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Yusuf Yayli - One of the best experts on this subject based on the ideXlab platform.
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Some variations of dual Euler–Rodrigues formula with an application to point–line geometry
Journal of Mathematical Analysis and Applications, 2018Co-Authors: Derya Kahveci̇, Yusuf YayliAbstract:This paper examines the Euler-Rodrigues formula in dual 3−space D 3 D 3 by analyisng its variations such as vectorial form, exponential map, point-line theory and quaternions which have some intrinsic relations. Contrary to the Euclidean case, dual rotation in dual 3−space corresponds to a screw motion in Euclidean 3−space. This paper begins by explaining dual motion in terms of the given dual axis and angle. It will then go on to express dual Euler-Rodrigues formula with algebraic methods. Furthermore, an application of dual Euler-Rodrigues formula to point-line geometry is accomplished and point-line displacement operator is obtained by dual Euler-Rodrigues formula. Finally, dual Euler-Rodrigues formula is presented with the help of dual Euler-Rodrigues parameters that is expressed as a dual quaternion.
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the geometrical and algebraic interpretations of euler Rodrigues formula in minkowski 3 space
International Journal of Geometric Methods in Modern Physics, 2016Co-Authors: Derya Kahveci, Yusuf YayliAbstract:The aim of this paper is to give the geometrical and algebraic interpretations of Euler–Rodrigues formula in Minkowski 3-space. First, for the given non-lightlike axis of a unit length in ℝ13 and angle, the spatial displacement is represented by a 3 × 3 semi-orthogonal rotation matrix using orthogonal projection. Second, we obtain the classifications of Euler–Rodrigues formula in terms of semi-skew-symmetric matrix corresponds to spacelike, timelike or lightlike axis and rotation angle with the help of exponential map. Finally, an alternative method is given to find rotation axis and the Euler–Rodrigues formula is expressed via split quaternions in Minkowski 3-space.
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The geometrical and algebraic interpretations of Euler–Rodrigues formula in Minkowski 3-space
International Journal of Geometric Methods in Modern Physics, 2016Co-Authors: Derya Kahveci̇, Yusuf YayliAbstract:The aim of this paper is to give the geometrical and algebraic interpretations of Euler–Rodrigues formula in Minkowski 3-space. First, for the given non-lightlike axis of a unit length in ℝ13 and angle, the spatial displacement is represented by a 3 × 3 semi-orthogonal rotation matrix using orthogonal projection. Second, we obtain the classifications of Euler–Rodrigues formula in terms of semi-skew-symmetric matrix corresponds to spacelike, timelike or lightlike axis and rotation angle with the help of exponential map. Finally, an alternative method is given to find rotation axis and the Euler–Rodrigues formula is expressed via split quaternions in Minkowski 3-space.
J J Jonas - One of the best experts on this subject based on the ideXlab platform.
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representation of orientation relationships in Rodrigues frank space for any two classes of lattice
Journal of Applied Crystallography, 2007Co-Authors: You Liang He, J J JonasAbstract:The fundamental zones of Rodrigues–Frank (R-F) space applicable to misorientations between crystals of any two Laue groups are constructed by using a unified formulation in terms of quaternion algebra. Some of these regions are fully bounded by planes that are determined solely by the symmetries of the groups, while others have at least one unbounded direction. Each of the bounded fundamental zones falls into one of nine geometrically distinct configurations. The maximum symmetry-reduced angles and the corresponding Rodrigues–Frank vectors for these fundamental zones are evaluated. The use of Rodrigues–Frank space for the representation of orientation relationships between crystals of any two symmetry groups is also addressed. Examples concerning the transition of phases of the same symmetry group, i.e. from face-centered cubic to body-centered cubic, and of different groups, i.e. from body-centered cubic to hexagonal close-packed, are given to illustrate the usefulness of this space for representing orientation relationships during phase transformation or precipitation.
Marcos Chor Maio - One of the best experts on this subject based on the ideXlab platform.
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brazilian physician nina Rodrigues analysis of a scientific career
Cadernos De Saude Publica, 1995Co-Authors: Marcos Chor MaioAbstract:One of the most productive ways of investigating the history of Brazilian medical practice at the turn of this century is to focus on the fruitful and ambiguous careers of those physicians that played an important role in the changes affecting the medical field at that time. This paper aims at analyzing the scientific career of physician-anthropologist Raimundo Nina Rodrigues, taking as its conceptual basis Pierrre Bourdieu's notion of "scientific field ". The paper's point of departure is the notion that the medical field is a space of confrontation that is structurally determined by previous conflicts in which physicians try to monopolize claims to scientific authority and competence. Nina Rodrigues' medical profile appears in this context as a precise indicator of the process of specialization and competition that took place during that period.
