysubstituted thieno[2,3‐c]pyridazines.     

Catalytic hydrogenation of 1-hexene with RuCl2(TPPMS)3(DMSO), Part I: Aqueous biphasic system

RuCl₂(TPPMS)₃(DMSO) (complex I) shows good catalytic 1-hexene hydrogenation activity in toluene/water biphasic medium under moderate conditions, reaching 90% conversion in 5 hours, with good hydrogenation selectivity and low isomerization products. The effect of various parameters (temperature, H₂ pressure, reaction time, substrate/catalyst ratio, added electrolytes and other additives) on the hydrogenation reaction were studied. Complex (I) shows good stability in the reaction medium and can be reused several times. This revised version was published online in August 2006 with corrections to the Cover Date.