This report has been compiled to document the thesis work carried out by Anton Andersson for Coresonic AB. The task was to develop an accelerator that could generate complex numbers suitable for fast fourier transforms (FFT) and tuning the phase of complex signals (NCO). Of many ways to achieve this, the CORDIC algorithm was chosen. It is very well suited since the basic implementation allows rotation of 2D-vectors using only shift and add operations. Error bounds and proof of convergence are derived carefully The accelerator was implemented in VHDL in such a way that all critical parameters were easy to change. Performance measures were extracted by simulating realistic test cases and then compare the output with reference data precomputed with high precision. Hardware costs were estimated by synthesizing a set of different configurations. Utilizing graphs of performance versus cost makes it possible to choose an optimal configuration. Maximum errors were extracted from simulations and seemed rather large for some configurations. The maximum error distribution was then plotted in histograms revealing that the typical error is often much smaller than the largest one. Even after trouble-shooting, the errors still seem to be somewhat larger than what other implementations of CORDIC achieve. However, precision was concluded to be sufficient for targeted applications. / Den här rapporten dokumenterar det examensarbete som utförts av AntonAndersson för Coresonic AB. Uppgiften bestod i att utveckla enaccelerator som kan generera komplexa tal som är lämpliga att använda försnabba fouriertransformer (FFT) och till fasvridning av komplexasignaler (NCO). Det finns en mängd sätt att göra detta men valet föllpå en algoritm kallad CORDIC. Den är mycket lämplig då den kan rotera2D-vektorer godtycklig vinkel med enkla operationer som bitskift ochaddition. Felgränser och konvergens härleds noggrannt. Acceleratorn implementerades i språket VHDL med målet att kritiskaparametrar enkelt skall kunna förändras. Därefter simuleradesmodellen i realistiska testfall och resulteten jämfördes medreferensdata som förberäknats med mycket hög precision. Dessutomsyntetiserades en mängd olika konfigurationer så att prestanda enkeltkan viktas mot kostnad.Ur de koefficienter som erhölls genom simuleringar beräknades detstörsta erhållna felet för en mängd olika konfigurationer. Felenverkade till en början onormalt stora vilket krävde vidareundersökning. Samtliga fel från en konfiguration ritades ihistogramform, vilket visade att det typiska felet oftast varbetydligt mindre än det största. Även efter felsökning verkar acceleratorngenerera tal med något större fel än andra implementationer avCORDIC. Precisionen anses dock vara tillräcklig för avsedda applikationer.

The fact that saving is one of the main factors to economic growth is unquestionable. Accumulated saving can be consider as the sources of capital stock to which play a crucial role in creating investment, production, and employment. And all these activities eventually enhance the economic growth. Therefore the main objective of this paper, ―The relationship between domestic saving and economic growth and convergence hypothesis: case study of Thailand‖, was to investigate the causality relationship between the domestic saving and economic growth of Thailand. This paper will analyze whether the direction of causality go from domestic saving to economic growth, or vice versa. Granger causality test were conducted by using time series annual data from 1960 to 2010, and the empirical result suggests that the direct of causality go from economic growth to domestic saving only. Aiming to grow its economy, Thailand had had development plans which used both saving and direct investment to stimulate economy. This paper examine whether the convergence hypothesis does hold in Thailand. This part would check whether or not Thailand is in the process of convergence, catching up, lagging behind, loose catching up, loose lagging behind or divergence over time compared with other developed countries. This test was conducted in pairwise between Thailand-Singapore, Thailand-United States, Thailand-United Kingdom, deployed data from 1970 to 2010, and the Augmented Dickey–Fuller (ADF) Test. The regression results demonstrate that convergence hypothesis does not hold in Thailand. Finally, the result of Granger Causality report that economic growth rate does matter lead to growth rate of domestic savings in Thailand only. Thus, in order to learn the effect of gross domestic saving per capita growth rate can help narrow the different of GDP between two countries concerned, this paper will examine the correlation of two variables, deployed the OSL methods to investigate the correlation between gross domestic saving growth rate and the different of GDP per capita between Thailand and Singapore. This test also examine whether saving does help support convergence hypothesis for Thailand or not. The test results shows that domestic saving growth rate does not help narrowing the range of different of income of Thailand and Singapore which mean that domestic saving growth rate does not support the convergence hypothesis in Thailand.

