993 resultados para Numerical Solutions
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The combination of two low-cost classical procedures based on titrimetric techniques is presented for the determination of pyridoxine hydrochloride in pharmaceuticals samples. Initially some experiments were carried out aiming to determine both pKa1 and pKa2 values, being those compared to values of literature and theoretical procedures. Commercial samples containing pyridoxine hydrochloride were electrochemically analysed by exploiting their acid-base and precipitation reactions. Potentiometric titrations accomplished the reaction between the ionizable hydrogens present in pyridoxine hydrochloride, being NaOH used as titrant; while the conductimetric method was based on the chemical precipitation between the chloride of pyridoxine hydrochloride molecule and Ag+ ions from de silver nitrate, changing the conductivity of the solution. Both methods were applied to the same commercial samples leading to concordant results when compared by statistical tests (95 and 98% confidence levels). Recoveries ranging from 99.0 to 108.1% were observed, showing no significant interference on the results.
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Adsorption is one of the most commonly used methods in water treatment processes. It is attractive due to it easy operation and the availability of a wide variety of commercial adsorbents. This doctoral thesis focuses on investigating and explaining the influence of external phase conditions (temperature, pH, ionic strength, acidity, presence of cosolutes) on adsorption phenomena. In order to cover a wide range of factors and phenomena, case studies were chosen from various fields where adsorption is applied. These include the adsorptive removal of surface active agents (used in cleaning chemicals, for example) from aqueous effluents, the removal of hormones (estradiol) from drinking water, and the adsorption of antibiotics onto silica. The latter can beused to predict the diffusion of antibiotics in the aquatic system if they are released into the environment. Also the adsorption of living cells on functionalized polymers to purify infected water streams was studied. In addition to these examples, the adsorptive separation of harmful compounds from internal water streams within a chemical process was investigated. The model system was removal of fermentation inhibitors from lignocelluloses hydrolyzates. The detoxification of the fermentation broth is an important step in the manufacture of bioethanol from wood, but has not been studied previously in connection with concentrated acid hydrolyzates. New knowledge on adsorption phenomena was generated for all of the applications investigated. In most cases, the results could be explained by combining classical theories for individual phenomena. As an example, it was demonstrated how liquid phase aggregation could explain abnormal-looking adsorption equilibrium data. In addition to the fundamental phenomena, also process performance was of interest. This aspect is often neglected in adsorption studies. It was demonstrated that adsorbents should not be selected for a target application based on their adsorption properties only, but regeneration of the spent adsorbent must be considered. It was found that using a suitable amount of organic co-solvent in the regeneration can significantly improve the productivity of the process.
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En del av de intressantaste fenomenen inom dagens materialfysik uppstår ur ett intrikat samspel mellan myriader av elektroner. Högtemperatursupraledare är det mest berömda exemplet. Varken klassiska teorier eller modeller där elektronerna är oberoende av varandra kan förklara de häpnadsväckande effekterna i de starkt korrelerade elektronsystemen. I vissa kopparoxider, till exempel La2CuO4, är det känt att valenselektronerna till följd av en stark ömsesidig växelverkan lokaliseras en och en till kopparatomerna i föreningens CuO2 plan. Laddningarnas inneboende magnetiska moment—spinnet—får då en avgörande roll för materialets elektriska och magnetiska egenskaper, vilka i exemplets fall kan beskrivas med Heisenbergmodellen som är den grundläggande teoretiska modellen för mikroskopisk magnetism. Men exakt varför föreningarna kan bli supraledande då de dopas med överskottsladdningar är än så länge en obesvarad fråga. Min avhandling undersöker orenheters inverkan på Heisenbergmodellens magnetiska egenskaper—ett problem av både experimentell och teoretisk relevans. En etablerad numerisk metod har använts—en kvantmekanisk Monte Carlo teknik—för att utföra omfattande datorsimuleringar av den matematiska modellen på två dedikerade Linux datorkluster. Arbetet hör till området beräkningsfysik. De teoretiska modellerna för starkt korrelerade elektronsystem, däribland Heisenbergmodellen, är ytterst invecklade matematiskt sett och de kan inte lösas exakt. Analytiska utredningar bygger för det mesta på antaganden och förenklingar vars inverkningar på slutresultatet är ofta oklara. I det avseende kan numeriska studier vara exakta, det vill säga de kan behandla modellerna som de är. Oftast behövs bägge tillvägagångssätten. Den röda tråden i arbetet har varit att numeriskt testa vissa högaktuella analytiska förutsägelser rörande effekterna av orenheter i Heisenbergmodellen. En del av dem har vi på basen av mycket noggranna data kunnat bekräfta. Men våra resultat har också påvisat felaktigheter i de analytiska prognoserna som sedermera delvis reviderats. En del av avhandlingens numeriska upptäckter har i sin tur stimulerat till helt nya teoretiska studier.
