Un matemático comprometido política, social y académicamente: José Luis Massera

Se analizan algunos aspectos de la vida de José Luis Massera, tanto académicos como políticos.

Análisis de las conceptualizaciones erróneas en conceptos de geometría y sistemas de ecuaciones: un estudio con estudiantes universitarios de primer ingreso

En el presente artículo se reportan los resultados de una investigación que clasifica las conceptualizaciones que tienen estudiantes de primer ingreso universitarios de Costa Rica en temas de geometría y sistemas de ecuaciones mediante el modelo SOLO Taxonómico (propuesto por Biggs & Collis, 1982). Inicialmente los estudiantes se ubican en los primeros niveles de razonamiento en los temas de geometría y en niveles intermedios en sistemas de ecuaciones, al final los estudiantes mostraron mejoría después de un curso introductorio de matemáticas.

La equivalencia de las representaciones de la solución particular por los métodos de reducción de orden y variación de parámetros

Usando el método de variación de parámetros, construimos la solución particular de una ecuación diferencial de segundo orden. Luego demostramos que es una representación diferente pero equivalente a aquella solución construida por el método de reducción de orden.

De la resolución de ecuaciones polinómicas al álgebra abstracta: un paseo a través de la historia

Realizaremos un paseo histórico a lo que ha sido la resolución de ecuaciones polinómicas y en general el desarrollo del álgebra. La intención es presentar una síntesis de algunas de las dificultades que se enfrentaron a lo largo de la historia, en la construcción de los significados y conceptos matemáticos, referidos principalmente a la resolución de ecuaciones polinómicas y al desarrollo del álgebra abstracta.

Replanteamiento de la Conjetura de Goldbach

En este ensayo se propone el uso de una razón que permite determinar la secuencia de las series cuyas sumas son cuadrados perfectos; estas soluciones las usamos posteriormente para determinar algunos primos de la forma 4n+1, descubrimos una nueva razón que relaciona la constante Pi y un número primo de diez cifras de la forma 4n+1. Más adelante describimos la relación de esta clase de números primos con los llamados primos gemelos, lo que nos permite replantear la Conjetura Binaria de Goldbach en términos de una igualdad que involucra exclusivamente las clases de números primos que nos ocupan.

Recta de Euler en cuadriláteros

El circuncentro (O), baricentro (G) y ortocentro (H) de todo triangulo estan alineados en la recta de Euler y verifican la relación mGH = 2 · mOG. En el presente artıculo se define baricentro (G) y ortocentro (H) de un cuadrilátero inscriptible de circuncentro (O) y se demuestra que dichos puntos están alineados y verifican la relación mGH = 3 · mOG.

Climate change and marine plankton

Understanding how climate change will affect the planet is a key issue worldwide. Questions concerning the pace and impacts of climate change are thus central to many ecological and biogeochemical studies, and addressing the consequences of climate change is now high on the list of priorities for funding agencies. Here, we review the interactions between climate change and plankton communities, focusing on systematic changes in plankton community structure, abundance, distribution and phenology over recent decades. We examine the potential socioeconomic impacts of these plankton changes, such as the effects of bottom-up forcing on commercially exploited fish stocks (i.e. plankton as food for fish). We also consider the crucial roles that plankton might have in dictating the future pace of climate change via feedback mechanisms responding to elevated atmospheric CO sub(2) levels. An important message emerges from this review: ongoing plankton monitoring programmes worldwide will act as sentinels to identify future changes in marine ecosystems.

Plankton and climate

Plankton has two roles with respect to climate: first as an indicator of climate change in present day populations and in the fossil record and second as a factor contributing to climate change through, for example, its role in the CO sub(2) cycle, in cloud formation via dimethylsulfide (DMS) production, and in altering the reflectivity of sea water as a component of suspended particulate matter. Current research on both the contribution of plankton to climate change and its role as an indicator of change are central to predicting potential scenarios that may occur in the future at a time when global mean temperatures are predicted to rise at an unprecedented rate by 1.5-6 degree C within the next 100 years.

Consistent increase in dimethyl sulfide (DMS) in response to high CO2 in five shipboard bioassays from contrasting NW European waters

The ubiquitous marine trace gas dimethyl sulfide (DMS) comprises the greatest natural source of sulfur to the atmosphere and is a key player in atmospheric chemistry and climate. We explore the short-term response of DMS production and cycling and that of its algal precursor dimethyl sulfoniopropionate (DMSP) to elevated carbon dioxide (CO₂) and ocean acidification (OA) in five 96 h shipboard bioassay experiments. Experiments were performed in June and July 2011, using water collected from contrasting sites in NW European waters (Outer Hebrides, Irish Sea, Bay of Biscay, North Sea). Concentrations of DMS and DMSP, alongside rates of DMSP synthesis and DMS production and consumption, were determined during all experiments for ambient CO₂ and three high-CO₂ treatments (550, 750, 1000 μatm). In general, the response to OA throughout this region showed little variation, despite encompassing a range of biological and biogeochemical conditions. We observed consistent and marked increases in DMS concentrations relative to ambient controls (110% (28–223%) at 550 μatm, 153% (56–295%) at 750 μatm and 225% (79–413%) at 1000 μatm), and decreases in DMSP concentrations (28% (18–40%) at 550 μatm, 44% (18–64%) at 750 μatm and 52% (24–72%) at 1000 μatm). Significant decreases in DMSP synthesis rate constants (μDMSP, d⁻¹) and DMSP production rates (nmol d⁻¹) were observed in two experiments (7–90% decrease), whilst the response under high CO₂ from the remaining experiments was generally indistinguishable from ambient controls. Rates of bacterial DMS gross consumption and production gave weak and inconsistent responses to high CO₂. The variables and rates we report increase our understanding of the processes behind the response to OA. This could provide the opportunity to improve upon mesocosm-derived empirical modelling relationships and to move towards a mechanistic approach for predicting future DMS concentrations.

