On the maximum principle for complete second-order elliptic operators in general domains

This paper is concerned with the maximum principle for second-order linear elliptic equations in a wide generality. By means of a geometric condition previously stressed by Berestycki-Nirenberg-Varadhan, Cabré was very able to improve the classical ABP estimate obtaining the maximum principle also in unbounded domains, such as infinite strips and open connected cones with closure different from the whole space. Now we introduce a new geometric condition that extends the result to a more general class of domains including the complements of hypersurfaces, as for instance the cut plane. The methods developed here allow us to deal with complete second-order equations, where the admissible first-order term, forced to be zero in a preceding result with Cafagna, depends on the geometry of the domain.     

Generalized Mukai conjecture for special Fano varieties

Let X be a Fano variety of dimension n, pseudoindex i _X and Picard number ρ_X. A generalization of a conjecture of Mukai says that ρ_X(i _X −1)≤n. We prove that the conjecture holds for a variety X of pseudoindex i _X ≥n+3/3 if X admits an unsplit covering family of rational curves; we also prove that this condition is satisfied if ρ_X> and either X has a fiber type extremal contraction or has not small extremal contractions. Finally we prove that the conjecture holds if X has dimension five.     

Internal standardization for the determination of cadmium,cobalt, chromium and manganese in saline produced water from petroleum industry by inductively coupled plasma optical emission spectrometry after cloud point extraction

In the present paper a procedure is proposed for the determination of traces of Cd, Co, Mn and Cr in petroleum industry produced water by inductively coupled plasma optical emission spectrometry. The procedure is based on cloud point extraction of these metals, as their dithizonate complexes, into the surfactant-rich phase of octylphenoxypolyethoxyethanol surfactant (Triton X-114). Extractions were carried out in solutions with salinities between 10‰ and 70‰. Since residual salinity in the surfactant-rich phase caused differences in its transport to the plasma, yttrium was used as an internal standard to correct for this effect. The simultaneous metal extraction procedure was optimized by response surface methodology using a Doehlert design and desirability function. Enhancement factors of 21, 21, 9 and 19, along with limits of quantification of 0.093, 0.20, 0.73 and 1.2 μg L^− 1, and precision expressed as relative standard deviation (n = 8, 20.0 μg L^− 1) of 5.8, 1.2, 1.7 and 5.7% were obtained for Cd, Co, Mn and Cr, respectively. The accuracy was evaluated by spike recovery tests on the high salinity water samples with salinity of 40 and 63‰.     

An experimental analysis of a population based approach for global optimization

In this paper we perform a computational analysis of a population based approach for global optimization, Population Basin Hopping (PBH), which was proven to be very efficient on very challenging global optimization problems by the authors (see ). The experimental analysis aims at understanding more deeply how the approach works and why it is successful on challenging problems.     

Mathematical and numerical analysis of a simplified time-dependent viscoelastic flow

A time-dependent model corresponding to an Oldroyd-B viscoelastic fluid is considered, the convective terms being disregarded. Global existence in time is proved in Banach spaces provided the data are small enough, using the implicit function theorem and a maximum regularity property for a three fields Stokes problem. A finite element discretization in space is then proposed. Existence of the numerical solution is proved for small data, so as a priori error estimates, using again an implicit function theorem. Supported by the Swiss National Science Foundation. Fellowship PBEL2–114311.     

How to assess and report the performance of a stochastic algorithm on a benchmark problem: mean or best result on a number of runs?

Some authors claim that reporting the best result obtained by a stochastic algorithm in a number of runs is more meaningful than reporting some central statistic. In this short note, we analyze and refute the main argument brought in favor of this statement.     

Memory effects in gas chromatographic detection with a microwave-induced plasma

Capillary gas chromatography coupled to microwave-inducedplasma detection furnishes sensitivity adequate for trace analysis when the signal is monitored at a carbon emission line. Work performed with one of these systems at high electronic gain for the carbon signal has revealed solvent band widths in excess of four minutes; these impeded quantification of peaks eluting after the solvent. This report discusses two phenomena which could be related to the unexpected intensity of this solvent response: photomultiplier tube saturation and carbon deposits in the quartz plasma discharge tube.     

Nonconservation of the net current of Dirac particles in Tolman-Bondi and Robertson-Walker geometries

A straightforward calculation shows that, in contrast to what happens for the Dirac equation in the Kerr metric, the net current of particles is not conserved in the case of the Dirac equation in the Tolman-Bondi and Robertson-Walker space-times.     

Numerical solution of eigenvalue problems for Hamiltonian systems

This paper discusses the numerical solution of eigenvalue problems for Hamiltonian systems of ordinary differential equations. Two new codes are presented which incorporate the algorithms described here; to the best of the author’s knowledge, these are the first codes capable of solving numerically such general eigenvalue problems. One of these implements a new new method of solving a differential equation whose solution is a unitary matrix. Both codes are fully documented and are written inPfort-verifiedFortran 77, and will be available in netlib/aicm/sl11f and netlib/aicm/sl12f.     

The liquid-crystalline properties of bis[N-[[4-[4-(alkoxy)benzoyloxy]2-hydroxyphenyl]methylene]alkanamino] complexes of Cu(II), Pd(II) and Ni(II). A general view

The thermotropic liquid-crystalline phase behaviour of a homologous set of bis[N-[[4-[4-(alkoxy)benzoyloxy]2-hydroxyphenyl]methylene]alkanamino] copper(II) complexes is examined. New data are reported and taken into account in addition to those previously reported in this Journal. The influence of alkoxy and alkanamine groups on the nature and stability of the mesophase is underlined. As a general trend, with some notable exception, smectic (C type) mesomorphism is favoured by longer alkoxy and alkanamine chains. Data concerning some Pd(II) and Ni(II) homologous complexes are also reported. The mesophase stability (nematic phase) is higher for palladium and nickel complexes than for the copper containing homologues.