The nonlinear pendulum always oscillates

It is shown that the nonlinear pendulum equation can be transformed into a linear harmonic oscillator in the phase space thanks to Kerner's method [12]. Moreover, as a mathematical divertissement, ..

LAGRANGIANS FOR EQUATIONS OF PAINLEVÉ TYPE BY MEANS OF THE JACOBI LAST MULTIPLIER

We apply the method of Jacobi Last Multiplier to the fifty second-order ordinary differential equations of Painleve type as given in Ince in order to obtain a Lagrangian and consequently solve the inverse problem of Calculus of Variations for those equations. The easiness and straightforwardness of Jacobi's method is underlined

Nonclassical Symmetries for a Class of Reaction-Diffusion Equations: the Method of Heir-Equations

The nonclassical symmetries method is applied to a class of reaction-diffusion equations with nonlinear source, i.e. u t =u xx +cu x +R(u, x). Several cases are obtained by using suitable solutions of the heir-equations as described in [M.C. Nucci, Nonclassical symmetries as special solutions of heir-equations, J. Math. Anal. Appl. 279 (2003) 168–179]

Singularity and symmetry analyses of mathematical models of epidemics

We present a summary of the methods of Lie symmetry and Painlevé singularity analyses and apply them to a number of well-known epidemiological models to demonstrate the utility of these analyses in the analysis of dynamical systems which arise during investigations of the evolution of diseases

MHD as a driver for Mixing in AGB Stars

We present analytical exact 2D and 3DMHD computations for the layers of an AGB star known to be affected by deep mixing phenomena, in order to verify previous suggestions that magnetic buoyancy may provide a sound explaination for the isotopic changes observed in AGB stars and in presolar grains. The structure of the relevant layers is similar to a polytrope of index 3 (a bubble of radiation), containing little mass. Due to this, the material is close to be unstable for expansion. Addition of any extra engine under the form of a magnetic dynamo generating toroidal structures unstable for buoyancy yields plasma phenomena that closely resemble those of the solar wind, in which almost ideal, non-resistive MHD allows for an easy analytical integration of the model equations. The results show that a further expansion occurs for magnetized domains (flux tubes). These last form close to thermonuclear shells and transport outward nucleosynthesis products with a velocity v ∼ r2, faster than for diffusion but slower than for convection, adequate to give a physical interpretation to extra-mixing processes in evolved stars. XIII Nuclei in the Cosmos 7-11 July, 2014 Debrecen, Hungar

Novel CaLB-like Lipase Found Using ProspectBIO, a Software for Genome-Based Bioprospection

Enzymes have been highly demanded in diverse applications such as in the food, pharmaceutical, and industrial fuel sectors. Thus, in silico bioprospecting emerges as an efficient strategy for discovering new enzyme candidates. A new program called ProspectBIO was developed for this purpose as it can find non-annotated sequences by searching for homologs of a model enzyme directly in genomes. Here we describe the ProspectBIO software methodology and the experimental validation by prospecting for novel lipases by sequence homology to Candida antarctica lipase B (CaLB) and conserved motifs. As expected, we observed that the new bioprospecting software could find more sequences (1672) than a conventional similarity-based search in a protein database (733). Additionally, the absence of patent protection was introduced as a criterion resulting in the final selection of a putative lipase-encoding gene from Ustilago hordei (UhL). Expression of UhL in Pichia pastoris resulted in the production of an enzyme with activity towards a tributyrin substrate. The recombinant enzyme activity levels were 4-fold improved when lowering the temperature and increasing methanol concentrations during the induction phase in shake-flask cultures. Protein sequence alignment and structural modeling showed that the recombinant enzyme has high similarity and capability of adjustment to the structure of CaLB. However, amino acid substitutions identified in the active pocket entrance may be responsible for the differences in the substrate specificities of the two enzymes. Thus, the ProspectBIO software allowed the finding of a new promising lipase for biotechnological application without the need for laborious and expensive conventional bioprospecting experimental steps

Morphometric and genetic characterization as tools for selection of Apis mellifera (Hymenoptera: Apidae) stocks in an area of natural hybridization in Argentina

