Measurement of fibre fracture toughness using an alternative specimen geometry

This paper presents an experimental and numerical study focused on the tensile fibre fracture toughness characterisation of hybrid plain weave composite laminates using non-standardized Overheight Compact Tension (OCT) specimens. The position as well as the strain field ahead of the crack tip in the specimens was determined using a digital speckle photogrammetry system. The limitation on the applicability of standard data reduction schemes for the determination of the intralaminar fibre fracture toughness of composites is presented and discussed. A methodology based on the numerical evaluation of the strain energy release rate using the J-integral method is proposed to derive new geometric correction functions for the determination of stress intensity factor for alternative composite specimen geometries. A comparison between different methods currently available to compute the intralaminar fracture toughness in composites is also presented and discussed. Good agreement between numerical and experimental results using the proposed methodology was obtained.

The Rossiter-McLaughlin effect reloaded: Probing the 3D spin-orbit geometry, differential stellar rotation, and the spatially-resolved stellar spectrum of star-planet systems

When a planet transits its host star, it blocks regions of the stellar surface from view; this causes a distortion of the spectral lines and a change in the line-of-sight (LOS) velocities, known as the Rossiter-McLaughlin (RM) effect. Since the LOS velocities depend, in part, on the stellar rotation, the RM waveform is sensitive to the star-planet alignment (which provides information on the system’s dynamical history). We present a new RM modelling technique that directly measures the spatially-resolved stellar spectrum behind the planet. This is done by scaling the continuum flux of the (HARPS) spectra by the transit light curve, and then subtracting the infrom the out-of-transit spectra to isolate the starlight behind the planet. This technique does not assume any shape for the intrinsic local profiles. In it, we also allow for differential stellar rotation and centre-to-limb variations in the convective blueshift. We apply this technique to HD 189733 and compare to 3D magnetohydrodynamic (MHD) simulations. We reject rigid body rotation with high confidence (>99% probability), which allows us to determine the occulted stellar latitudes and measure the stellar inclination. In turn, we determine both the sky-projected (λ ≈ −0.4 ± 0.2◦) and true 3D obliquity (ψ ≈ 7+12 −4 ◦ ). We also find good agreement with the MHD simulations, with no significant centre-to-limb variations detectable in the local profiles. Hence, this technique provides a new powerful tool that can probe stellar photospheres, differential rotation, determine 3D obliquities, and remove sky-projection biases in planet migration theories. This technique can be implemented with existing instrumentation, but will become even more powerful with the next generation of high-precision radial velocity spectrographs.

Object segregation and local gist vision using low-level geometry

Multi-scale representations of lines, edges and keypoints on the basis of simple, complex and end-stopped cells can be used for object categorisation and recognition (Rodrigues and du Buf, 2009 BioSystems 95 206-226). These representations are complemented by saliency maps of colour, texture, disparity and motion information, which also serve to model extremely fast gist vision in parallel with object segregation. We present a low-level geometry model based on a single type of self-adjusting grouping cell, with a circular array of dendrites connected to edge cells located at several angles.

Drilling tool geometry evaluation for reinforced composite laminates

In this work, a comparative study on different drill point geometries and feed rate for composite laminates drilling is presented. For this goal, thrust force monitoring during drilling, hole wall roughness measurement and delamination extension assessment after drilling is accomplished. Delamination is evaluated using enhanced radiography combined with a dedicated computational platform that integrates algorithms of image processing and analysis. An experimental procedure was planned and consequences were evaluated. Results show that a cautious combination of the factors involved, like drill tip geometry or feed rate, can promote the reduction of delamination damage.