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This study aimed to identify the value components of nurse call solutions. The value creation of such systems was analyzed by using a framework that was created based on the existing customer value literature. The empirical part of the study was conducted as a multiple-case study by using qualitative research methods. The data for the analysis was gathered through structured interviews in ten Finnish eldercare centers. The results indicate that a nurse call solution creates value for eldercare centers by increasing the safety of the residents, and by improving the efficiency of the staff while also providing cost savings.
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Whenever a spacecraft is launched it is essential that the algorithms in the on-board software systems and at ground control are efficient and reliable over extended periods of time. Geometric numerical integrators, and in particular variational integrators, have both these characteristics. In "Numerics of Spacecraft Dynamics" new numerical integrators are presented and analysed in depth. These algorithms have been designed specifically for the dynamics of spacecraft and artificial satellites in Earth orbits. Full analytical solutions to a class of integrable deformations of the two-body problem in classical mechanics are derived, and a systematic method to compute variational integrators to arbitrary order with a computer algebra system is introduced.
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Carboxylic acids are commonly used organic acids and have many applications in industries producing food and pharmaceutical products, surfactants and detergents. Especially formic, acetic, propionic and butyric acid are important organic chemicals. These compounds can be found in many side streams and plant effluents. Recovery costs of carboxylic acids are high when they are removed from dilute solution. Conventional processes for the recovery of carboxylic acids from aqueous solutions are classical distillation or extractive distillation, azeotropic distillation or liquid-liquid extraction. The literature part of this Master’s of Science Thesis comprises possible extractants in liquid-liquid extraction of carboxylic acids from aqueous solutions and methods for their regeneration form the extract. The experimental part of this Thesis investigates liquid-liquid extraction of carboxylic acids from aqueous solutions. The aim of this work was to find a suitable extractant for liquid-liquid extraction and suitable process conditions to recover carboxylic acids from aqueous solutions. Also, back extraction of carboxylic acids and their thermal decomposition in relation to distillation of were. Experiments showed that there is more than one possible extractant for liquid-liquid extraction of carboxylic acids. Results also showed that it is possible to separate carboxylic acids and regenerate all the used extractants by vacuum distillation at suitable temperature.
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The objective of this dissertation is to improve the dynamic simulation of fluid power circuits. A fluid power circuit is a typical way to implement power transmission in mobile working machines, e.g. cranes, excavators etc. Dynamic simulation is an essential tool in developing controllability and energy-efficient solutions for mobile machines. Efficient dynamic simulation is the basic requirement for the real-time simulation. In the real-time simulation of fluid power circuits there exist numerical problems due to the software and methods used for modelling and integration. A simulation model of a fluid power circuit is typically created using differential and algebraic equations. Efficient numerical methods are required since differential equations must be solved in real time. Unfortunately, simulation software packages offer only a limited selection of numerical solvers. Numerical problems cause noise to the results, which in many cases leads the simulation run to fail. Mathematically the fluid power circuit models are stiff systems of ordinary differential equations. Numerical solution of the stiff systems can be improved by two alternative approaches. The first is to develop numerical solvers suitable for solving stiff systems. The second is to decrease the model stiffness itself by introducing models and algorithms that either decrease the highest eigenvalues or neglect them by introducing steady-state solutions of the stiff parts of the models. The thesis proposes novel methods using the latter approach. The study aims to develop practical methods usable in dynamic simulation of fluid power circuits using explicit fixed-step integration algorithms. In this thesis, twomechanisms whichmake the systemstiff are studied. These are the pressure drop approaching zero in the turbulent orifice model and the volume approaching zero in the equation of pressure build-up. These are the critical areas to which alternative methods for modelling and numerical simulation are proposed. Generally, in hydraulic power transmission systems the orifice flow is clearly in the turbulent area. The flow becomes laminar as the pressure drop over the orifice approaches zero only in rare situations. These are e.g. when a valve is closed, or an actuator is driven against an end stopper, or external force makes actuator to switch its direction during operation. This means that in terms of accuracy, the description of laminar flow is not necessary. But, unfortunately, when a purely turbulent description of the orifice is used, numerical problems occur when the pressure drop comes close to zero since the first derivative of flow with respect to the pressure drop approaches infinity when the pressure drop approaches zero. Furthermore, the second derivative becomes