Note on Radius Problems for Certain Class of Analytic Functions

MSC 2010: 30C45

Growth Theorem and the Radius of Starlikeness of Close-to-Spirallike Functions

AMS Subj. Classification: 30C45

Charge compensation and Ce3+ formation in trivalent doping of the CeO2(110) surface: The key role of dopant ionic radius

In this paper, we use density functional theory corrected for on-site Coulomb interactions (DFT + U) and hybrid DFT (HSE06 functional) to study the defects formed when the ceria (110) surface is doped with a series of trivalent dopants, namely, Al3+, Sc3+, Y3+, and In 3+. Using the hybrid DFT HSE06 exchange-correlation functional as a benchmark, we show that doping the (110) surface with a single trivalent ion leads to formation of a localized MCe / + O O • (M = the 3+ dopant), O- hole state, confirming the description found with DFT + U. We use DFT + U to investigate the energetics of dopant compensation through formation of the 2MCe ′ +VO ̈ defect, that is, compensation of two dopants with an oxygen vacancy. In conjunction with earlier work on La-doped CeO2, we find that the stability of the compensating anion vacancy depends on the dopant ionic radius. For Al3+, which has the smallest ionic radius, and Sc3+ and In3+, with intermediate ionic radii, formation of a compensating oxygen vacancy is stable. On the other hand, the Y3+ dopant, with an ionic radius close to that of Ce4+, shows a positive anion vacancy formation energy, as does La3+, which is larger than Ce4+ (J. Phys.: Condens. Matter 2010, 20, 135004). When considering the resulting electronic structure, in Al3+ doping, oxygen hole compensation is found. However, Sc 3+, In3+, and Y3+ show the formation of a reduced Ce3+ cation and an uncompensated oxygen hole, similar to La3+. These results suggest that the ionic radius of trivalent dopants strongly influences the final defect formed when doping ceria with 3+ cations. In light of these findings, experimental investigations of these systems will be welcome.

One-dimensional Model for Fluids of Third-grade in Tubes with Constant Radius

Our goal in this paper is to extend previous results obtained for Newtonian and secondgrade fluids to third-grade fluids in the case of an axisymmetric, straight, rigid and impermeable tube with constant cross-section using a one-dimensional hierarchical model based on the Cosserat theory related to fluid dynamics. In this way we can reduce the full threedimensional system of equations for the axisymmetric unsteady motion of a non-Newtonian incompressible third-grade fluid to a system of equations depending on time and on a single spatial variable. Some numerical simulations for the volume flow rate and the the wall shear stress are presented.

Submesoscale features in regions with different baroclinic deformation radius

In questo studio, un modello nidificato "child" ad alta risoluzione (risoluzione 1/48°) è ottenuto attraverso la piattaforma SURF. Il modello "child" è ottenuto tramite "downscaling" dei campi medi giornalieri dal modello globale "parent" (1/12°). Questo permette di osservare le caratteristiche della sottomesoscala in due regioni dell'oceano Atlantico settentrionale, Azzorre e Bermuda, dal 4 al 12 gennaio 2021. Questa tesi si propone di condurre un'analisi preliminare della relazione fra il raggio di deformazione baroclino e l'esordio dell'attività di sottomesoscala, nelle regioni di interesse. A questo scopo, vengono effettuati molti confronti fra i campi risultanti dal "parent" e dal "child". In particolare, ci concentriamo sulla Mixed-Layer Instability (MLI) studiata attraverso variabili come la Mixed-Layer Depth (MLD), la vorticità relativa, le velocità orizzontali e verticali, l'energia cinetica e la frequenza di Brunt-Vaisala. Dai risultati, mentre il modello "parent" sembra inadeguato, quello "child" è in grado di rilevare la MLI e la presenza di filamenti e scie topografiche in entrambe le regioni, riproducendo meglio le correnti orizzontali e verticali alla sottomesoscala. Ciò fornisce una connessione tra mesoscala e sottomesoscala: mentre nelle Azzorre la MLI sembra svolgere un ruolo chiave nella ristratificazione della colonna d'acqua, lo stesso non sembra nelle Bermuda dove i vortici di mesoscala sono più ampi, influendo maggiormente sulla stratificazione verticale. Qui, i processi di ristratificazione sembrerebbero correlati alle mesoscale piuttosto che alle sottomesoscale. La MLI giocherebbe comunque un ruolo nella generazione di correnti alla sottomesoscala, insieme ad altri processi come la frontogenesi e le scie topografiche. In conclusione, il valore del raggio di deformazione baroclino non sembra influenzare l'attivazione dei processi di sottomesoscala, mentre sembrerebbe determinare l'importanza della MLI nel processo di ristratificazione.

