Algebraic treatment of the confluent Natanzon potentials

Using the so(2,1) Lie algebra and the Baker, Campbell and Hausdorff formulas, the Green's function for the class of the confluent Natanzon potentials is constructed straightforwardly. The bound-state energy spectrum is then determined. Eventually, the three-dimensional harmonic potential, the three-dimensional Coulomb potential and the Morse potential may all be considered as particular cases.Comment: 9 page

New family of iterative methods with high order of convergence for solving nonlinear systems

In this paper we present and analyze a set of predictor-corrector iterative methods with increasing order of convergence, for solving systems of nonlinear equations. Our aim is to achieve high order of convergence with few Jacobian and/or functional evaluations. On the other hand, by applying the pseudocomposition technique on each proposed scheme we get to increase their order of convergence, obtaining new high-order and efficient methods. We use the classical efficiency index in order to compare the obtained schemes and make some numerical test.This research was supported by Ministerio de Ciencia y Tecnología MTM2011-28636-C02-02 and by FONDOCYT 2011-1-B1-33, República Dominicana.Cordero Barbero, A.; Torregrosa Sánchez, JR.; Penkova Vassileva, M. (2013). New family of iterative methods with high order of convergence for solving nonlinear systems. En Numerical Analysis and Its Applications. Springer Verlag. 222-230. https://doi.org/10.1007/978-3-642-41515-9_23S222230Cordero, A., Hueso, J.L., Martínez, E., Torregrosa, J.R.: A modified Newton-Jarratt’s composition. Numer. Algor. 55, 87–99 (2010)Cordero, A., Hueso, J.L., Martínez, E., Torregrosa, J.R.: Efficient high-order methods based on golden ratio for nonlinear systems. Applied Mathematics and Computation 217(9), 4548–4556 (2011)Cordero, A., Torregrosa, J.R.: Variants of Newton’s Method using fifth-order quadrature formulas. Applied Mathematics and Computation 190, 686–698 (2007)Cordero, A., Torregrosa, J.R.: On interpolation variants of Newton’s method for functions of several variables. Journal of Computational and Applied Mathematics 234, 34–43 (2010)Cordero, A., Torregrosa, J.R., Vassileva, M.P.: Pseudocomposition: a technique to design predictor-corrector methods for systms of nonlinear equtaions. Applied Mathematics and Computation 218(23), 11496–11504 (2012)Nikkhah-Bahrami, M., Oftadeh, R.: An effective iterative method for computing real and complex roots of systems of nonlinear equations. Applied Mathematics and Computation 215, 1813–1820 (2009)Ostrowski, A.M.: Solutions of equations and systems of equations. Academic Press, New York (1966)Shin, B.-C., Darvishi, M.T., Kim, C.-H.: A comparison of the Newton-Krylov method with high order Newton-like methods to solve nonlinear systems. Applied Mathematics and Computation 217, 3190–3198 (2010

Ostrogradski approach for the Regge-Teitelboim type cosmology

We present an alternative geometric inspired derivation of the quantum cosmology arising from a brane universe in the context of {\it geodetic gravity}. We set up the Regge-Teitelboim model to describe our universe, and we recover its original dynamics by thinking of such field theory as a second-order derivative theory. We refer to an Ostrogradski Hamiltonian formalism to prepare the system to its quantization. Our analysis highlights the second-order derivative nature of the RT model and the inherited geometrical aspect of the theory. A canonical transformation brings us to the internal physical geometry of the theory and induces its quantization straightforwardly. By using the Dirac canonical quantization method our approach comprises the management of both first- and second-class constraints where the counting of degrees of freedom follows accordingly. At the quantum level our Wheeler-De Witt Wheeler equation agrees with previous results recently found. On these lines, we also comment upon the compatibility of our approach with the Hamiltonian approach proposed by Davidson and coworkers.Comment: 11 pages, 2 figures, accepted for publication in Phys. Rev.