discontinuous, which causes numerical noise and an infinitely small integration step when a variable step integrator is used. A numerically efficient model for the orifice flow is proposed using a cubic spline function to describe the flow in the laminar and transition areas. Parameters for the cubic spline function are selected such that its first derivative is equal to the first derivative of the pure turbulent orifice flow model in the boundary condition. In the dynamic simulation of fluid power circuits, a tradeoff exists between accuracy and calculation speed. This investigation is made for the two-regime flow orifice model. Especially inside of many types of valves, as well as between them, there exist very small volumes. The integration of pressures in small fluid volumes causes numerical problems in fluid power circuit simulation. Particularly in realtime simulation, these numerical problems are a great weakness. The system stiffness approaches infinity as the fluid volume approaches zero. If fixed step explicit algorithms for solving ordinary differential equations (ODE) are used, the system stability would easily be lost when integrating pressures in small volumes. To solve the problem caused by small fluid volumes, a pseudo-dynamic solver is proposed. Instead of integration of the pressure in a small volume, the pressure is solved as a steady-state pressure created in a separate cascade loop by numerical integration. The hydraulic capacitance V/Be of the parts of the circuit whose pressures are solved by the pseudo-dynamic method should be orders of magnitude smaller than that of those partswhose pressures are integrated. The key advantage of this novel method is that the numerical problems caused by the small volumes are completely avoided. Also, the method is freely applicable regardless of the integration routine applied. The superiority of both above-mentioned methods is that they are suited for use together with the semi-empirical modelling method which necessarily does not require any geometrical data of the valves and actuators to be modelled. In this modelling method, most of the needed component information can be taken from the manufacturer’s nominal graphs. This thesis introduces the methods and shows several numerical examples to demonstrate how the proposed methods improve the dynamic simulation of various hydraulic circuits.
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Adsorbents functionalized with chelating agents are effective in removal of heavy metals from aqueous solutions. Important properties of such adsorbents are high binding affinity as well as regenerability. In this study, aminopolycarboxylic acid, EDTA and DTPA, were immobilized on the surface of silica gel, chitosan, and their hybrid materials to achieve chelating adsorbents for heavy metals such as Co(II), Ni(II), Cd(II), and Pb(II). New knowledge about the adsorption properties of EDTA- and DTPA-functionalizedadsorbents was obtained. Experimental work showed the effectiveness, regenerability, and stability of the studied adsorbents. Both advantages and disadvantages of the adsorbents were evaluated. For example, the EDTA-functionalized chitosan-silica hybrid materials combined the benefits of the silica gel and chitosan while at the same time diminishing their observed drawbacks. Modeling of adsorption kinetics and isotherms is an important step in design process. Therefore, several kinetic and isotherm models were introduced and applied in this work. Important aspects such as effect of error function, data range, initial guess values, and linearization were discussed and investigated. The selection of the most suitable model was conducted by comparing the experimental and simulated data as well as evaluating the correspondence between the theory behind the model and properties of the adsorbent. In addition, modeling of two-component data was conducted using various extended isotherms. Modeling results for both one- and twocomponent systems supported each other. Finally, application testing of EDTA- and DTPA-functionalized adsorbents was conducted. The most important result was the applicability of DTPA-functionalized silica gel and chitosan in the capturing of Co(II) from its aqueous EDTA-chelate. Moreover, these adsorbents were efficient in various solution matrices. In addition, separation of Ni(II) from Co(II) and Ni(II) and Pb(II) from Co(II) and Cd(II) was observed in two- and multimetal systems. Lastly, prior to their analysis, EDTA- and DTPA-functionalized silica gels were successfully used to preconcentrate metal ions from both pure and salty waters
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Tämän diplomityön tavoitteena oli kehittää seisontamaksuprosessia löytämällä keinot tehostaa informaation kulkua prosessin eri osapuolten välillä, parantaa prosessin läpimenoaikaa, yhtenäistää toimintakäytäntöjä, sekä vähentää virheellisten seisontamaksulaskujen lähettämistä asiakkaille. Tietoa kerättiin haastatteluin, sähköpostikeskusteluja tutkimalla, sekä analysoimalla numeerista aineistoa seisontamaksuista. Työn teoriaosassa käsiteltiin prosesseja ja niiden kehittämistä yleisesti, muutoksen hallintaa, sekä prosessien kehittämisessä apuna toimivia valmiita kehittämismalleja. Työn empiirisessä osassa kuvattiin seisontamaksuprosessi ja löydettiin siitä suurimmat ongelmakohdat. Tiedonkulku prosessin eri osapuolten välillä osoittautui suurimmaksi ongelmien aiheuttajaksi. Ongelmiin kehitettiin ratkaisut, joiden pohjalta luotiin optimaalinen toimintamalli seisontamaksuprosessista. Lisäksi prosessin tulevan toiminnan seuraamiseksi ehdotettiin erilaisia mittareita. Kehitettyjen ratkaisujen katsottiin täyttäneen kaikki yrityksen asettamat tavoitteet, mutta ratkaisujen tarkemmat vaikutukset prosessin toimintaan näkyvät kuitenkin vasta niiden käyttöönoton jälkeen.