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This thesis investigates whether developments associated with globalization and regional integration have caused the levels of government support provided to agricultural producers in Canada and the United States to converge in a downward direction. The literature is sharply divided as to whether governments retain the ability to pursue an independent agricultural policy course. To shed light on this debate, the levels of government assistance payments made to farmers in six contiguous Canadian provinces and American states (Manitoba, Saskatchewan, Alberta, North Dakota, South Dakota, and Montana) are compared over the 1990-2001 period. This time-frame allows for sufficient periods both before and after the establishment of NAFTA and the WTO to study the effects of these developments on the relevant policy outcomes. After outlining the programs and policy changes that drove the shifts in levels of government support provided to farmers, the paper argues that although the levels of government payments made to farmers in the six sub-units converged in the mid-1990s, they diverged thereafter. The evidence drawn from this examination supports the contention that governments do possess considerable room to manoeuvre in the agricultural policy making arena and significant ability to chart an independent policy course.

The introduction of deregulation and subsequent open access policy in electricity sector has brought competition in energy market. Allocation of transmission loss has become a contentious issue among the electricity producers and consumers. A closed form solution for transmission loss allocation does not exist due to the fact that transmission loss is a highly non-linear function of system states and it is a non-separable quantity. In absence of a closed form solution different utilities use different methods for transmission loss allocation. Most of these techniques involve complex mathematical operations and time consuming computations. A new transmission loss allocation tool based on artificial neural network has been developed and presented in this thesis. The proposed artificial neural network computes loss allocation much faster than other methods. A relatively short execution time of the proposed method makes it a suitable candidate for being a part of a real time decision making process. Most independent system variables can be used as inputs to this neural network which in turn makes the loss allocation procedure responsive to practical situations. Moreover, transmission line status (available or failed) was included in neural network inputs to make the proposed network capable of allocating loss even during the failure of a transmission line. The proposed neural networks were utilized to allocate losses in two types of energy transactions: bilateral contracts and power pool operation. Two loss allocation methods were utilized to develop training and testing patterns; the Incremental Load Flow Approach was utilized for loss allocation in the context of bilateral transaction and the Z-bus allocation was utilized in the context of pool operation. The IEEE 24-bus reliability network was utilized to conduct studies and illustrate numerical examples for bilateral transactions and the IEEE 14-bus network was utilized for pool operation. Techniques were developed to expedite the training of the neural networks and to improve the accuracy of results.

Abstract: Considering the Schrödinger equation $\Delta_x u = i\partial{u}/\partial{t}$, we have a solution $u$ on the form $$u(x, t)= (2\pi)^{-n} \int_{\RR} {e^{i x\cdot \xi}e^{it|\xi|^2}\widehat{f}(\xi)}\, d \xi, x \in \RR, t \in \mathbf{R}$$ where $f$ belongs to the Sobolev space. It was shown by Sjögren and Sjölin, that assuming $\gamma : \mathbf{R}_+ \rightarrow \mathbf{R}_+ $ being a strictly increasing function, with $\gamma(0) = 0$ and $u$ and $f$ as above, there exists an $f \in H^{n/2} (\RR)$ such that $u$ is continuous in $\{ (x, t); t>0 \}$ and $$\limsup_{(y,t)\rightarrow (x,0),|y-x|<\gamma (t), t>0} |u(y,t)|= + \infty$$ for all $x \in \RR$. This theorem was proved by choosing $$\widehat{f}(\xi )=\widehat{f_a}(\xi )= | \xi | ^{-n} (\log | \xi |)^{-3/4} \sum_{j=1}^{\infty} \chi _j(\xi)e^{- i( x_{n_j} \cdot \xi + t_j | \xi | ^a)}, \, a=2,$$ where $\chi_j$ is the characteristic function of shells $S_j$ with the inner radius rapidly increasing with respect to $j$. The purpose of this essay is to explain the proof given by Sjögren and Sjölin, by first showing that the theorem is true for $\gamma (t)=t$, and to investigate the result when we use $$S^a f_a (x, t)= (2 \pi)^{-n}\int_{\RR} {e^{i x\cdot \xi}e^{it |\xi|^a}\widehat{f_a}(\xi)}\, d \xi$$ instead of $u$.

The location of the Inter-Tropical Convergence Zone plays an important role in the climatology of tropical regions. Yet, despite its importance, the basic physics that determine the location of the ITCZ are not fully understood. Observational analyses show that, where the cross-equatorial pressure gradient is strong, the maximum convection is not necessarily associated with the highest sea surface temperature,or correspondingly, the lowest sea level pressure. Tomas and Webster (1997) argue that if a strong enough cross-equatorial pressure gradient exists and the system is inertialy unstable, secondary ameliorating circulations will drive strong off-equatorial convection in regions where ITCZ location is determined by low tropospheric dynamics. The observational record is re-examined to test the inertial instability hypothesis using the new ECMWF reanalysis data set. Composite analyses are performed to study the structure of the summer meridional circulation for the tropical Eastern Pacific Ocean and Atlantic Ocean. In agreement with Tomas and Webster theory, we find that the magnitude of the cross-equatorial pressure difference appears to determine the intensity of convection with low values of outgoing longwave radiation always to the north of the zero absolute vorticity line, and the absolute vorticity advection equatorward of the this line. Also the observed oscillation period of the disturbance for the studied regions coincides with theoretical oscillation period of the inertial flow.

