Fekete-Szegoe problem for certain subclasses of analytic functions with respect to symmetric points

MSC 2010: 30C45

Freak waves and modulational dynamics in plasmas with negative ions

The nonlinear dynamics of modulated electrostatic wavepackets propagating in negativeion plasmas is investigated from first principles. A nonlinear Schrödinger equation is derived by adopting a multiscale technique. The stability of breather- like (bright envelope soliton) structures, considered as a precursor to freak wave (rogue wave) formation, is investigated and then tested via numerical simulations.

Series representations of the remainders in the expansions for certain functions with applications

We present a summary of the series representations of the remainders in the expansions in ascending powers of t of 2/(et+1)2/(et+1) , sech t and coth t and establish simple bounds for these remainders when t>0t>0 . Several applications of these expansions are given which enable us to deduce some inequalities and completely monotonic functions associated with the ratio of two gamma functions. In addition, we derive a (presumably new) quadratic recurrence relation for the Bernoulli numbers Bn.

Class-D audio amplifiers with negative feedback

There are many different designs for audio amplifiers. Class-D, or switching, amplifiers generate their output signal in the form of a high-frequency square wave of variable duty cycle (ratio of on time to off time). The square-wave nature of the output allows a particularly efficient output stage, with minimal losses. The output is ultimately filtered to remove components of the spectrum above the audio range. Mathematical models are derived here for a variety of related class-D amplifier designs that use negative feedback. These models use an asymptotic expansion in powers of a small parameter related to the ratio of typical audio frequencies to the switching frequency to develop a power series for the output component in the audio spectrum. These models confirm that there is a form of distortion intrinsic to such amplifier designs. The models also explain why two approaches used commercially succeed in largely eliminating this distortion; a new means of overcoming the intrinsic distortion is revealed by the analysis. Copyright (2006) Society for Industrial and Applied Mathematics

Complex functions with Geogebra

Complex functions, generally feature some interesting peculiarities, seen as extensions real functions, complementing the study of real analysis. However, the visualization of some complex functions properties requires the simultaneous visualization of two-dimensional spaces. The multiple Windows of GeoGebra, combined with its ability of algebraic computation with complex numbers, allow the study of the functions defined from ℂ to ℂ through traditional techniques and by the use of Domain Colouring. Here, we will show how we can use GeoGebra for the study of complex functions, using several representations and creating tools which complement the tools already provided by the software. Our proposals designed for students of the first year of engineering and science courses can and should be used as an educational tool in collaborative learning environments. The main advantage in its use in individual terms is the promotion of the deductive reasoning (conjecture / proof). In performed the literature review few references were found involving this educational topic and by the use of a single software.

Risk factors associated with negative in-vivo diagnostic results in bovine tuberculosis-infected cattle in Spain

BACKGROUND Despite great effort and investment incurred over decades to control bovine tuberculosis (bTB), it is still one of the most important zoonotic diseases in many areas of the world. Test-and-slaughter strategies, the basis of most bTB eradication programs carried out worldwide, have demonstrated its usefulness in the control of the disease. However, in certain countries, eradication has not been achieved due in part to limitations of currently available diagnostic tests. In this study, results of in-vivo and post-mortem diagnostic tests performed on 3,614 animals from 152 bTB-infected cattle herds (beef, dairy, and bullfighting) detected in 2007-2010 in the region of Castilla y León, Spain, were analyzed to identify factors associated with positive bacteriological results in cattle that were non-reactors to the single intradermal tuberculin test, to the interferon-gamma (IFN-γ) assay, or to both tests applied in parallel (Test negative/Culture + animals, T-/C+). The association of individual factors (age, productive type, and number of herd-tests performed since the disclosure of the outbreak) with the bacteriology outcome (positive/negative) was analyzed using a mixed multivariate logistic regression model. RESULTS The proportion of non-reactors with a positive post-mortem result ranged from 24.3% in the case of the SIT test to 12.9% (IFN-γ with 0.05 threshold) and 11.9% (95% CI 9.9-11.4%) using both tests in parallel. Older (>4.5 years) and bullfighting cattle were associated with increased odds of confirmed bTB infection by bacteriology, whereas dairy cattle showed a significantly lower risk. Ancillary use of IFN-γ assay reduced the proportion of T-/C + animals in high risk groups. CONCLUSIONS These results demonstrate the likelihood of positive bacteriological results in non-reactor cattle is influenced by individual epidemiological factors of tested animals. Increased surveillance on non-reactors with an increased probability of being false negative could be helpful to avoid bTB persistence, particularly in chronically infected herds. These findings may aid in the development of effective strategies for eradication of bTB in Spain.

