Asymptotic Expansions of Jacobi Polynomials for Large Values of Beta

Asymptotic approximations of Jacobi polynomials are given for large values of the Beta-parameter and of their zeros. The expansions are given in terms of Laguerre polynomials and of their zeros. The levels of accuracy of the approximations are verified by numerical examples.This work was supported by Ministerio de Econom a y Competitividad, project MTM2015-67142-P (MINECO/FEDER, UE). NMT thanks CWI, Amsterdam, for scienti c support

Fast, reliable and unrestricted iterative computation of Gauss-Hermite and Gauss-Laguerre quadratures

Methods for the computation of classical Gaussian quadrature rules are described which are effective both for small and large degree. These methods are reliable because the iterative computation of the nodes has guaranteed convergence, and they are fast due to their fourth-order convergence and its asymptotic exactness for an appropriate selection of the variables. For Gauss?Hermite and Gauss?Laguerre quadratures, local Taylor series can be used for computing efficiently the orthogonal polynomials involved, with exact initial values for the Hermite case and first values computed with a continued fraction for the Laguerre case. The resulting algorithms have almost unrestricted validity with respect to the parameters. Full relative precision is reached for the Hermite nodes, without any accuracy loss and for any degree, and a mild accuracy loss occurs for the Hermite and Laguerre weights as well as for the Laguerre nodes. These fast methods are exclusively based on convergent processes, which, together with the high order of convergence of the underlying iterative method, makes them particularly useful for high accuracy computations. We show examples of very high accuracy computations (of up to 1000 digits of accuracy)

On the computation and inversion of the cumulative noncentral beta distribution function

The computation and inversion of the noncentral beta distribution Bp,q(x, y) (or the noncentral F-distribution, a particular case of Bp,q(x, y)) play an important role in different applications. In this paper we study the stability of recursions satisfied by Bp,q(x, y) and its complementary function and describe asymptotic expansions useful for computing the function when the parameters are large. We also consider the inversion problem of finding x or y when a value of Bp,q(x, y) is given. We provide approximations to x and y which can be used as starting values of methods for solving nonlinear equations (such as Newton) if higher accuracy is needed

Asymptotic inversion of the binomial and negative binomial cumulative distribution functions

ABSTRACT: The computation and inversion of the binomial and negative binomial cumulative distribution functions play a key role in many applications. In this paper, we explain how methods used for the central beta distribution function (described in Gil, Segura, and Temme, [Numer. Algorithms, 74 (2017), pp. 77?91]) can be utilized to obtain asymptotic representations of these functions and also for their inversion. The performance of the asymptotic inversion methods is illustrated with numerical examples.Acknowledgments. The authors thank the anonymous referees for their constructive comments and suggestions. This work was supported by Ministerio de Ciencia e Innovación, Spain, projects MTM2015-67142-P (MINECO/FEDER, UE) and PGC2018-098279-B-I00 (MCIU/AEI/FEDER, UE). NMT thanks CWI, Amsterdam, for scientific support

NUEVOS REGISTROS DE COPÉPODOS PARÁSITOS (COPEPODA: PANDARIDAE, EUDACTYLINIDAE, CALIGIDAE) EN CINCO ESPECIES DE TIBURONES (PISCES: ELASMOBRANCHIA) EN EL GOLFO DE MÉXICO

El presente estudio es parte de una investigación en curso de los copépodos parásitos de peces de las aguas costeras en el Estado de Campeche (sur del Golfo de México). El objetivo de este trabajo fue describir las especies de copépodos parásitos que se encontraron en cinco especies de tiburones: Carcharhinus leucas (Müller & Henle, 1839), Carcharhinus limbatus (Müller & Henle, 1839), Carcharhinus plumbeus (Nardo, 1827), Rhizoprionodon terraenovae (Richardson, 1836), y Sphyrna tiburo (Linnaeus, 1758). Aexcepción de R. terraenovae, todas las especies de tiburones estuvieron infectados al menos con una especie de copépodo. Un total de ocho especies de copépodos fueron encontrados: Nesippus orientalis Heller, 1865, Nemesis sp. y Paralebion elongatusWilson C.B., 1911 en C. leucas (n = 6); Tuxophorus caligodesWilson C.B., 1908, Lepeophtheirus longispinosus Wilson C.B., 1908 y Pandarus sinuatus Say, 1818 en C. limbatus (n = 9); Pandarus sp. en C. plumbeus (n = 4); y Eudactylina longispina Bere, 1936 en S. tiburo (n = 24). La ocurrencia de estas especies de copépodos en estos tiburones del Golfo de México constituye nuevos registros de hospedero y extienden su distribución geográfica conocida, y contribuye al conocimiento de la biodiversidad de los copépodos parásitos en México

