Dithered quantization and noise shaping is well known in the audio community. The image processing community seems to be aware of this same theory only in bits and pieces, and frequently under conflicting terminology. This thesis attempts to show that dithered quantization of images is an extension of dithered quantization of audio signals to higher dimensions. Dithered quantization, or ``threshold modulation'', is investigated as a means of suppressing undesirable visual artifacts during the digital quantization, or requantization, of an image. Special attention is given to the statistical moments of the resulting error signal. Afterwards, noise shaping, or ``error diffusion'' methods are considered to try to improve on the dithered quantization technique. We also take time to develop the minimum-phase property for two-dimensional systems. This leads to a natural extension of Jensen's Inequality and the Hilbert transform relationship between the log-magnitude and phase of a two-dimensional system. We then describe how these developments are relevant to image processing.

In recent years, the moments of L-functions has been a topic of growing interest in the field of analytic number theory. New techniques, including applications of Random Matrix Theory and multiple Dirichlet series, have lead to many well-posed theorems and conjectures for the moments of various L-functions. In this thesis, we theoretically and numerically examine the integral moments of quadratic Dirichlet $L$-functions. In particular, we exhibit and discuss the conjectures for the moments which result from the applications of Random Matrix Theory, number theoretic heuristics, and the theory of multiple Dirichlet series. In the case of the cubic moment, we further numerically investigate the possible existence of additional lower order main terms.

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Vad är avgörande vändpunkter i psykoterapi? Detta är en kvalitativ studie av konfidenters upplevelser av avgörande ögonblick/vändpunkter. Studien utgår från konfidenternas upplevelser och beskrivning av dessa vändpunkter. Metoden är fenomenologisk och utgår ifrån EPP- metoden. Samtliga sex informanter har gått i terapi över 25 timmar och alla har gått i en psykodynamisk terapi. Resultatet visade inte på några avgörande ögonblick/vändpunkter i form av aha-upplevelser. Konfidenterna lyfte istället fram vändpunkter i form av insikter över tid. Två gemensamma drag trädde fram i materialet. Konfidenterna framhöll hur de med terapins hjälp fick syn på hur de suttit fast i mönster och försvar i sina tidiga objektrelationer. Konfidenterna framhöll också vikten av ett "eget rum" att möta sig själv tillsammans med terapeuten. / What is the crucial turning point in psychotherapy? This is a qualitative study of patients' experiences of the crucial moments/ turning points in their psychotherapy. This study examined patients' experiences and their description of these. The method is phenomenological and is called the EPP- method. The six informants have all attended more than 25 hours of therapy they have all attended psychodynamic therapy. The results revealed no crucial moments/ turning points such as "aha moment". Instead the patients emphasized turning points and insights over time. Two common features emerged in the material. The patients emphasized how they due to the therapy became aware of how they have been stuck in patterns and defense systems due to their early object relations. The patients also emphasized the importance of a "private room" of their own where they could meet themselves together with the therapist.

Dithered quantization and noise shaping is well known in the audio community. The image processing community seems to be aware of this same theory only in bits and pieces, and frequently under conflicting terminology. This thesis attempts to show that dithered quantization of images is an extension of dithered quantization of audio signals to higher dimensions. Dithered quantization, or ``threshold modulation'', is investigated as a means of suppressing undesirable visual artifacts during the digital quantization, or requantization, of an image. Special attention is given to the statistical moments of the resulting error signal. Afterwards, noise shaping, or ``error diffusion'' methods are considered to try to improve on the dithered quantization technique. We also take time to develop the minimum-phase property for two-dimensional systems. This leads to a natural extension of Jensen's Inequality and the Hilbert transform relationship between the log-magnitude and phase of a two-dimensional system. We then describe how these developments are relevant to image processing.

In recent years, the moments of L-functions has been a topic of growing interest in the field of analytic number theory. New techniques, including applications of Random Matrix Theory and multiple Dirichlet series, have lead to many well-posed theorems and conjectures for the moments of various L-functions. In this thesis, we theoretically and numerically examine the integral moments of quadratic Dirichlet $L$-functions. In particular, we exhibit and discuss the conjectures for the moments which result from the applications of Random Matrix Theory, number theoretic heuristics, and the theory of multiple Dirichlet series. In the case of the cubic moment, we further numerically investigate the possible existence of additional lower order main terms.

In this thesis the entanglement properties of atom-atom, atom-photon, and photon-photon are investigated. The recent developments of quantum computation as well as quantum information and communication have attracted much interest in the generation of these entanglements in the laboratory. To generate atom-photon entanglement, I discuss a model system in the cavity QED setup. By using a four-level atom and two resonant cavity modes, we can generate atom-photon entanglement almost deterministically. An extension of the above model to a six-level atom and again two resonant cavity modes can generate entangled photon pairs by appropriately adjusting system parameters. I then investigate the atom-atom entanglement in a 1D harmonic trap. I show the dependence of the pair entanglement on the scattering length and temperature, as well as the particle symmetry requirement (bosons or fermions). Among many peculiar properties in a 1D system, we briefly discuss the Fermi-Bose duality". While the entanglement properties of a single-channel model have recently been obtained for 1D and 3D systems, I thus study the entanglement of a multi-channel process in a cylindrical harmonic trap. I discuss the dependence of entanglement on the trap geometry. Finally I present detailed studies of the spin mixing between two Rb87 atoms in a single lattice site. The topic is emphasized on various motional state approximations and dipolar effect. Various motional state approximations can cause up to 20% error to experimental data. I also find that the dipolar interaction can lead to an experimentally observable frequency shift in a cylindrical harmonic trap with very large aspect ratio. The spin mixing of spin-2 manifold has also been discussed.

