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Optimal Scheduling Results for Parallel Computing1996In: Applications on advanced architecture computers / [ed] Astfalk, Greg, Philadelphia, USA: SIAM , 1996, p. 155-164Chapter in book (Refereed)

Load balancing is one of many possible causes of poor performance on parallel machines. If good load balancing of the decomposed algorithm or data is not achieved, much of the potential gain of the parallel algorithm is lost to idle processors. Each of the two extremes of load balancing - static allocation and dynamic allocation - has advantages and disadvantages. This chapter illustrates the relationship between static and dynamic allocation of tasks.

Optimal Worst Case Formulas Comparing Cache Memory Associativity1995Report (Other academic)

Consider an arbitrary program $P$ which is to be executed on a computer with two alternative cache memories. The first cache is set associative or direct mapped. It has $k$ sets and $u$ blocks in each set, this is called a (k,u)$-cache. The other is a fully associative cache with$q$blocks - a$(1,q)$-cache. We present formulas optimally comparing the performance of a$(k,u)$-cache compared to a$(1,q)$-cache for worst case programs. Optimal mappings of the program variables to the cache blocks are assumed. Let$h(P,k,u)$denote the number of cache hits for the program$P$, when using a$(k,u)$-cache and an optimal mapping of the program variables of$P$to the cache blocks. We establish an explicit formula for the quantity $$\inf_P \frac{h(P,k,u)}{h(P,1,q)},$$ where the infimum is taken over all programs$P$which contain$n$variables. The formula is a function of the parameters$n,k,u$and$q$only. We also deduce a formula for the infimum taken over all programs of any number of variables, this formula is a function of$k,u$and$q$. We further prove that programs which are extremal for this minimum may have any hit ratio, i.e. any ratio$h(P,1,q)/m(P)$. Here$m(P)$is the total number of memory references for the program P. We assume the commonly used LRU replacemant policy, that each variable can be stored in one memory block, and is free to be stored in any block. Since the problems of finding optimal mappings are NP-hard, the results provide optimal bounds for NP-hard quantities. The results on cache hits can easily be transformed to results on access times for different cache architectures. • 303. Lennerstad, Håkan Optimal worst case formulas comparing cache memory associativity2000In: SIAM journal on computing (Print), ISSN 0097-5397, E-ISSN 1095-7111, p. 872-905Article in journal (Refereed) In this paper we derive a worst case formula comparing the number of cache hits for two different cache memories. From this various other bounds for cache memory performance may be derived. Consider an arbitrary program P which is to be executed on a computer with two alternative cache memories. The rst cache is set-associative or direct-mapped. It has k sets and u blocks in each set; this is called a (k, u)-cache. The other is a fully associative cache with q blocks-a (1, q)-cache. We derive an explicit formula for the ratio of the number of cache hits h(P, k, u) for a(k, u)-cache compared to a (1, q)-cache for a worst case program P. We assume that the mappings of the program variables to the cache blocks are optimal. The formula quantifies the ratio [GRAPHICS] where the in mum is taken over all programs P with n variables. The formula is a function of the parameters n, k, u, and q only. Note that the quantity h ( P, k, u) is NP-hard. We assume the commonly used LRU (least recently used) replacement policy, that each variable can be stored in one memory block, and that each variable is free to be mapped to any set. Since the bound is decreasing in the parameter n, it is an optimal bound for all programs with at most n variables. The formula for cache hits allows us to derive optimal bounds comparing the access times for cache memories. The formula also gives bounds ( these are not optimal, however) for any other replacement policy, for direct-mapped versus set-associative caches, and for programs with variables larger than the cache memory blocks. • 304. Blekinge Institute of Technology, School of Engineering, Department of Mathematics and Natural Sciences. Åtta IKT-projekt för matematiken i skolan: empiri och analys2012Report (Other (popular science, discussion, etc.)) Denna rapport presenterar empiri och analys av en granskning av åtta projekt som mottagit medel från Skolverket för att tillämpa IKT i skolans matematikundervisning. Empirin är organiserad enligt aktivitetsteorin, vilken sätter relationerna mellan människa, miljö, aktiviteter och mål i förgrunden. Empirin som presenteras är till stor del sammanställda repliker från lärare och elever vid intervjuerna, organi¬sera¬de för att belysa verksamhetens olika relationer. Det betyder att presentationen är till stor del på de verksammas villkor, och på deras språk. Ett stort antal konkreta slutsatser framkommer ur detta material. En av dem är att