Constant Mean Curvature Spacelike Surfaces in Three-Dimensional Generalized Robertson–Walker Spacetimes

Several uniqueness and non-existence results on complete constant mean curvature spacelike surfaces lying between two slices in certain three-dimensional generalized Robertson–Walker spacetimes are given. They are obtained from a local integral estimation of the squared length of the gradient of a distinguished smooth function on a constant mean curvature spacelike surface, under a suitable curvature condition on the ambient spacetime. As a consequence, all the entire bounded solutions to certain family of constant mean curvature spacelike surface differential equations are found.     

Integrable Hénon-Heiles Hamiltonians: A Poisson algebra approach

The three integrable two-dimensional Hénon-Heiles systems and their integrable perturbations are revisited. A family of new integrable perturbations is found, and N-dimensional completely integrable generalizations of all these systems are constructed by making use of sl(2,R)⊕h₃ as their underlying Poisson symmetry algebra. In general, the procedure here introduced can be applied in order to obtain N-dimensional integrable generalizations of any 2D integrable potential of the form , and the formalism gives the explicit form of all the integrals of the motion. Further applications of this algebraic approach in different contexts are suggested.     

Biological significance of polymorphism in legume protease inhibitors from the Bowman-Birk family

Naturally occurring protease inhibitors (PI) of the Bowman-Birk type constitute a major PI family in cereal and legume seeds. The family name is derived from the names of the two investigators who characterised the first inhibitor of this type, the Bowman-Birk inhibitor from soybean (BBI). These proteins have the capacity to inhibit one or more of a range of serine proteases, including the digestive enzymes trypsin and chymotrypsin. PI from this family interact with the active sites of serine proteases in a 'canonical', i.e. substrate-like, manner via exposed reactive site loops of conserved conformation within the inhibitor. Multiple BBI variants can be found within and among species. A limited number of amino acids located within the inhibitory domain is responsible for the primary functional and biological activities of BBI-like proteins. However, sequence variation in binding loops, post-translational modifications at the amino- and carboxy-terminal ends, as well as differences in the multimeric nature of the inhibitors may act in combination to influence the functional properties and the physiological role of BBI-like proteins. Recently, BBI and proteins homologous to BBI (BBI-like proteins) have emerged as highly promising cancer chemopreventive agents. BBI has been shown to be capable of preventing or suppressing carcinogenic processes in a wide variety of in vitro and in vivo animal model systems. The potential exploitation of BBI-like proteins in human health-promotion programmes will depend on elucidating in detail the molecular basis for the variation in biological activities among the many variant forms. New knowledge, derived both from the use of synthetic cyclic peptides that mimic the inhibitory loops of BBI-like proteins, and from genomic data pertaining to the structure of BBI gene classes, together facilitate the manipulation, screening and selection of appropriate variants through biotechnology.     

Development and validation of an integrated computational approach for the modeling of cw-ESR spectra of free radicals in solution: p-(methylthio)phenyl nitronylnitroxide in toluene as a case study

In this work we address the interpretation, via an ab initio integrated computational approach, of continuous wave electron spin resonance (cw-ESR) spectra of p-(methylthio)phenyl nitronylnitroxide (MTPNN) dissolved in toluene. Our approach is based on the determination of the spin Hamiltonian, averaged with respect to fast vibrational motions, with magnetic tensor parameters (Zeeman and hyperfine tensors) characterized by quantum mechanical density functional calculations. The system is then described by a stochastic Liouville equation, with inclusion of diffusive rotational dynamics. Parametrization of diffusion rotational tensor is provided by a hydrodynamic model. Cw-ESR spectra of MTPNN are simulated for a wide range of temperatures (155-292 K) with minimal resorting to fitting procedures, proving that the combination of sensitive ESR spectroscopy and sophisticated modeling can be highly helpful in providing structural and dynamic information on molecular systems.     

Researching how professional mathematicians construct new mathematical definitions: a case study

In this work, we study the mathematical practice of defining by mathematics researchers. Since research is an important part of many professional mathematicians, understanding how they do research is a necessary step before thinking about future researchers’ undergraduate and postgraduate education. We focus on the defining process associated with the generalization of existing definitions as a way of constructing new ones. Data of this qualitative study come from a case study whose subject is a mathematics researcher in the area of differential geometry. We have interviewed this researcher and collected her research documents. From our analysis of the data, we have identified four phases in the defining process (Finding an opportunity to generalize an existing concept, Proposing a new definition, Justifying that the new definition is valid and Continuing the chain of definitions), which we will describe in detail in Section 4.     

