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G?del and the Incompleteness of Arithmetic  [PDF]
Pinheiro
Advances in Pure Mathematics (APM) , 2016, DOI: 10.4236/apm.2016.68042
Abstract: People normally believe that Arithmetic is not complete because GÖdel launched this idea a long time ago, and it looks as if nobody has presented sound evidence on the contrary. We here intend to do that perhaps for the first time in history. We prove that what Stanford Encyclopedia has referred to as Theorem 3 cannot be true, and, therefore, if nothing else is presented in favour of GÖdel’s thesis, we actually do not have evidence on the incompleteness of Arithmetic: All available evidence seems to point at the extremely opposite direction.
First Note on the Definition of S2-Convexity  [PDF]
Pinheiro Marcia
Advances in Pure Mathematics (APM) , 2011, DOI: 10.4236/apm.2011.11001
Abstract: In this short, but fundamental, note, we start progressing towards a mathematically sound definition of the real functional classes 2sK
Minima Domain Intervals and the S-Convexity, as well as the Convexity, Phenomenon  [PDF]
I. M. R. Pinheiro
Advances in Pure Mathematics (APM) , 2012, DOI: 10.4236/apm.2012.26069
Abstract: In this paper, we propose a refinement in the analytical definition of the s2-convex classes of functions aiming to progress further in the direction of including s2-convexity properly in the body of Real Analysis.
First Note on the Definition of s1-Convexity  [PDF]
I. M. R. Pinheiro
Advances in Pure Mathematics (APM) , 2014, DOI: 10.4236/apm.2014.412076
Abstract:

In this note, we analyze a few major claims about . As a consequence, we rewrite a major theorem, nullify its proof and one remark of importance, and offer a valid proof for it. The most important gift of this paper is probably the reasoning involved in all: We observe that a constant, namely t, has been changed into a variable, and we then tell why such a move could not have been made, we observe the discrepancy between the claimed domain and the actual domain of a supposed function that is created and we then explain why such a function could not, or should not, have been created, along with others.

Second Note on the Definition of S1-Convexity  [PDF]
I. M. R. Pinheiro
Advances in Pure Mathematics (APM) , 2015, DOI: 10.4236/apm.2015.53015
Abstract: In this note, we discuss the definition of the S1-convexity Phenomenon. We first make use of some results we have attained for??\"\" in the past, such as those contained in [1], to refine the definition of the phenomenon. We then observe that easy counter-examples to the claim \"\" extends K0 are found. Finally, we make use of one theorem from [2] and a new theorem that appears to be a supplement to that one to infer that?\"\" does not properly extend K0 in both its original and its revised version.
Marginal Distributions of Random Vectors Generated by Affine Transformations of Independent Two-Piece Normal Variables
Maximiano Pinheiro
Journal of Probability and Statistics , 2012, DOI: 10.1155/2012/758975
Abstract: Marginal probability density and cumulative distribution functions are presented for multidimensional variables defined by nonsingular affine transformations of vectors of independent two-piece normal variables, the most important subclass of Ferreira and Steel's general multivariate skewed distributions. The marginal functions are obtained by first expressing the joint density as a mixture of Arellano-Valle and Azzalini's unified skew-normal densities and then using the property of closure under marginalization of the latter class. 1. Introduction In the literature on probability distributions, there are several approaches for extending the multivariate normal distribution with the introduction of some sort of skewness. Arellano-Valle et al. [1] provide a unified view of this literature. The largest group of contributions was initiated by Azzalini and Dalla Valle [2] and Azzalini and Capitanio [3] and generalizes the univariate skew-normal (SN) distribution studied by Azzalini [4, 5]. These “multivariate skew-normal distributions” are generated from a normal distribution either by conditioning on a truncated variable or by a convolution mechanism. An alternative approach was proposed by Ferreira and Steel [6–8] and is based on nonsingular affine transformations of random vectors with independent components, each having a skewed distribution with probability density function (pdf) constructed from a symmetric distribution using the inverse scaling factor method introduced by Fernández and Steel [9]. (Arellano-Valle et al. [10] consider a general class of asymmetric univariate distributions that includes the distributions generated according to the procedure proposed by Fernández and Steel [9] as a special case.) If the univariate symmetric distribution is the standard normal, then the corresponding univariate skewed distribution becomes (with a different parameterization) the two-piece normal (tpn) analyzed by John [11] (see also Johnson et al. [12]). To overcome an issue of overparameterization, Ferreira and Steel [7, 8] pay particular attention to the subclass associated with transformation matrices that can be factorized as the product of an orthogonal matrix and a diagonal positive definite matrix. Villani and Larsson [13] studied this subclass when the basic univariate skewed distribution is the tpn and named these distributions “multivariate split normal.” Under the acronym SUN (standing for “unified skew-normal”), Arellano-Valle and Azzalini [14] suggested a formulation for the first approach that encompasses the most relevant coexisting variants
