Homotopical linking and Morse index estimates in min-max theorems

The authors extend some well-known Morse estimates for critical points of saddle point type to some linking conditions recently considered in the literature. Applications are given for multiplicity results in PDE and existence of subharmonic solutions for a class of conservative ODE. Research supported by Program STRIDE (contract STRDA/C/CEN/531/92) and EC (contract ERBCHRXCT940555).     

Single-phase natural circulation in a tilted square loop

Natural circulation of water in a tilted square loop of circular cross-section is studied in this paper. Heating is by an electrical resistance and cooling through a heat exchanger. Heating and cooling are at opposite sides of the square loop. The natural convection flow is determined experimentally as a function of the heating flux and the tilt angle. Multiplicity of steady-state velocities is experimentally confirmed.

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Einphasiger Naturumlauf in einem geneigten quadratischen Loop

Zusammenfassung In dem Aufsatz wird der Naturumlauf von Wasser in einem geneigten quadratischen Loop mit Rohren kreisförmigen Querschnittes behandelt. Die Beheizung erfolgt über einen elektrischen Widerstand und die Kühlung über einen Wärmetauscher. Heizung und Kühlung sind auf den gegenüberliegenden Seiten des quadratischen Loops angeordnet. Der Naturumlauf wird experimentell als Funktion des Wärmestromes und des Neigungswinkels bestimmt. Es wird die Vielfältigkeit von stationären Geschwindigkeiten experimentell bestätigt.

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Nomenclature Q input heat flow - V fluid velocity - V _m maximum fluid velocity - tilt angle - _c critical tilt angle - T temperature difference     

Isothermal mass transfer in annular liquid jets with Sievert's solubility law

Summary A study of isothermal gas absorption by underpressurized, axisymmetric, thin, inviscid, incompressible, annular liquid jets which form enclosed volumes, where hazardous wastes may be burned, is presented. The study considers the nonlinear dynamical coupling between the fluid dynamics of, and the gases enclosed by, the annular liquid jet. It assumes equilibrium conditions at the interfaces, and employs Sievert's solubility law to determine the gas concentration at the gas-liquid interfaces. Both steady-state and transient conditions are considered. Under steady-state conditions, the fluid dynamics and mass transfer phenomena are uncoupled, and the rate of generation of combustion gases is equal to the mass absorption rate by the liquid. The transient behaviour of the annular jet is determined from initial conditions corresponding to steady-state operation, once there is no gas generation by the combustion of hazardous wastes. It is shown that, for most of the conditions considered in this paper, there is no leakage of gaseous combustion products through the jet's outer interface, and that the amount of gases dissolved in the liquid at the nozzle exit and the solubility ratio play a paramount role in determining the mass fluxes of hazardous combustion products at the annular jet's interfaces.The research reported in this paper was supported by Project PB91-0767 from the C.I.C.Y.T. of spain.     

An indefinite concave-convex equation under a Neumann boundary condition I

We investigate the problem (P _λ) ?Δu = λb(x)|u| ^q?2 u + a(x)|u| ^p?2 u in Ω, ?u/?n = 0 on ?Ω, where Ω is a bounded smooth domain in R ^N (N ≥ 2), 1 < q < 2 < p, λ ∈ R, and a, b ∈ \({C^\alpha }\left( {\overline \Omega } \right)\) with 0 < α < 1. Under certain indefinite type conditions on a and b, we prove the existence of two nontrivial nonnegative solutions for small |λ|. We then characterize the asymptotic profiles of these solutions as λ → 0, which in some cases implies the positivity and ordering of these solutions. In addition, this asymptotic analysis suggests the existence of a loop type component in the non-negative solutions set. We prove the existence of such a component in certain cases, via a bifurcation and a topological analysis of a regularized version of (P _λ).     

Transient natural convection in a cavity with heat input and a constant temperature wall on opposite sides

The transient natural convection of a fluid with Prandtl number of order 200 in a two-dimensional square cavity has been numerically studied. One of the vertical walls of the cavity is kept at a constant (ambient) temperature and a constant heat flux is applied on the opposite wall. The other walls are adiabatic. Initially, a boundary layer is formed near the heated wall; subsequently, a large vortical structure is generated, together with an upper intrusion layer. As time progresses, the average temperature in the cavity increases, and a descending boundary layer is formed near the constant temperature wall. During the transition to the steady-state regime, a thermal stratification pattern is formed. The results are compared with the scale analysis presented by Patterson and Imberger (1980).     

In situ assessment of atorvastatin impurity using MALDI mass spectrometry imaging (MALDI-MSI)

The analysis of impurities and degradation products in pharmaceutical preparations are usually performed by chromatographic techniques such as high-performance liquid chromatography (HPLC). This approach demands extensive analysis time, mostly due to extraction and separation phases. These steps must be carried out in samples in order to adapt them to the requirements of the analytical method of choice. In the present contribution, matrix-assisted laser desorption/ionization mass spectrometry imaging (MALDI-MSI) was employed to quantify an important degradation product in atorvastatin calcium 80 mg tablets: the atorvastatin lactone. Through the standard of the impurity, it was possible to perform quantitative analysis directly on the drug tablet, using a quick and novel approach, suitable for quality control processes in the pharmaceutical industry.     

Surfactant-free miniemulsion polymerization as a simple synthetic route to a successful encapsulation of magnetite nanoparticles

Due to the existing interest in new hybrid particles in the colloidal range based on both magnetic and polymeric materials for applications in biotechnological fields, this work is focused on the preparation of magnetic polymer nanoparticles (MPNPs) by a single-step miniemulsion process developed to achieve better control of the morphology of the magnetic nanocomposite particles. MPNPs are prepared by surfactant-free miniemulsion polymerization using styrene (St) as a monomer, hexadecane (HD) as a hydrophobe, and potassium persulfate (KPS) as an initiator in the presence of oleic acid (OA)-modified magnetite nanoparticles. The effect of the type of cross-linker used [divinylbenzene (DVB) and bis[2-(methacryloyloxy)ethyl] phosphate (BMEP)] together with the effect of the amount of an aid stabilizer (dextran) on size, particle size distribution (PSD), and morphology of the hybrid nanoparticles synthesized is analyzed in detail. The mixture of different surface modifiers produces hybrid nanocolloids with various morphologies: from a typical core-shell composed by a magnetite core surrounded by a polymer shell to a homogeneously distributed morphology where the magnetite is uniformly distributed throughout the entire nanocomposite.