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Brazilian physician Nina Rodrigues: analysis of a scientific career
Cadernos De Saude Publica, 1995Co-Authors: Marcos Chor MaioAbstract:Uma das maneiras mais proficuas de se pesquisar a historia da medicina brasileira na passagem do seculo XIX para o XX e a investigacao da trajetoria profissional de determinados medicos que tiveram posicoes de relevo no processo de mudancas que atingiu o campo medico a epoca. Neste sentido, este artigo tem por objetivo analisar a carreira academico-profissional de Raimundo Nina Rodrigues, a partir da nocao de campo cientifico de Pierre Bourdieu. Partindo do principio de que o campo medico e um espaco de confrontos estruturalmente determinado pelos embates passados, onde os medicos buscam monopolizar a autoridade/competencia cientifica, considero que o perfil medico de Nina Rodrigues e um indicador preciso do processo de especializacao e concorrencia que se desenvolveu naquele momento.
Fawzi M Mahomoodally - One of the best experts on this subject based on the ideXlab platform.
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ethnopharmacological analysis of medicinal plants used against non communicable diseases in Rodrigues island indian ocean
Journal of Ethnopharmacology, 2015Co-Authors: Anne Kathie Samoisy, Fawzi M MahomoodallyAbstract:Abstract Ethnopharmacological relevance Rodrigues is an autonomous outer island that form part of the Republic of Mauritius and one of three islands that constitute the Mascarene archipelago in the Indian Ocean. Though herbal medicine is in common use in Rodrigues, there has been no ethnopharmacological study to document quantitatively such traditional practise particularly against non-communicable diseases (NCD) which is currently a growing major health issue on the island. The aim of the present study was to collect, analyse and document traditionally used medicinal plants (MP) from key informants and traditional medicine practitioners (TMP) in the tropical island of Rodrigues to treat and/or manage common NCD. Materials and methods Data was collected via face-to-face interviews with MP users ( n =113) and TMP (n =9). Seven quantitative ethnopharmacological indices, namely family use value (FUV), use value (UV), informant agreement ratio (IAR), relative frequency of citation (RFC), fidelity level (FL), relative importance (RI) and ethnobotanicity index (EI) were calculated. Results Hundred and three plants belonging to 55 families were recorded for the treatment and/or management of 27 different NCD. Three of the MP ( Terminalia bentzoe (L.) L.F , Sarcostemma cf. adontolepis Balf.f. and Clerodendrum laciniatum Balf.f.) recorded are endemic to Rodrigues and 2 ( Carissa xylopicron Thouars. , Phyllanthus casticum Willemet f.) endemic to the Mascarene Islands. The most solicited MP family was Asteraceae with a total of 8 species. Citrus aurantifolia (Christm.) Swingle scored the highest RFC (RFC=1.02) value. Ten plants were found to score 100% FL and the highest IAR (0.98) was observed for the disease category of certain conditions originating in the perinatal period. Arecaceae scored the highest FUV value and Ayapana triplinervis (Vahl) R.M. King et H.Rob highest UV (UV= 2.72). Conclusion Given the dearth of updated information on traditional medicine of Rodrigues, this study can provide an opportunity to establish valuable primary information on the different MP used by the local people and hence can open new perspectives for further pharmacological research.
Antonio J. Durán - One of the best experts on this subject based on the ideXlab platform.
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Rodrigues’ formulas for orthogonal matrix polynomials satisfying second-order difference equations
Integral Transforms and Special Functions, 2014Co-Authors: Antonio J. Durán, Vanesa Sánchez-canalesAbstract:We develop a method to find discrete Rodrigues’ formulas for orthogonal matrix polynomials which are also eigenfunctions of a second-order difference operator. Using it, we produce Rodrigues’ formulas for two illustrative examples of arbitrary size.
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Rodrigues’ Formulas for Orthogonal Matrix Polynomials Satisfying Second-Order Differential Equations
International Mathematics Research Notices, 2009Co-Authors: Antonio J. DuránAbstract:We develop a method to find Rodrigues’ formulas for orthogonal matrix polynomials satisfying second-order differential equations with coefficients independent of n. Using it, we produce Rodrigues’ formulas for three illustrative examples of arbitrary size.
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Orthogonal matrix polynomials, scalar-type Rodrigues' formulas and Pearson equations
Journal of Approximation Theory, 2005Co-Authors: Antonio J. Durán, F. Alberto GrünbaumAbstract:Some families of orthogonal matrix polynomials satisfying second-order differential equations with coefficients independent of n have recently been introduced (see [Internat. Math. Res. Notices 10 (2004) 461-484]). An important difference with the scalar classical families of Jacobi, Laguerre and Hermite, is that these matrix families do not satisfy scalar type Rodrigues' formulas of the type (@F^nW)^(^n^)W^-^1, where @F is a matrix polynomial of degree not bigger than 2. An example of a modified Rodrigues' formula, well suited to the matrix case, appears in [Internat. Math. Res. Notices 10 (2004) 482]. In this note, we discuss some of the reasons why a second order differential equation with coefficients independent of n does not imply, in the matrix case, a scalar type Rodrigues' formula and show that scalar type Rodrigues' formulas are most likely not going to play in the matrix valued case the important role they played in the scalar valued case. We also mention the roles of a scalar-type Pearson equation as well as that of a noncommutative version of it.