Global bifurcation of solutions of the mean curvature spacelike equation in certain Friedmann–Lemaître–Robertson–Walker spacetimes

We study the existence of spacelike graphs for the prescribed mean curvature equation in the Friedmann–Lemaître–Robertson–Walker (FLRW) spacetime. By using a conformal change of variable, this problem is translated into an equivalent problem in the Lorentz–Minkowski spacetime. Then, by using Rabinowitz's global bifurcation method, we obtain the existence and multiplicity of positive solutions for this equation with 0-Dirichlet boundary condition on a ball. Moreover, the global structure of the positive solution set is studied.     

Lie algebroid structures on double vector bundles and representation theory of Lie algebroids

A VB-algebroid is essentially defined as a Lie algebroid object in the category of vector bundles. There is a one-to-one correspondence between VB-algebroids and certain flat Lie algebroid superconnections, up to a natural notion of equivalence. In this setting, we are able to construct characteristic classes, which in special cases reproduce characteristic classes constructed by Crainic and Fernandes. We give a complete classification of regular VB-algebroids, and in the process we obtain another characteristic class of Lie algebroids that does not appear in the ordinary representation theory of Lie algebroids.     

Modeling the synergy level in a vertical collaborative supply chain through the IMP interaction model and DEA framework

This work develops a mathematical programming model that characterizes the main variables present in the interaction dynamics of each agent in a collaborative vertical logistical system, such as a supply chain, and measures the synergy level of such system. The model is based on the interaction model developed by the IMP (Industrial Marketing and Purchasing) group and also on the DEA (Data Envelopment Analysis) framework. The basics of these two approaches allow modeling of the characteristics of an agent as well as the collaborative relationships with other agents within the chain. The model was validated using information of supply chain of leather and its products, classified by DANE (Departamento Nacional de Estadistica—Colombia) as the sector CIIU323.     

Distribution of <Superscript>137</Superscript>Cs, <Superscript>40</Superscript>K, <Superscript>232</Superscript>Th and <Superscript>238</Superscript>U in coastal marine sediments of Margarita Island,Venezuela

This work presents the results of ¹³⁷Cs, ⁴⁰K, ²³²Th and ²³⁸U concentration (Bq kg⁻¹) values in coastal marine sediments collected from 38 sites along the coastline of the island of Margarita, Venezuela. The purpose was to determine baseline values for these radionuclides in surface marine sediments and to detect if there were any anomalously high concentration values. Only three of the 38 sediments analyzed had measurable values above the detection limit of 0.9 Bq kg⁻¹ for ¹³⁷Cs and the highest only being 1.4 Bq kg⁻¹. While, the concentration (Bq kg⁻¹) ranges for the primordial radionuclides, ⁴⁰K, ²³²Th and ²³⁸U were as follows: 12.2–211.7, <1.5–9.8 and <4.4–20.7, respectively. These concentration ranges for the primordial radionuclides can be considered as baseline values for surface marine sediments for areas that are considered not polluted by man or contaminated by nature. Finally, the concentration range of ¹³⁷Cs can also be employed as baseline values, which only seem to have been the result of the atmospheric testing of nuclear weapons in the past.     

Study of elution behaviour with gradient voltage in CEC using methacrylate monolithic columns

A theoretical study on the retention behaviour and chromatographic performance of neutral solutes using a lauryl methacrylate‐based monolithic column under voltage gradient mode in CEC was carried out. Through a flexible mathematical function based on a modified Gaussian model, the peak shape of compounds was firstly fitted under constant and gradient voltage. Using the peak shape parameters and retention time, the estimation of global chromatographic performance, efficiency and peak capacity under several voltage conditions was performed. The influence of voltage gradient on the separation efficiency is discussed and simple equations are presented to calculate retention and peak widths under voltage gradient conditions. A comparison in terms of chromatographic performance of a test mixture of neutral solutes under constant and gradient voltage modes was also carried out. The experiments carried out under gradient voltage showed better efficiencies (172 000 plates/m) and lower peak widths than those obtained under constant voltage (52 000 plates/m).