Strength improvement of adhesively-bonded joints using a reverse-bent geometry

Adhesive bonding of components has become more efficient in recent years due to the developments in adhesive technology, which has resulted in higher peel and shear strengths, and also in allowable ductility up to failure. As a result, fastening and riveting methods are being progressively replaced by adhesive bonding, allowing a big step towards stronger and lighter unions. However, single-lap bonded joints still generate substantial peel and shear stress concentrations at the overlap edges that can be harmful to the structure, especially when using brittle adhesives that do not allow plasticization in these regions. In this work, a numerical and experimental study is performed to evaluate the feasibility of bending the adherends at the ends of the overlap for the strength improvement of single-lap aluminium joints bonded with a brittle and a ductile adhesive. Different combinations of joint eccentricity were tested, including absence of eccentricity, allowing the optimization of the joint. A Finite Element stress and failure analysis in ABAQUS® was also carried out to provide a better understanding of the bent configuration. Results showed a major advantage of using the proposed modification for the brittle adhesive, but the joints with the ductile adhesive were not much affected by the bending technique.

A theoretical study on modelling the respiratory tract with ladder networks by means of intrinsic fractal geometry

Fractional order modeling of biological systems has received significant interest in the research community. Since the fractal geometry is characterized by a recurrent structure, the self-similar branching arrangement of the airways makes the respiratory system an ideal candidate for the application of fractional calculus theory. To demonstrate the link between the recurrence of the respiratory tree and the appearance of a fractional-order model, we develop an anatomically consistent representation of the respiratory system. This model is capable of simulating the mechanical properties of the lungs and we compare the model output with in vivo measurements of the respiratory input impedance collected in 20 healthy subjects. This paper provides further proof of the underlying fractal geometry of the human lungs, and the consequent appearance of constant-phase behavior in the total respiratory impedance.

An algebraic operator approach to the analysis of Gerber-Shiu functions

We introduce an algebraic operator framework to study discounted penalty functions in renewal risk models. For inter-arrival and claim size distributions with rational Laplace transform, the usual integral equation is transformed into a boundary value problem, which is solved by symbolic techniques. The factorization of the differential operator can be lifted to the level of boundary value problems, amounting to iteratively solving first-order problems. This leads to an explicit expression for the Gerber-Shiu function in terms of the penalty function.

Many valued algebraic structures as measures of comparison

This thesis studies the properties and usability of operators called t-norms, t-conorms, uninorms, as well as many valued implications and equivalences. Into these operators, weights and a generalized mean are embedded for aggregation, and they are used for comparison tasks and for this reason they are referred to as comparison measures. The thesis illustrates how these operators can be weighted with a differential evolution and aggregated with a generalized mean, and the kinds of measures of comparison that can be achieved from this procedure. New operators suitable for comparison measures are suggested. These operators are combination measures based on the use of t-norms and t-conorms, the generalized 3_-uninorm and pseudo equivalence measures based on S-type implications. The empirical part of this thesis demonstrates how these new comparison measures work in the field of classification, for example, in the classification of medical data. The second application area is from the field of sports medicine and it represents an expert system for defining an athlete's aerobic and anaerobic thresholds. The core of this thesis offers definitions for comparison measures and illustrates that there is no actual difference in the results achieved in comparison tasks, by the use of comparison measures based on distance, versus comparison measures based on many valued logical structures. The approach has been highly practical in this thesis and all usage of the measures has been validated mainly by practical testing. In general, many different types of operators suitable for comparison tasks have been presented in fuzzy logic literature and there has been little or no experimental work with these operators.

代微積拾級Dai wei ji shi ji.Loomis' Analytical Geometry and Differential and Integral Calculus.

Traduction de Wylie, rédigée par Li Shan lan ; préfaces Chinoises des deux traducteurs (1859) ; préface anglaise, écrite à Shang hai par A. Wylie (juillet 1859). Liste de termes techniques en anglais et en Chinois. Gravé à la maison Mo hai (1859).18 livres.

