Computer integrated manufacturing environments and competition among companies to meet customer requirements raise the need for the use of online methodologies in combination with traditional Statistical Process Control tools. This study focuses on detecting the change point, when a shift in mean occurs, in a normal bivariate process using two different approaches. First, Multivariate Cumulative Sum (MCUSUM) and Multivariate Exponentially Weighted Moving Average (MEWMA) statistical procedures were used in detecting the mean shift in the process. Then the step-change detection and neural network approaches were applied to the outputs of MCUSUM and MEWMA statistical procedures to identify the time of the change. The results show that the step-change and neural network approaches are capable of detecting the time of the change earlier than either the MCUSUM or MEWMA statistical procedure.

We develop several continuous method models for convex quadratic programming (CQP) problems with di.erent types of constraints. The essence of the continuous method is to construct one ordinary di.erential equation (ODE) system such that its limiting equilibrium point corresponds to an optimal solution of the underlying optimization problem. All our continuous method models share the main feature of the interior point methods, i.e., starting from any interior point, all the solution trajectories remain in the interior of the feasible regions. First, we present an a.ne scaling continuous method model for nonnegativity constrained CQP. Under the boundedness assumption of the optimal set, a thorough study on the properties of the ordinary di.erential equation is provided, strong con­vergence of the continuous trajectory of the ODE system is proved. Following the features of this ODE system, a new ODE system for solving box constrained CQP is also presented. Without projection, the whole trajectory will stay inside the box region, and it will converge to an optimal solution. Preliminary simulation results illustrate that our continuous method models are very encouraging in obtaining the optimal solutions of the underlying optimization problems. For CQP in the standard form, the convergence of the iterative .rst-order a.ne scaling algorithm is still open. Under boundedness assumption of the optimal set and nondegeneracy assumption of the constrained region, we discuss the properties of the ODE system induced by the .rst-order a.ne scaling direction. The strong convergence of the continuous trajectory of the ODE system is also proved. Finally, a simple iterative scheme induced from our ODE is presented for find­ing an optimal solution of nonnegativity constrained CQP. The numerical results illustrate the good performance of our continuous method model with this iterative scheme. Keywords: ODE; Continuous method; Quadratic programming; Interior point method; A.ne scaling.

No description available.

The main aim of this research is to develop an on-line tool wear condition monitoring intelligent system for single-point turning operations. This is to provide accurate and reliable information on the different states of tool wear. Calibrated acoustic emission and vibration techniques were implemented to monitor the progress of wear on carbide tool tips. Previous research has shown that acoustic emission (AE) is sensitive to tool wear. However, AE, as a monitoring technique, is still not widely adopted by industry. This is because it is as yet impossible to achieve repeatable measurements of AE. The variability is due to inconsistent coupling of the sensor with structures and the fact that the tool structure may have different geometry and material property. Calibration is therefore required so that the extent of variability becomes quantifiable, and hence accounted for or removed altogether. Proper calibration needs a well-defined and repeatable AE source. In this research, various artificial sources were reviewed in order to assess their suitability as an AE calibration source for the single-point machining process. Two artificial sources were selected for studying in detail. These are an air jet and a pulsed laser; the former produces continuous-type AE and the latter burst type AE. Since the air jet source has a power spectrum resembling closely the AE produced from single-point machining and since it is readily available in a machine shop, not to mention its relative safety compared to laser, an air-jet source is a more appealing choice. The calibration procedure involves setting up an air jet at a fixed stand-off distance from the top rake of the tool tip, applying in sequence a set of increasing pressures and measuring the corresponding AE. It was found that the root-mean-square value of the AE obtained is linearly proportional to the pressure applied. Thus, irrespective of the layout of the sensor and AE source in a tool structure, AE can be expressed in terms of the common currency of 'pressure' using the calibration curve produced for that particular layout. Tool wear stages can then be defined in terms of the 'pressure' levels. In order to improve the robustness of the monitoring system, in addition to AE, vibration information is also used. In this case, the acceleration at the tool tip in the tangential and feed directions is measured. The coherence function between these two signals is then computed. The coherence is a function of the vibration frequency and has a value ranging from 0 to 1, corresponding to no correlation and full correlation respectively between the two acceleration signals. The coherence function method is an attempt to provide a solution, which is relatively insensitive to the dynamics and the process variables except tool wear. Three features were identified to be sensitive to tool wear and they are; AErms, and the coherence function of the acceleration at natural frequency (2.5-5.5 kHz) of the tool holder and at high frequency end (18-25kHz) respectively. A belief network, based on Bayes' rule, was created providing fusion of data from AE and vibration for tool wear classification. The conditional probabilities required for the belief network to operate were established from examples. These examples were presented to the belief network as a file of cases. The file contains the three features mentioned earlier, together with cutting conditions and the tool wear states. Half of the data in this file was used for training while the other half was used for testing the network. The performance of the network gave an overall classification error rate of 1.6 % with the WD acoustic emission sensor and an error rate of 4.9 % with the R30 acoustic emission sensor.