Above ground biomass functions with vegetation indices for multiple use systems of two evergreen oaks

Remote sensing is a promising approach for above ground biomass estimation, as forest parameters can be obtained indirectly. The analysis in space and time is quite straight forward due to the flexibility of the method to determine forest crown parameters with remote sensing. It can be used to evaluate and monitoring for example the development of a forest area in time and the impact of disturbances, such as silvicultural practices or deforestation. The vegetation indices, which condense data in a quantitative numeric manner, have been used to estimate several forest parameters, such as the volume, basal area and above ground biomass. The objective of this study was the development of allometric functions to estimate above ground biomass using vegetation indices as independent variables. The vegetation indices used were the Normalized Difference Vegetation Index (NDVI), Enhanced Vegetation Index (EVI), Simple Ratio (SR) and Soil-Adjusted Vegetation Index (SAVI). QuickBird satellite data, with 0.70 m of spatial resolution, was orthorectified, geometrically and atmospheric corrected, and the digital number were converted to top of atmosphere reflectance (ToA). Forest inventory data and published allometric functions at tree level were used to estimate above ground biomass per plot. Linear functions were fitted for the monospecies and multispecies stands of two evergreen oaks (Quercus suber and Quercus rotundifolia) in multiple use systems, montados. The allometric above ground biomass functions were fitted considering the mean and the median of each vegetation index per grid as independent variable. Species composition as a dummy variable was also considered as an independent variable. The linear functions with better performance are those with mean NDVI or mean SR as independent variable. Noteworthy is that the two better functions for monospecies cork oak stands have median NDVI or median SR as independent variable. When species composition dummy variables are included in the function (with stepwise regression) the best model has median NDVI as independent variable. The vegetation indices with the worse model performance were EVI and SAVI.

Board of directors and top management team: a study on CEO relative power and financial return

Best corporate governance practices published in the primers of Brazilian Securities and Exchange Commission and the Brazilian Corporate Governance Institute promote board independence as much as possible, as a way to increase the effectiveness of governance mechanism (Sanzovo, 2010). Therefore, this paper aims at understanding if what the managerial literature portraits as being self-evident - stricter governance, better performance - can be observed in actual evidence. The question answered is: do companies with a stricter control and monitoring system perform better than others? The method applied in this paper consists on comparing 116 companies in respect to the their independence level between top management team and board directors– being that measured by four parameters, namely, the percentage of independent outsiders in the board, the separation of CEO and chairman, the adoption of contingent compensation and the percentage of institutional investors in the ownership structure – and their financial return measured in terms return on assets (ROA) from the latest Quarterly Earnings release of 2012. From the 534 companies listed in the Stock Exchange of Sao Paulo – Bovespa – 116 were selected due to their level of corporate governance. The title “Novo Mercado” refers to the superior level of governance level within companies listed in Bovespa, as they have to follow specific criteria to assure shareholders ´protection (BM&F, 2011). Regression analyses were conducted in order to reveal the correlation level between two selected variables. The results from the regression analysis were the following: the correlation between each parameter and ROA was 10.26%; the second regression analysis conducted measured the correlation between the independence level of top management team vis-à-vis board directors – namely, CEO relative power - and ROA, leading to a multiple R of 5.45%. Understanding that the scale is a simplification of the reality, the second part of the analysis transforms all the four parameters into dummy variables, excluding what could be called as an arbitrary scale. The ultimate result from this paper led to a multiple R of 28.44%, which implies that the combination of the variables are still not enough to translate the complex reality of organizations. Nonetheless, an important finding can be taken from this paper: two variables (percentage of outside directors and percentage of institutional investor ownership) are significant in the regression, with p-value lower than 10% and with negative coefficients. In other words, counter affirming what the literature very often portraits as being self-evident – stricter governance leads to higher performance – this paper has provided evidences to believe that the increase in the formal governance structure trough outside directors in the board and ownership by institutional investor might actually lead to worse performance. The section limitations and suggestions for future researches presents some reasons explaining why, although supported by strong theoretical background, this paper faced some challenging methodological assumptions, precluding categorical statements about the level of governance – measured by four selected parameters – and the financial return in terms of financial on assets.

Sobre a integração indefinida de funções racionais complexas: teoria e implementação de algoritmos racionais

We present indefinite integration algorithms for rational functions over subfields of the complex numbers, through an algebraic approach. We study the local algorithm of Bernoulli and rational algorithms for the class of functions in concern, namely, the algorithms of Hermite; Horowitz-Ostrogradsky; Rothstein-Trager and Lazard-Rioboo-Trager. We also study the algorithm of Rioboo for conversion of logarithms involving complex extensions into real arctangent functions, when these logarithms arise from the integration of rational functions with real coefficients. We conclude presenting pseudocodes and codes for implementation in the software Maxima concerning the algorithms studied in this work, as well as to algorithms for polynomial gcd computation; partial fraction decomposition; squarefree factorization; subresultant computation, among other side algorithms for the work. We also present the algorithm of Zeilberger-Almkvist for integration of hyperexpontential functions, as well as its pseudocode and code for Maxima. As an alternative for the algorithms of Rothstein-Trager and Lazard-Rioboo-Trager, we yet present a code for Benoulli’s algorithm for square-free denominators; and another for Czichowski’s algorithm, although this one is not studied in detail in the present work, due to the theoretical basis necessary to understand it, which is beyond this work’s scope. Several examples are provided in order to illustrate the working of the integration algorithms in this text

