Der Beitrag unterteilt sich in zwei Teile: Teil 1 (vgl. Informationen/07; 1976,05) und Teil 2 (cp. Informationen/07; 1976,06). Teil 1 enthält eine Einleitung und Grenzwertsätze für unabhängige und identisch verteilte Zufallsgrößen und die Übertragung der betrachteten Grenzwertsätze auf den Fall der Existenz einseitiger Momente. Teil 2 enthält Grenzwertsätze für mittlere Abweichungen für Summen unabhängiger nichtidentisch verteilter Zufallsgrößen (Serienschema) und eine Diskussion der erhaltenen Ergebnisse und schließlich einige Literaturangaben. Sei F_n(x) die Verteilungsfunktion der Summe X_1+X_2+...+X_n, wobei X_1, X_2, ...,X_n unabhängige und identisch verteilte Zufallsgrößen mit Erwartungswert 0 und Streuung 1 und endlichen absoluten Momenten c_m, m>2, sind, und sei Phi die standardisierte Normalverteilungsfunktion. Es werden absolute Konstanten L_i derart berechnet, dass wir Fehlerabschätzungen im unleichmäßigen zentralen Grenzwertsätzen in verschiedenen Fällen angeben können, wobei sich der Index i in L_i auf folgende fünf Fälle bezieht: kleine x, mittlere Abweichungen für x, große Abweichungen für x, kleine n und große n. Im Fall der Existenz einseitiger Momente werden obere Schanken für 1-F_n(x) angegeben für x>D_m*n^(1/2)*ln(n) bzw. x>D_m*n^(1/2)*(ln(n))^(1/2), womit Ergebnisse von S.V.NAGAEV(1965) präzisiert werden. Der Beitrag unterteilt sich in zwei Teile: Teil 1 (vgl. Informationen/07; 1976,05) und Teil 2 (cp. Informationen/07; 1976,06). Teil 1 enthält eine Einleitung und Grenzwertsätze für unabhängige und identisch verteilte Zufallsgrößen und die Übertragung der betrachteten Grenzwertsätze auf den Fall der Existenz einseitiger Momente. Teil 2 enthält Grenzwertsätze für mittlere Abweichungen für Summen unabhängiger nichtidentisch verteilter Zufallsgrößen (Serienschema) und eine Diskussion der erhaltenen Ergebnisse und schließlich einige Literaturangaben. Sei F_n(x) die Verteilungsfunktion der Summe X_1+X_2+...+X_n, wobei X_1, X_2, ...,X_n unabhängige und identisch verteilte Zufallsgrößen mit Erwartungswert 0 und Streuung 1 und endlichen absoluten Momenten c_m, m>2, sind, und sei Phi die standardisierte Normalverteilungsfunktion. Es werden absolute Konstanten L_i derart berechnet, dass wir Fehlerabschätzungen im unleichmäßigen zentralen Grenzwertsätzen in verschiedenen Fällen angeben können, wobei sich der Index i in L_i auf folgende fünf Fälle bezieht: kleine x, mittlere Abweichungen für x, große Abweichungen für x, kleine n und große n. Im Fall der Existenz einseitiger Momente werden obere Schanken für 1-F_n(x) angegeben für x>D_m*n^(1/2)*ln(n) bzw. x>D_m*n^(1/2)*(ln(n))^(1/2), womit Ergebnisse von S.V.NAGAEV(1965) präzisiert werden. / The paper is divided in two parts: part 1 (cp. Informationen/07; 1976,05) and part 2 (cp. Informationen/07; 1976,06). Part 1 contains an introduction and limit theorems for iid random variables and the transfer of the considered limit theorems to the case of the existence of onesided moments. Part 2 contains limit theorems of moderate deviations for sums of series of non iid random variables and a discussion of all obtained results in part 1 and 2 and finally some references. Let F_n(x) be the cdf of X_1+X_2+...+X_n, where X_1, X_2, ...,X_n are iid random variables with mean 0 and variance 1 and with m-th absolute moment c_m, m>2, and Phi the cdf of the unit normal law. Explicit universal constants L_i are computed such that we have an error estimate in the nonuniform central limit theorem with the L_i, where i corresponds to the five cases considered: small x, moderate deviations for x, large deviations for x, small n , large n. Additional upper bounds for 1-F_n(x) are obtained if the one-sided moments of order m, m>2, are finite and if x>D_m*n^(1/2)*ln(n) and x>D_m*n^(1/2)*(ln(n))^(1/2) respectively improving results by S.V.NAGAEV (1965).

