From Treatises to Late Baroque Architecture in Val di Noto

2019 ◽  
pp. 302-328
Author(s):  
Rita Valenti ◽  
Lucia Trigilia ◽  
Maria Elena Ragno ◽  
Emanuela Paternò
Keyword(s):  
Point Of View ◽  
Church Architecture ◽  
Urban Centers ◽  
Building Site ◽  
Baroque Architecture ◽  
Geometric Point

Val di Noto is an area geographically corresponding to southeastern Sicily and it is arranged as an integrated context. Within the Baroque in Sicily, it is necessary to remember the earthquake of 1693 which ravaged the area across, destroying lots of populated centers. After the earthquake, a lot of urban centers were rebuilt transforming the area around Val di Noto into a big building site. The research develops a critical methodological investigation of the works of the period concerning church architecture with sinusoidal facades. The instrumental survey is particularly suitable to draw comparisons with the treatises known at the time. The present study refers to the ichnographies of Mazza collection by Rosario Gagliardi, prominent figure of the Sicilian Baroque. The adopted methodology highlighted analogies and formal geometric differences between the model represented by Gagliardi's ichnographies and the churches previously identified. The chapter provides a useful instrument for the research of a technical, scientific and geometric point of view.

scholarly journals Laws of the iterated logarithm on covering graphs with groups of polynomial volume growth

2020 ◽  
Vol 0 (0) ◽  
Author(s):  
Ryuya Namba
Keyword(s):  
Random Walks ◽  
Quadratic Forms ◽  
Volume Growth ◽  
Moderate Deviation ◽  
Point Of View ◽  
Iterated Logarithm ◽  
Large Numbers ◽  
Geometric Point ◽  
Rate Functions ◽  
The Given

AbstractModerate deviation principles (MDPs) for random walks on covering graphs with groups of polynomial volume growth are discussed in a geometric point of view. They deal with any intermediate spatial scalings between those of laws of large numbers and those of central limit theorems. The corresponding rate functions are given by quadratic forms determined by the Albanese metric associated with the given random walks. We apply MDPs to establish laws of the iterated logarithm on the covering graphs by characterizing the set of all limit points of the normalized random walks.

Dynamics of Multibody Systems: Generalized Mass Metric in Riemannian Velocity Space and Recursive Momentum Formulation

2007 ◽  
Author(s):  
Qiang Zhao ◽  
Hong Tao Wu
Keyword(s):  
Point Of View ◽  
Velocity Space ◽  
Motion Equations ◽  
Closed Loop Systems ◽  
Dynamics Of Multibody Systems ◽  
Operator Factorization ◽  
Geometric Point ◽  
Mass Tensor ◽  
Generalized Momentum ◽  
Serial Chains

This paper describes two aspects of multibody system (MBS) dynamics on a generalized mass metric in Riemannian velocity space and recursive momentum formulation. Firstly, we present a detailed expression of the Riemannian metric and operator factorization of a generalized mass tensor for the dynamics of general-topology rigid MBS. The derived expression allows a clearly understanding the components of the generalized mass tensor, which also constitute a metric of the Riemannian velocity space. It is being the fact that there does exist a common metric in Lagrange and recursive Newton-Euler dynamic equation, we can determine, from the Riemannian geometric point of view, that there is the equivalent relationship between the two approaches to a given MBS. Next, from the generalized momentum definition in the derivation of the Riemannian velocity metrics, recursive momentum equations of MBS dynamics are developed for progressively more complex systems: serial chains, topological trees, and closed-loop systems. Through the principle of impulse and momentum, a new method is proposed for reorienting and locating the MBS form a given initial orientation and location to desired final ones without needing to solve the motion equations.

scholarly journals Trajetória intelectual e identidade do educador: Anísio Teixeira (1900-1971)

2019 ◽  
Vol 81 (197) ◽  
Author(s):  
Clarice Nunes
Keyword(s):  
Point Of View ◽  
Education History ◽  
Urban Centers ◽  
Brazilian Society ◽  
Urban Representations ◽  
Main Representative

Celebrar a trajetória de Anísio Teixeira é trazer para o centro das nossas reflexões momentos decisivos da nossa história da educação. Ele fez parte de uma geração de intelectuais urbanos a quem coube, sobretudo, na passagem do século 19 para o século 20, grande responsabilidade pela discussão do tema da modernidade e dos projetos políticos que lhe diziam respeito, a partir de certa visão de sociedade brasileira e de povo brasileiro. Ao trabalhar nos maiores e mais importantes centros urbanos do País, liderando as famosas reformas de instrução pública, nos anos 20 e 30, esses intelectuais criaram não só a possibilidade de estruturar um campo de identificação dos educadores mas, sobretudo, interferiram na ordenação simbólica das cidades, armando novas representações do urbano e do seu papel profissional dentro dele. Compreender o móvel dessa ação é, em parte, meu objetivo neste texto. Para tanto, tomo como caso a trajetória de Anísio Teixeira, o maior representante da tradição pedagógica democrática em nosso País. Palavras-chave: Anísio Teixeira; biografia. Abstract If still alive, Anísio Teixeira would complete one hundred years old. Celebrating his trajectory is to bring to the center of our reflections decisive moments of education history. He was part of an urban intellectual generation that, mainly lasted from the passage of 19 to the 20 century, took the responsibility of discussing the modernity of political projects from the point of view of the Brazilian society and public. Working in the major urban centers in Brazil, leading the famous public instructions reforms in the 1920's and 30's, these intellectual created not only the possibility of structuring the educators identification, but above all, they interfere in the symbolic ordination of cities, creating new urban representations and new roles for the professionals. Comprehend the mobile of this action is in part the objective of this text. For this reason, it is consider the trajectory of Anísio Teixeira, the main representative of the Pedagogical democracy tradition of our country. Keywords: Anísio Teixeira; biography.