The electronic spectra and the determination of the excited state geometry of 3A" propynal /|nby Chhiu-Tsu Lin. -- 260 St. Catharines, Ont. : [s. n.],

Impurity free eluission spectra of HCCCHO and DCCCHO have been rephotographed using the electronic-energy-exchange method with benzene as a carrier gas. The near ultraviolet spectra of ReeCHO and DCCCHO were photographed in a sorption under conditions of high resolution with absorption path lengths up to 100 meters. The emission and absorption spectra of Propynal resulting from 3 n 1 t 1\ - A excitation has been reanalyzed in som.e detail. Botrl of the eH out-of-plane wagging modes were found to have negative anharmonicity. A barrier height of 56.8/0.0 cm- 1 and a nonplanar oft , , equilibrium angle of 17 3 /30 are calculated for the V 10/ lJ 11 modes. The in-plane and out-of-plane v1. brational modes in the 3A." and 1a~. ' elec ronic states of Propynal were subjected to a normal coordinate treatment in the approximat :on of tIle Urey-Bradley force field. From the relative oscillator strengths of the trans1·t1·0ns connect i ng t he v ibrat1•0n1ess lA' , state and t,he V1· bron1·C 3· if levels of the A state, the differences in equilibrium configuration were evaluated from an approximate Franck-Condon analysis based on the ground state normal coordinates. As this treatment gave 512 possible geometrical structures for the upper state, it 4 was necessary to resort to a comparison of the observed and calculated moments of inertia along with chemical intuition to isolate the structure. A test of the correctness of the calculated structure change and the vibrational assignment was raade by evaluating the intensities of the inplane and out-oi-plane fundarnental, sequence, and cross sequellce transitions y the exact Franck-Condon method.

Automatic Structure Generation using Genetic Programming and Fractal Geometry

Three dimensional model design is a well-known and studied field, with numerous real-world applications. However, the manual construction of these models can often be time-consuming to the average user, despite the advantages o ffered through computational advances. This thesis presents an approach to the design of 3D structures using evolutionary computation and L-systems, which involves the automated production of such designs using a strict set of fitness functions. These functions focus on the geometric properties of the models produced, as well as their quantifiable aesthetic value - a topic which has not been widely investigated with respect to 3D models. New extensions to existing aesthetic measures are discussed and implemented in the presented system in order to produce designs which are visually pleasing. The system itself facilitates the construction of models requiring minimal user initialization and no user-based feedback throughout the evolutionary cycle. The genetic programming evolved models are shown to satisfy multiple criteria, conveying a relationship between their assigned aesthetic value and their perceived aesthetic value. Exploration into the applicability and e ffectiveness of a multi-objective approach to the problem is also presented, with a focus on both performance and visual results. Although subjective, these results o er insight into future applications and study in the fi eld of computational aesthetics and automated structure design.

An Abstract Algebraic Theory of L-Fuzzy Relations for Relational Databases

Classical relational databases lack proper ways to manage certain real-world situations including imprecise or uncertain data. Fuzzy databases overcome this limitation by allowing each entry in the table to be a fuzzy set where each element of the corresponding domain is assigned a membership degree from the real interval [0…1]. But this fuzzy mechanism becomes inappropriate in modelling scenarios where data might be incomparable. Therefore, we become interested in further generalization of fuzzy database into L-fuzzy database. In such a database, the characteristic function for a fuzzy set maps to an arbitrary complete Brouwerian lattice L. From the query language perspectives, the language of fuzzy database, FSQL extends the regular Structured Query Language (SQL) by adding fuzzy specific constructions. In addition to that, L-fuzzy query language LFSQL introduces appropriate linguistic operations to define and manipulate inexact data in an L-fuzzy database. This research mainly focuses on defining the semantics of LFSQL. However, it requires an abstract algebraic theory which can be used to prove all the properties of, and operations on, L-fuzzy relations. In our study, we show that the theory of arrow categories forms a suitable framework for that. Therefore, we define the semantics of LFSQL in the abstract notion of an arrow category. In addition, we implement the operations of L-fuzzy relations in Haskell and develop a parser that translates algebraic expressions into our implementation.