Point processes are mechanisms that beget point patterns. Realisations of point processes are observed in many contexts, for example, locations of stars in the sky, or locations of trees in a forest. Inferring the mechanisms that drive point processes relies on the development of models that appropriately account for the dependencies inherent in the data. Fitting models that adequately capture the complex dependency structures in either space, time, or both is often problematic. This is commonly due to—but not restricted to—the intractability of the likelihood function, or computational burden of the required numerical operations. This thesis primarily focuses on developing point process models with some hierarchical structure, and specifically where this is a latent structure that may be considered as one of the following: (i) some unobserved construct assumed to be generating the observed structure, or (ii) some stochastic process describing the structure of the point pattern. Model fitting procedures utilised in this thesis include either (i) approximate-likelihood techniques to circumvent intractable likelihoods, (ii) stochastic partial differential equations to model continuous spatial latent structures, or (iii) improving computational speed in numerical approximations by exploiting automatic differentiation. Moreover, this thesis extends classic point process models by considering multivariate dependencies. This is achieved through considering a general class of joint point process model, which utilise shared stochastic structures. These structures account for the dependencies inherent in multivariate point process data. These models are applied to data originating from various scientific fields; in particular, applications are considered in ecology, medicine, and geology. In addition, point process models that account for the second order behaviour of these assumed stochastic structures are also considered.

On s'intéresse, dans cette thèse, à des questions concernant le nombre maximum de points rationnels d'une courbe singulière définie sur un corps fini, sujet qui, depuis Weil, a été amplement abordé dans le cas lisse. Cette étude se déroule en deux temps. Tout d'abord on présente une construction de courbes singulières de genres et corps de base donnés, possédant un grand nombre de points rationnels : cette construction, qui repose sur des notions et outils de géométrie algébrique et d'algèbre commutative, permet de construire, en partant d'une courbe lisse X, une courbe à singularités X', de telle sorte que X soit la normalisée de X', et que les singularités ajoutées soient rationnelles sur le corps de base et de degré de singularité prescrit. Ensuite, en utilisant une approche euclidienne, on prouve une nouvelle borne sur le nombre de points fermés de degré deux d'une courbe lisse définie sur un corps fini.La combinaison de ces résultats, à priori indépendants, permet notamment d'étudier le problème de savoir quand la borne d'Aubry-Perret, analogue de la borne de Weil dans le cas singulier, est atteinte. Cela nous amène de façon naturelle à l'étude des propriétés des courbes maximales et, lorsque la cardinalité du corps de base est un carré, à l'analyse du spectre des genres de ces dernières. / In this PhD thesis, we focus on some issues about the maximum number of rational points on a singular curve defined over a finite field. This topic has been extensively discussed in the smooth case since Weil's works. We have split our study into two stages. First, we provide a construction of singular curves of prescribed genera and base field and with many rational points: such a construction, based on some notions and tools from algebraic geometry and commutative algebra, yields a method for constructing, given a smooth curve X, another curve X' with singularities, such that X is the normalization of X', and the added singularities are rational on the base field and with the prescribed singularity degree. Then, using a Euclidian approach, we prove a new bound for the number of closed points of degree two on a smooth curve defined over a finite field.Combining these two a priori independent results, we can study the following question: when is the Aubry-Perret bound (the analogue of the Weil bound in the singular case) reached? This leads naturally to the study of the properties of maximal curves and, when the cardinality of the base field is a square, to the analysis of the spectrum of their genera.

Nonlinear programming is a very important tool for optimizing many systems in science and engineering. The interior point solver IPOPT has become one of the most popular solvers for NLP because of its high performance. However, certain types of problems are still challenging for IPOPT. This dissertation considers three improvements or extensions to IPOPT to improve performance on several practical classes of problems. Compared to active set solvers that treat inequalities by identifying active constraints and transforming to equalities, the interior point method is less robust in the presence of degenerate constraints. Interior point methods require certain regularity conditions on the constraint set for the solution path to exist. Dependent constraints commonly appear in applications such as chemical process models and violate the regularity conditions. The interior point solver IPOPT introduces regularization terms to attempt to correct this, but in some cases the required regularization terms either too large or too small and the solver will fail. To deal with these challenges, we present a new structured regularization algorithm, which is able to numerically delete dependent equalities in the KKT matrix. Numerical experiments on hundreds of modified example problems show the effectiveness of this approach with average reduction of more than 50% of the iterations. In some contexts such as online optimization, very fast solutions of an NLP are very important. To improve the performance of IPOPT, it is best to take advantage of problem structure. Dynamic optimization problems are often called online in a control or stateestimation. These problems are very large and have a particular sparse structure. This work investigates the use of parallelization to speed up the NLP solution. Because the KKT factorization is the most expensive step in IPOPT, this is the most important step to parallelize. Several cyclic reduction algorithms are compared for their performance on generic test matrices as well as matrices of the form found in dynamic optimization. The results show that for very large problems, the KKT matrix factorization time can be improved by a factor of four when using eight processors. Mathematical programs with complementarity constraints (MPCCs) are another challenging class of problems for IPOPT. Several algorithmic modifications are examined to specially handle the difficult complementarity constraints. First, two automatic penalty adjustment approaches are implemented and compared. Next, the use of our structured regularization is tested in combination with the equality reformulation of MPCCs. Then, we propose an altered equality reformulation of MPCCs which effectively removes the degenerate equality or inequality constraints. Using the MacMPEC test library and two applications, we compare the efficiency of our approaches to previous NLP reformulation strategies.