NONLINEARITY AND LEAST SQUARES

CISM journal ◽  
1988 ◽  
Vol 42 (4) ◽  
pp. 321-330 ◽  
Author(s):  
P.J.G. Teunissen ◽  
E.H. Knickmeyer
Keyword(s):  
Least Squares ◽  
Covariance Structure ◽  
Point Of View ◽  
Helmert Transformation ◽  
Know How ◽  
Least Squares Estimators ◽  
Functional Relations ◽  
Geometric Point ◽  
Rotational Invariant ◽  
Almost All

Since almost all functional relations in our geodetic models are nonlinear, it is important, especially from a statistical inference point of view, to know how nonlinearity manifests itself at the various stages of an adjustment. In this paper particular attention is given to the effect of nonlinearity on the first two moments of least squares estimators. Expressions for the moments of least squares estimators of parameters, residuals and functions derived from parameters, are given. The measures of nonlinearity are discussed both from a statistical and differential geometric point of view. Finally, our results are applied to the 2D symmetric Helmert transformation with a rotational invariant covariance structure.

scholarly journals A teaching proposal for the study of Eigenvectors and Eigenvalues

2017 ◽  
Vol 7 (1) ◽  
pp. 100 ◽  
Author(s):  
María José Beltrán Meneu ◽  
Marina Murillo Arcila ◽  
Enrique Jordá Mora
Keyword(s):  
Rigid Body ◽  
Mathematical Thinking ◽  
Point Of View ◽  
Moment Of Inertia ◽  
Geometric Point ◽  
The Moment ◽  
Eigenvectors And Eigenvalues

In this work, we present a teaching proposal which emphasizes on visualization and physical applications in the study of eigenvectors and eigenvalues. These concepts are introduced using the notion of the moment of inertia of a rigid body and the GeoGebra software. The proposal was motivated after observing students’ difficulties when treating eigenvectors and eigenvalues from a geometric point of view. It was designed following a particular sequence of activities with the schema: exploration, introduction of concepts, structuring of knowledge and application, and considering the three worlds of mathematical thinking provided by Tall: embodied, symbolic and formal.

scholarly journals Improvements of Rackwitz–Fiessler Method for Correlated Structural Reliability Analysis

2019 ◽  
Vol 17 (06) ◽  
pp. 1950077 ◽  
Author(s):  
Sheng-Tong Zhou ◽  
Qian Xiao ◽  
Jian-Min Zhou ◽  
Hong-Guang Li
Keyword(s):  
Structural Reliability ◽  
Pearson Correlation ◽  
Computational Cost ◽  
Transformation Process ◽  
Point Of View ◽  
Gaussian Copula ◽  
Normal Space ◽  
Copula Theory ◽  
Geometric Point ◽  
Nataf Transformation

Rackwitz–Fiessler (RF) method is well accepted as an efficient way to solve the uncorrelated non-Normal reliability problems by transforming original non-Normal variables into equivalent Normal variables based on the equivalent Normal conditions. However, this traditional RF method is often abandoned when correlated reliability problems are involved, because the point-by-point implementation property of equivalent Normal conditions makes the RF method hard to clearly describe the correlations of transformed variables. To this end, some improvements on the traditional RF method are presented from the isoprobabilistic transformation and copula theory viewpoints. First of all, the forward transformation process of RF method from the original space to the standard Normal space is interpreted as the isoprobabilistic transformation from the geometric point of view. This viewpoint makes us reasonably describe the stochastic dependence of transformed variables same as that in Nataf transformation (NATAF). Thus, a corresponding enhanced RF (EnRF) method is proposed to deal with the correlated reliability problems described by Pearson linear correlation. Further, we uncover the implicit Gaussian copula hypothesis of RF method according to the invariant theorem of copula and the strictly increasing isoprobabilistic transformation. Meanwhile, based on the copula-only rank correlations such as the Spearman and Kendall correlations, two improved RF (IRF) methods are introduced to overcome the potential pitfalls of Pearson correlation in EnRF. Later, taking NATAF as a reference, the computational cost and efficiency of above three proposed RF methods are also discussed in Hasofer–Lind reliability algorithm. Finally, four illustrative structure reliability examples are demonstrated to validate the availability and advantages of the new proposed RF methods.

Fourier-Mukai Transforms in Algebraic Geometry

2007 ◽  
Author(s):  
D. Huybrechts
Keyword(s):  
Algebraic Geometry ◽  
Smooth Projective Variety ◽  
Derived Category ◽  
Point Of View ◽  
Basic Knowledge ◽  
Research Directions ◽  
Coherent Sheaves ◽  
Geometric Point ◽  
Singular Cohomology

This book provides a systematic exposition of the theory of Fourier-Mukai transforms from an algebro-geometric point of view. Assuming a basic knowledge of algebraic geometry, the key aspect of this book is the derived category of coherent sheaves on a smooth projective variety. The derived category is a subtle invariant of the isomorphism type of a variety, and its group of autoequivalences often shows a rich structure. As it turns out — and this feature is pursued throughout the book — the behaviour of the derived category is determined by the geometric properties of the canonical bundle of the variety. Including notions from other areas, e.g., singular cohomology, Hodge theory, abelian varieties, K3 surfaces; full proofs and exercises are provided. The final chapter summarizes recent research directions, such as connections to orbifolds and the representation theory of finite groups via the McKay correspondence, stability conditions on triangulated categories, and the notion of the derived category of sheaves twisted by a gerbe.

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