Nonoperative treatment of slipped capital femoral epiphysis: a scientific study
Pedro Pinheiro
Journal of Orthopaedic Surgery and Research , 2011, DOI: 10.1186/1749-799x-6-10
Abstract: The research was performed based on the study of the following variables: symptomatology, and the degree of slipping. A hip spica cast and bilateral short/long leg casts in abduction, internal rotation with anti-rotational bars were used for immobilizing the patient's hip for twelve weeks. Statistical analysis was accomplished by Wilcoxon's marked position test and by the Fisher accuracy test at a 5% level.A satisfactory result was obtained in the acute group, 70.5%; 94%; in the chronic group (chronic + acute on chronic). Regarding the degree of the slipping, a satisfactory result was obtained in 90.5% of hips tested with a mild slip; in 76% with moderate slip and 73% in the severe slip. The statistical result revealed that a significant improvement was found for flexion (p = 0.0001), abduction (p = 0.0001), internal rotation (p = 0.0001) and external rotation (p = 0.02). Chondrolysis was present in 11.3% of the hips tested. One case of pseudoarthrosis with aseptic capital necrosis was presented. There was no significant variation between age and chondrolysis (p = 1.00).Significant variation between gender/non-white patients versus chondrolysis (p = 0.031) and (p = 0.037), respectively was verified.No causal association between plaster cast and chondrolysis was observed (p = 0.60). In regard to the symptomatology group and the slip degree versus chondrolysis, the p value was not statistically significant in both analyses, p = 0.61 and p = 0.085 respectively.After analyzing the nonoperative treatment of slipped capital femoral epiphysis and chondrolysis, we conclude that employment of the treatment revealed that the method was functional, efficient, valid, and reproducible; it also can be used as an alternative therapeutic procedure regarding to this specific disease.The contributions and reasons for the use of the non-operative management of Slipped Capital Femoral Epiphysis (SCFE) are as follows:- applicability: non-operative treatment of SCFE allows the use of thi
Contingência e análise infinita em Leibniz
Pinheiro, Ulysses;
Kriterion: Revista de Filosofia , 2001, DOI: 10.1590/S0100-512X2001000200004
Abstract: leibniz says in various occasions that infinite analysis is the key concept to explain the compatibillity of determinism and contingence. it is not evident, however, why the analogical use of a mathematical concept, such as infinitesimal calculus, could solve this ontological problem, nor in what sense one should understand such analogy. the aim of this paper is to elucidate these two points.
Omiss?es
Pinheiro, Ulysses;
Kriterion: Revista de Filosofia , 2006, DOI: 10.1590/S0100-512X2006000100009
Abstract: at first sight, actions and omissions do not share the same properties. some authors hold that an illustration of this assimetry is causality: actions must be explained as the instantiation of a causal relation between an agent and certain facts, while omissions seem to have to be explained as the absence of causal relations between a person and the relevant facts. in this paper, i will show that actions and omissions are, contrary to appearances, simetrical regarding the attribution of genuine causality.
A "doen?a dos eruditos" e a triangularidade da ideia de triangulo: uma análise do conceito de espa?o no tratado de Hume
Pinheiro, Ulysses;
Kriterion: Revista de Filosofia , 2010, DOI: 10.1590/S0100-512X2010000100004
Abstract: hume's analysis of the concept of space in the treatise of human nature commits him to a series of positive assertions on its nature and on the content represented by its idea: space is finitely divisible, and its idea is composed of colored or tactile non-extended points, which leads him to conclude that the idea of space is itself spatial. these assertions seem to commit hume to an idealistic theory of space. in this paper, i propose to elucidate hume's arguments for his positive theses and to examine his commitment to idealism through a characterization of the nature of treatise's propositions.
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