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The aim of this study was to create a Balanced Scorecard to the DigiCup solution. The first goal was to create process descriptions to the few critical processes. The second goal was to define appropriate measurements, according to customer survey as well as following the Balanced Scorecard process description, to manage the critical success factors. The overall goal of this study was to create a performance measurement system for the solution which guides the operation towards continuous improvement. This study was conducted by using both qualitative and quantitative methods, and the analysis was done by using a case study method. The material was gathered from the current customers, the management and the employees using structured, semi-structured and open group and individual interviews. The current customers were divided into retailers and direct customers of the DigiCup solution. The questions which the customers were asked were related to the information about interviewee, company, business strategy, market, satisfaction survey and future requirements. The management defined the strategy and took part in specifying the perspectives, objectives and measurements to the Balanced Scorecard of the DigiCup solution. The employees participated into the choosing of the metrics. The material consisted from altogether sixteen interviews. At the beginning of the study the product development, the order-delivery as well as the printing processes was chosen to be the critical processes of the DigiCup solution. These processes were concentrated on already in the literature review while trying to find the characteristics of these processes as well as the critical success factors and the appropriate measurements, which could be utilized when creating the Balanced Scorecard to the DigiCup solution according to the customer survey. The appropriate perspectives, objectives and measurements were found to the DigiCup solution. The chosen measures works as a basis for the development of IT-reporting tool. As a conclusion it can be stated that when discussing a new business, where the objectives are changing according to which development’s phases the company is in, the measurement should be updated often enough.
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Alumiiniveneissä hitsauksen aiheuttamat muodonmuutokset ovat usein erittäin haitallisia, koska niiden aiheuttamat mittamuutokset ja ulkonäölliset haitat alentavat tuotteen laatua sekä arvoa. Monissa tapauksissa myös hitsausliitoksen suorituskyky heikentyy ja lisäksi hitsausmuodonmuutokset voivat aiheuttaa toiminnallisia ongelmia alumiiniveneiden runkorakenteisiin. Tästä johtuen hitsausmuodonmuutosten hallinta ja minimointi ovat erityisen tärkeitä tekijöitä pyrittäessä parantamaan alumiiniveneiden laatua ja kustannustehokkuutta sekä kasvattamaan alumiinivenealan kilpailukykyä. Tässä diplomityössä tutkittiin robotisoidun kaasukaarihitsauksen aiheuttamia muodonmuutoksia sekä niiden hallintaa alumiinista valmistettujen työ- ja huviveneiden runkorakenteissa. Työssä perehdyttiin nykyaikaiseen alumiinivenevalmistukseen sekä hitsattujen rakenteiden yleisiin lujuusopin teorioihin ja käyttäytymismalleihin. Alumiinin hitsausmuodonmuutosten tutkimuksissa suoritettiin käytännön hitsauskokeita, joiden kohteina olivat alumiiniveneissä käytetyt rakenneratkaisut ja liitostyypit. Työn tavoitteena oli määrittää alumiinin hitsauksessa syntyviin muodonmuutoksiin keskeisesti vaikuttavia tekijöitä ja parametreja. Tutkimustulosten perusteella pyrittiin esittämään ratkaisuja alumiiniveneiden rakenteisiin aiheutuvien hitsausmuodonmuutosten vähentämiseksi ja hallitsemiseksi. Alumiinirakenteissa hitsausmuodonmuutokset ovat hyvin tapauskohtaisia, koska usein niiden syntyminen määräytyy monen tekijän yhteisvaikutuksesta. Teräsrakenteille käytetyt yleiset analyyttiset laskentakaavat ja käyttäytymismallit eivät sovellu suoraan alumiinirakenteille, mikä johtuu alumiinin erilaisista materiaaliominaisuuksista ja käyttäytymisestä hitsauksen aikana. Tulevaisuudessa empiiristen koejärjestelyiden ja analyyttisten mallien lisäksi sovellettavan numeerisen elementtimenetelmän avulla voidaan parantaa alumiinin hitsauksessa aiheutuvien muodonmuutosten kokonaisvaltaista hallintaa.
