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  • About
  • The Global ETD Search service is a free service for researchers to find electronic theses and dissertations. This service is provided by the Networked Digital Library of Theses and Dissertations.
    Our metadata is collected from universities around the world. If you manage a university/consortium/country archive and want to be added, details can be found on the NDLTD website.
1

The structure of spaces of valuations and the local uniformization problem

2013 September 1900 (has links)
The problem of resolution of singularities is a major problem in algebraic geometry. Local uniformization can be seen as its local version. For varieties over fields of characteristic zero, local uniformization was proved by Zariski in 1940 and resolution of singularities was proved by Hironaka in 1964. For algebraic varieties over fields of positive characteristic both problems are open in dimension greater than 3. Zariski's idea to solve the resolution of singularities problem for an algebraic variety was to prove local uniformization for all valuations of the associated function field and use the compactness of the Zariski space of valuations to glue the solutions together and construct a global resolution. Hence, his approach deals with two aspects: proving local uniformization and using structural properties of spaces of valuations to glue the local solutions. In this thesis, we present our contribution to both aspects. In most of the successful cases, local uniformization was first proved for rank one valuations and then extended to the general case. Local uniformization can be stated as a property of a valuation centered at a local ring R. One of our contributions to the local uniformization problem (which is joint work with Spivakovsky) is that in order to prove local uniformization for valuations centered at local rings in a category M which is closed under taking homomorphic images, finitely generated birational extensions and localizations, it is enough to prove that rank one valuations centered at members of M admit local uniformization. We also obtain this reduction for different versions of local uniformization, for instance, for embedded local uniformization and inseparable local uniformization. Our proofs are particularly important because they do not depend on the nature of the category M. We also work with henselian elements. Henselian elements are roots of polynomials appearing in Hensel's Lemma. We summarize unpublished results of Kuhlmann, van den Dries and Roquette to obtain that for a finite field extension (F|L,v), if F is contained in the absolute inertia field of L, then the valuation ring OF of (F,v) is generated as an OL-algebra by henselian elements. Moreover, we obtain a list of equivalent conditions under which OF is generated over OL by finitely many henselian elements. We prove that if the chain of prime ideals of OL is well-ordered by inclusion, then these conditions are satisfied. We give an example of a finite inertial extension (F|L,v) for which OF is not a finitely generated OL-algebra. We also present a theorem with a simple proof that relates the problem of local uniformization with the theory of henselian elements. This theorem shows, in particular, that if we obtain elimination of ramification for a function field for a good transcendence basis, then the valuation admits local uniformization. In our studies of spaces of valuations we define new topologies on spaces of valuations which extend naturally known topologies. We compare these topologies and show that in general they are not equal. We also obtain criteria under which the space of valuations taking values in a fixed ordered abelian group G is a closed subset in the space of all functions taking values in G. We study the works of Favre and Jonsson and Granja on the valuative tree. Favre and Jonsson prove that the set of all valuations centered at C[[x,y]] admits a tree structure, which they call the valuative tree. Granja extends this result to any two-dimensional regular local ring. In both works, the definition of non-metric rooted tree is not satisfactory. This is because the definition does not guarantee the existence of an infimum for any non-empty set of valuations. This infimum is necessary in order to define and study many concepts related to such trees. We give a more general definition of a rooted non-metric tree and prove that the set of all valuations satisfies this more general definition, namely, we prove that every non-empty set of valuations centered at a two-dimensional regular domain admits an infimum. We also generalize some topological results related to a non-metric tree, for instance that the weak tree topology is always coarser than the metric topology given by any parametrization.
2

Some Fundamental Properties of Valuations Defined on a Field

Doerr, James C. 01 1900 (has links)
The purpose of this thesis is to develop some properties of a special class of functions called valuations. The study begins with and examination of the properties of valuations defined on an arbitrary field, F, and later, consideration is given to valuations defined on the field of rational numbers. The concept of a pseud-valuation is introduced and an investigation is made of the properties of pseudo-valuations.
3

Valuations and Places

Lo, Louis M. T. 01 1900 (has links)
The purpose of this paper is devoted to investigating some fundamental properties of valuations and places.
4

Mirror, Mirror, on the wall, will the market rise or will it fall? A study into the effectiveness of Japanese Candlestick Charting on the Johannesburg Stock Exchange from 2010 to 2019

