The objects studied in this thesis are families of cycles on schemes. A space — the Chow variety — parameterizing effective equidimensional cycles was constructed by Chow and van der Waerden in the first half of the twentieth century. Even though cycles are simple objects, the Chow variety is a rather intractable object. In particular, a good functorial description of this space is missing. Consequently, descriptions of the corresponding families and the infinitesimal structure are incomplete. Moreover, the Chow variety is not intrinsic but has the unpleasant property that it depends on a given projective embedding. A main objective of this thesis is to construct a closely related space which has a good functorial description. This is partly accomplished in the last paper. The first three papers are concerned with families of zero-cycles. In the first paper, a functor parameterizing zero-cycles is defined and it is shown that this functor is represented by a scheme — the scheme of divided powers. This scheme is closely related to the symmetric product. In fact, the scheme of divided powers and the symmetric product coincide in many situations. In the second paper, several aspects of the scheme of divided powers are discussed. In particular, a universal family is constructed. A different description of the families as multi-morphisms is also given. Finally, the set of k-points of the scheme of divided powers is described. Somewhat surprisingly, cycles with certain rational coefficients are included in this description in positive characteristic. The third paper explains the relation between the Hilbert scheme, the Chow scheme, the symmetric product and the scheme of divided powers. It is shown that the last three schemes coincide as topological spaces and that all four schemes are isomorphic outside the degeneracy locus. The last paper gives a definition of families of cycles of arbitrary dimension and a corresponding Chow functor. In characteristic zero, this functor agrees with the functors of Barlet, Guerra, Kollár and Suslin-Voevodsky when these are defined. There is also a monomorphism from Angéniol's functor to the Chow functor which is an isomorphism in many instances. It is also confirmed that the morphism from the Hilbert functor to the Chow functor is an isomorphism over the locus parameterizing normal subschemes and a local immersion over the locus parameterizing reduced subschemes — at least in characteristic zero. / QC 20100908

ABSTRACT ROBUST CONTROL CHARTS &Ccedil / etiny&uuml / rek, Aysun M. Sc., Department of Statistics Supervisor: Dr. BariS S&uuml / r&uuml / c&uuml / Co-Supervisor: Assoc. Prof. Dr. Birdal Senoglu December 2006, 82 pages Control charts are one of the most commonly used tools in statistical process control. A prominent feature of the statistical process control is the Shewhart control chart that depends on the assumption of normality. However, violations of underlying normality assumption are common in practice. For this reason, control charts for symmetric distributions for both long- and short-tailed distributions are constructed by using least squares estimators and the robust estimators -modified maximum likelihood, trim, MAD and wave. In order to evaluate the performance of the charts under the assumed distribution and investigate robustness properties, the probability of plotting outside the control limits is calculated via Monte Carlo simulation technique.

Under the consideration of ¡§avoiding the overusing the ground water¡¨, ¡§proper planning for the utilization of the land in the land-subsidence areas¡¨, and ¡§facilitating the exploitation of surface water and substitute water¡¨, we take eight counties included in the ground-water-constrained areas in Kaohsiung as illustrations to discuss the issue of optimal planning for matching the land-use and the demand of water resource. Compared with the traditional Linear Programming, Fuzzy Linear Programming has received a great deal of attention in the recent years for its strength on working out results more fitting in with the uncertainty faced while making decisions in practice, and we adopt this model to solve the problem in this study. By separately following the Zimmermann¡¦s Symmetric Model, Werners¡¦s Symmetric Model and combining model of Delgado¡¦s Model and Flexible Programming, we show that setting 2006 as the target year, our models can properly describe linguistic objective and vague constraints after taking the uncertainty of the result into account and work out the optimal-alterative-based planning.