The Basic Reproduction Number Obtained From Jacobian And Next Generation Matrices - A Case Study Of Dengue Transmission Modelling.

The basic reproduction number is a key parameter in mathematical modelling of transmissible diseases. From the stability analysis of the disease free equilibrium, by applying Routh-Hurwitz criteria, a threshold is obtained, which is called the basic reproduction number. However, the application of spectral radius theory on the next generation matrix provides a different expression for the basic reproduction number, that is, the square root of the previously found formula. If the spectral radius of the next generation matrix is defined as the geometric mean of partial reproduction numbers, however the product of these partial numbers is the basic reproduction number, then both methods provide the same expression. In order to show this statement, dengue transmission modelling incorporating or not the transovarian transmission is considered as a case study. Also tuberculosis transmission and sexually transmitted infection modellings are taken as further examples.

Aplicação de indentação instrumentada na caracterização mecânica de poliuretana derivada de óleo de mamona

Neste trabalho são investigadas as propriedades mecânicas de poliuretana derivada do óleo de mamona, utilizando a técnica de indentação instrumentada com penetradores de geometrias piramidal e esférica. Foi analisada a influência da forma do penetrador utilizado nos ensaios de indentação instrumentada para se obter valores das propriedades mecânicas de polímero derivado de óleo de mamona. Os penetradores utilizados são de pontas piramidais dos tipos Berkovich e canto de cubo e esférico de raio igual a 150 μm em um Nanoindenter XP TM com cargas aplicadas entre 1 e 200 mN. As penetrações variam de acordo com o formato do penetrador, sendo maiores para pontas agudas. A dureza e o módulo de elasticidade foram determinados, utilizando o método de Oliver e Pharr. Verificou-se que os valores medidos para a dureza são maiores para penetradores mais agudos. Os valores obtidos com a ponta piramidal Berkovich foram de 0,14 GPa para pequenas penetrações e 0,12 GPa para maiores penetrações. Já os valores obtidos com ponta canto de cubo foram 25 a 30% maiores. Isso está relacionado com os volumes das regiões que apresentam deformações plásticas elevadas, no caso de penetradores agudos comparados com os volumes das regiões que sofrem deformações viscoelásticas. A viscosidade aparente determinada, utilizando penetrador esférico em testes de força aplicada constante, é igual a (22 ± 2) × 10(12) Pa.s.

Spectroscopic characterization and investigation of the dynamic of charge compensation process of supramolecular films derived from tetra-2-pyridyl-1,4-pyrazine ligand

This work describes the infrared spectroscopy characterization and the charge compensation dynamics in supramolecular film FeTPPZFeCN derived from tetra-2-pyridyl-1,4-pyrazine (TPPZ) with hexacyanoferrate, as well as the hybrid film formed by FeTPPZFeCN and polypyrrole (PPy). For supramolecular film, it was found that anion flux is greater in a K+ containing solution than in Li+ solution, which seems to be due to the larger crystalline ionic radius of K+. The electroneutralization process is discussed in terms of electrostatic interactions between cations and metallic centers in the hosting matrix. The nature of the charge compensation process differs from others modified electrodes based on Prussian blue films, where only cations such as K+ participate in the electroneutralization process. In the case of FeTPPZFeCN/PPy hybrid film, the magnitude of the anions’s flux is also dependent on the identity of the anion of the supporting electrolyte.

