We know that the best linear combination of the intra- and inter-block estimates is Intra-estimatexInter-variance+Inter-estimatexIntra-variance / Intra-variance + Inter-variance ; however, this combined estimate is merely theoretical, since we do not know in practice the exact inter- and intra-variances. A reasonable solution is to use a random weight which can be computed from the data of our experiment, but so far there has been no practical solution without severe restrictions on the size of the experiment, and no solution at all for a clear answer to the question of how much we recovered. In fact, the experimenter applying the methodology available to him now, cannot be sure that he is really improving the accuracy of his estimation. This research has achieved the following: 1. A new method of combining two independent estimates has been developed. This method has its use in incomplete block designs, in similar experiments, and in randomized block designs with heterogeneous variances. The improvement introduced by this method is very satisfactory, compared with the utmost possible theoretical improvement. 2. A procedure for recovering the inter-block information in B.I.B. designs was given, which is applicable in experiments as small as t = 4. 3. It has been proven that the practical utilization of inter-block information is possible in any P.B.I.B. with seven treatments or more. 4. A general procedure for recovering the inter-block information in P.B.I.B.'s with two associate classes was given. 5. An inter-block analysis of singular and semi-regular group divisible designs was discussed, which makes a partial utilization of the inter-information possible. In general, this work has two merits: 1. It makes possible the utilization of the interblock information in small and moderate size experiments. 2. As a ratio of the utmost possible theoretical recovery (by combining linearly), either exactly or a lower bound of the ratio of recovery is always computable. Tables which enable the experimenter to use the procedures described in this dissertation were given. The ratios of recovery listed in these tables show that the new method gives good results where the old method is not applicable, and when the old method starts, hopefully, to be valid, the ratio of recovery achieved by the new method starts to approach the theoretical value that can be achieved, assuming the intra- and inter-variance are known. / Ph. D.

The work of Kramer and Bradley on the use of factorials in incomplete block designs bas been extended to permit both the intra-block and combined intra- and inter-block analyses of factorials in balanced and partially balanced incomplete block designs. In particular, we have obtained a combined intra- and inter-block analysis for factorials in balanced incomplete block designs, group divisible designs, and Latin Square types of partially balanced, incomplete block designs. For the class of Latin Square sub-type L₃ designs both the intra-block and combined intra- and inter-block analyses have been developed. In general, factorial treatment combinations were assigned to the association schemes by permitting the rows of the association schemes to represent the levels of one factor and the columns to represent the levels of a second factor. The extension to multifactor factorials was then carried out by sub-dividing the levels of the basic two-factor factorial, the levels in the sub-divisions representing the levels of the multi-factor factorials. Estimators for the factorial effects have been obtained along with their variances and covariances. Sums of squares in terms of the factorial estimators have been derived and can be used to carry out tests of significance. These sums of squares were shown, for the combined intra- and inter-block analyses, to be independently distributed as χ²-variates with the appropriate numbers of degrees of freedom. Suitable sums of squares for tests of significance are not possible in general for Latin Square sub-type L₃ designs. In situations such as these, we can only consider contrasts among the estimators and use their variances to perform tests of significance. However, for the special cases of factorials in the 4 x 4 Latin Square sub-type L₃ design, a complete analysis yielding the adjusted sums of squares for the factorial effects is possible if the factorial treatments are applied to the association scheme in a different manner. Single-degree-of-freedom contrasts are obtained in much the usual way as for factorials in complete block designs. The method of incorporating a fractional replicate of a factorial into incomplete block designs is also considered. Numerical examples have been worked in detail for a group divisible design and a Latin Square sub-type L₂ design. The procedure for analyzing a Latin Square sub-type L₃ design is also discussed. / Ph. D.

We take a critical view of the standard approach to finance and growth. The mapping between the theory and empirics is shown to be poorly understood, and this is traced to deficiencies in our understanding of the microeconomics at play. By looking at both primary and secondary historical evidence we argue that issues of aggregation are critical, and that spatial factors are also prevalent. Further, we suggest that these disaggregated elements can change over the course of an industrial revolution. A model in the spirit of standard finance and growth theories is extended to consider these further effects, and we calibrate the model to data on historical growth paths. In order to advance our understanding of the microeconomic factors that cause the observed phenomena in the finance-growth nexus, we develop a general equilibrium theory of financial intermediation in which exchange costs are endogenously determined by technologies, endowments and preferences. We suggest that incomplete contracts might be central to these phenomena. We link this framework to an understanding of power and political economy in a setting with heterogeneous agents. We develop these results numerically, showing a number of interesting interactions between markets, exchange costs and institutions in economies with different levels of wealth. The model of endogenous exchange costs can be thought of in terms of the findings coming out of our historical analysis. We outline in some detail the further steps that need to be taken before we can speak of the microfoundations of finance and growth with any confidence. First, a fully dynamic model of markets and coalitions must be embedded within a story of economic growth that can match the dynamic observations. Second, we must develop our conception of incomplete contracting and the link with institutions and political economy. The thesis thus opens a number of interesting avenues for future research.

