A stochastic process or sometimes called random process is the counterpart to a deterministic process in theory. A stochastic process is a random field, whose domain is a region of space, in other words, a random function whose arguments are drawn from a range of continuously changing values. In this case, Instead of dealing only with one possible 'reality' of how the process might evolve under time (as is the case, for example, for solutions of an ordinary differential equation), in a stochastic or random process there is some indeterminacy in its future evolution described by probability distributions. This means that even if the initial condition (or starting point) is known, there are many possibilities the process might go to, but some paths are more probable and others less. However, in discrete time, a stochastic process amounts to a sequence of random variables known as a time series. Over the past decades, the problems of synergetic are concerned with the study of macroscopic quantitative changes of systems belonging to various disciplines such as natural science, physical science and electrical engineering. When such transition from one state to another take place, fluctuations i.e. (random process) may play an important role. Fluctuations in its sense are very common in a large number of fields and nearly every system is subjected to complicated external or internal influences that are often termed noise or fluctuations. Fokker-Planck equation has turned out to provide a powerful tool with which the effects of fluctuation or noise close to transition points can be adequately be treated. For this reason, in this thesis work analytical and numerical methods of solving Fokker-Planck equation, its derivation and some of its applications will be carefully treated. Emphasis will be on both for one variable and N- dimensional cases.
Galerkinmetoden studeras för att lösa ingegralekvationer med randvärden för Laplacepoperatorn för non-smooth områden. Konvergens visas med ett villkor på nätstorleken., vilket består av den lokala krökningen för approximerande områden. Feluppskattningar är härledda, och resultaten generaliserar för system av ekvationer.
ireless Communication is one of the fields of Telecommunications which is growing with the tremendous speed. With the passage of time wireless communication devices are becoming more and more common. It is not only the technology of business but now people are using it to perform their daily tasks, be it for calling, shopping, checking their emails or transfer their money. Wireless communication devices include cellular phones, cordless phones and satellite phones, smart phones like Personal Digital Assistants (PDA), two way pagers, and lots of their devices are on their way to improve this wireless world. In order to establish two way communications, a wireless link may be using radio waves or Infrared light. The Wireless communication technologies have become increasingly popular in our everyday life. The hand held devices like Personal Digital Assistants (PDA) allow the users to access calendars, mails, addresses, phone number lists and the internet. Personal digital assistants (PDA) and smart phones can store large amounts of data and connect to a broad spectrum of networks, making them as important and sensitive computing platforms as laptop PCs when it comes to an organization’s security plan. Today’s mobile devices offer many benefits to enterprises. Mobile phones, hand held computers and other wireless systems are becoming a tempting target for virus writers. Mobile devices are the new frontier for viruses, spam and other potential security threats. Most viruses, Trojans and worms have already been created that exploit vulnerabilities. With an increasing amount of information being sent through wireless channels, new threats are opening up. Viruses have been growing fast as handsets increasingly resemble small computers that connect with each other and the internet. Hackers have also discovered that many corporate wireless local area networks (WLAN) in major cities were not properly secured. Mobile phone operators say that it is only a matter of time before the wireless world is hit by the same sorts of viruses and worms that attack computer software.
Fuzzy relation equations are becoming extremely important in order to investigate the optimal solution of the inverse problem even though there is a restrictive condition for the availability of the solution of such inverse problems. We discussed the methods for finding the optimal (maximum and minimum) solution of inverse problem of fuzzy relation equation of the form $R \circ Q = T$ where for both cases R and Q are kept unknown interchangeably using different operators (e.g. alpha, sigma etc.). The aim of this study is to make an in-depth finding of best project among the host of projects, depending upon different factors (e.g. capital cost, risk management etc.) in the field of civil engineering. On the way to accomplish this aim, two linguistic variables are introduced to deal with the uncertainty factor which appears in civil engineering problems. Alpha-composition is used to compute the solution of fuzzy relation equation. Then the evaluation of the projects is orchestrated by defuzzifying the obtained results. The importance of adhering to such synopsis, in the field of civil engineering, is demonstrated by an example.