A new species of Baurusuchus (Crocodyliformes, Mesoeucrocodylia) from the Upper Cretaceous of Brazil, with the first complete postcranial skeleton described for the family Baurusuchidae

The present work describes a new species of Baurusuchidae from Upper Cretaceous sediments of the Bauru Basin, and provides the first complete postcranial description for the family. Many postcranial features observed in the new species are also present in other notosuchian taxa, and are thus considered plesiomorphic for the genus. These are: long cervical neural spines; robust deltopectoral crest of the humerus; large proximal portion in the radiale that contacts the ulna; ulnare anterior distal projection; supra-acetabular crest well developed laterally; post-acetabular process posterodorsally deflected; presence of an anteromedial crest in the femur; fourth trocanter of femur posteriorly positioned; tibia with a laterally curved shaft; calcaneum tuber posteroventrally oriented; osteoderms ornamented with grooves and imbricated in the tail. On the other hand, we found the following sacral and carpal features to be unique among all mesoeucrocodylians analyzed: transverse processes of sacral vertebrae dorsolaterally deflected; presence of a longitudinal crest in the lateral surface of sacral vertebrae; pisiform carpal with a condyle-like surface. The majority of these cited features corroborates a cursorial locomotion for the new species described in the present study, suggesting that members of the family Baurusuchidae were also cursorial species.

Utilização dos subprodutos da fresagem do osso subcondral em substituição ao enxerto autólogo esponjoso em artrodeses de carpo de cães

A artrodese rádio-cárpica é procedimento radical usado no tratamento de fraturas e luxações do carpo, com danos à fibrocartilagem palmar e às estruturas ligamentares de sustentação, decorrentes de hiperextensão. Para este estudo foram selecionados 15 cães, submetidos à artrodese rádio-cárpica, entre abril/02 e julho/04. Foram estudados os casos quanto à formação de calo ósseo e às complicações pós-cirúrgicas. A técnica consistiu na ostectomia da superfície articular do rádio, expondo-a e retificando-a. Os subprodutos desta fresagem foram reintroduzidos como enxerto após sua redução em tamanho com rugina. Para a estabilização articular, em todos os casos, foram usadas placas compressivas. Foram realizados exames radiográficos imediatamente à intervenção cirúrgica e em intervalos de 30 dias, até a total fusão articular. Os resultados obtidos neste estudo, com fusão da articulação em até 300 dias de pós-cirúrgico em 80% dos casos estudados, foram semelhantes aos dispostos para as técnicas que utilizam enxertos autólogos esponjosos, sendo que, em 68% dos pacientes, a recuperação se deu sem qualquer complicação significativa. Pequenas complicações, como o aumento de volume, foram observadas em 22% dos casos, não determinando qualquer alteração no resultado final. Tais resultados viabilizam a técnica descrita, demonstrando a exeqüibilidade da utilização dos subprodutos da fresagem do osso subcondral como enxerto em artrodeses de carpo em cães.

Quasinormal modes of black holes in anti-de Sitter space: A numerical study of the eikonal limit

Using series solutions and time-domain evolutions, we probe the eikonal limit of the gravitational and scalar-field quasinormal modes of large black holes and black branes in anti-de Sitter backgrounds. These results are particularly relevant for the AdS/CFT correspondence, since the eikonal regime is characterized by the existence of long-lived modes which (presumably) dominate the decay time scale of the perturbations. We confirm all the main qualitative features of these slowly damped modes as predicted by Festuccia and Liu [G. Festuccia and H. Liu, arXiv:0811.1033.] for the scalar-field (tensor-type gravitational) fluctuations. However, quantitatively we find dimensional-dependent correction factors. We also investigate the dependence of the quasinormal mode frequencies on the horizon radius of the black hole (brane) and the angular momentum (wave number) of vector- and scalar-type gravitational perturbations.