NUEVOS REGISTROS DE COPÉPODOS PARÁSITOS (CALIGIDAE: SIPHONOSTOMATOIDA) EN LA RAYA MANCHADA, AETOBATUS NARINARI (ELASMOBRANCHII: MYLIOBATIDAE) DEL GOLFO DE MEXICO

El objetivo de este estudio, fue investigar la ocurrencia de copépodos parásitos (Caligidae: Siphonostomatoida) en la raya pinta Aetobatus narinari considerada una especie amenazada mundialmente. En el sur de México, la raya manchada representa una fuente tradicional de alimento, alcanzando el valor económico más alto con respecto a otros elasmobranquios. Durante un reciente estudio de parásitos de peces de tres localidades del estado de Campeche (sur del Golfo de México), ocho individuos de A. narinari capturados por pescadores locales fueron examinados por ectoparásitos y cinco especies diferentes de copépodos fueron registrados en la piel de este pez: Alebion sp. Krøyer, 1863; Caligus dasyaticus Rangnekar, 1957; Caligus haemulonis Krøyer, 1863; Euryphorus sp., Milne Edwards H., 1840; Lepeophtheirus acutus Heegaard, 1943 and Lepeophtheirus marginatus Bere, 1936. Este trabajo es el primero en documentar; i) un copépodo parásito (piojo de mar) registrado para la raya pinta A. narinari como especie de importancia comercial, ii) un nuevo hospedero para el género Euryphorus que no había sido reportado previamente para México y iii) C. dasyaticus representa una nueva registro geográfico en el Sur del Golfo de México. El presente estudio registra un nuevo hospedero y registro geográfico para seis especies de copépodos parásitos en el Estado de Campeche, México y contribuye al conocimiento de la biodiversidad de los copépodos parásitos en México. No hay duda de que el número de registros de especies de este grupo de parásitos se incrementará con nuevos estudios

Bionate biocompatibility: in vivo study in rabbits

Response to foreign materials includes local tissue reaction, osteolysis, implant loosening, and migration to lymph nodes and organs. Bionate 80A human explants show minor wear and slight local tissue reaction, but we do not know the response at the spinal cord, nerve roots, lymph nodes, or distant organs. This study aims to figure out reactions against Bionate 80A when implanted at the spinal epidural space of 24 20-week-old New Zealand white rabbits. In one group of 12 rabbits, we implanted Bionate 80A on the spinal epidural space, and another group of 12 rabbits was used as the control group. We studied tissues, organs, and tissue damage markers on blood biochemistry, urine tests, and necropsy. The animals' clinical parameters and weight showed no statistically significant differences. At 3 months, the basophils increased slightly in the implant group, platelets decreased in all, and at 6 months, implanted animals showed slight eosinophilia, but none of these changes was statistically significant. External, organ, and spinal tissue examination showed neither toxic reaction, inflammatory changes, or noticeable differences between groups or survival periods. Under microscopic examination, the Bionate 80A particles induced a chronic granulomatous response always outside the dura mater, with giant multinucleated cells holding phagocytized particles and no particle migration to lymph nodes or organs. Thus, it was concluded that Bionate particles, when implanted in the rabbit lumbar epidural space, do not generate a significant reaction limited to the surrounding soft tissues with giant multinucleated cells. In addition, the particles did not cross the dura mater or migrate to lymph nodes or organs

Observation of magnetic order in the double-layer system La2MCu2O6+δ (M=Ca,Sr)