Conclusions In the theory section, we have shown two fundamental principles of fluid flow, conservation of mass (continuity equation) and conservation of momentum (the Cauchy equation) of fluid motion. To get to Euler equations we employed the Navier-Stokes equations for incompressible flow, by neglecting fluid viscosity making μ=0 [21], with this assumption Navier-Stokes equations take the form of Euler equations, detailed discussions and derivations might be found at Atil’s lecture notes[21][23] The second last step is derivation of exact solutions to the Navier-Stokes quations, the Hagen–Poiseuille eqautions, by applying basic physics with the assumptions of laminar flow, constant viscosity and straight pipe with circular cross-section, we derived Hagen–Poiseuille eqautions, this led to a relationship between pressure changes over a length L of pipe, and a friction factor associated with viscous effects We then applied Euler equations to derive well known Bernoulli equation, which signifies that when the velocity increases in a fluid stream, the pressure decreases and when velocity decreases the pressure increases [31] [15] We must highlight that all of these equations have their roots in the Navier– Stokes equations, once again underscoring the universality of these equations in the context of describing the motion of fluids [10] Why did we have to derive all these equations? It is important when applying any equation that we are aware of the restrictions on its use, the restrictions are normally seen in the derivation of the equation when certain simplifying assumptions about the nature of the problem are made. If we ignore the restrictions, we may get inaccurate results from the equation. e.g. an equation was derived while assuming that the flow was incompressible, which means that the speed of the flow is much less than the speed of sound. If you use this form for a supersonic flow, the answer will be wrong [32] In the Modeling and simulations section, the following steps have been completed as given on the goal statement: To broaden our level of understanding and interactions of different components we shown simplified model of the UDS To ensure model meets requirements and fulfills its intended use we have verified (e.g. Right flow, pressure, and mass flow rate) To gain confidence in the model we have validated by comparing model with the real system data and found acceptable agreement We have also shown Effects of various parameters of the system, such as Volumetric Efficiency of the pump, return restriction diameter variations, relationship between flow rate and speed Finally we have demonstrated Adblue density as function of pressure and temperature, and effects of the temperature on Dynamic and Kinematic viscosity of the Adblue, more Adblue fluid properties is also given on Appendix B
To be successful in today's competitive market, service providers should look at user's satisfaction as a critical key. In order to gain a better understanding of customers' expectations, a proper evaluations which considers intrinsic characteristics of perceived quality of service is needed. Due to the subjective nature of quality, the vagueness of human judgment and the uncertainty about the degree of users' linguistic satisfaction, fuzziness is associated with quality of experience. Considering the capability of Fuzzy logic in dealing with imprecision and qualitative knowledge, it would be wise to apply it as a powerful mathematical tool for analyzing the quality of experience (QoE). This thesis proposes a fuzzy procedure to evaluate the quality of experience. In our proposed methodology, we provide a fuzzy relationship between QoE and Quality of Service (QoS) parameters. To identify this fuzzy relationship a new term called Fuzzi ed Opinion Score (FOS) representing a fuzzy quality scale is introduced. A fuzzy data mining method is applied to construct the required number of fuzzy sets. Then, the appropriate membership functions describing fuzzy sets are modeled and compared with each other. The proposed methodology will assist service providers for better decision-making and resource management.
Nonlinear self-adjointness of the anisotropic nonlinear heat equation is investigated. Mathematical models of heat conduction in anisotropic media with a source are considered and a class of self-adjoint models is identified. Conservation laws corresponding to the symmetries of the equations in question are computed.
In the present paper, the recent method of conservation laws for constructing exact solutions for systems of nonlinear partial differential equations is applied to the gasdynamic equations describing one-dimensional and three-dimensional polytropic flows. In the one-dimensional case singular solutions are constructed in closed forms. In the threedimensional case several conservation laws are used simultaneously. It is shown that the method of conservation laws leads to particular solutions different from group invariant solutions.
Recently, the financial market has become an area of increased research interest for mathematician and statisticians. The Black and Scholes breakthrough in this area triggered a lot of new research activity. Commonly the research concerns the log returns of assets (shares, bond, foreign exchange, option). The variation in the log returns is called volatility and it is widely studied and because of its relevance for applications in the financial world. The volatility is mostly used for measuring the risk and also for forecasting future prices. In this research work a process of trading activities is considered. It is assumed that at a random time-point a parameter change in the laws of the trading occurs, indicating changed trading behaviour. For inferential matters about the process it is of vital importance to be able to state that such change has occurred quickly and accurately. The methods used to this end are called stopping rules which signal alarm as soon as some statistics based on-line observations goes beyond some boundary. The model considered for this process of log returns is the family of Autoregressive Conditional Heteroskedastic (ARCH) model. It is widely accepted that this well describes a lot of phenomena in the financial market. In this work statements about this process will be derived, the stopping rule will be defined, evaluated and their properties discussed.
In real word many problems, most of criteria have interdependent or interactive characteristics, which cannot be evaluated by additive measures exactly. For the human subjective evaluation processes it will be more better to apply Choquet and Sugeno integrals model together with the definition of lambda − fuzzy measure, in which the property of additivity is not necessary. My thesis presents the application of fuzzy integrals as tool for criteria aggregation in the decision problems. Finally, this research gives the examples of evaluating medicine with illustrations of hierarchicalstructure of lambda− fuzzy measure for Choquet and Sugeno integrals model.