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<p>This master thesis deals with steel girders subjected to patch loading caused by concentrated moments. There exist no good methods to calculate by hand the ultimate resistance for this load case. In “tunnplåtshandboken”, (Handbook for sheet metal, which is published by SSAB), one calculation method is presented. It’s however fairly difficult to use, because of many calculation steps and many graphs. This study concentrates on how to calculate the resistance for this load case in a better way. The load case arises for example when a small steel plate (attachment) is welded to the flange above the web of a girder and the attachment is pulled in a direction parallel to the beam. It’s possible view the load as two components, a moment and a horizontal load. The moment will push the attachment into the girder and finally yielding in combination with web buckling will govern the ultimate resistance. In this report, only the moment part of the load is studied.</p><p>This study was made in three steps. First an FE-model was built. This model was verified against physical tests on patch loading from a force acting perpendicular to the beam axis. This approach was taken because no tests were found for the load case with a local moment. As step number two the FE-model was numerically adjusted to work for tests with patch loading caused by a local moment. A number of experiments were made, for which two parameters were varied, the thickness of the web and the length of the attachment. The loaded attachment was made very stiff, because it should not be deformed in order to simulate a sharp concentrated moment. In the last step a hand calculation model was developed for the investigated load case.</p><p>The FE-model that was created for comparison to the physical experiments gave resistances 10 % below the resistances, from the physical tests. This was mainly due to the sensitivity of the girder to initial imperfections and that the most severe buckling mode was used in the modeling of the imperfections.</p><p>The handcalculation model was developed to imitate the one for patch loading in EN 1993-1- 5 (EC3), because it may then work as an addition to EC3. The model was developed in three steps: yield resistance, critical elastic buckling load and the resistance function. The model for yield resistance is analytical and has a form equivalent to the one in EC3. The expressions for the critical elastic buckling load were taken as simple as possible, since they are the main area of this study. The method essentially uses the same equations as EC3 except from two small changes. The results are on the safe side but the safety margin increases when the length of the loaded attachment decreases and the slenderness of the web panel increase. Consequently formulas for calculating the critical load may be improved. The chosen reduction function was slightly increased compared to the function in EC3 but the results will still have a good safety margin. The complete model gives results where the safety margin increases as the length of the loaded attachment decreases. The calculation model was designed to be easy to use. In comparison to the FE-analysis, all the tested beams except a few with low slenderness gave results on the safe side.</p> / <p>Detta examensarbete behandlar stålbalkar utsatta för lokal intryckning orsakade av en lokal momentbelastning. För lastfallet finns ännu inga bra handräkningsmetoder, i plåthandboken som ges ut av SSAB finns en beräkningsmetod presenterad. Den är väldigt krånglig med många beräkningssteg och diagram. Denna studie är inriktad på att utreda hur man kan räkna på belastningsfallet på ett enklare och bättre sätt. Lastfallet uppkommer t.ex. då en lastögla svetsas till flänsen rakt över livet på en balk. Om lastöglan dras parallellt med balkens riktning så kan belastningen ses som två komponenter, ett moment och en horisontalkraft. Momentet kommer att trycka in lastöglan i balken och till slut blir det ett brott p.g.a. en blandning av att materialet flyter och att livet bucklar. I den här rapporten behandlas bara momentdelen av lasten.</p><p>Studien är gjord i tre steg. Först byggdes en FE-modell i Abaqus. Denna modell verifierades mot fysiska försök på lokal intryckning från en vertikal kraft, eftersom inga försök hittades på intryckning av ett lokalt moment. Som steg nummer två anpassades FE-modellen till försök med lokal intryckning från ett moment. Ett antal experiment gjordes med variation av två parametrar, livplåtens tjocklek och lastöglans längd. Lastöglan var väldigt styv eftersom den bara skulle skapa momentbelastningen. Sista steget var att utifrån resultaten ta fram en beräkningsmodell för lastfallet.</p><p>FE-modellen som skapades för testerna visade sig ge bärförmågor ca 10% under bärförmågan från de fysiska försöken. Detta berodde mycket på att balken var känslig för hur initialimperfektionerna såg ut och att första bucklingsmodens form användes vid modelleringen av de geometriska imperfektionerna.</p><p>Beräkningsmodellen utvecklades så att den skulle efterlikna den som gäller för lokal intryckning från vertikal last i EN 1993-1-5. Detta för att modellen skulle kunna användas som ett tillägg till EK3. Modellen utvecklades i tre delar, flytbärförmågan, kritiska bucklingslasten och reduktionsfaktorn för buckling. Modellen för flytbärförmågan togs fram analytiskt och fick en form som efterliknar den i EK3. Beräkningsmetoden för den kritiska bucklingslasten använder sig i princip av formlerna i EK3 förutom två små ändringar. Reduktionsfunktionen som valdes är en liten ökning av funktionen i EK3 men resultaten ligger ändå med bra marginal på säkra sidan. Den kompletta beräkningsmodellen ger resultat där säkerhetsmarginalen ökar vid minskande längd på lastöglan. Den har utformats så att den är lätt att använda och vid jämförelse med FE-försök gav beräkningsmodellen resultat på säkra sidan för alla balkar förutom några få av balkarna med låg slankhet. </p>

Thèse de doctorat : Electronique : Lille 1 : 2001. / N° d'ordre (Lille) : 3048. Résumé en français et en anglais. Bibliogr. en fin de chapitres.