Mukansi, Tintswalo 07 March 2022 (has links)
Using the methodology developed by Caginalp and Laurent (1998), this study tests the predictive ability of eight three-day reversal candlestick patterns on a sample of sixty listed shares on the Johannesburg Stock Exchange (JSE) from 1 January 2010 to 31 December 2019. The study further investigates the predictability of the patterns on three sub-sectors of the JSE; this included the resource, financial and industrial sectors. As the final step, the study tests the use of the candlestick pattern as a trading strategy before and after costs. To the authors knowledge, it is the first study of candlestick patterns on South Africa's JSE. However, similar studies have been conducted in other emerging markets such as Thailand, Taiwan and Brazil. The study finds that only one of the candlestick patterns, the Three Outside Down pattern, has predictive ability on the JSE. However, when looking at the JSE sub-sectors, the results are more divergent. Candlestick patterns have no predictive ability on the resources and financial sector but on the industrial sector three patterns (Three Inside Up, Three Black Crows and Morning Star) were significant at the ten percent level of significance; and the Three Outside Up and Three Outside Down were at the five percent level of significance. The study finds that after fees the use of candlestick patterns is unable to outperform passive benchmarks. The evidence suggests some violations of the Random Walk Theory, but the study finds that the JSE and its sub-indices are weak-form efficient in terms of the Efficient Market Hypothesis. The Thai and Brazilian markets were also found to be weak-form efficient.
5

Comparison of Logistic Regression and Classification Trees to Forecast Short Term Defaults on Repeat Consumer Loans

Naicker, Keeland 08 March 2022 (has links)
This dissertation highlights the performance comparison between two popular contemporary consumer loan credit scoring techniques, namely logistic regression and classification trees. Literature has shown logistic regression to perform better than classification trees in terms of predictiveness and robustness when forecasting consumer loan default events over standard twelve-month outcome periods. One of the major shortcomings with classification trees is its tendency to overfit data eroding its robustness, making it vulnerable to underlying population characteristic shifts. Classification trees remains a popular technique due to its ease of application (algorithm machine learning basis) and model interpretation. Past research has found classification trees to perform marginally better than logistic regression with respect to predictiveness and robustness when modelling short term consumer credit default outcomes related to previously unseen new customer credit loan applications. This dissertation independently tested this finding on reloan consumer loan data, repeat customers who renewed loan facilities at a significant South African micro lender. This dissertation tests the finding if the classification tree technique would outperform logistic regression when modelling this new type of loan data. Credit scoring models were built and tested for each respective technique across identical data sets with the intent to eliminate bias. Robustness tests were constructed via careful iterative data splits. Performance tests measuring predictiveness and robustness were conducted via the weighted sums of squared error evaluation approach. Results reveal logistic regression to outperform classification trees on predictiveness and robustness across the designed uniform iterative data splits, which suggests that logistic regression remains the superior technique when modelling short term credit default outcomes on reloan consumer loan data.
6

The relationship between foreign exchange reserves, Pula exchange rate and inflation in Botswana

Israel, Bofelo 04 July 2023 (has links) (PDF)
This study examines the relationship between foreign exchange reserve, Pula exchange rate and inflation in Botswana over the period 1995-2020. The period covered contains recent data on level of foreign exchange reserves through global events like Covid-19 pandemic in which significant drawdowns in foreign reserves were experienced and not covered in prior studies. Secondary time series data was sourced from Bank of Botswana financial statistics bulletin and a linear regression was run for two models using R studio statistical software. Unit root and correlation tests were run on the data to ensure the variables were stationery and error terms correlation was eliminated in the time series. Regression equation showed that the relationship between foreign exchange reserves and inflation was negative. Similarly, the second regression revealed that the correlation between foreign exchange reserves and foreign exchange rates was negative. Empirical results further revealed that foreign exchange reserves have no statistically significant impact on inflation and exchange rates in Botswana. The statistically insignificant relationship results between the variables implies that foreign exchange reserves have not significantly influenced exchange rate and inflation which may be due to sterilization by the central bank, therefore, other factors may be responsible for changes in exchange rate and inflation locally. This may indicate that the monetary policy framework which requires foreign exchange reserves have served the country well as it maintained a stable exchange rate and did not stir inflation. However, monetary authorities should note that the current framework may not be sustainable given the tremendous pressure that foreign reserved faced in recent years and a move to a floating exchange regime should be considered as a long-term policy goal. The negative correlation of foreign reserves with inflation and exchange rate further suggest to the monetary authorities that Botswana's economy may be influenced by endogenous monetary policies rather than external variables. The relationship between exchange rates and foreign reserves is consistent with elasticity approach and economic theory of modern mercantilism which predict a negative relationship between the two variables. This may provide monetary authorities and policy makers with a framework that explains the link of Botswana's foreign reserves and exchange rates.
7

Valuations on Fields

Walker, Catherine A. 05 1900 (has links)
This thesis investigates some properties of valuations on fields. Basic definitions and theorems assumed are stated in Capter I. Chapter II introduces the concept of a valuation on a field. Real valuations and non-Archimedean valuations are presented. Chapter III generalizes non-Archimedean valuations. Examples are described in Chapters I and II. A result is the theorem stating that a real valuation of a field K is non-Archimedean if and only if $(a+b) < max4# (a), (b) for all a and b in K. Chapter III generally defines a non-Archimedean valuation as an ordered abelian group. Real non-Archimedean valuations are either discrete or nondiscrete. Chapter III shows that every valuation ring identifies a non-Archimedean valuation and every non-Archimedean valuation identifies a valuation ring.
8