Analysis of the tip roundness effects on the micro- and macroindentation response of elastic-plastic materials

In this work, the effects of indenter tip roundness oil the load-depth indentation curves were analyzed using finite element modeling. The tip roundness level was Studied based on the ratio between tip radius and maximum penetration depth (R/h(max)), which varied from 0.02 to 1. The proportional Curvature constant (C), the exponent of depth during loading (alpha), the initial unloading slope (S), the correction factor (beta), the level of piling-up or sinking-in (h(c)/h(max)), and the ratio h(max)/h(f) are shown to be strongly influenced by the ratio R/h(max). The hardness (H) was found to be independent of R/h(max) in the range studied. The Oliver and Pharr method was successful in following the variation of h(c)/h(max) with the ratio R/h(max) through the variation of S with the ratio R/h(max). However, this work confirmed the differences between the hardness values calculated using the Oliver-Pharr method and those obtained directly from finite element calculations; differences which derive from the error in area calculation that Occurs when given combinations of indented material properties are present. The ratio of plastic work to total work (W(p)/W(t)) was found to be independent of the ratio R/h(max), which demonstrates that the methods for the Calculation of mechanical properties based on the *indentation energy are potentially not Susceptible to errors caused by tip roundness.

The role of crystalline anisotropy in mechanical property extractions through Berkovich indentation

This work uses crystal plasticity finite element simulations to elucidate the role of elastoplastic anisotropy in instrumented indentation P-h(s) curve measurements in face-centered Cubic (fcc) crystals. It is shown that although the experimental fluctuations in the loading stage of the P-h(s) curves can be attributed to anisotropy, the variability in the unloading stage of the experiments Is much greater than that resulting from anisotropy alone. Moreover, it is found that the conventional procedure used to evaluate the contact variables ruling the unloading P-h(s) curve introduces all uncertainty that approximates to the more fundamental influence of anisotropy. In view of these results, a robust procedure is proposed that uses contact area measurements in addition to the P-h(s) curves to extract homogenized J(2)-Plasticity-equivalent mechanical properties from single crystals.

LOCAL HEAD LOSS OF NON-COAXIAL EMITTERS INSERTED IN POLYETHYLENE PIPE

The design of a lateral line for drip irrigation requires accurate evaluation of head losses in not only the pipe but in the emitters as well. A procedure was developed to determine localized head losses within the emitters by the formulation of a mathematical model that accounts for the obstruction caused by the insertion point. These localized losses can be significant when compared with tire total head losses within the system due to the large number of emitters typically installed along the lateral line. Air experiment was carried out by altering flow characteristics to create Reynolds numbers (R) from 7,480 to 32,597 to provide turbulent flow and a maximum velocity of 2.0 m s(-1). The geometry of the emitter was determined by an optical projector and sensor An equation was formulated to facilitate the localized head loss calculation using the geometric characteristics of the emitter (emitter length, obstruction ratio, and contraction coefficient). The mathematical model was tested using laboratory measurements on four emitters. The local head loss was accurately estimated for the Uniram (difference of +13.6%) and Drip Net (difference of +7.7%) emitters, while appreciable deviations were found for the Twin Plus (-21.8%) and Tiran (+50%) emitters. The head loss estimated by the model was sensitive to the variations in the obstruction area of the emitter However, the variations in the local head loss did not result in significant variations in the maximum length of the lateral lines. In general, for all the analyzed emitters, a 50% increase in the local head loss for the emitters resulted in less than an 8% reduction in the maximum lateral length.

Electromagnetic energy within magnetic spheres

Consider that an incident plane wave is scattered by a homogeneous and isotropic magnetic sphere of finite radius. We determine, by means of the rigorous Mie theory, an exact expression for the time-averaged electromagnetic energy within this particle. For magnetic scatterers, we find that the value of the average internal energy in the resonance picks is much larger than the one associated with a scatterer with the same nonmagnetic medium properties. This result is valid even, and especially, for low size parameter values. Expressions for the contributions of the radial and angular field components to the internal energy are determined. For the analytical study of the weak absorption regime, we derive an exact expression for the absorption cross section in terms of the magnetic Mie internal coefficients. We stress that, although the electromagnetic scattering by particles is a well-documented topic, almost no attention has been devoted to magnetic scatterers. Our aim is to provide some new analytical results, which can be used for magnetic particles, and emphasize the unusual properties of the magnetic scatters, which could be important in some applications. (C) 2010 Optical Society of America