Der Beitrag stellt eine Verallgemeinerung der Ergebnisse dar, die in den Informationen/07; 1976,05 veröffentlicht wurden. Sei F_n(x) die Verteilungsfunktion der Summe X_1+X_2+...+X_n, wobei X_1, X_2, ...,X_n unabhängige und nicht notwendig identisch verteilte Zufallsgrößen mit endlichen absoluten Momenten c_m, m>2, sind, und sei Phi die standardisierte Normalverteilungsfunktion. Es werden absolute Konstanten L_m derart berechnet, dass wir Fehlerabschätzungen im unleichmäßigen zentralen Grenzwertsatz explizit angeben können. Als Spezialfall ergibt sich die ungleichmäßige Fehlerschranke von A.BIKELIS (1966) im Fall der Existenz dritter absoluter Momente. Weiterhin werden Grenzwertsätze unter Voraussetzung einseitiger Momente betrachtet. Es werden einige Literaturhinweise angegeben. / The paper is a generalization of the results, published by the author in Informationen/07; 1976,05. Let F_n(x) be the cdf of X_1+X_2+...+X_n, where X_1, X_2, ...,X_n are non iid random variables with m-th absolute moment c_m, m>2, and Phi the cdf of the unit normal law. Explicit universal constants L_m are computed such that we have some error estimates in the nonuniform central limit theorem. A special case is the nonuniform error bound by A.BIKELIS (1966) in the case of existence of third absolute moments. Furthermore limit theorems with assumption of onesided moments are considered. Some references are given.

Es wird eine Folge unabhängiger zentrierter Zufallsgrößen betrachtet, die absolute Momente der Ordnung m, 2<m<3, besitzen mögen. Dann gelten für die normierte Verteilungsfunktion der Zufallssumme X_1+X_2+...+X_n der zentrale Grenzwertsatz und insbesondere eine ungleichmäßige Fehlerabschätzung von A.BIKELIS (1966). In der vorliegenden Note werden die analytische Struktur der in dieser Fehlerabschätzung auftretenden Konstanten L=L(m) genauer untersucht sowie dazu erzielte numerische Resultate vorgelegt. Abschließend werden einige Literaturhinweise angegeben. Der Fall m=3 wurde bereits in der Dissertation (TU Dresden 1977) des Autors untersucht. / We consider a sequence of centered and independent random variables with moments of order m, 2<m<3. Now the central limit theorem for the distribution function of the normed sum X_1+X_2+...+X_n and especially a nonuniform error estimate by A.BIKELIS (1966) hold. In this paper the analytical structure of the appearing constant L=L(m) of the error bound and numerical results are presented. Finally some references are given. The case m=3 was already studied in the thesis (Dissertation TU Dresden, 1977) by the author.

This thesis describes the implementation of a real-time, full search, 16x16 bidirectional motion estimation at 24 frames per second with the record performance of 155 Gop/s (1538 ops/pixel) at a high clock rate of 125 MHz. The core of bidirectional motion estimation uses close to 100% FPGA resources with 7 Gbit/s bandwidth to external memory. The architecture allows extremely controlled, macro level floor-planning with parameterized block size, image size, placement coordinates and data words length. The FPGA chip is part of the board that was developed at the Institute of Computer &amp; Communication Networking Engineering, Technical University Braunschweig Germany, in collaboration with Grass Valley Germany in the FlexFilm research project. The goal of the project was to develop hardware and programming methodologies for real-time digital film image processing. Motion estimation core uses FlexWAFE reconfigurable architecture where FPGAs are configured using macro components that consist of weakly programmable address generation units and data stream processing units. Bidirectional motion estimation uses two cores of motion estimation engine (MeEngine) forming main data processing unit for backward and forward motion vectors. The building block of the core of motion estimation is an RPM-macro which represents one processing element and performs 10-bit difference, a comparison, and 19-bit accumulation on the input pixel streams. In order to maximize the throughput between elements, the processing element is replicated and precisely placed side-by-side by using four hierarchal levels, where each level is a very compact entity with its own local control and placement methodology. The achieved speed was further improved by regularly inserting pipeline stages in the processing chain.

Series Active Filters (SAF) are designed for harmonic isolation and load voltage regulation of single-phase and three-phase voltage harmonic source type nonlinear loads. The novel Absolute Value Method (AVM) for load voltage harmonic extraction is proposed and applied in the control algorithm of SAF. The SAF compensated systems are represented by simplified linear models such that SAF controller gains can be easily determined. Harmonic isolation and load voltage regulation performances of 2.5 kW single-phase and 10 kW three-phase SAF compensated systems are evaluated by detailed simulations. Laboratory prototype single-phase and three-phase SAFs and loads are designed and manufactured. Digital signal processor based control platform is employed. Exclusive laboratory tests are conducted. Via laboratory experiments and simulations it is shown that AVM yields superior harmonic isolation and load voltage regulation performance compared to the conventional low/high pass filtering method. Theory, simulations, and experiments are well correlated and illustrate the feasibility of the proposed method.