Solventless continuous flow homogeneous hydroformylation of 1-octene

The hydroformylation of 1-octene under continuous flow conditions is described. The system involves dissolving the catalyst, made in situ from [ Rh(acac)(CO)(2)] (acacH = 2,4- pentanedione) and [RMIM][TPPMS] ( RMIM = 1-propyl (Pr), 1-pentyl (Pn) or 1-octyl (O)-3-methyl imidazolium, TPPMS = Ph2P(3-C6H4SO3)), in a mixture of nonanal and 1-octene and passing the substrate, 1-octene, together with CO and H-2 through the system dissolved in supercritical CO2 (scCO(2)). [PrMIM][TPPMS] is poorly soluble in the medium so heavy rhodium leaching (as complexes not containing phosphine) occurs in the early part of the reaction. [PnMIM][ PPMS] affords good rates at relatively low catalyst loadings and relatively low overall pressure (125 bar) with rhodium losses <1 ppm, but the catalyst precipitates at higher catalyst loadings, leading to lower reaction rates. [OMIM][ TPPMS] is the most soluble ligand and promotes high reaction rates, although preliminary experiments suggested that rhodium leaching was high at 5-10 ppm. Optimisation aimed at balancing flows so that the level within the reactor remained constant involved a reactor set up based around a reactor fitted with a sight glass and sparging stirrer with the CO2 being fed by a cooled head HPLC pump, 1-octene by a standard HPLC pump and CO/H-2 through a mass flow controller. The pressure was controlled by a back pressure regulator. Using this set up, [OMIM][ TPPMS] as the ligand and a total pressure of 140 bar, it was possible to control the level within the reactor and obtain a turnover frequency of ca. 180 h(-1). Rhodium losses in the optimised system were 100 ppb. Transport studies showed that 1-octene is preferentially transported over the aldehydes at all pressures, although the difference in mol fraction in the mobile phase was less at lower pressures. Nonanal in the mobile phase suppresses the extraction of 1-octene to some extent, so it is better to operate at high conversion and low pressure to optimise the extraction of the products relative to the substrate. CO and H2 in the mobile phase also suppress the extraction effciency by as much as 80%.

Cobalt(II) Complexes of Nitrile-Functionalized Ionic Liquids

A series of nitrile-functionalized ionic liquids were found to exhibit temperature-dependent miscibility (thermomorphism) with the lower alcohols. Their coordinating abilities toward cobalt(II) ions were investigated through the dissolution process of cobalt(II) bis(trifluoromethylsulfonyl)imide and were found to depend on the donor abilities of the nitrile group. The crystal structures of the cobalt(II) solvates [Co(C1C1CNPyr)2(Tf2N)4] and [Co(C1C2CNPyr)6][Tf2N]8, which were isolated from ionic-liquid solutions, gave an insight into the coordination chemistry of functionalized ionic liquids. Smooth layers of cobalt metal could be obtained by electrodeposition of the cobalt-containing ionic liquids.

Ionic Liquids Containing Boron Cluster Anions

The combination of different boron cluster anions and some of the cations typically found in the composition of ionic liquids has been possible by straightforward metathetic reactions, producing new low melting point salts; the imidazolium cations have been systematically studied, [C(n)mim](+) (when [C(n)mim](+) = 1-alkyl-3-methylimidazolium; n = 2, 4, 6, 8, 10, 12, 14, 16, or 18). Melting points increase in the anionic order [Co(C2B9H11)(2)](-) =-34 degrees C). The salts [C(n)mim](2)[X] ([X](2-) = [B10Cl10](2-) or [B12Cl12](2-), n = 16 or 18) show liquid crystal phases between the solid and liquid states. Tetraalkylphosphonium salts of [B10Cl10](2-) have also been prepared. Physical properties, such as thermal stability, density, or viscosity, have been measured for some selected samples. The presence of the perhalogenated dianion [B12Cl12](2-) in the composition of the imidazolium salts renders highly thermally stable compounds. For example, [C(2)mim](2)[B12Cl12] starts to decompose above 480 degrees C in a dynamic TGA analysis under a dinitrogen atmosphere. Crystal structures of [C(2)mim][Co(C2B9H11)(2)] and [C(2)mim](2)[B12Cl12] have been determined. H-1 NMR spectra of selected imidazolium-boron cluster anion salts have been recorded from solutions as a function of the concentration, showing trends related to the cation-anion interactions.