När undervisningsmaterial översätts kan text baserade exempel förlora sin mening, analogier bli meningslösa, alfabet oförenliga, etc. Vi fokuserar på några principer för att undervisningsexempel ska fungera i helt olika språk och kulturer. Vi presenterar en fallstudie baserad på material som är fritt tillgängligt från CSunplugged.org. Det engelska materialet har anpassats till japanska, kinesiska, koreanska och svenska förhållande. (Dataundervisning, Kinestetisk lärande, Översättning)
Nowadays, cognitive radio (CR) is a promising concept to improve the radio spectrum exploitation. CR has tremendous ability to enhance spectrum efficiency by allowing secondary users (SUs) to access licensed radio spectrum resource which is currently not being used by primary users (PUs). One basic challenge of that paradigm is securing the quality of service (QoS) of the primary link transmission while increasing the rate of the secondary links transmission. Cooperative relaying is an encouraging technology which offers the opportunity to maximize the transmission diversity gain significantly in the rapid development growth of wireless communication which contains cognitive radio networks. On the other hand, effective capacity (EC) which is designed to provide a maximum constant arrival rate that a statistical wireless channels can support while satisfying statistical QoS requirements. In this thesis, the performance enhancement analysis of cognitive radio relay network (CRRN) by exploiting the direct communication link has been investigated in Rayleigh fading channel where peak interference power constraint is taken into consider. A spectrum sharing technique is considered in this thesis where a restriction of spectrum sharing is applied by the PUs. Here, an SU can coexist simultaneously with the PU for transmitting data as long as a certain threshold on the peak interference power applied on the primary receiver is not overstepped by the SUs transmission. In addition, it is supposed that there are multiple intermediate relay nodes available to transmit their signal to the destination along with a direct communication link for secondary transmission. Moreover, the SU transmission has to meet a random delay QoS constraint. By providing this QoS constraint, the maximum arrival data rate of SUs can be achieved with small error of probability. Specifically, this thesis also acquires closed-form expressions of EC for CRRN. It is evident that if the channel quality and the interference threshold set by the PU are changed, then the capacity of the channel is also to be changed. In addition, it is also verified that the direct communication link together with multiple relay nodes has significantly higher capacity gains compare to non-direct communication link for CRRN. Matlab simulations are presented to find out theoretical results and Monte-Carlo simulations are carried out to support these numerical results. Both the simulation results and the analytical results match very well.
We find the Lie point symmetries of the Novikov equation and demonstrate that it is strictly self-adjoint. Using the self-adjointness and the recent technique for constructing conserved vectors associated with symmetries of differential equations, we find the conservation law corresponding to the dilation symmetry and show that other symmetries do not provide nontrivial conservation laws. Then we investigate the invariant solutions.
We find the Lie point symmetries of a coupled variable-coefficient modified Korteweg–de Vries system in a two-layer fluid model. Then we establish its quasi self-adjointness and corresponding conservation laws.
This book is the main course literature in the course Computational Engineering, which comprises 22,5 ECTS (European Credit Transfer System), within the programme of Master of Science in Mechanical Engineering with emphasis on Structural Mechanics at Blekinge Institute of Technology. The book starts with rather simple numerical methods for ordinary differential equations and ends with advanced topics such as finite element procedures for systems of transient, non-linear and coupled partial differential equations. Several topics from physics and engineering are included to support the study of the numerical methods.
In curve of growth, traditionally equivalent width is found for absorption lines of Gaussian, Lorentz and Voigt profile against flat continuum. Here, absorption against non-flat distributions is examined. These non-flat distributions are Gaussian and Lorentz distribution. Analytically equivalent widths for absorption against non-flat continuum are complicated integrals. It is impossible to solve these integrals analytically so I have solved them numerically. At low μ the absorption is independent on profile while the growth of absorption depends on profile at high μ, where μ is width.
The propagation of intensive acoustic noise is of fundamental interest in nonlinear acoustics. Some of the simplest models describing such phenomena are generalized Burgers’ equations for finite amplitude sound waves. An important problem in this field is to find the wave’s behavior far from the emitting source for stochastic initial waveforms. The method of numerical solution of generalized Burgers equation proposed is step-by-step calculation supported on using Fast Fourier Transform of the considered signal. The general idea is to keep only Fourier image of concerned signal and update it recursively (in space). For simulating the wave evolution we used 4096 (212) point realizations and took averaging over 1000 realizations. Also the object of the present study is a numerical analysis of the spectral and bispectral functions of the intense random signals propagating in nondispersive nonlinear media. The possibility of recovering the input spectrum from the measured spectrum and bispectrum at the output of the nonlinear medium is discusses. The analytical estimations are supported by numerical simulation. For two different types of primary spectrum evolution of jet noise were numerically simulates at a short distance and assayed bispectrum and a spectrum analysis of the signals.