Uniformisation locale simultanée par monomialisation d'éléments clefs / Simultaneaous local uniformization by monomialization of key elements

Decaup, Julie 06 July 2018 (has links)
Le théorème d'uniformisation locale est un résultat important en théorie des singularités. Connu en caractéristique nulle, il reste ouvert en caractéristique positive. Dans cette thèse, nous donnons une version simultanée de ce théorème en caractéristique nulle. On considère R un anneau local régulier muni d'une valuation centrée en son idéal maximal. Nous démontrons l'uniformisation locale par monomialisation simultanée des éléments de R. La preuve apportée ici est nouvelle et riche de trois choses : tout d'abord, nous monomialisons tous les éléments avec la même suite d'éclatements. De plus, cette suite est explicite et nous connaissons les coordonnées pas à pas. Pour finir, nous ne faisons aucune supposition sur le rang de la valuation. Afin de faire cela, nous utilisons une théorie intimement liée à la théorie des valuations : celle des éléments clefs, une généralisation des polynômes clefs, qui est détaillée dans le deuxième chapitre du manuscrit. On y donne une nouvelle définition des polynômes clefs et on étudie leur rapport précis avec les polynômes clefs de MacLane et Vaquié. Enfin, le dernier chapitre est dédié à un cadre plus général : celui des anneaux locaux d'équicaractéristique nulle quasi-excellents intègres. Dans ce cas, la théorie des éléments clefs, bien que nécessaire, n'est plus suffisante. Il nous faudra utiliser l'idéal premier implicite H d'un tel anneau R et montrer que l'on peut réduire l'étude à la régularisation du quotient du complété de R par H. / The local uniformization theorem is an important result in theory of singularities. Known in characteristic zero, it is an open problem in positive characteristic. In this thesis, we give a simultaneous version of this theorem in zero characteristic. We consider a regular local ring R with a valuation centered in its maximal ideal. We prove the local uniformization theorem by monomializing simultaneously the elements of R. The proof given is new and rich in three respects : first, we monomialize every element with the same sequence of blow-ups. Furthermore, this sequence is explicit and we know the coordinates at each step. In addition, the construction is independent of any hypothesis on the rank of the valuation. To this end, we use a theory intimately linked to that of valuations based on the notion of key elements, a generalization of key polynomials, which is explained in detail in the second chapter of this manuscript. We give a new definition of key polynomials and we study their precise relation with key polynomials of Mac Lane and Vaquié. The last chapter is devoted to the more general framework of local quasi-excellent domains of equicharacteristic zero. In this case, although still necessary, the theory of key elements is no longer sufficient. We need to use the implicit prime ideal H of such a ring R and show that the problem can be reduced to the desingularisation of the quotient of the completion of R by H.
9

Earnings Smoothness and Investment Sensitivity to Stock Prices

Huang, Xiaochuan 07 May 2011 (has links)
Existing research suggests that market misvaluations affect corporate investment, often leading to suboptimal investment. I examine whether earnings smoothness reduces the impact of market valuations on corporate investment and in turn enhances investment efficiency. I find that earnings smoothness has a strong negative effect on the sensitivity of corporate investment to stock prices. Further analyses indicate that this negative effect is driven by both innate and discretionary components of earnings smoothness and is more pronounced for firms operating in more volatile business environments. I complement these findings by demonstrating that firms with smoother earnings have lower over- (under-)investment and higher future operating performance. Collectively, the evidence suggests that earnings smoothness improves corporate investment efficiency by reducing the impact of market valuations on investment.
10

The long run impact of rights issues on share price performance and operating performance

Setati, Kwena January 2013 (has links)
Rights issues continue to be a well-researched topic within the field of corporate finance. The focus of this study was to consider the long-run impact of rights issue on company performance both in terms of share price performance and operating performance. The long-run perspective taken in this study adds to the literature, which usually looks at the immediate share price reaction to a rights issue announcement. The study also looked at whether the intended use of capital stated in the SENS announcement had any post-issue effect on the share price. The study found significantly negative cumulative average abnormal returns within the first year after the rights issue. This study confirms the expected negative share price reaction to a rights issue announcement. The study also found evidence that companies that use the proceeds to repay debt, invest or for general purposes had a negative share price reaction to a rights issue announcement. Companies that were vague about the intended purpose of the rights issue had the largest post-issue underperformance. The study did not find any statistically significant evidence that the rights issue announcement had any effect on the operating performance. These findings suggest that rights issues have more impact on a company’s share price, and no clear impact on the operating performance of the issuing company. / Dissertation (MBA)--University of Pretoria, 2013. / lmgibs2014 / Gordon Institute of Business Science (GIBS) / MBA / Unrestricted

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