In this Thesis, the problems of the Free Flexural (or Bending) Vibrations of Composite, Orthotropic Plates and/or Panels with Various Bonded Joints are formulated and investigated in detail. The composite bonded plate system is composed of Plate Adherends adhesively bonded by relatively very thin adhesive layers. The general problem is considered in terms of the three Main PROBLEMS, namely Main PROBLEM I, Main PROBLEM II and Main PROBLEM III. The theoretical formulation of the Main PROBLEMS is based on Mindlin Plate Theory which is a First Order Shear Deformation Plate Theory (FSDPT). Thus, the transverse shear deformations, the transverse and the rotary moments of inertia of the plates are included in the formulation. Very thin, elastic deformable adhesive layers are considered as continua with transverse normal and shear stresses. The damping effects in the plates and the adhesive layers are neglected. The entire composite bonded joint assembly is assumed to be simple supported along the two opposite edges, so that the Classical Levy&amp / #8217 / s Solutions can be applied in this direction. The dynamic equations of the Bonded Joint System which combines together the Mindlin Plate dynamic equations with the adhesive layer equations are reduced to a system of First Order Ordinary Differential Equations in the state vector form. This special form of the Governing System of the First Order Ordinary Differential Equations are numerically integrated by means of the Modified Transfer Matrix Method which is a combination of the Classical Levy&amp / #8217 / s Method, the Transfer Matrix Method and the Integrating Matrix Method (with Interpolation Polynomials and/or Chebyshev Polynomials). The Main PROBLEMS are investigated and presented in terms of the mode shapes and the corresponding natural frequencies for various sets of boundary conditions. The significant effects of the hard and the soft adhesive layer elastic constants on the mode shapes and on the natural frequencies are demonstrated. Some important parametric studies such as the influences of the Joint Length Ratio, the Joint Position Ratio, the Bending Stiffness Ratio, etc. on the natural frequencies are computed and plotted for the hard and soft adhesive cases for several support conditions.

Made available in DSpace on 2015-05-14T13:21:10Z (GMT). No. of bitstreams: 0 Previous issue date: 2011-05-06 / Coordenação de Aperfeiçoamento de Pessoal de Nível Superior / Neste trabalho, estabelecemos a existência de uma solução simétrica positiva, como também uma solução não-simétrica que muda de sinal, para o problema elíptico semilinear u + V (z)u = f(z; u); u 2 H1(RN); onde N 4; V : RN ! R é um potencial não-negativo e f : RNR ! R é uma função contínua. Para obtermos os resultados, usamos o Teorema do Passo da Montanha, o Princípio de Criticalidade e resultados de compacidade.

Made available in DSpace on 2015-05-15T11:46:00Z (GMT). No. of bitstreams: 1 arquivototal.pdf: 527317 bytes, checksum: 8813dca2fcd848a18ab218a0f8fa470b (MD5) Previous issue date: 2011-05-06 / Coordenação de Aperfeiçoamento de Pessoal de Nível Superior / In this work, we establish the existence of a positive symmetric solution and a nonsymmetric solution which changes sing, for the semilinear elliptic problem ---u + V (z)u = f(z; u); u 2 H1(RN); where N - 4; V : RN ! R is a non-negative potential and f : RN-R ! R is a continuous function. To achieve these results, we use the Mountain Pass Theorem, the Principle of Symmetric Criticality and compactness results. / Neste trabalho, estabelecemos a existência de uma solução simétrica positiva, como também uma solução não-simétrica que muda de sinal, para o problema elíptico semilinear ---u + V (z)u = f(z; u); u 2 H1(RN); onde N - 4; V : RN ! R é um potencial não-negativo e f : RN - R ! R é uma função contínua. Para obtermos os resultados, usamos o Teorema do Passo da Montanha, o Princípio de Criticalidade e resultados de compacidade.