As shown from the study, different geometries give different results at different flow conditions (Reynolds number/ mass-flow rate). The choice of appropriate plate geometry does not always depend on high Nusselt number values, but predictability and almost constant behaviour through a large Reynolds number range, plays an important role as shown by the chevron design.
The purpose of this study was to investigate and implement fuzzy decision algorithms based on unequal objectives and minimization of regret to retrieve an optimal decision in business intelligence. Another aim was to compare these two models; those have been applied in business intelligence area. The use of unequal objectives and minimization of regret methods based on the essential concept of the fuzzy decision were applied on the business intelligence model. The first method uses Saaty’s approach of comparison objectives to determine the weight of the objectives, while the second method uses the regression of objectives which acts as a filter for high values by divesting them of their decisive power. In a complex business problem, we have used knowledge of experts in verbal expressions, converted these verbal expressions into linguistic variables and then used fuzzy decision making models to retrieve best decision. The implementation’s results of the two methods were the same regarding to the final decision set. The first model results indicated the effect of the influential factors on the products, while the second model results showed the payoff for the influential factors and its effectives on the products.
Den globala ekonomiska härdsmälta som påverkade börserna över hela världen hade också en negativ effekt på mindre utvecklingsländernas aktiemarknaderna. Som ett resultat av den härdsmälta, förlorade investerarna förtroende börsen. Monetära myndigheter i både Nigeria och Ghana hade försökt på flera sätt att återställa investerarnas förtroende och därmed ett av de viktigaste verktyg som regeringen använder för att uppnå makroekonomisk mål är penningpolitiken. Det blev ett behov av att undersöka hur penningpolitiska förändringar påverkar avkastningen på aktiemarknaden i nigerianska och ghananska börserna utbyte. Detta dokument bygger på jämförande studie av Nigerianska och Ghanas aktiemarknaderna i andra för att ta reda hur penningpolitiken inriktas nämligen räntan och penningmängden (m2) påverkar avkastning på aktiemarknaden. Genomförde vi ett enkelt test regressionsanalys baserat på årliga 20 års data (1990-2010). Resultatet visar att penningpolitiken har mer inverkan på avkastningen på aktiemarknaden i Ghanas ekonomin än den nigerianska ekonomin, och som sådan skulle kunna fungera som en marknad signal för investerare i Ghanas börsen marknaden. Medan den nigerianska börsen marknaden är okänslig för förändringar i penningpolitiken som sådan, skulle en förändring av penningpolitiken fungerar inte som en marknad signal för investerare i den nigerianska börsen marknaden.
Boken beskriver på ett enhetligt sätt ickelinjär akustik i gaser och vätskor (fluider) med lika stor vikt på matematik som fysik.
Aims. The main aim of this work was to investigate if the radiative process photoexcitation by accidental resonance (PAR) is producing Fe II lines in the UV region of NGC 4151. At the same time I searched for collisionally excited Fe II emission. While doing so, the broad line region (BLR), intermediate line region (ILR) and narrow line region (NLR) contributions to the Mg II resonance doublet were also investigated. Methods. The focus was on the 2000 to 3000 Å wavelength region, in which decay from both the collisionally and PAR excited Fe II levels would form emission lines. I examined three archived Space Telescope Imaging Spectrograph (STIS) spectra of NGC 4151. Theoretical spectra based on calculated ranges for possible fluxes of the collisionally excited lines and pumping rates through the Fe II channels were then fitted to the observed spectra Results. I show that the UV region is influenced by PAR and that the Fe II fluorescence lines are clearly needed to explain the spectrum between 2000 to 3000 Å. The best fit of the theoretical spectra to the STIS spectra was obtained by assuming a similar radiation power of Fe+ ions and Mg+ ions. Conclusions. The PAR is active in the BLR of NGC 4151 and the total power of the Fe II fluorescence is a significant fraction of the total emission in the 2000 to 3000 wavelength region. Therefore it is important to incorporate this in models of NGC 4151 and possibly also in models of other active galactic nuclei. There are also many collisionally excited Fe II lines that are blended by each other and are therefore not individually observable in the NGC 4151 spectra.
Two nonlinear dispersive wave equations arising in elasto-plastic flow have been investigated for self-adjointness. For these equations their symmetries are calculated and conservation laws are constructed using two different methods: an old method based on Noether´s Theorem and a new one developed by Prof. Nail Ibragimov. The new method works for a larger number of equations than the old one. It is complementing the old one in the way that it gives some conservation laws that otherwise would have been impossible to obtain.