Elementos of geometry and trigonometry : from the works of A.M. Legendre, adapted to the course of mathematical instruction in the United State

UANL

An elementary treatise on analytic geometry, embracing plane geometry and an introduction to geometry of threee dimensions with numerous examples.

UANL

Quotients d'une variété algébrique par un groupe algébrique linéairement réductif et ses sous-groupes maximaux unipotents

La construction d'un quotient, en topologie, est relativement simple; si $G$ est un groupe topologique agissant sur un espace topologique $X$, on peut considérer l'application naturelle de $X$ dans $X/G$, l'espace d'orbites muni de la topologie quotient. En géométrie algébrique, malheureusement, il n'est généralement pas possible de munir l'espace d'orbites d'une structure de variété. Dans le cas de l'action d'un groupe linéairement réductif $G$ sur une variété projective $X$, la théorie géométrique des invariants nous permet toutefois de construire un morphisme de variété d'un ouvert $U$ de $X$ vers une variété projective $X//U$, se rapprochant autant que possible d'une application quotient, au sens topologique du terme. Considérons par exemple $X\subseteq P^{n}$, une $k$-variété projective sur laquelle agit un groupe linéairement réductif $G$ et supposons que cette action soit induite par une action linéaire de $G$ sur $A^{n+1}$. Soit $\widehat{X}\subseteq A^{n+1}$, le cône affine au dessus de $\X$. Par un théorème de la théorie classique des invariants, il existe alors des invariants homogènes $f_{1},...,f_{r}\in C[\widehat{X}]^{G}$ tels que $$C[\widehat{X}]^{G}= C[f_{1},...,f_{r}].$$ On appellera le nilcone, que l'on notera $N$, la sous-variété de $\X$ définie par le locus des invariants $f_{1},...,f_{r}$. Soit $Proj(C[\widehat{X}]^{G})$, le spectre projectif de l'anneau des invariants. L'application rationnelle $$\pi:X\dashrightarrow Proj(C[f_{1},...,f_{r}])$$ induite par l'inclusion de $C[\widehat{X}]^{G}$ dans $C[\widehat{X}]$ est alors surjective, constante sur les orbites et sépare les orbites autant qu'il est possible de le faire; plus précisément, chaque fibre contient exactement une orbite fermée. Pour obtenir une application régulière satisfaisant les mêmes propriétés, il est nécessaire de jeter les points du nilcone. On obtient alors l'application quotient $$\pi:X\backslash N\rightarrow Proj(C[f_{1},...,f_{r}]).$$ Le critère de Hilbert-Mumford, dû à Hilbert et repris par Mumford près d'un demi-siècle plus tard, permet de décrire $N$ sans connaître les $f_{1},...,f_{r}$. Ce critère est d'autant plus utile que les générateurs de l'anneau des invariants ne sont connus que dans certains cas particuliers. Malgré les applications concrètes de ce théorème en géométrie algébrique classique, les démonstrations que l'on en trouve dans la littérature sont généralement données dans le cadre peu accessible des schémas. L'objectif de ce mémoire sera, entre autres, de donner une démonstration de ce critère en utilisant autant que possible les outils de la géométrie algébrique classique et de l'algèbre commutative. La version que nous démontrerons est un peu plus générale que la version originale de Hilbert \cite{hilbert} et se retrouve, par exemple, dans \cite{kempf}. Notre preuve est valide sur $C$ mais pourrait être généralisée à un corps $k$ de caractéristique nulle, pas nécessairement algébriquement clos. Dans la seconde partie de ce mémoire, nous étudierons la relation entre la construction précédente et celle obtenue en incluant les covariants en plus des invariants. Nous démontrerons dans ce cas un critère analogue au critère de Hilbert-Mumford (Théorème 6.3.2). C'est un théorème de Brion pour lequel nous donnerons une version un peu plus générale. Cette version, de même qu'une preuve simplifiée d'un théorème de Grosshans (Théorème 6.1.7), sont les éléments de ce mémoire que l'on ne retrouve pas dans la littérature.