The main objective of this project is to develop a "black-box" multigrid preconditioner for the iterative solution of finite element discretisations of the convection-diffusion equation with dominant convection. This equation can be considered a stand alone scalar problem or as part of a more complex system of partial differential equations, such as the Navier-Stokes equations. The project will focus on the stand alone scalar problem. Multigrid is considered an optimal preconditioner for scalar elliptic problems. This strategy can also be used for convection-diffusion problems, however an appropriate robust smoother needs to be developed to achieve mesh-independent convergence. The focus of the thesis is on the development of such a smoother. In this context a novel smoother is developed referred to as truncated incomplete factorisation (tILU) smoother. In terms of computational complexity and memory requirements, the smoother is considerably less expensive than the standard ILU(0) smoother. At the same time, it exhibits the same robustness as ILU(0) with respect to the problem and discretisation parameters. The new smoother significantly outperforms the standard damped Jacobi smoother and is a competitor to the Gauss-Seidel smoother (and in a number of important cases tILU outperforms the Gauss-Seidel smoother). The new smoother depends on a single parameter (the truncation ratio). The project obtains a default value for this parameter and demonstrated the robust performance of the smoother on a broad range of problems. Therefore, the new smoothing method can be regarded as "black-box". Furthermore, the new smoother does not require any particular ordering of the nodes, which is a prerequisite for many robust smoothers developed for convection-dominated convection-diffusion problems. To test the effectiveness of the preconditioning methodology, we consider a number of model problems (in both 2D and 3D) including uniform and complex (recirculating) convection fields discretised by uniform, stretched and adaptively refined grids. The new multigrid preconditioner within block preconditioning of the Navier-Stokes equations was also tested. The numerical results gained during the investigation confirm that tILU is a scalable, robust smoother for both geometric and algebraic multigrid. Also, comprehensive tests show that the tILU smoother is a competitive method.

Ziel der vorliegenden Untersuchung ist die Beschreibung der Varietäten der italienischen Sprache, wie sie von in Berlin lebenden italienischen Auswanderern gesprochen werden. Die Stichprobe, die sich aus 64 Informanten zusammensetzt, wurde ausgehend von deren Bildungsgrad in zwei Gruppen aufgeteilt, die wiederum nach erster und zweiter Generation unterteilt wurden. Die insgesamt vier Gruppen bestehen aus jeweils 16 Informanten. Die Analysen erfolgten auf soziolinguistischer und sprachlicher Ebene. Für die erste Untersuchung wurde eine Studie zum Phänomen des language shift durchgeführt, bei der die Einstellungen zu den Sprachen im Repertoire der Gemeinschaft untersucht wurden. Die Analyse ergab zum einen, dass es zwei verschiedene Sprachgemeinschaften mit zwei Repertoires gibt, die sich nicht vollkommen überschneiden, und zum anderen, dass ein unterschiedlicher Grad der Integration innerhalb der deutschen Gemeinschaft festzustellen ist. Die soziolinguistischen Ergebnisse wurden durch die anschließende Analyse der sprachlichen Merkmale bestätigt, die die beiden Gruppen der ersten Generation nach dem Bildungsgrad und der unterschiedlichen Dialektverwendung unterscheiden. In der Gruppe mit niedrigem bis mittlerem Bildungsgrad zeigt sich eine Verschiebung von der varietà popolare hin zur Umgangssprache, während in der Gruppe mit mittlerem bis hohem Bildungsgrad eine Verschiebung vom neo-standard hin zur Umgangssprache erkennbar ist. Interessant ist jedoch die Analyse der jeweiligen Gruppen der zweiten Generation, aus der – unabhängig von der Herkunft der Eltern – viele gemeinsame Merkmale ersichtlich werden. Dies lässt sich tendenziell durch den längeren Kontakt mit der deutschen Gesellschaft erklären, der zu einem Rückgang des Italienischgebrauchs führt. / The present dissertation investigates the varieties of spoken Italian used by members of the Italian community in Berlin from a sociolinguistic perspective. The aim is to determine whether there are different Italian linguistic communities in Berlin and how they differentiate from one another. The sample consists of 64 participants, 32 from the first generation and 32 from the second, further divided according to their educational degree. The study takes into account the relationship between linguistic codes and domains of language use, whilst exploring the language shift phenomenon. The qualitative analysis of the data reveals that two linguistic communities with two specific repertoires have gradually taken shape. This is confirmed by the linguistic analysis of the Italian varieties spoken by the participants. The educational degree and the different use of the heritage Italo-Romance dialect of the informants emerged as sociolinguistic variable. The variety of the first generation with low educational degree and extensive use of the dialect shares linguistic features both of the “italiano popolare“ (i.e. the variety of Italian spoken by those individuals who learned as their native language an Italo-Romance dialect) and of the colloquial variety of Italian. On the contrary, the variety of the first generation with a high educational degree and a restricted use of the dialect shares linguistic traits both of the neo-standard and of the colloquial variety. Findings of the second generation groups indicate that the parent's background seems to have a marginal effect on the linguistic variety. This could be due to the second generation participants being exposed to the German society for a longer period of time, causing a decline in their competency of the Italian language.