The financial market has become an area of increasing research interest for mathematicians and statisticians in recent years. Mathematical models and methods are increasingly being applied to study various parameters of the market. One of the parameters that have attracted lots of interest is `volatility'. It is the measure of variability of prices of instruments (e.g. stock, options etc.) traded in the market. It is used mainly to measure risk and to predict future prices of assets. In this paper, the volatility of financial price processes is studied using the Ornstein-Uhlenbeck process. The process is a mean reverting model which has good and well documented properties to serve as a model for financial price processes. At some random time point, a parameter change in the distribution of the price process occurs. In order to control the development of prices, it is important to detect this change as quickly as possible. The methods for detecting such changes are called `stopping rules'. In this work, stopping rules will be derived and analysed. Using simulations and analytical methods, the properties of these stopping rules will be evaluated.
The Buck Converter is a voltage regulator consisted on an electronic circuit composed by a mosfet, a diode, an inductor and a capacitor. There are some implicit losses which depend on the choice of the different components. Therefore, the topic of this thesis is focused on that choice and the simulation with the components chosen shows the efficiency achieved. To simulate, it is necessary to make the mathematical analysis of the converter.
The first chapter introduces the thesis work. The second chapter presents the background of decision making models, their process, and the classification of decision making models. The third chapter presents the research methodology we have used in different phases which aims to answer the research questions. The fourth chapter gives a detailed literature study of how decision models can be used in application security. The fifth chapter evaluates selected decision models. The sixth chapter concludes the thesis and presents future work.
Basic mathematic analysis of how financial markets work and different valuation models such as the Stochastic Market Price Estimator, valuation model created by the author.
This thesis investigates the performance of cognitive radio relay networks (CRRN) in Rayleigh fading channel under various power constraints. Here spectrum sharing approach is considered, whereby a secondary user (SU) may be allowed to transmit simultaneously with a primary user (PU) as long as SU interference to PU remains below a tolerable level. In addition, SU has to meet certain quality of service (QoS) constraints of its own link. To support these QoS constraints, the maximal data rate that can be reliably transmitted with arbitrarily small error of probability is found. It is observed that this capacity is affected by channel quality and interference limit allowed by PU. Ergodic capacity and outage capacity which are two well known capacities, are analysed for CRRN under interference power constraints. This thesis also finds effective capacity for CRRN, a link layer channel model that models the effect of channel fading on queuing behaviour of the link. Effective capacity under interference and secondary transmitter power constraints is also investigated. The way of analysing effective capacity under interference and transmit power constraints is extended to ergodic capacity and outage capacity. Here it is observed that, capacity is affected by the minimum of transmit power and interference power constraints. Monte-Carlo simulations are carried out to support theoretical results obtained in this thesis.
This book is devoted to a symplectic approach of classical and quantum mechanics
Louise Petrén is an interesting person in the history of Swedish mathematics. In her PhD thesis defended in Lund in 1911, she extended to higher-order equations Laplace’s method of integration of second-order linear hyperbolic equations with two independent variables. It is interesting to consider her results from point of view of invariants of differential equations and compare with the theory of the Laplace invariants. However, L. Petrén’s research was not known until recently among mathematicians working in group analysis. The aim of our talk is to introduce Louise Petrén as a person and to discuss her generalization of Laplace’s method. Lars Haikola will contribute with a family background of Louise Petrén.
There is presently no wildfire model developed for Swedish conditions, only a fire danger rating system (FWI) has been developed for Swedish conditions. The demand for a wildfire model has not been great in the past in Sweden but the climate changes now taking place increases the risk of large and intensive wildfires in Sweden. The need for additional and better tools for sizing-up wildfires will be in great demand in the future. This pre-study is aimed at: - Presenting what has been done in the wildfire modeling field during the years and mainly the last twenty years. - Giving recommendations on the continued work with developing a Swedish wildfire model. The method that was used was literature and article survey. The study also looks into the required input data for a wildfire model and the input data available at the moment. This issue is highly crucial as the quality of the output of a wildfire model is depending upon the quality of the input data. During the study, a primitive wildfire model was constructed and refined in order to get an insight in the complexities and problems with developing an operational model. The following characterization of wildfire models was used during the study: - Statistical models: based primarily on statistics from earlier or experimental fires. They do not explicitly consider the controlling physical processes. - Semi-empirical models: based on physical laws, but enhanced with some empirical factors, often by lumping all physical mechanisms for heat transfer together. - Physical models: based on physical principles and distinguishing between physical mechanisms for heat transfer. The