Singular analysis of stereoscopic serif

The article is devoted to the development of a methodological apparatus for evaluating the influence of geometric survey conditions on the ratio of errors in the planned and altitude components of determining the terrain points’ spatial coordinates. For this purpose, an approach based on the singular analyzing the matrix of the system of equations for intersecting lines in the basis plane is used. It is shown that singular numbers characterize the ellipse of coordinate definition errors in plane and height. They are calculated for the most typical cases of stereo surveying. It is noted that the geometric conditions of stereo photography are mainly determined by the serif angle. By interpolating the results of calculating singular numbers, the formulas characterizing the direct and inverse dependence of the ratio of the stereo-cut in plan and height on the serif angle errors’ are obtained. The author considers the practical issues of using the developed methodological apparatus to justify the solutions related to the assessment of the ratio between the errors in determining the plane coordinates and the heights of terrain points from stereo images.

A singular analysis—attribution of illegality following Singularis v Daiwa

This article considers the Supreme Court’s judgment in Singularis Holdings Ltd (In Official Liquidation) v Daiwa Capital Markets Europe Ltd [2019] UKSC 50. In particular, it examines the court’s ruling in relation to attribution of illegality. This clarifies that, when determining if the knowledge and actions of a director are to be attributed to a company, the answer is to be found in a consideration of the context and purpose for which the attribution is relevant, and not in the identification of the “directing mind and will” of the company.

Between THe aacient and the modern world: war and community in Max Weber’s city typology

Economy and Society, one of the most influential oeuvres of the early twentieth century, with impact in several branches of the Human Sciences, has in one of its parts a text of particular interest to researchers of Ancient History, the Typology of Cities. Although Max Weber’s significant aims in composing his text were, blatantly, to evaluate the contemporary world, the density of the Weberian text, the fruit of a unique erudition, revealed an in-depth and singular analysis of the ancient Greek city. The purpose of this article is to analyze Weber’s interpretive choices, in the light of historiographical criticism and a careful analysis of the Typology, in articular as regards the ideal types which he made to understand the city of the ancient Greeks.

Genetic and biophysical modelling evidence of generational connectivity in the intensively exploited, Western North Atlantic red grouper (Epinephelus morio)

Understanding the connectivity of reef organisms is important to assist in the conservation of biological diversity and to facilitate sustainable fisheries in these ecosystems. Common methods to assess reef connectivity include both population genetics and biophysical modelling. Individually, these techniques can offer insight into population structure; however, the information acquired by any singular analysis is often subject to limitations, underscoring the need for a multi-faceted approach. To assess the connectivity dynamics of the red grouper (Epinephelus morio), an economically important reef fish species found throughout the Gulf of Mexico and USA western Atlantic, we utilized two sets of genetic markers (12 microsatellite loci and 632 single nucleotide polymorphisms) to resolve this species’ population genetic structure, along with biophysical modelling to deliver a spatial forecast of potential larval “sources” and “sinks” across these same regions and spatial scale. Our genetic survey indicates little, if any, evidence of population genetic structure and modelling efforts indicate the potential for ecological connectivity between sampled regions over multiple generations. We offer that using a dual empirical and theoretical approach lessens the error associated with the use of any single method and provides an important step towards the validation of either of these methodologies.

The exponential map at a cuspidal singularity

We study spaces with a cuspidal (or horn-like) singularity embedded in a smooth Riemannian manifold and analyze the geodesics in these spaces which start at the singularity. This provides a basis for understanding the intrinsic geometry of such spaces near the singularity. We show that these geodesics combine to naturally define an exponential map based at the singularity, but that the behavior of this map can deviate strongly from the behavior of the exponential map based at a smooth point or at a conical singularity: While it is always surjective near the singularity, it may be discontinuous and non-injective on any neighborhood of the singularity. The precise behavior of the exponential map is determined by a function on the link of the singularity which is an invariant of the induced metric. Our methods are based on the Hamiltonian system of geodesic differential equations and on techniques of singular analysis. The results are proved in the more general natural setting of manifolds with boundary carrying a so-called cuspidal metric.

ANÁLISE DE SÉRIES TEMPORAIS DA TEMPERATURA DO AR E UMIDADE RELATIVA EM CUIABÁ ATRAVÉS DO MÉTODO DE ANÁLISE DE ESPECTRO SINGULAR (ANALYSIS OF TIME SERIES OF AIR TEMPERATURE AND RELATIVE HUMIDITY IN CUIABÁ THROUGH THE METHOD OF ANALYSIS OF SINGULAR SPECTRUM)

Nos últimos anos o método de Análise de Espectro Singular (SSA- Singular Spectrum Analysis) tem sido utilizado como uma técnica na análise de séries temporais de dados meteorológicos e climáticos, possibilitando extrair informações úteis a partir de séries temporais estudadas. Nessa pesquisa, essa técnica foi utilizada no estudo das variáveis de temperatura do ar e umidade relativa em Cuiabá dos anos de 2000 a 2013, utilizando dados fornecidos pelo Instituto Nacional de Meteorologia (INMET). O foco principal do estudo foi extrair informações sobre as tendências e efeitos sazonais das séries temporais. A ação conjunta desses dois fatores é particularmente evidente no caso da temperatura, que apresenta, comumente, dois máximos anuais.