In chapter 1, we show (i) that the risk-return characteristics of our sample of 17 developed stock markets of the world have converged significantly toward each other during our study period 1974 2004, and (ii) that this international convergence in risk-return characteristics is driven mainly by the declining country effect, rather than the rising industry effect, suggesting that the convergence is associated with international market integration. Specifically, we first compute the risk-return distance among international stock markets based on the Euclidean distance and find that the distance thus computed has been deceasing significantly over time, implying a mean-variance convergence. In particular, the average risk-return distance has decreased by about 43% over our sample period. The speed of convergence, however, varies greatly across individual markets, largely reflecting the initial distance of each individual market from the international average risk-return characteristic. Lastly, we document that the risk-return characteristics of our sample of 14 emerging markets have been converging rapidly toward those of developed markets in recent years. This development notwithstanding, emerging markets still remain as a distinct asset class. In chapter 2, we examine the historical evolution of international earnings-to-price ratios for a sample of 17 markets over the period 1980 2004. We introduce a distance measure of earnings-to-price ratios among international stock markets and find that earnings-to-price ratios of 17 markets have significantly converged toward each other during the period. The average distance measure for 17 markets has decreased by about 80 percent during the period. The speed of convergence for individual markets varies and mainly reflects the initial distance of individual markets from the international average. We also find that although both country and industry effects account for convergence in earnings-to-price ratios among the sample markets, country effect dominates industry effect in terms of the magnitude. We further examine what could explain the declining country effect and document that the time trend of dividend-yield distance measure closely follows that of earnings-to-price distance measure. This result suggests that convergence in earnings-to-price ratio is mainly due to convergence in economic factors such as growth opportunities or discount rates rather than due to convergence in accounting practices.

In this thesis, for the under-determined system Fx = b with the matrix F ∈m¡Ñn (m ≤ n), new error bounds involving the traditional condition number and the effective condition number are established. Such error bounds are simple than those of over-determined system. The errors results implies that for stability, the condition number and the effective condition numbers are important if the perturbation of matrix F and vector b are dominant, respectively. This thesis is also devoted to the application of Neumann problems, where the consistent condition holds to guarantee the existence of multiple solutions. For the traditional Neumann conditions, the discrete consistent condition has to be satisfied to guarantee the existence of numerical solutions. Such a discrete consistent condition can be removed, to greatly simplify the numerical algorithms, and to retain the same convergence rates. For Neumann Problems, we may solve its ordinal discrete linear equations, or the underdetermined systems by ignoring some dependent equations, or the fixed variables methods. Moreover, we may choose different equations to be ignored, and different variables to be fixed. The comparisons of these different methods and choices are important in applications. In this thesis, the new comparisons and relations of stability and accuracy are first explored, and some interesting results and new discoveries are found. Numerical examples of Neumann problem in 1D are carried out, to support the analysis made. However, the algorithms and stability analysis can be applied to the complicated Nuemann problems in 2D and 3D, such as the traction problems in linear elastic problems.

When a multicultural team is formed of say six individuals of different cultural backgrounds, there will be potential conflicts and greater varieties. However, there will be a ¡§normal¡¨ curve forms the range and permissible boundaries of a team. In concept, this normal distribution is the ¡§calm¡¨ state when the team is not active (norms). The potential is the range of team members¡¦ abilities/differences (divergences). To be able to reach the potential and perform is part of the team¡¦s goal (convergences & attributions). But to expect something more than expected is cultural synergy (break the original boundaries). The factors that will be considered as diverging forces are the differences that are born (already exists) when the team is formed. In order to model these cultural factors and estimate these cultural differences, Hofstede cultural dimensions are used. The factors that will be considered as converging forces are what each individual believe in such as perspective taking and self-leadership. These values are projected from the assessments of team individuals. The factors that will be considered as supporting forces (attribution factors) are how each member interacts with one another during the process. These are each individual behavior and personality. Therefore, from the perspective of divergence and convergence to see how cultural differences influence the teams and talk about their possible behaviors and reasons behind them is a conceptual way to look at the team. Based on the concept described above, the analysis of these different forces on multicultural teams is conducted. Using these factors, the paper explains/examines: l Cultural and individual values differences l Wish to base on the findings from the research to make helpful inferences on the learning and performance of multicultural teams. l Cultural divergent factors l Individual convergent factors l Individual attribution factors l Cultural synergy