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Min avhandling behandlar hur oordnade material leder elektrisk ström. Bland materialen som studeras finns ledande polymerer, d.v.s. plaster som leder ström, och mer allmänt organiska halvledare. Av de här materialen har man kunnat bygga elektroniska komponenter, och man hoppas på att kunna trycka hela kretsar av organiska material. För de här tillämpningarna är det viktigt att förstå hur materialen själva leder elektrisk ström. Termen oordnade material syftar på material som saknar kristallstruktur. Oordningen gör att elektronernas tillstånd blir lokaliserade i rummet, så att en elektron i ett visst tillstånd är begränsad t.ex. till en molekyl eller ett segment av en polymer. Det här kan jämföras med kristallina material, där ett elektrontillstånd är utspritt över hela kristallen (men i stället har en väldefinierad rörelsemängd). Elektronerna (eller hålen) i det oordnade materialet kan röra sig genom att tunnelera mellan de lokaliserade tillstånden. Utgående från egenskaperna för den här tunneleringsprocessen, kan man bestämma transportegenskaperna för hela materialet. Det här är utgångspunkten för den så kallade hopptransportmodellen, som jag har använt mig av. Hopptransportmodellen innehåller flera drastiska förenklingar. Till exempel betraktas elektrontillstånden som punktformiga, så att tunneleringssannolikheten mellan två tillstånd endast beror på avståndet mellan dem, och inte på deras relativa orientation. En annan förenkling är att behandla det kvantmekaniska tunneleringsproblemet som en klassisk process, en slumpvandring. Trots de här grova approximationerna visar hopptransportmodellen ändå många av de fenomen som uppträder i de verkliga materialen som man vill modellera. Man kan kanske säga att hopptransportmodellen är den enklaste modell för oordnade material som fortfarande är intressant att studera. Man har inte hittat exakta analytiska lösningar för hopptransportmodellen, därför använder man approximationer och numeriska metoder, ofta i form av datorberäkningar. Vi har använt både analytiska metoder och numeriska beräkningar för att studera olika aspekter av hopptransportmodellen. En viktig del av artiklarna som min avhandling baserar sig på är att jämföra analytiska och numeriska resultat. Min andel av arbetet har främst varit att utveckla de numeriska metoderna och applicera dem på hopptransportmodellen. Därför fokuserar jag på den här delen av arbetet i avhandlingens introduktionsdel. Ett sätt att studera hopptransportmodellen numeriskt är att direkt utföra en slumpvandringsprocess med ett datorprogram. Genom att föra statisik över slumpvandringen kan man beräkna olika transportegenskaper i modellen. Det här är en så kallad Monte Carlo-metod, eftersom själva beräkningen är en slumpmässig process. I stället för att följa rörelsebanan för enskilda elektroner, kan man beräkna sannolikheten vid jämvikt för att hitta en elektron i olika tillstånd. Man ställer upp ett system av ekvationer, som relaterar sannolikheterna för att hitta elektronen i olika tillstånd i systemet med flödet, strömmen, mellan de olika tillstånden. Genom att lösa ekvationssystemet fås sannolikhetsfördelningen för elektronerna. Från sannolikhetsfördelningen kan sedan strömmen och materialets transportegenskaper beräknas. En aspekt av hopptransportmodellen som vi studerat är elektronernas diffusion, d.v.s. deras slumpmässiga rörelse. Om man betraktar en samling elektroner, så sprider den med tiden ut sig över ett större område. Det är känt att diffusionshastigheten beror av elfältet, så att elektronerna sprider sig fortare om de påverkas av ett elektriskt fält. Vi har undersökt den här processen, och visat att beteendet är väldigt olika i endimensionella system, jämfört med två- och tredimensionella. I två och tre dimensioner beror diffusionskoefficienten kvadratiskt av elfältet, medan beroendet i en dimension är linjärt. En annan aspekt vi studerat är negativ differentiell konduktivitet, d.v.s. att strömmen i ett material minskar då man ökar spänningen över det. Eftersom det här fenomenet har uppmätts i organiska minnesceller, ville vi undersöka om fenomenet också kan uppstå i hopptransportmodellen. Det visade sig att det i modellen finns två olika mekanismer som kan ge upphov till negativ differentiell konduktivitet. Dels kan elektronerna fastna i fällor, återvändsgränder i systemet, som är sådana att det är svårare att ta sig ur dem då elfältet är stort. Då kan elektronernas medelhastighet och därmed strömmen i materialet minska med ökande elfält. Elektrisk växelverkan mellan elektronerna kan också leda till samma beteende, genom en så kallad coulombblockad. En coulombblockad kan uppstå om antalet ledningselektroner i materialet ökar med ökande spänning. Elektronerna repellerar varandra och ett större antal elektroner kan leda till att transporten blir långsammare, d.v.s. att strömmen minskar.
