The Four Bars Problem

A four-bar linkage is a mechanism consisting of four rigid bars which are joined by their endpoints in a polygonal chain and which can rotate freely at the joints (or vertices). We assume that the linkage lies in the 2-dimensional plane so that one of the bars is held horizontally fixed. In this paper we consider the problem of reconfiguring a four-bar linkage using an operation called a \emph{pop}. Given a polygonal cycle, a pop reflects a vertex across the line defined by its two adjacent vertices along the polygonal chain. Our main result shows that for certain conditions on the lengths of the bars of the four-bar linkage, the neighborhood of any configuration that can be reached by smooth motion can also be reached by pops. The proof relies on the fact that pops are described by a map on the circle with an irrational number of rotation.Comment: 18 page

Calculation of the hull and of the car-suspension systems of airships

Differential and integral curves are presented and well as numerous calculations relating to hulls. Some of the calculations include those relating to hulls, those relating to the invariability of the shape of the hulls, and those relating to the suspension of the hull

SPATIAL STATISTICS ON AMAZON RAINFOREST ASSESSMENT: SPATIALLY STRATIFIED INVENTORY PROCESSING

Biomass and wood volume estimates in forest ecosystems are fundamental to a variety of studies focusing at forest dynamics. These estimates are usually carried out through forest inventory techniques which rely upon statistical computations. This work aims at providing a new methodological approach to forest inventory processing when data is georeferenced. Specifically, geostatistical modelling is performed through ordinary co-kriging using tree basal area and tree richness as a cofactor in an Amazonian rainforest site. The spatial interpolation provided the tools for the creation of two disjoint forest strata, which are processed following the principles of Stratified Forest Inventory. The spatially stratified forest inventory processing has shown a 14.29% decrease in error as directly compared to simple random sampling processing. Only two strata have been used following spatial interpolation, albeit it is argued that theoretically any number of them could be generated. The procedure is methodologically feasible and offers a framework to future research on its development and reach. Particularly, the geometries of forest strata and the behavior of spatial interpolation along a gradient of forest vertical structures are of potential interest in future work

Aquatics reconstruction software: the design of a diagnostic tool based on computer vision algorithms

Computer vision methods can be applied to a variety of medical and surgical applications, and many techniques and algorithms are available that can be used to recover 3D shapes and information from images range and volume data. Complex practical applications, however, are rarely approachable with a single technique, and require detailed analysis on how they can be subdivided in subtasks that are computationally treatable and that, at the same time, allow for the appropriate level of user-interaction. In this paper we show an example of a complex application where, following criteria of efficiency, reliability and user friendliness, several computer vision techniques have been selected and customized to build a system able to support diagnosis and endovascular treatment of Abdominal Aortic Aneurysms. The system reconstructs the geometrical representation of four different structures related to the aorta (vessel lumen, thrombus, calcifications and skeleton) from CT angiography data. In this way it supports the three dimensional measurements required for a careful geometrical evaluation of the vessel, that is fundamental to decide if the treatment is necessary and to perform, in this case, its planning. The system has been realized within the European trial AQUATICS (IST-1999-20226 EUTIST-M WP 12), and it has been widely tested on clinical data

On the eigenvalue distribution of adjacency matrices for connected planar graphs

This paper describes the previously unknown statistical distribution of adjacency matrix spectra for planar graphs, also known as spatial weights matrices, in terms of the following three readily available eigenvalue properties: extremes, rank orderings, and sums of powers. This distribution is governed by at most six parameters that, once known, allow accurate approximations of eigenvalues to be computed without resorting to numerical matrix methods applied on a case-by-case basis. Parameter estimates for illustrative real-world examples are obtained using nonlinear least squares regression techniques. Three conjectures are proposed, and graphical and trend results are reported for a diverse set of planar graph-based matrices

Combinatorial and analytic techniques for lattice path enumeration

This bachelor s degree thesis studies two type of combinatorial objects. The first ones are exact models of which we can get exact counting formulas, whereas the second type of models are the ones of which we don t have enumerative exact results. The first part of the work focuses on the exact models and two methods useful to find counting formulas are described: the Symbolic method and the Kernel method. In the second part of this thesis, an specific type of non exact model is addressed: self-avoiding walks. Although there are no exact counting formulas, we are going to study its asymptotic behaviour and we will proof a theorem which states that the connective constant of self-avoiding walks in the hexagonal lattice H equals √2 + √2

Transonic liquid bells

http://www.irphe.univ-mrs.fr/~clanet/PaperFile/PHFBell.pdfThe shape of a liquid bell resulting from the overflow of a viscous liquid out of a circular dish is investigated experimentally and theoretically. The main property of this bell is its ability to sustain the presence of a ‘‘transonic point,'' where the liquid velocity equals the speed of antisymmetric—or sinuous—surface waves. Their shape and properties are thus rather different from usual ‘‘hypersonic'' water bells. We first show that the bell shape can be calculated very accurately, starting from the sonic point.We then demonstrate the extreme sensitivity of the shape of these bells to the difference of pressure across the interface, making them a perfect barometer. Finally, we discuss the oscillations of the bell which occur close to the bursting limit