I detta arbete har lösningar till ekvationen xn+yn= 1 i en ändlig kropp av primtalsordning studerats. Både konkreta lösningar för vissa givna förutsättningar samt resultat gällande antalet lösningar har varit målet för dessa studier. I uppsatsen redovisas även de metoder som använts för att nå nämnda resultat. Eftersom ekvationen kan studeras för en oändlig mängd kroppar presenteras inget heltäckande resultat. Vissa resultat är dock generella under premissen att antingen kroppen eller ekvationen fixeras för något primtal p respektive exponent n. För sådana specialfall presenteras flera exempel. Huvudresultatet i arbetet visar att det alltid finns många icke-triviala lösningar för ekvationen över stora ändliga kroppar.

<p>In this bachelor thesis a complete prototype of an industrial vibration measurement platform has been developed. By measuring a number of variables such as acceleration, temperature and speed conclusions can be drawn on machinery health. The aim is to evaluate hardware and software solutions for a possible future product. Based on a requirement specification a proper hardware design has be developed. The hardware consists of a four-layer PCB with an ARM Cortex-M3 microcontroller and about 250 other components. The PCB was designed, assembled, tested and finally housed in a box. Measures have been taken to protect the prototype against external disturbances such as inappropriate supply voltages and transients on the input stages.Software has been written for the microcontroller to perform the various measurements required by the prototype. These include RMS, integration and filtering. Special attention was paid to the latter by implementing filters based on lattice wave digital structures. This structure results in a very efficient implementation. Consideration is taken to be able to generate arbitrary filters independent of the characteristics and design method. To save time the microcontroller implements all the algorithms without any floating point numbers.Furthermore, both hardware and software are adapted for future industrial use. The finished prototype supports a number of communication interfaces in which Modbus (RS-485) and current loop communication can be mentioned.The final result is a very good performing platform with strong future potential.The work was commissioned by the consulting firm Syncore Technologies AB at their office in Mjärdevi, Linköping. The project has, in total, taken 10 weeks and occurred during spring 2010.In this bachelor thesis a complete prototype of an industrial vibration measurement platform has been developed. By measuring a number of variables such as acceleration, temperature and speed conclusions can be drawn on machinery health. The aim is to evaluate hardware and software solutions for a possible future product. Based on a requirement specification a proper hardware design has be developed. The hardware consists of a four-layer PCB with an ARM Cortex-M3 microcontroller and about 250 other components. The PCB was designed, assembled, tested and finally housed in a box. Measures have been taken to protect the prototype against external disturbances such as inappropriate supply voltages and transients on the input stages.Software has been written for the microcontroller to perform the various measurements required by the prototype. These include RMS, integration and filtering. Special attention was paid to the latter by implementing filters based on lattice wave digital structures. This structure results in a very efficient implementation. Consideration is taken to be able to generate arbitrary filters independent of the characteristics and design method. To save time the microcontroller implements all the algorithms without any floating point numbers.Furthermore, both hardware and software are adapted for future industrial use. The finished prototype supports a number of communication interfaces in which Modbus (RS-485) and current loop communication can be mentioned.The final result is a very good performing platform with strong future potential.The work was commissioned by the consulting firm Syncore Technologies AB at their office in Mjärdevi, Linköping. The project has, in total, taken 10 weeks and occurred during spring 2010.</p>

In this bachelor thesis a complete prototype of an industrial vibration measurement platform has been developed. By measuring a number of variables such as acceleration, temperature and speed conclusions can be drawn on machinery health. The aim is to evaluate hardware and software solutions for a possible future product. Based on a requirement specification a proper hardware design has be developed. The hardware consists of a four-layer PCB with an ARM Cortex-M3 microcontroller and about 250 other components. The PCB was designed, assembled, tested and finally housed in a box. Measures have been taken to protect the prototype against external disturbances such as inappropriate supply voltages and transients on the input stages.Software has been written for the microcontroller to perform the various measurements required by the prototype. These include RMS, integration and filtering. Special attention was paid to the latter by implementing filters based on lattice wave digital structures. This structure results in a very efficient implementation. Consideration is taken to be able to generate arbitrary filters independent of the characteristics and design method. To save time the microcontroller implements all the algorithms without any floating point numbers.Furthermore, both hardware and software are adapted for future industrial use. The finished prototype supports a number of communication interfaces in which Modbus (RS-485) and current loop communication can be mentioned.The final result is a very good performing platform with strong future potential.The work was commissioned by the consulting firm Syncore Technologies AB at their office in Mjärdevi, Linköping. The project has, in total, taken 10 weeks and occurred during spring 2010.In this bachelor thesis a complete prototype of an industrial vibration measurement platform has been developed. By measuring a number of variables such as acceleration, temperature and speed conclusions can be drawn on machinery health. The aim is to evaluate hardware and software solutions for a possible future product. Based on a requirement specification a proper hardware design has be developed. The hardware consists of a four-layer PCB with an ARM Cortex-M3 microcontroller and about 250 other components. The PCB was designed, assembled, tested and finally housed in a box. Measures have been taken to protect the prototype against external disturbances such as inappropriate supply voltages and transients on the input stages.Software has been written for the microcontroller to perform the various measurements required by the prototype. These include RMS, integration and filtering. Special attention was paid to the latter by implementing filters based on lattice wave digital structures. This structure results in a very efficient implementation. Consideration is taken to be able to generate arbitrary filters independent of the characteristics and design method. To save time the microcontroller implements all the algorithms without any floating point numbers.Furthermore, both hardware and software are adapted for future industrial use. The finished prototype supports a number of communication interfaces in which Modbus (RS-485) and current loop communication can be mentioned.The final result is a very good performing platform with strong future potential.The work was commissioned by the consulting firm Syncore Technologies AB at their office in Mjärdevi, Linköping. The project has, in total, taken 10 weeks and occurred during spring 2010.