Beekeepers around the world select bees’ characteristics that facilitate and favor production. In regions where hybridization among lineages is taking place, this selection is a challenge, given that these regions are “natural laboratories”, where the action of evolutionary processes of a population or species occurs in real time. A natural honeybee (Apis mellifera) hybrid zone exists in Argentina between 28° and 35° South, where Africanized (AHB) and European (EHB) populations converge. In this zone, beekeepers use selected genetic resources of European origin mostly, since the local Africanized bees show a higher defensive behavior, which is not desirable for management. Although EHB colonies have many advantages for honey production, they are not fully adapted to the subtropical climate and are susceptible to certain parasitosis such as varroosis. In addition, both AHB and EHB mate in drone congregation areas (DCAs), where males and virgin queens fly to meet, resulting in variability in the desired characteristics. In this study, we explored the degree of hybridization within a DCA and its reference apiary, located in the province of Entre Ríos, by applying two complementary techniques. First, morphotypes with different degrees of hybridization between European and African subspecies were observed in the reference apiary, indicating a high sensitivity of this morphometric approach to detect hybridization in these populations. Second, a genetic analysis revealed haplotypes of both origins for drones in DCAs, with a higher prevalence of European haplotypes, while all the colonies from the reference apiary exhibited European haplotypes. Overall, our results are in line with the strong impact that commercial beekeeping has on the genetics of DCAs. We show how wing morphometry may be used to monitor hybridization between European and African subspecies, a tool that may be evaluated in other regions of the world where hybridization occurs.Instituto de GenéticaFil: Litvinoff, Leonardo. Reinas del Litoral SRL; ArgentinaFil: Menescardi, Francisco. Reinas del Litoral SRL; ArgentinaFil: Porrini, Leonardo. Instituto de Investigaciones en Producción, Sanidad y Ambiente (CONICET-UNSAM). Centro de Investigación en Abejas Sociales; ArgentinaFil: Porrini, Leonardo. Consejo Nacional de Investigaciones Científicas y Técnicas; ArgentinaFil: Russo, Romina Maria. Instituto Nacional de Tecnología Agropecuaria (INTA). Instituto de Genética; ArgentinaFil: Russo, Romina Maria. Instituto Nacional de Tecnología Agropecuaria (INTA). Instituto de Agrobiotecnología y Biología Molecular; ArgentinaFil: Russo, Romina Maria. Consejo Nacional de Investigaciones Científicas y Técnicas; ArgentinaFil: Liendo, María Clara. Instituto Nacional de Tecnología Agropecuaria (INTA). Instituto de Genética; ArgentinaFil: Liendo, María Clara. Instituto Nacional de Tecnología Agropecuaria (INTA). Instituto de Agrobiotecnología y Biología Molecular; ArgentinaFil: Liendo, María Clara. Consejo Nacional de Investigaciones Científicas y Técnicas; ArgentinaFil: Nucci, Alejandro. Instituto de Investigaciones en Producción, Sanidad y Ambiente (CONICET-UNSAM). Centro de Investigación en Abejas Sociales; ArgentinaFil: Nucci, Alejandro. Consejo Nacional de Investigaciones Científicas y Técnicas; ArgentinaFil: Lusarreta, Esteban. Instituto de Investigaciones en Producción, Sanidad y Ambiente (CONICET-UNSAM). Centro de Investigación en Abejas Sociales; ArgentinaFil: Lusarreta, Esteban. Consejo Nacional de Investigaciones Científicas y Técnicas; ArgentinaFil: Ventura, Rocio. Instituto de Investigaciones en Producción, Sanidad y Ambiente (CONICET-UNSAM). Centro de Investigación en Abejas Sociales; ArgentinaFil: Ventura, Rocio. Consejo Nacional de Investigaciones Científicas y Técnicas; ArgentinaFil: Espasadin, Luna. Fundación Miguel Lillo. Instituto de Entomología; ArgentinaFil: Monmany-Garzia, A. Carolina. Universidad Nacional de Tucumán. Instituto de Ecología Regional; ArgentinaFil: Monmany-Garzia, A. Carolina. Consejo Nacional de Investigaciones Científicas y Técnicas; ArgentinaFil: Scannapieco, Alejandra Carla. Instituto Nacional de Tecnología Agropecuaria (INTA). Instituto de Genética; ArgentinaFil: Scannapieco, Alejandra Carla. Instituto Nacional de Tecnología Agropecuaria (INTA). Instituto de Agrobiotecnología y Biología Molecular; ArgentinaFil: Scannapieco, Alejandra Carla. Consejo Nacional de Investigaciones Científicas y Técnicas; ArgentinaFil: Galindo Cardona, Alberto. Fundación Miguel Lillo. Instituto de Entomología; ArgentinaFil: Galindo Cardona, Alberto. Consejo Nacional de Investigaciones Científicas y Técnicas; Argentin

Using Lie symmetries in epidemiology

Lie symmetry method has been and still is successfully applied in different problems of physics for about a hundred years, but its application in epidemiology has been rare perhaps because the ordinary differential equations studied in this field are generally of first-order in contrast with those in physics which are usually of second-order. Here we exemplify the use of Lie symmetry method in the study of mathematical models in epidemiology, and show how it complements the mathematical techniques (qualitative and numerical analysis) traditionally used

Iterations of the nonclassical symmetries and conditional Lie-Bäcklund symmetries

Iterations of the non-classical symmetries method give rise to new nonlinear equations, which inherit the Lie point symmetry algebra of the original equation. Invariant solutions of these heir equations supply new solutions of the original equation. We show that particular cases of such invariant solutions correspond to Zhdanov's conditional Lie-Backlund symmetries