Neste trabalho foi proposto o modelo linear parcial generalizado simétrico, com base nos modelos lineares parciais generalizados e nos modelos lineares simétricos, em que a variável resposta segue uma distribuição que pertence à família de distribuições simétricas, considerando um preditor linear que possui uma parte paramétrica e uma não paramétrica. Algumas distribuições que pertencem a essa classe são as distribuições: Normal, t-Student, Exponencial potência, Slash e Hiperbólica, dentre outras. Uma breve revisão dos conceitos utilizados ao longo do trabalho foram apresentados, a saber: análise residual, influência local, parâmetro de suavização, spline, spline cúbico, spline cúbico natural e algoritmo backfitting, dentre outros. Além disso, é apresentada uma breve teoria dos modelos GAMLSS (modelos aditivos generalizados para posição, escala e forma). Os modelos foram ajustados utilizando o pacote gamlss disponível no software livre R. A seleção de modelos foi baseada no critério de Akaike (AIC). Finalmente, uma aplicação é apresentada com base em um conjunto de dados reais da área financeira do Chile. / In this work we propose the symmetric generalized partial linear model, based on the generalized partial linear models and symmetric linear models, that is, the response variable follows a distribution that belongs to the symmetric distribution family, considering a linear predictor that has a parametric and a non-parametric component. Some distributions that belong to this class are distributions: Normal, t-Student, Power Exponential, Slash and Hyperbolic among others. A brief review of the concepts used throughout the work was presented, namely: residual analysis, local influence, smoothing parameter, spline, cubic spline, natural cubic spline and backfitting algorithm, among others. In addition, a brief theory of GAMLSS models is presented (generalized additive models for position, scale and shape). The models were adjusted using the package gamlss available in the free R software. The model selection was based on the Akaike criterion (AIC). Finally, an application is presented based on a set of real data from Chile\'s financial area.

Résumé de la thèse :ce travail porte sur la notion d'espace symétrique symplectique extrinsèque. Ces espaces sont des espaces symétriques symplectiques dont la structure est induite par le plongement dans variété symplectique ambiante munie d'une connexion.<p><p>Par analogie à la théorie standard des espaces symétriques, nous démontrons un théorème d'équivalence entre les espaces symétriques symplectiques extrinsèques d'une variété qui est elle-même un espace symétrique symplectique.<p><p>La définition d'un espace symétrique symplectique extrinsèque fait intervenir l'existence d'affinités globales de la variété ambiante, les ``symétries extrinsèques', qui induisent la structure symétrique de la sous-variété ;ceci mène à poser une question du type :quelles sont les variétés possédant ``beaucoup' de ces affinités~? Une question précise ainsi qu'une réponse sont fournies dans un contexte où la variété ambiante est seulement supposée munie d'une structure<p>symplectique et d'une connexion symplectiques. Nous considérons également le cas où ces symétries commutent avec un champ $K$ d'endomorphismes symplectiques fixé de la variété, de carré $pmId$. Nous définissons une notion de courbure sectionnelle pour plans $K$-stables et montrons que les espaces à $K$-courbure sectionnelle constantes sont localement symétriques de type Ricci.<p><p>Par suite nous étudions les espaces symétriques symplectiques extrinsèques dans un espace vectoriel symplectique. Nous montrons par exemple qu'un tel espace, s'ils est de dimension deux, est forcément intrinsèquement plat (c.-à-d. à courbure intrinsèque nulle), mais que son image n'est pas forcément un plan affin de l'espace vectoriel ambiant. Nous décrivons en fait explicitement tous les espaces<p>symétriques symplectiques extrinsèques, dans un espace vectoriel, dont la courbure intrinsèque s'annule identiquement. Nous décrivons également une famille d'exemples d'espaces extrinsèques, dont nous montrons qu'elle fournit la totalité des espaces extrinsèques de codimension $2$, dans un espace vectoriel.<p><p>Enfin, nous décrivons quelques exemples d'espaces symétriques symplectiques extrinsèques qui sont totalement géodésiques, dans un espace de type Ricci particulier.<p> / Doctorat en Sciences / info:eu-repo/semantics/nonPublished

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The main objective of this dissertation is the development of CUSUM procedures based on signed and unsigned sequential ranks. These CUSUMs can be applied to detect changes in the location or dispersion of a process. The signed and unsigned sequential rank CUSUMs are distribution-free and robust against the effect of outliers in the data. The only assumption that these CUSUMs require is that the in-control distribution is symmetric around a known location parameter. These procedures specifically do not require the existence of any higher order moments. Another advantage of these CUSUMs is that Monte Carlo simulation can readily be applied to deliver valid estimates of control limits, irrespective of what the underlying distribution may be. Other objectives of this dissertation include a brief discussion of the results and refinements of the CUSUM in the literature. We justify the use of a signed sequential rank statistic. Also, we evaluate the relative efficiency of the suggested procedure numerically and provide three real-world applications from the engineering and financial industries. / MSc (Risk Analysis), North-West University, Potchefstroom Campus, 2015