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This study was conducted in order to learn how companies’ revenue models will be transformed due to the digitalisation of its products and processes. Because there is still only a limited number of researches focusing solely on revenue models, and particularly on the revenue model change caused by the changes at the business environment, the topic was initially approached through the business model concept, which organises the different value creating operations and resources at a company in order to create profitable revenue streams. This was used as the base for constructing the theoretical framework for this study, used to collect and analyse the information. The empirical section is based on a qualitative study approach and multiple-case analysis of companies operating in learning materials publishing industry. Their operations are compared with companies operating in other industries, which have undergone comparable transformation, in order to recognise either similarities or contrasts between the cases. The sources of evidence are a literature review to find the essential dimensions researched earlier, and interviews 29 of managers and executives at 17 organisations representing six industries. Based onto the earlier literature and the empirical findings of this study, the change of the revenue model is linked with the change of the other dimen-sions of the business model. When one dimension will be altered, as well the other should be adjusted accordingly. At the case companies the transformation is observed as the utilisation of several revenue models simultaneously and the revenue creation processes becoming more complex.
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This thesis studies the use of heuristic algorithms in a number of combinatorial problems that occur in various resource constrained environments. Such problems occur, for example, in manufacturing, where a restricted number of resources (tools, machines, feeder slots) are needed to perform some operations. Many of these problems turn out to be computationally intractable, and heuristic algorithms are used to provide efficient, yet sub-optimal solutions. The main goal of the present study is to build upon existing methods to create new heuristics that provide improved solutions for some of these problems. All of these problems occur in practice, and one of the motivations of our study was the request for improvements from industrial sources. We approach three different resource constrained problems. The first is the tool switching and loading problem, and occurs especially in the assembly of printed circuit boards. This problem has to be solved when an efficient, yet small primary storage is used to access resources (tools) from a less efficient (but unlimited) secondary storage area. We study various forms of the problem and provide improved heuristics for its solution. Second, the nozzle assignment problem is concerned with selecting a suitable set of vacuum nozzles for the arms of a robotic assembly machine. It turns out that this is a specialized formulation of the MINMAX resource allocation formulation of the apportionment problem and it can be solved efficiently and optimally. We construct an exact algorithm specialized for the nozzle selection and provide a proof of its optimality. Third, the problem of feeder assignment and component tape construction occurs when electronic components are inserted and certain component types cause tape movement delays that can significantly impact the efficiency of printed circuit board assembly. Here, careful selection of component slots in the feeder improves the tape movement speed. We provide a formal proof that this problem is of the same complexity as the turnpike problem (a well studied geometric optimization problem), and provide a heuristic algorithm for this problem.
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Thesis talks about relay protection for microgrids. Microgrid operation sets more challenges than traditional utility grid protection because of lower fault current levels. Solutions for these challenges are discussed in this paper. Thesis also studies available relay protection solutions and figures out how they would fit for microgrid protection.