Theoretical and experimental correlations of gas dissolution, diffusion, and thermodynamic properties in determination of gas permeability and selectivity in supported ionic liquid membranes

Supported ionic liquid membranes (SILMs) has the potential to be a new technological platform for gas/organic vapour separation because of the unique non-volatile nature and discriminating gas dissolution properties of room temperature ionic liquids (ILs). This work starts with an examination of gas dissolution and transport properties in bulk imidazulium cation based ionic liquids [C_nmim][NTf2] (n = 2.4, 6, 8.10) from simple gas H₂, N₂, to polar CO₂, and C₂H₆, leading to a further analysis of how gas dissolution and diffusion are influenced by molecular specific gas-SILMs interactions, reflected by differences in gas dissolution enthalpy and entropy. These effects were elucidated again during gas permeation studies by examining how changes in these properties and molecular specific interactions work together to cause deviations from conventional solution–diffusion theory and their impact on some remarkably contrasting gas perm-selectivity performance. The experimental perm-selectivity for all tested gases showed varied and contrasting deviation from the solution–diffusion, depending on specific gas-IL combinations. It transpires permeation for simpler non-polar gases (H₂, N₂) is diffusion controlled, but strong molecular specific gas-ILs interactions led to a different permeation and selectivity performance for C₂H₆ and CO₂. With exothermic dissolution enthalpy and large order disruptive entropy, C₂H₆ displayed the fastest permeation rate at increased gas phase pressure in spite of its smallest diffusivity among the tested gases. The C₂H₆ gas molecules “peg” on the side alkyl chain on the imidazulium cation at low concentration, and are well dispersed in the ionic liquids phase at high concentration. On the other hand strong CO₂-ILs affinity resulted in a more prolonged “residence time” for the gas molecule, typified by reversed CO₂/N₂ selectivity and slowest CO₂ transport despite CO₂ possess the highest solubility and comparable diffusivity in the ionic liquids. The unique transport and dissolution behaviour of CO₂ are further exploited by examining the residing state of CO₂ molecules in the ionic liquid phase, which leads to a hypothesis of a condensing and holding capacity of ILs towards CO₂, which provide an explanation to slower CO₂ transport through the SILMs. The pressure related exponential increase in permeations rate is also analysed which suggests a typical concentration dependent diffusion rate at high gas concentration under increased gas feed pressure. Finally the strong influence of discriminating and molecular specific gas-ILs interactions on gas perm-selectivity performance points to future specific design of ionic liquids for targeted gas separations.

Use of adhesion counts to help predict symptomatic infection and the ability of fluoroquinolones to penetrate bacterial biofilms on the bladder cells of spinal cord injured patients

There were three objectives to the present study: (1) compare the bladder infection rate and extent of biofilm formation for seven untreated spinal cord injured (SCI) patients and seven given prophylactic co-trimoxazole, (2) identify a level of bacterial adhesion to bladder cells which could be used to help predict symptomatic infection, and (3) determine from in vivo and in vitro studies whether fluoroquinolones were effective at penetrating bacterial biofilms. The results showed that the infection rate had not changed with the introduction of prophylaxis. However, the uropathogenic population had altered subsequent to the introduction of prophylaxis with E. coli being replaced by E. faecalis as the most common cause of infection. In 63% of the specimens from asymptomatic patients, the bacterial counts per cell were <20, while 81% of specimens from patients with at least one sign and one symptom of urinary tract infection (UTI) had > 20 adherent bacteria per bladder cell. Therefore, it is proposed that counts of > 20 bacteria adherent to sediment transitional epithelial bladder cells may be predictive of symptomatic UTI. Clinical data showed that fluoroquinolone therapy reduced the adhesion counts to <20 per cell in 63% of cases, while trimethoprim-sulfamethoxazole only did so in 44%. Further in vitro testing showed that ciprofloxacin (0.1, 0.5 and 1.0 micrograms/ml) partially or completely eradicated adherent biofilms from 92% of spinal cord injured patients' bladder cells, while ofloxacin did so in 71% cases and norfloxacin in 56%. These findings have important implications for the detection and treatment of bacteriuria in spinal cord injured patients.

Adsorption properties of HKUST-1 toward hydrogen and other small molecules monitored by IR

Among microporous systems metal organic frameworks are considered promising materials for molecular adsorption. In this contribution infrared spectroscopy is successfully applied to highlight the positive role played by coordinatively unsaturated Cu2+ ions in HKUST-1, acting as specific interaction sites. A properly activated material, obtained after solvent removal, is characterized by a high fraction of coordinatively unsaturated Cu2+ ions acting as preferential adsorption sites that show specific activities towards some of the most common gaseous species (NO, CO2, CO, N-2 and H-2). From a temperature dependent IR study, it has been estimated that the H-2 adsorption energy is as high as 10 kJ mol(-1). A very complex spectral evolution has been observed upon lowering the temperature. A further peculiarity of this material is the fact that it promotes ortho-para conversion of the adsorbed H-2 species.