Power system state estimation (PSSE) is an energy management system function responsible for the computation of the most likely values of state variables viz., bus voltage magnitudes and angles. The state estimation is obtained within a network at a given instant by solving a system of mostly non-linear equations whose parameters are the redundant measurements, both static such as transformer/line parameters and dynamic such as, status of circuit breakers/isolators, transformer tap positions, active/reactive power flows, generator active/reactive power outputs etc. PSSE involves solving an over determined set of nonlinear equations by minimizing a weighted norm of the measurement residuals. Typically, the L1 and L2 norms are employed. The use of L2 norm leads to state estimation based on the weighted least squares (WLS) criterion. This method is known to exhibit efficient filtering capability when the errors are Gaussian but fails in the case of presence of bad data. The method of hypothesis testing identification can be incorporated into the WLS estimator to detect and identify bad data. Nevertheless, it is prone to failure when the measurement is a leverage point. On the other hand state estimation based on the weighted least absolute value (WLAV) criterion using L1 norm, has superior bad data suppression capability. But it also fails in rejecting bad data measurements associated with leverage points. Leverage points are highly influential measurements that attract the state estimator solution towards them. Consequently, much research effort has focused recently, on producing a LAV estimator that remains robust in the presence of bad leverage measurements. This problem has been addressed in the thesis work. Two methods, which aims development of robust estimator that are insensitive to bad leverage points, have been proposed viz., (i) The objective function used here is obtained by linearizing L2 norm of the error function. In addition to the constraints corresponding to measurement set, constraints corresponding to bounds of state variables are also involved. Linear programming (LP) optimization is carried out using upper bound optimization technique. (ii) A hybrid optimization algorithm which is combination of”upper bound optimization technique” and ”an improved algorithm for discrete l1 linear approximation”, to restrict the state variables not to leave the basis during optimization process. Linear programming optimization, with bounds of state variables as additional constraints is carried out using the proposed hybrid optimization algorithm. The proposed state estimator algorithms are tested on 24-bus EHV equivalent of southern power network, 36-bus EHV equivalent of western grid, 205-bus interconnected grid system of southern region and IEEE-39 bus New England system. Performances of the proposed two methods are compared with the WLAV estimator in the presence of bad data associated with leverage points. Also, the effect of bad leverage measurements on the interacting bad data, which are non-leverage, has been compared. Results show that proposed state estimator algorithms rejects bad data associated with leverage points efficiently.