statistical models make no attempt to involve physical processes, as they are merely a statistical description of test fires. Thus the lack of a physical basis means that statistical models must be used carefully outside the test conditions. Semi-empirical models are often based on conservation of energy principles but do not make any difference between conduction, convection and radiation heat transfer. The semi-empirical model has low computational requirements and includes variables that are generally easy to measure in the field. So despite the issue with limited accuracy, the speed and simplicity of these models make them useful for operational use. Physical models have the advantage that they are based on known relationships and thus facilitating their scaling. Thus we can expect that physical models would provide the most accurate predictions and have the widest applicability. But the work on physical models is suffering of for example the lack of understanding of several processes, such as the characterization of the chemical processes taking place during combustion, the resulting flame characteristics and the isolation and quantification of physical processes governing heat transfer. The input data available today are generally not detailed enough for physical models. As a result, a very detailed physical model will still only give imprecise predictions. As better and more detailed input will be available, the use of physical models will be more justified. A semi-empirical model is recommended being developed in Sweden. This conclusion is based upon the following factors: - The accuracy of a semi-empirical model is generally much better than for a statistical model, also the use of a semi-empirical model is much wider than the use of a statistical model. - The amount of work required for developing a semi-empirical model will not differ much from the amount of work required for a statistical model. In both cases a number of test fires will have to be conducted to define and calibrate a number of fuel models representative of Sweden. - Presently the performance and application of physical models is not at an acceptable level (due to for example the complexity which they are to model and the computational capabilities of the PC’s of today) for operational use. The semi-empirical model for Sweden is recommended to be built upon Swedish conditions (i.e. built upon the type of vegetation found in Sweden) instead of trying to retrofit the local Swedish conditions into an existing model. This would most likely give the best output for Swedish conditions. A system for better input data - weather and fuel data – should be worked on as well. This could for example take advantage of the results of the very promising “Alarm”-project that is being conducted in western part of Sweden. Regarding the issue on better fuel data, new technology for satellite images or aerial photos and image classification techniques must be monitored as one major problem to be solved is distinguishing between the canopy fuel and the ground fuel. For more specific conclusions and reflections, please see the analysis and discussion, and conclusions sections of this report.
This paper focuses on the grounding methods for distribution systems and the characteristics and behavior of earth fault currents. At First different existing grounding methods such as isolated neutral, solidly grounded, Resonant grounding, low and high impedance groundings are introduced. Secondly, focus is placed on further describing these methods and the viability of each of these methods in different scenarios. Then these methods are further analyzed by using equivalent circuit designs. Using the equivalent circuit helps to derive the formulations and equations. It is shown that the designing of these systems in fact follows basic electrical properties such as voltage dividing and current dividing principles. The derived equations are further tested experimentally to prove the characteristics and behavior of these methods. Finally, the report is concluded by testing some of these methods (isolated neutral and grounding via resistor methods) in the laboratory and the results obtained are analyzed with the theoretical results to determine the characteristics and behavior of these methods. In this manner it is shown experimentally that in case of isolated neutral systems the summation of currents through all the phases (current flow through the line model) is zero when there is no earth fault. In case of an earth fault occurring across one of the phases the neutral-to-ground voltage becomes equal to the voltage across the faulted phase and also the sum of currents passing through the healthy phases is equal to the current flowing through the faulted phase. This phenomenon is proved in the second experiment. The third experiment proves the relation between the earth fault current and current via the resistor and the currents via the healthy phases whereby it is shown that the fault current is equal to the root square summation of currents of resistor and healthy phases. This is one of the characteristics of grounded via resistor system. The next experimental setup also focuses on the characteristics of grounded via resistor system whereby it is shown that the fault current and the total phase current are independent of any external load. The last experiment proves the phenomenon that phase-to-phase voltage remains intact during times of earth fault and the system continues the operation uninterrupted as it should be in case of isolated neutral grounding system.
A simple mechanical system containing a low-frequency vibration mode and set of high-frequency acoustic modes is considered. The frequency response is calculated. Nonlinear behaviour and interaction between modes is described by system of functional equations. Two types of nonlinearities are taken into account. The first one is caused by the finite displacement of a movable boundary, and the second one is the volume nonlinearity of gas. New mathematical models based on nonlinear equations are suggested. Some examples of nonlinear phenomena are discussed on the base of derived solutions.