Under the terms of the Creative Commons Attribution License 3.0 (CC-BY).-- et al.Measurements of the spin rotation and depolarization of implanted positive muons have revealed that La2SrCu2O6+δ, La2CaCu2O6+δ, and La1.9Y0.1CaCu2O6+δ, members of the double-layer perovskite family La2MCu2O6+δ (M=Ca,Sr), display magnetic ordering similar to that of La2−xSrxCuO4−y and YBa2Cu3Ox Their magnetic order parameters are remarkably close to those of the other layered cuprates. A superconducting minority phase has been detected in La2CaCu2O6+δ (δ≥0.02), with onset at ∼45 K and accompanied by a change in the muon-spin-precession signals from the majority antiferromagnetic phase, phenomena absent in La2SrCu2O6+δ. This behavior was attributed to mobility and local clustering of intercalated oxygen excess in the layer between the CuO2 planes.This work was supported by NSERC (Canada), DOE Grant No. DE-FG05-88ER45353, the CICYT and the MIDAS project (Spain), and the CEE.Peer Reviewe

Barbed Dental Ti6Al4V Alloy Screw : Design and Bench Testing

Background context. Dental implants are designed to replace a missing tooth. Implant stability is vital to achieving osseointegration and successful implantation. Although there are many implants available on the market, there is room for improvement. Purpose. We describe a new dental implant with improved primary stability features. Study design. Lab bench test studies. Methods. We evaluated the new implant using static and flexion-compression fatigue tests with compression loads, 35 Ncm tightening torque, displacement control, 0.01 mm/s actuator movement speed, and 9-10 Hz load application frequency, obtaining a cyclic load diagram. We applied variable cyclic loadings of predetermined amplitude and recorded the number of cycles until failure. The test ended with implant failure (breakage or permanent deformation) or reaching five million cycles for each load. Results. Mean stiffness was 1151.13 ± 133.62 SD N/mm, mean elastic limit force 463.94 ± 75.03 SD N, and displacement 0.52 ± 0.04 SD mm, at failure force 663.21 ± 54.23 SD N and displacement 1.56 ± 0.18 SD mm, fatigue load limit 132.6 ± 10.4 N, and maximum bending moment 729.3 ± 69.43 mm/N. Conclusions. The implant fatigue limit is satisfactory for incisor and canine teeth and between the values for premolars and molars for healthy patients. The system exceeds five million cycles when subjected to a 132.60 N load, ensuring long-lasting life against loads below the fatigue limit

Bionate Lumbar Disc Nucleus Prosthesis : Biomechanical Studies in Cadaveric Human Spines

Design: cadaveric spine nucleus replacement study. Objective: determining Bionate 80A nucleus replacement biomechanics in cadaveric spines. Methods: in cold preserved spines, with ligaments and discs intact, and no muscles, L3-L4, L4-L5, and L5-S1 nucleus implantation was done. Differences between customized and overdimensioned implants were compared. Flexion, extension, lateral bending, and torsion were measured in the intact spine, nucleotomy, and nucleus implantation specimens. Increasing load or bending moment was applied four times at 2, 4, 6, and 8 Nm, twice in increasing mode and twice in decreasing mode. Spine motion was recorded using stereophotogrammetry. Expulsion tests: cyclic compression of 50-550 N for 50,000 cycles, increasing the load until there was extreme flexion, implant extrusion, or anatomical structure collapse. Subsidence tests were done by increasing the compression to 6000 N load. Results: nucleotomy increased the disc mobility, which remained unchanged for the adjacent upper level but increased for the lower adjacent one, particularly in lateral bending and torsion. Nucleus implantation, compared to nucleotomy, reduced disc mobility except in flexion-extension and torsion, but intact mobility was no longer recovered, with no effect on upper or lower adjacent segments. The overdimensioned implant, compared to the customized implant, provided equal or sometimes higher mobility. Lamina, facet joint, and annulus removal during nucleotomy caused more damaged than that restored by nucleus implantation. No implant extrusion was observed under compression loads of 925-1068 N as anatomical structures collapsed before. No subsidence or vertebral body fractures were observed under compression loads of 6697.8-6812.3 N. Conclusions: nucleotomized disc and L1-S1 mobility increased moderately after cadaveric spine nucleus implantation compared to the intact status, partly due to operative anatomical damage. Our implant had shallow expulsion and subsidence risks