Precise measurements of both absolute frequencies and small frequency differences of atomic energy levels have played an important role in the development of physics. For example, high precision measurements of absolute frequencies of the 2S½ → 2P ½ transition (D1 line) of alkali atoms form an important link in the measurement of the fine structure constant, α. Similarly, precise interferometric measurements of the local gravitational acceleration (g) rely on the knowledge of the absolute frequencies of the 2S½ → 2P 3/2 transition (D2line) in alkali atoms. Difference frequency measurements of hyperfine structure and isotope shifts of atomic energy levels provide valuable information about the structure of the nucleus, which in turn helps in fine tuning the atomic wave functions used in theoretical calculations. The work reported in this thesis starts with the development and refinement of high precision measurement of absolute frequencies using a ring-cavity resonator. The measurement technique is relatively simple and cost-effective, but the accuracy is comparable to that achieved with the frequency comb technique (10¯11) when the accuracy is limited by the natural linewidth of the transition being measured. The technique combines the advantages of using tunable diode lasers to access atomic transitions with the fact that the absolute frequency of the D2 line in87Rb is known with an accuracy of 6 kHz. A frequency-stabilized diode laser locked to this line is used as a frequency reference, along with a ring-cavity resonator whose length is locked to the reference laser. For a given cavity length, an unknown laser locked to an atomic transition has a small frequency offset from the nearest cavity resonance. We use an acousto-optic modulator (AOM) to compensate for this frequency offset. The measured offset is combined with the cavity mode number to obtain a precise value for the frequency of The unknown laser. We have used this technique for absolute frequency measurements Of the D lines in133Cs and 6,7Li, and the 398.8nm line in Yb. We have also developed a technique to measure the ‘difference frequency’ of atomic energy levels using a single diode laser and an AOM. In this technique, the laser is first locked to a given hyperfine transition. The laser frequency is then shifted using the AOM to another hyperfine transition and the AOM frequency is locked to this difference. Thus the AOM frequency directly gives a measurement of the hyperfine interval. Applying this AOM technique we have measured the hyperfine interval of the D1 lines of all alkali atoms with high precision. We have further developed a technique of coheren-tcontrol spectroscopy (CCS) using co-propagating control and probe beam that is useful for highresolution spectroscopy. In this technique, the probe beam is locked to a transition and its absorption signal is monitored while the control beam is scanned through neighbouring transition. As the control comes into resonance with another transition, the probe absorption is reduced and the signal shows a Doppler free dip. This technique allows us to resolve transitions that are otherwise swamped by crossover resonances in conventional saturated absorption spectroscopy (SAS). We have applied this technique to measure hyperfine intervals in the D2 line of several alkali atoms. Thus, we were able to do high-precision measurements of both absolute and difference frequency of atomic transitions. The precision of the absolute frequency measurement is finally limited by the accuracy of 6 kHz with which the reference frequency is known. The nearby two photon transition in Rb, i.e. the 5S1/2→5D3/2 transition at 778 nm, is known with an accuracy of 1 kHz. In future, we hope to improve the accuracy of our technique using this transition as the reference. This thesis is organized as follows: In Chapter1,we give a brief introduction to our work.. We review the importance of frequency measurements and precision spectroscopy, followed by a comparison of the frequency comb and our ring cavity technique. In Chapter2, we describe measurements of the absolute frequency of the D lines of 133Cs using the ring cavity. We give a detailed discussion of the technique, the Possible sources of errors, and ways to check for the errors. The measurement of the absolute frequency of the D lines of Cs allows a direct comparison to frequency comb measurements, and thus acts as a good check on our technique. In Chapter 3, we describe the absolute frequency and isotope shift measurements in the 398.8 nm line in Yb. We probed this line by frequency doubling the output of a tunable Ti:Sapphire laser. We obtained< 60 kHz precision in our measurements and were able to resolve several discrepancies in previous measurements on this line. In Chapter 4, we describe the measurement of hyperfine structure in the D1 lines of alkali atoms. We used conventional saturated-absorption spectroscopy in a vapor cell to probe different hyperfine transitions and then used our AOM technique to measure the hyperfine interval with high precision. In Chapter 5 we discuss our measurements of hyperfine structure in the D2 lines of several alkali atoms. In the case of 23Na and 39K, the closely-spaced hyperfine transitions are not completely resolved in conventional saturatedabsorption spectroscopy due to the presence of cross over resonances. We have used coherent control spectroscopy to obtain crossover-free spectra and then measured the hyperfine intervals using an AOM. This technique was also used for high resolution spectroscopy in the D2 line of 133Cs. Finally, we describe our measurements of hyperfine structure in the D2 line of Rb using normal saturated absorption spectroscopy. Chapter 6, describes the relative and absolute frequency measurements in the D lines of6,7 Li at 670nm. High-precision measurements in lithium are of special interest because theoretical calculations of atomic properties in this simple three electron system are fairly advanced. Lithium spectroscopy poses an experimental challenge and we describe our efforts in doing highresolution spectroscopy on this system. Chapter 7 describes the hyperfine spectroscopy on the1P 1 state of 173Yb. Measurement of hyperfine structure in 173Yb has a problem because two of the hyperfine transitions overlap with the transition in 172Yb. In our earlier work (described in chapter 4), we had solved this problem by using multipeak fitting to the partially resolved spectrum. Here, we directly resolve the hyperfine transitions by using transverse laser cooling to selectively deflect the 173Yb isotope. In Chapter 8 , we give a broad conclusion to the work reported in this thesis and suggest future avenues of research to continue the work commenced here.