In this master’s thesis the width of the <img src="http://www.diva-portal.org/cgi-bin/mimetex.cgi?%5Ceta'" /> meson is studied as a function of temperature. We consider a background medium consisting of a pion gas and assume a vanishing net baryon chemical potential. The width is obtained in the framework of large <img src="http://www.diva-portal.org/cgi-bin/mimetex.cgi?N_%7Bc%7D" /> chiral perturbation theory and we consider terms up to next-to-leading order in the effective Lagrangian. We use a low-density approximation to calculate the width increase due to scattering with pions from the heat bath. The results suggest that the in-medium width for the <img src="http://www.diva-portal.org/cgi-bin/mimetex.cgi?%5Ceta'" /> may become of considerable size: at a temperature <img src="http://www.diva-portal.org/cgi-bin/mimetex.cgi?T%5Capprox%2075" /> MeV we find a width increase of <img src="http://www.diva-portal.org/cgi-bin/mimetex.cgi?%5CDelta%5CGamma%5Capprox%203-4" /> MeV, comparable to the inverse lifetime of the fireball created in a heavy-ion collision. The <img src="http://www.diva-portal.org/cgi-bin/mimetex.cgi?%5Ceta'" /> is of particular interested since it is intimately connected to the <img src="http://www.diva-portal.org/cgi-bin/mimetex.cgi?U(1)_%7BA%7D" /> anomaly of Quantum Chromodynamics (QCD). It has been speculated that <img src="http://www.diva-portal.org/cgi-bin/mimetex.cgi?U(1)_%7BA%7D" /> may become a symmetry of QCD at high temperatures and studies of the <img src="http://www.diva-portal.org/cgi-bin/mimetex.cgi?%5Ceta'" /> could indicate if that is the case. Depending on for how large temperatures the results from large <img src="http://www.diva-portal.org/cgi-bin/mimetex.cgi?N_%7Bc%7D" /> can be trusted, they indicate that the <img src="http://www.diva-portal.org/cgi-bin/mimetex.cgi?%5Ceta'" /> may be possible to study experimentally in heavy-ion collisions due to its sizable in-medium width.

Ever since Bengt Sigurd laid out the first comprehensive description of Swedish phonotactics in 1965, it has been the main point of reference within the field. This thesis attempts a new approach, by presenting a computational and statistical model of Swedish phonotactics, which can be built by any corpus of IPA phonetic script. The model is a weighted trie, represented as a finite state automaton, where states are phonemes linked by transitions in valid phoneme sequences, which adds the benefits of being probabilistic and expressible by regular languages. It was implemented using the Nordisk Språkteknologi (NST) pronunciation lexicon and was used to test against a couple of rulesets defined in Sigurd relating to initial two consonant clusters of phonemes and phoneme classes. The results largely agree with Sigurd's rules and illustrated the benefits of the model, in that it effectively can be used to pattern match against phonotactic information using regular expression-like syntax. / Ända sedan Bengt Sigurd lade fram den första övergripande beskrivningen av svensk fonotax 1965, så har den varit den främsta referenspunkten inom fältet. Detta examensarbete försöker sig på en ny infallsvinkel genom att presentera en beräkningsbar och statistisk modell av svensk fonotax som kan byggas med en korpus av fonetisk skrift i IPA. Modellen är en viktad trie, representerad som en ändlig automat, vilket har fördelarna av att vara probabilistisk och kunna beskrivas av reguljära språk. Den implementerades med hjälp av uttalslexikonet från Nordisk Språkteknologi (NST) och användes för att testa ett par regelgrupper av initiala två-konsonant kluster av fonem och fonemklasser definierad av Sigurd. Resultaten stämmer till större del överens med Sigurds regler och visar på fördelarna hos modellen, i att den effektivt kan användas för att matcha mönster av fonotaktisk information med hjälp av en liknande syntax för reguljära uttryck.