A Microarray study of Carpet-Shell Clam (Ruditapes decussatus) shows common and organ-specific growth-related gene expression Differences in gills and digestive gland

Growth rate is one of the most important traits from the point of view of individual fitness and commercial production in mollusks, but its molecular and physiological basis is poorly known. We have studied differential gene expression related to differences in growth rate in adult individuals of the commercial marine clam Ruditapes decussatus. Gene expression in the gills and the digestive gland was analyzed in 5 fast-growing and five slow-growing animals by means of an oligonucleotide microarray containing 14,003 probes. A total of 356 differentially expressed genes (DEG) were found. We tested the hypothesis that differential expression might be concentrated at the growth control gene core (GCGC), i. e., the set of genes that underlie the molecular mechanisms of genetic control of tissue and organ growth and body size, as demonstrated in model organisms. The GCGC includes the genes coding for enzymes of the insulin/ insulin-like growth factor signaling pathway (IIS), enzymes of four additional signaling pathways (Raf/ Ras/ Mapk, Jnk, TOR, and Hippo), and transcription factors acting at the end of those pathways. Only two out of 97 GCGC genes present in themicroarray showed differential expression, indicating a very little contribution of GCGC genes to growth-related differential gene expression. Forty eight DEGs were shared by both organs, with gene ontology (GO) annotations corresponding to transcription regulation, RNA splicing, sugar metabolism, protein catabolism, immunity, defense against pathogens, and fatty acid biosynthesis. GO termenrichment tests indicated that genes related to growth regulation, development and morphogenesis, extracellular matrix proteins, and proteolysis were overrepresented in the gills. In the digestive gland overrepresented GO terms referred to gene expression control through chromatin rearrangement, RAS-related small GTPases, glucolysis, and energy metabolism. These analyses suggest a relevant role of, among others, some genes related to the IIS, such as the ParaHox gene Xlox, CCAR and the CCN family of secreted proteins, in the regulation of growth in bivalves.Direccion General de Investigacion Cientifica y Tecnica of the Spanish Government [AGL2010-16743, AGL2013-49144-C3-3-R]; COMPETE Program; Portuguese National Funds [PEst-255 C/MAR/LA0015/2011]; Portuguese FCT [UID/Multi/04326/2013]; Generalitat Valenciana; Ministry of Education, Culture, and Sports of the Spanish Government; Association of European Marine Biology Laboratoriesinfo:eu-repo/semantics/publishedVersio

Strichartz Estimates for the Vibrating Plate Equation

We study the dispersive properties of the linear vibrating plate (LVP) equation. Splitting it into two Schr\"odinger-type equations we show its close relation with the Schr\"odinger equation. Then, the homogeneous Sobolev spaces appear to be the natural setting to show Strichartz-type estimates for the LVP equation. By showing a Kato-Ponce inequality for homogeneous Sobolev spaces we prove the well-posedness of the Cauchy problem for the LVP equation with time-dependent potentials. Finally, we exhibit the sharpness of our results. This is achieved by finding a suitable solution for the stationary homogeneous vibrating plate equation.Comment: 18 pages, 4 figures, some misprints correcte

Low-temperature phase transformations of PZT in the morphotropic phase-boundary region

We present anelastic and dielectric spectroscopy measurements of PbZr(1-x)Ti(x)O(3) with 0.455 < x < 0.53, which provide new information on the low temperature phase transitions. The tetragonal-to-monoclinic transformation is first-order for x < 0.48 and causes a softening of the polycrystal Young's modulus whose amplitude may exceed the one at the cubic-to-tetragonal transformation; this is explainable in terms of linear coupling between shear strain components and tilting angle of polarization in the monoclinic phase. The transition involving rotations of the octahedra below 200 K is visible both in the dielectric and anelastic losses, and it extends within the tetragonal phase, as predicted by recent first-principle calculations.Comment: 4 pages, 4 figure