<p>The theory of economic growth predicts that poorer regions will eventually converge towards the income level of the wealthier regions (Barro & Sala-i-Martin, 2004). The aim of this Bachelor thesis is to establish if absolute convergence in Gross Regional Product (GRP) growth rates exists across LA-regions in Sweden during the period 1994-2004. The variables used in the model of absolute convergence are; the level of initial GRP per capita in the year 1994 and the growth rate of GRP per capita. The authors of this thesis find support of absolute convergence among Swedish LA-regions of 1.67 percent per year. Convergence estimations are also performed for high-, mid-, and low-performing groups of regions in respect to their income level per capita. The low-performing group of regions is in fact converging faster towards the income level of the wealthier regions in Sweden than the mid- and high-performing group. Alternative measurement of convergence is the so called sigma-convergence. The authors find that it only holds for the group of high-performing regions. However, this measurement cannot be considered reliable, as the existence of absolute convergence is necessary for sigma-convergence, but it is not sufficient.</p> / <p>Ekonomisk tillväxtteori förutspår att fattigare regioner med tiden kommer att konvergera mot samma inkomst nivå som rikare regioner har (Barro & Sala-i-Martin, 2004). Syftet med denna Kandidatuppsats är undersöka ifall det förekommer betingad konvergenstillväxt av Brutto Regional Produkt (BRP) nivåer mellan svenska LA-regioner under perioden 1994-2004. Variablerna som används i modellen för betingad konvergens är den ursprungliga nivån av BRP per capita under år 1994, och tillväxtnivån av BRP per capita under perioden 1994-2004. Författarna av denna uppsats har funnit stöd för betingad konvergens bland svenska LA-regioner med en konvergenstakt på 1,67 procent per år. En estimering av konvergens är därtill utförd för hög-, mellan- och lågpresterande grupper av regioner med respekt till deras inkomstnivå per capita. Den lågpresterande gruppen har en snabbare konvergeringstakt mot den inkomstnivå de rikare regionerna i Sverige har, än vad de mellan- och högpresterande grupperna. Ett alternativt mått på konvergens är den så kallade sigma-konvergensen. Författarna finner att detta mått endast håller för gruppen av högpresterande regioner. Emellertid kan inte detta mått räknas som tillförlitligt, då förekomsten av betingad konvergens är nödvändigt för sigma-konvergens, men det är inte tillräckligt.</p>

No description available.

Since the time of Cauchy, integration theory has in the main been an attempt to regain the Eden of Newton. In that idyllic time [. . . ] derivatives and integrals were [. . . ] different aspects of the same thing. -Peter Bullen, as quoted in [24] The theory of integration has gone through many changes in the past centuries and, in particular, there has been a tension between the Riemann and the Lebesgue approach to integration. Riemann's definition is often the first integral to be introduced in undergraduate studies, while Lebesgue's integral is more powerful but also more complicated and its methods are often postponed until graduate or advanced undergraduate studies. The integral presented in this paper is due to the work of Ralph Henstock and Jaroslav Kurzweil. By a simple exchange of the criterion for integrability in Riemann's definition a powerful integral with many properties of the Lebesgue integral was found. Further, the generalized Riemann integral expands the class of integrable functions with respect to Lebesgue integrals, while there is a characterization of the Lebesgue integral in terms of absolute integrability. As this definition expands the class of functions beyond absolutely integrable functions, some theorems become more cumbersome to prove in contrast to elegant results in Lebesgue's theory and some important properties in composition are lost. Further, it is not as easily abstracted as the Lebesgue integral. Therefore, the generalized Riemann integral should be thought of as a complement to Lebesgue's definition and not as a replacement. / Ända sedan Cauchys tid har integrationsteori i huvudsak varit ett försök att åter finna Newtons Eden. Under den idylliska perioden [. . . ] var derivator och integraler [. . . ] olika sidor av samma mynt.-Peter Bullen, citerad i [24] Under de senaste århundradena har integrationsteori genomgått många förändringar och framförallt har det funnits en spänning mellan Riemanns och Lebesgues respektive angreppssätt till integration. Riemanns definition är ofta den första integral som möter en student pa grundutbildningen, medan Lebesgues integral är kraftfullare. Eftersom Lebesgues definition är mer komplicerad introduceras den först i forskarutbildnings- eller avancerade grundutbildningskurser. Integralen som framställs i det här examensarbetet utvecklades av Ralph Henstock och Jaroslav Kurzweil. Genom att på ett enkelt sätt ändra kriteriet for integrerbarhet i Riemanns definition finner vi en kraftfull integral med många av Lebesgueintegralens egenskaper. Vidare utvidgar den generaliserade Riemannintegralen klassen av integrerbara funktioner i jämförelse med Lebesgueintegralen, medan vi samtidigt erhåller en karaktärisering av Lebesgueintegralen i termer av absolutintegrerbarhet. Eftersom klassen av generaliserat Riemannintegrerbara funktioner är större än de absolutintegrerbara funktionerna blir vissa satser mer omständiga att bevisa i jämforelse med eleganta resultat i Lebesgues teori. Därtill förloras vissa viktiga egenskaper vid sammansättning av funktioner och även möjligheten till abstraktion försvåras. Integralen ska alltså ses som ett komplement till Lebesgues definition och inte en ersättning.