In this thesis, we first obtain coincidence and common fixed point theorems for a pair of generalized non-expansive type mappings in a normed space. Then we discuss two types of convergence theorems, namely, the convergence of Mann iteration procedures and the convergence and stability of fixed points. In addition, we discuss the viscosity approximations generated by (ψ ,ϕ)-weakly contractive mappings and a sequence of non-expansive mappings and then establish Browder and Halpern type convergence theorems on Banach spaces. With regard to iteration procedures, we obtain a result on the convergence of Mann iteration for generalized non-expansive type mappings in a Banach space which satisfies Opial's condition. And, in the case of stability of fixed points, we obtain a number of stability results for the sequence of (ψ,ϕ)- weakly contractive mappings and the sequence of their corresponding fixed points in metric and 2-metric spaces. We also present a generalization of Fraser and Nadler type stability theorems in 2-metric spaces involving a sequence of metrics.

Background: Tobacco marketing has been established as the main motivator for tobacco use among youth. A proliferation of tobacco promotional activities in retail stores has been observed yet little is known about its impact on adolescent smoking behaviours. The purpose of this study is to use secondary data to describe the prevalence of retail tobacco point-of-purchase (PoP) activities, examine its associations with adolescent smoking behaviours, and determine what ecological factors moderate the relationship between PoP activities and student smoking behaviours in British Columbia. Methods: This cross-sectional study surveyed grade 10-11 students from 22 randomly-selected schools in BC on student smoking behaviour and conducted observations in 57 retail stores on tobacco PoP activities located within a 1 km radius of these schools. Descriptive analysis was conducted on retail tobacco PoP variables. Individual data on smoking behaviour and school level data on retailers were linked to analyse the association between retail tobacco PoP activities and student smoking behaviour using logistic regression. Moderating effects of contextual factors were also examined. GIS maps were generated to illustrate study findings. Result: A moderate to strong presence of tobacco PoP activities was observed in all tobacco retail stores located in BC school neighbourhoods. Nearly all stores displayed cigarette products in a visible manner (98.25%) and posted tobacco control signage (94.74%). In this model, proportion of stores in the school neighbourhood with presence of tobacco advertising increased the odds of a student being a smoker (OR = 1.28-3.27). Proportion of stores in the school neighbourhood with presence of tobacco control signage decreased the odds of a student being a smoker (OR = 0.11-0.66). The odds of a student being a smoker increased if they resided on the island compared to living in the lower mainland (OR = 1.11-1.75). Discussion: Convenience stores exhibited more tobacco PoP activities than other store types. Retailers in the school neighbourhood that had tobacco advertisements and tobacco control signage exhibited both detrimental and protective effects on student smoking. This provides supportive evidence to ban tobacco advertising in retail stores and increase efforts for creating an anti-tobacco environment in neighbourhood retail stores. Maps generated served descriptive and hypothesis generating purposes. / Medicine, Faculty of / Population and Public Health (SPPH), School of / Graduate

A fixed point of a mapping is an element in the domain of the mapping that is mapped into itself by the mapping. The study of fixed points has been a field of interests to mathematicians since the discovery of the Banach contraction theorem, i.e. if is a complete metric space and is a contraction mapping (i.e. there exists such that for all ), then has a unique fixed point. The Banach contraction theorem has found many applications in pure and applied mathematics. Due to fixed point theory being a mixture of analysis, geometry, algebra and topology, its applications to other fields such as physics, economics, game theory, chemistry, engineering and many others has become vital. The theory is nowadays a very active field of research in which many new theorems are published, some of them applied and many others generalized. Motivated by all of this, we give an exposition of some generalizations of fixed point theorems in metric fixed point theory, which is a branch of fixed point theory about results of fixed points of mappings between metric spaces, where certain properties of the mappings involved need not be preserved under equivalent metrics. For instance, the contractive property of mappings between metric spaces need not be preserved under equivalent metrics. Since metric fixed point theory is wide, we limit ourselves to fixed point theorems for self and non-self-mappings on Banach and metric spaces. We also take a look at some open problems on this topic of study. At the end of the dissertation, we suggest our own problems for future research.