This thesis concerns the integration of agent technology and mathematical optimization for improved decision support within the domain of analysis and planning of production and transportation. These two approaches have often been used separately in this domain but the research concerning how to combine them is very limited. The studied domain is considered to be complex due to the fact that many decision makers, which influence each other, often are involved in the decision making process. Moreover, problems in the domain are typically large and combinatorial, which makes them more difficult to solve. We argue that the integration of agent-based approaches and mathematical optimization has a high potential to improve analysis and planning of production and transportation. In order to support this hypothesis, we have developed and analyzed three different approaches to the integration of agent technology and mathematical optimization. First, we present a Multi-Agent-Based Simulation (MABS) model called TAPAS for simulation of decision-making and physical activities in supply chains. By using agent technology and optimization, we were able to simulate the decision-making of the involved actors as well as the interaction between them, which is difficult using traditional simulation techniques. In simulation experiments, TAPAS has been used to study the effects of different types of governmental taxes, and synchronization of timetables. Moreover, we provide an analysis of existing MABS applications with respect to a number of criteria. Also, we present a framework containing a number of abstract roles, responsibilities, and interactions, which can be used to simplify the process of developing MABS models. Second, we present an approach for efficient planning and execution of intermodal transports. The approach provides agent-based support for key tasks, such as, finding the optimal sequence of transport services (potentially provided by different transport operators) for a particular goods transport, and monitoring the execution of transports. We analyzed the requirements of such an approach and described a multi-agent system architecture meeting these requirements. Finally, an optimization model for a real world integrated production, inventory, and routing problem was developed. For solving and analyzing the problem, we developed an agent-based solution method based on the principles of Dantzig-Wolfe decomposition. The purpose was to improve resource utilization and to analyze the potential effects of introducing VMI (Vendor Managed Inventory). In a case study, we conducted simulation experiments, which indicated that an increased number of VMI customers may give a significant reduction of the total cost in the system.
En industriellt använd LCC-kraftomvandlare är modellerad som ett hybrid-system. Det visas att för en given parameteruppsättning och olika begynnelsevillkor har systemet tre olika gränscykler, en stabil och två olika instabila assymmetriska gränscykler. Effekter för den industriella tillämpningen analyseras.
En industriellt tillämpad LCC omvandlare är modellerad som ett hybridsystem. Det hybrida systemet modelleras med tre kontinuerliga tillstånd och ett logiskt tillstånd. Givet den industriella parameteruppsättningen och olika differentialvärden har systemet lösningar som bland annat en sluten bana och två gränscykler. Andra lösningar är inikerade.
One of the most fundamental notions in pure and applied sciences is the concept of a relation. Science has been described as the discovery of relations between objects, states and events. Fuzzy relations generalize the concept of relations in the same manner as fuzzy sets generalize the fundamental idea of sets. This work presents an overview of comparison between classical and fuzzy relations. Some important compositions of fuzzy relations have been described and using these compositions a model for predicting score in cricket is developed. Finally it deals with the restoration and the identification of the causes (diagnosis) through the observed effects (symptoms) on the basis of fuzzy relations.
The main purpose of this thesis is to use modern goal-oriented adaptive methods of Lie group analysis to construct the optimal sys- tem of Black-Scholes equation. We will show in this thesis how to obtain all invariant solutions by constructing what has now become so popular, optimal system of sub-algebras, the main Lie algebra admit- ted by the Black-Scholes equation. First, we obtain the commutator table of already calculated symmetries of the Black-Scholes equation. We then followed with the calculations of transformation of the gen- erators with the Lie algebra L6 which provides one-parameter group of linear transformations for the operators. Here we make use of the method of Lie equations to solve the partial di®erential equations. Next, we consider the construction of optimal systems of the Black- Scholes equation where the method requires a simpli¯cation of a vector to a general form to each of the transformations of the generators. Further, we construct the invariant solutions for each of the op- timal system. This study is motivated by the analysis of Lie groups which is being taken to another level by ALGA here in Blekinge In- stitute Technology, Sweden. We give a practical and in-depth steps and explanation of how to construct the commutator table, the calcu- lation of the transformation of the generators and the construction of the optimal system as well as their invariant solutions. Keywords: Black-Scholes Equation, commutators, commutator table, Lie equa- tions, invariant solution, optimal system, generators, Airy equation, structure constant,
The present paper is a survey of results [1], [2] on extension of Euler’s method for solving hyperbolic equations with one spatial variable to parabolic equations. The new method, based on the invariants of parabolic equations, allows one to identify all linear parabolic equations reducible to the heat equation and find their general solution. The method is illustrated by several examples.
Volume 3 contains 6 articles: Lars Haikola, Louise Petrén-Overton, min mormor; Lars Haikola, Louise Petr´en-Overton, my grandmother. Traslations: Louise Petrén, Extension of Laplace's method to the equations...; E. Bessel-Hagen, On conservation laws of electrodynamics. Nail H. Ibragimov, The answer to the question put to me by L.V. Ovsyannikov 33 years ago; Nail H. Ibragimov, Raisa Khamitova, Bo Thidé, Adjoint system and conservation laws for symmetrized electromagnetic equations with a dual Ohm's law.
Volume 5 contains 3 articles by N.Ibragimov, an article by R. Khamitova and the English translation of V.P.Ermakov's article "Second order differential equations:conditions of complete integrability".