A large literature has related the failure of interest rate parity in the foreign exchange market to the existence of a time-varying risk premium. Nevertheless, most modern open economy DSGE models imply a (near) perfect interest rate parity condition. This paper presents a stylized two-country incomplete-markets model in which countries have strong precautionary motives because they face international liquidity constraints, the presence of which successfully generates a time-varying risk premium: the country that has accumulated debt after experiencing relative worse times has stronger precautionary motives and its asset carries a risk premium. (author's abstract) / Series: Department of Economics Working Paper Series

The concomitance of prosperity and poverty come as an enigma in today's world.As some people in this world benefit greatly from advanced technologies andglobalization, others are still suffering heavily from poverty. One noticeable fact is thatalmost all developing countries have their own distinguished "poor area". Such poorareas seem to persist regardless of robust economic growth enjoyed by the overalleconomy.By decomposing the developing country into two regions, one rich coastal regionand one poor inland region, this research establishes a new classical general equilibrium3X2 Ricardian model to investigate how trade liberalization will affect the participationin the division of labor by poor individuals in the inland region in a developing countryand their associated welfare change under different trading conditions.Our model of division of labor on poverty delineates the interdependentrelationship between individuals in the poor inland region, the rich coastal region and thedeveloped country. Market integration plays a very important role in suchinterdependency. Low transaction efficiency is the bottle-neck constraint on the poorinland region's integration into international division of labor through international trade.Thus, it is critical for the poor inland region to improve the market transaction efficiencyin order to enjoy gains from trade.Our marginal and inframarginal analysis show that as an important part of tradeliberalization policy, tariff reduction may not always be a good policy choice for thedeveloping country to alleviate the poverty. Whether tariff reduction makes the inlandregion better off depends on the initial general equilibrium market structure and thedeveloping country's power of influencing its terms of trade. If the developing country islarge enough to determine the terms of trade in international trade with the developedcountry, the developing country may increase the welfare level of the poor inland regionby increasing its tariff rate. But the developed country will oppose it because the tariffrate increase in the developing country will hurt its welfare. Trade negotiation is thennecessary to determine the final tariff rate and the share of gains of trade to each countryand region.

Symmetric generalized eigenvalue problems arise in many physical applications and frequently only a few of the eigenpairs are of interest. Typically, the problems are large and sparse, and therefore traditional methods such as the QZ algorithm may not be considered. Moreover, it may be impractical to apply shift-and-invert Lanczos, a favored method for problems of this type, due to difficulties in applying the inverse of the shifted matrix. With these difficulties in mind, Golub and Ye developed an inverse free Krylov subspace algorithm for the symmetric generalized eigenvalue problem. This method does not rely on shift-and-invert transformations for convergence acceleration, but rather a preconditioner is used. The algorithm suffers, however, in the presence of multiple or clustered eigenvalues. Also, it is only applicable to the location of extreme eigenvalues. In this work, we extend the method of Golub and Ye by developing a block generalization of their algorithm which enjoys considerably faster convergence than the usual method in the presence of multiplicities and clusters. Preconditioning techniques for the problems are discussed at length, and some insight is given into how these preconditioners accelerate the method. Finally we discuss a transformation which can be applied so that the algorithm extracts interior eigenvalues. A preconditioner based on a QR factorization with respect to the B-1 inner product is developed and applied in locating interior eigenvalues.

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In this thesis, we follow the incomplete contract model developed by Freixas and Rochet (1997). They model the decision of a bank regulator for continuing the sound bank or restructuring the failing bank as a game between bank equity owners, the bank manager, and the regulator under the incomplete contract framework. In this essay, we apply this incomplete contract model to Taiwan empirical data. After using several kinds of financial ratios as our indicators, we select nine ratios to process our empirical examination. And we find that: there are two banks appeared in the “ex-post efficient interference” segment except two ratios and also another two banks shown in the “ex-post efficient passivity” segment except one ratio. / In this thesis, we follow the incomplete contract model developed by Freixas and Rochet (1997). They model the decision of a bank regulator for continuing the sound bank or restructuring the failing bank as a game between bank equity owners, the bank manager, and the regulator under the incomplete contract framework. In this essay, we apply this incomplete contract model to Taiwan empirical data. After using several kinds of financial ratios as our indicators, we select nine ratios to process our empirical examination. And we find that: there are two banks appeared in the “ex-post efficient interference” segment except two ratios and also another two banks shown in the “ex-post efficient passivity” segment except one ratio.