Boundaries for algebras of holomorphic functions

Let A_u(B_G) be the Banach algebra of all complex valued functions defined on the closed unit ball B_G of a complex Banach space G which are uniformly continuous on B_G and holomorphic in the interior of B_G, endowed with the sup norm. A characterization of the boundaries for A_u(B_G) is given in case G belongs to a class of Banach spaces that includes the pre-dual of a Lorentz sequence space studied by Gowers in Israel J. Math. 69 (1990) 129-151. The non-existence of the Shilov boundary for A_u(B_G) is also proved.     

The Calogero–Bogoyavlenskii–Schiff Equation in 2+1 Dimensions

We use the classical and nonclassical methods to obtain symmetry reductions and exact solutions of the (2+1)-dimensional integrable Calogero–Bogoyavlenskii–Schiff equation. Although this (2+1)-dimensional equation arises in a nonlocal form, it can be written as a system of differential equations and, in potential form, as a fourth-order partial differential equation. The classical and nonclassical methods yield some exact solutions of the (2+1)-dimensional equation that involve several arbitrary functions and hence exhibit a rich variety of qualitative behavior.     

Three solutions for a mixed boundary value problem involving the one-dimensional p-Laplacian

This paper deals with two mixed nonlinear boundary value problems depending on a parameter λ. For each of them we prove the existence of at least three generalized solutions when λ lies in an exactly determined open interval. Usefulness of this information on the interval is then emphasized by means of some consequences. Our main tool is a very recent three critical points theorem stated in [Topol. Methods Nonlinear Anal. 22 (2003) 93-104].     

The generalized second law in phantom dominated universes in the presence of black holes

This Letter considers the generalized second law of gravitational thermodynamics in two scenarios featuring a phantom dominated expansion plus a black hole. The law is violated in both scenarios.     

Annealing effects on the magnetization of Co–Ni–B amorphous nanoparticles

Chemically prepared (Co_xNi_1−x)_1−yB_y (x=0.5, 0.75, 1; y≈0.4) amorphous fine particles were characterized by X-ray diffraction, DTA and TGA, and in situ magnetic measurement as a function of annealing temperature in an inert atmosphere. Magnetic measurement performed in as-prepared and 150°C annealed samples shows an increase of the saturation magnetization and magnetic moment after thermal treatment. Room temperature magnetization increases by factors of 3.5, 1.8, and 1.5, for x=0.5, 0.75, and 1, respectively. These measurements may indicate a local re-ordering of the amorphous phase at temperatures much lower than the full crystallization temperature.     

Generating well-behaved utility functions for compromise programming

The purpose of this paper is to seek utility functions satisfying a weak condition which guarantees that the utility optimum always belongs to the compromise set. This set is a special subset of the attainable or feasible set, which is generated through the application of the well-known operational research approach called compromise programming. It is shown that there are large families of utility functions satisfying this condition, thus reinforcing the value of compromise programming as a good surrogate of the traditional utility optimum.Thanks are due to the reviewers for their helpful suggestions. The English editing by Ms. Christine Méndez is appreciated. The authors have been supported by the Comisión Interministerial de Ciencia y Tecnología (CICYT), Madrid, Spain.     

A comparative study of several HPLC methods for determining free amino acid profiles in honey

A study of the viability of three derivatizing reagents for obtaining amino acid profiles in honey through high performance liquid chromatography (HPLC) is presented. A method using diode array detection based on a reaction with diethyl ethoxymethylene malonate (DEMM) and two other methods using fluorescence detection based on derivatization with fluorenylmethyl chloroformate (FMOC-Cl) and 6-aminoquinolyl-N-hydroxysuccinimidyl carbamate (AQC) have been developed. The three methods yield detection limits close to the ppb level, but vary in relation to other analytical characteristics. The use of methyl chloroformate derivatives allows the profile to be obtained with the greatest sensitivity within a short time frame. On applying such methods to honey samples of diverse botanical origin, we observe that the proline values obtained are always lower than those found using the official spectrophotometric method, thereby underlining the advisability of using HPLC methods to reduce uncertainty in these results.     

New aspects on the transuranics transfer in the Palomares marine environment

The environmental contamination of transuranics following the Palomares accident in 1966 (Southern Spain) has been continuous monitored on land and scientific programs are still running. The study of the land to sea transfer of the contamination started in 1986, focussed on the depositional history recorded in marine sediments. At the continental shelf, south of the mouth of the Almanzora river, enhanced levels of plutonium and americium were found which could be related to the accident. Additional analysis of marine sediments, collected far from the impact point, showed the presence of a hot particle. The study of the chronology of this sediment core and the isotopic ratios are given in this paper to assess the origin and pathway of the particle. The route of this particle was found to be the aerial transfer at the time of the accident.