Volume 6 contains 6 articles: Nail H. Ibragimov, Utilization of canonical variables for integration of systems of first-order differential equations; Nail H. Ibragimov and Ranis N. Ibragimov, Group analysis of nonlinear internal waves in oceans. I: Self-adjointness, conservation laws, invariant solutions; Nail H. Ibragimov, Ranis N. Ibragimov and Vladimir F. Kovalev, Group analysis of nonlinear internal waves in oceans. II: The symmetries and rotationally invariant solution; Nail H. Ibragimov and Ranis N. Ibragimov, Group analysis of nonlinear internal waves in oceans. III: Additional conservation laws; Nail H. Ibragimov Alternative presentation of Lagrange's method of variation of parameters; Nail H. Ibragimov Application of group analysis to liquid metal systems.
Linear and nonlinear waves in anisotropic media are used in various fields, e.g. in biomechanics, biomedical acoustics, etc. The present paper is devoted to discussion of nonlinear anisotropic wave equations with a source from point of view of their conservation laws and exact solutions associated with conservation laws. Nonlinearly self-adjoint wave equations with special source terms are singled out. The conservation laws associated with symmetries of the nonlinearly self-adjoint wave equations are computed and used for constructing exact solutions. The obtained solutions are different from group invariants solutions, in particular, from steady state and traveling wave solutions. The paper is designed for the application oriented readers. Its main goal is to introduce readers, interested in solutions of mathematical models having real world applications, to the recent method of conservation laws for constructing exact solutions of partial differential equations using conservation laws. © 2017 Elsevier Ltd
The concept of nonlinear self-adjointness of differential equations, introduced by the author in 2010, is discussed in detail. All linear equations and systems are nonlinearly self-adjoint. Moreover, the class of nonlinearly self-adjoint equations includes all nonlinear equations and systems having at least one local conservation law. It follows, in particular, that the integrable systems possessing infinite set of Lie-Backlund symmetries (higher-order tangent transformations) are nonlinearly self-adjoint. An explicit formula for conserved vectors associated with symmetries is provided for all nonlinearly self-adjoint differential equations and systems. The number of equations contained in the systems under consideration can be different from the number of dependent variables. A utilization of conservation laws for constructing exact solutions is discussed and illustrated by computing non-invariant solutions of the Chaplygin equations in gas dynamics.
Advanced topics to be added to my textbook "A Practical Course in Differential Equations and Mathematical Modelling".
This volume is dedicated to the memory of my teacher and friend Lev Vasilyevich Ovsyannikov (22.04.1919{23.05.2014).
Volume V contains preprints written during 2008-2014 as advanced topics to be added to the textbook. They include, e.g. a discussion of a wide class of linear ordinary differential equations whose integration is reducible to solution of algebraic equations. This class contains the constant coefficient equations and Eulers equations as particular cases. The recent method of nonlinear self-adjointness for constructing conservations laws associated with symmetries of partial differential equations is also presented in this volume.
A bridge between Lie symmetry groups for differential equations and Galois groups for algebraic equations is suggested. It is based on calculation of Lie symmetries for algebraic equations and their restriction of the roots of the equations under consideration. The approach is illustrated by several examples. An alternative representation of Lie symmetries, called the Galois representation, is provided for differential equations.
The evolutionary part of Maxwell's equations has a Lagrangian written in terms of the electric and magnetic fields, but admit neither Lorentz nor conformal transformations. The additional equations on vanishing the divergences of the electric and magnetic fields guarantee the Lorentz and conformal invariance, but the resulting overdetermined system does not have a Lagrangian. The aim of the present paper is to attain a harmony between these two contradictory properties.
A general theorem on conservation laws for arbitrary differential equations is proved. The theorem is valid also for any system of differential equations where the number of equations is equal to the number of dependent variables. The new theorem does not require existence of a Lagrangian and is based on a concept of an adjoint equation for non-linear equations suggested recently by the author. It is proved that the adjoint equation inherits all symmetries of the original equation. Accordingly, one can associate a conservation law with any group of Lie, Lie-Backlund or non-local symmetries and find conservation laws for differential equations without classical Lagrangians.
A practical course in differential equations and mathematical modelling is a unique blend of the traditional methods with Lie group analysis enriched by author’s own theoretical developments. The main objective of the book is to develop new mathematical curricula based on symmetry and invariance principles. This approach helps to make courses in differential equations, mathematical modelling, distributions and fundamental solution, etc. easy to follow and interesting for students. The book is based on author’s long-term experience of teaching at Novosibirsk and Moscow Universities in Russia, Collège de France, Georgia Tech and Stanford University in USA, Universities in South Africa, Cyprus, Turkey, and Blekinge Institute of Technology (BTH) in Sweden. The new curriculum prepares the students for solving modern nonlinear problems and attracts essentially more students than the traditional way of teaching mathematics. The book can be used as a main textbook by undergraduate and graduate students and their teachers in applied mathematics, physics and engineering sciences.