Bieberbach's Conjecture, the de Branges and Weinstein Functions and the Askey-Gasper Inequality

The Bieberbach conjecture about the coefficients of univalent functions of the unit disk was formulated by Ludwig Bieberbach in 1916 [Bieberbach1916]. The conjecture states that the coefficients of univalent functions are majorized by those of the Koebe function which maps the unit disk onto a radially slit plane. The Bieberbach conjecture was quite a difficult problem, and it was surprisingly proved by Louis de Branges in 1984 [deBranges1985] when some experts were rather trying to disprove it. It turned out that an inequality of Askey and Gasper [AskeyGasper1976] about certain hypergeometric functions played a crucial role in de Branges' proof. In this article I describe the historical development of the conjecture and the main ideas that led to the proof. The proof of Lenard Weinstein (1991) [Weinstein1991] follows, and it is shown how the two proofs are interrelated. Both proofs depend on polynomial systems that are directly related with the Koebe function. At this point algorithms of computer algebra come into the play, and computer demonstrations are given that show how important parts of the proofs can be automated.

Smoothness of scale functions for spectrally negative Lévy processes

Scale functions play a central role in the fluctuation theory of spectrally negative Lévy processes and often appear in the context of martingale relations. These relations are often require excursion theory rather than Itô calculus. The reason for the latter is that standard Itô calculus is only applicable to functions with a sufficient degree of smoothness and knowledge of the precise degree of smoothness of scale functions is seemingly incomplete. The aim of this article is to offer new results concerning properties of scale functions in relation to the smoothness of the underlying Lévy measure. We place particular emphasis on spectrally negative Lévy processes with a Gaussian component and processes of bounded variation. An additional motivation is the very intimate relation of scale functions to renewal functions of subordinators. The results obtained for scale functions have direct implications offering new results concerning the smoothness of such renewal functions for which there seems to be very little existing literature on this topic.

Potential Analysis for Hypoelliptic Second Order PDEs with Nonnegative Characteristic Form

In this Thesis we consider a class of second order partial differential operators with non-negative characteristic form and with smooth coefficients. Main assumptions on the relevant operators are hypoellipticity and existence of a well-behaved global fundamental solution. We first make a deep analysis of the L-Green function for arbitrary open sets and of its applications to the Representation Theorems of Riesz-type for L-subharmonic and L-superharmonic functions. Then, we prove an Inverse Mean value Theorem characterizing the superlevel sets of the fundamental solution by means of L-harmonic functions. Furthermore, we establish a Lebesgue-type result showing the role of the mean-integal operator in solving the homogeneus Dirichlet problem related to L in the Perron-Wiener sense. Finally, we compare Perron-Wiener and weak variational solutions of the homogeneous Dirichlet problem, under specific hypothesis on the boundary datum.

A method for the design of MRI radiofrequency coils based on triangular and pulse basis functions

This paper presents a numerical technique for the design of an RF coil for asymmetric magnetic resonance imaging (MRI) systems. The formulation is based on an inverse approach where the cylindrical surface currents are expressed in terms of a combination of sub-domain basis functions: triangular and pulse functions. With the homogeneous transverse magnetic field specified in a spherical region, a functional method is applied to obtain the unknown current coefficients. The current distribution is then transformed to a conductor pattern by use of a stream function technique. Preliminary MR images acquired using a prototype RF coil are presented and validate the design method. (C) 2002 Elsevier Science B.V. All rights reserved.

Stochastic delay differential equations driven by fractional Brownian motion with Hurst parameter H 1/2

We consider the Cauchy problem for a stochastic delay differential equation driven by a fractional Brownian motion with Hurst parameter H>¿. We prove an existence and uniqueness result for this problem, when the coefficients are sufficiently regular. Furthermore, if the diffusion coefficient is bounded away from zero and the coefficients are smooth functions with bounded derivatives of all orders, we prove that the law of the solution admits a smooth density with respect to Lebesgue measure on R.

Functions satisfying holonomic q-differential equations

In a similar manner as in some previous papers, where explicit algorithms for finding the differential equations satisfied by holonomic functions were given, in this paper we deal with the space of the q-holonomic functions which are the solutions of linear q-differential equations with polynomial coefficients. The sum, product and the composition with power functions of q-holonomic functions are also q-holonomic and the resulting q-differential equations can be computed algorithmically.