klass¬upp-sätt¬ningar av datorer är sällan framgångsrika, på grund av att teknisk support ofta var otillräcklig, och att lärarna inte kan veta hur mycket eleverna använder datorerna till icke-skol-verk¬sam¬het. Dessa problem finns inte för interaktiva skrivtavlor. De framstår däremot som ett socialt verktyg, som gör utbyte och dialog om ämnet lättare att få till stånd. I flera fall framkom indirekt, men ändå tydligt, att utbildningen på tekniken hade varit otillräcklig, trots att lärarna inte uttryckte ett tydligt missnöje med den. Skrivtavlan ökade lärarnas motivation för samarbete. En framåtriktad slutsats är att en lärargrupp som har ett fungerande samarbete och goda didaktiska, ämnesmässiga, ledar- och relationella kompe¬tenser med en interaktiv skrivtavla har en möjlighet att komma längre med elevernas måluppfyllelse. • 305. Lindberg, Vanja First principles study of CO reactivity on metallic nano particles2007Conference paper (Refereed) The activity of a surface is determined by the local electronic structure. When nano particles are adsorbed, the catalytic properties will change. Surfaces with adsorbed nano particles often show a significantly higher chemical reactivity than the clean counterpart. Gold, for instance, shows an extra high activity towards many reactions, such as low-temperature catalytic combustion, partial oxidation of hydrocarbons and CO oxidation when dispersed as ultra-fine particles on metal oxide surfaces. In the case of CO oxidation, the activity has been observed to depend critically on the nano particle size, the nature of the support and the detailed synthetic procedure. Since it has been observed experimentally that the chemical reactivity of a nanoparticulated surface tend to depend on the size of the adatom structures, suggesting a quantum size effect, we find it well motivated to perform a theoretical investigation with focus on the cluster-size dependence. We have chosen to model CO interaction with sodium nano particles with focus on small particles, containing only a few atoms, since we expect the eventual quantum effects to be most pronounced for these. Further, we limit our investigation to unsupported nano particles because our previous investigations [1] have shown that it is predominately states localized to the nano particle region that contribute to the local electronic structure above the particle itself. The calculations have been performed in the context of density functional theory applying the MIKA real-space program package [2], using norm-conserving pseudo-potentials for the molecule. The nano particle has been modeled as a cylindrically symmetric quantum dot. For further details, see [3,4]. Our results show that the charge transfer between the nano particle and the CO molecule depends critically on the nano particle size, and that this dependence is intimately connected to the local electronic structure at the point where the molecule approaches the particle. The key factor for charge transfer turns out to be the presence of states with the symmetry of the chemically active molecular orbital at the Fermi level. [1] T. Torsti, V. Lindberg, M. J. Puska ,and B. Hellsing, Phys. Rev. B 66, 235420 (2002). [2] M. Heiskanen, T. Torsti, M. J. Puska, and R. M. Nieminen, Phys. Rev. B 63, 245106 (2001). [3] V. Lindberg and B. Hellsing, J. Phys. Condens. Matter 17, S1075 (2005). [4] V. Lindberg, T. Petersson, and B. Hellsing, Surf. Sci. 600, 6 (2006). • 306. Blekinge Institute of Technology, School of Engineering. Single view metrology applied for dynamic control of sink height for children2011Independent thesis Basic level (degree of Bachelor)Student thesis ABSTRACT In our modern society, the design and implementation of intelligent equipments for autonomous physical services become more and more important. In line with this, the proposed Intelligent Vision Agent System, IVAS, is able to automatically detect and identify a target for a specific task by surveying human activities space. One of IVAS’ applications can be the adjustment of sink height for different height of people. Usually, the sink is fixed in one place, however, the height of sink could be too high to use for children. It becomes a real problem and may bring much of inconvenience and insecurity for the little boys and girls. The equipment for dynamical adjustment of sink height is rare in today’s society. The most common sink height adjustments are of two types. The first way is to place two sinks, one for adult and one for a kid individually. The second way is to use a spring device to adjust the height of sink. But, the both solutions have some limitations. The disadvantage of first method is that it takes too much space, and not all bathrooms can accommodate two sinks at the same time. The weakness of second way is a need to manually adjust the height of sink. In order to achieve an optimal design of adjustable sink high, the author uses a camera fixed on wall connected to an intelligent agent controlling suitable actuators. The camera captures a photo of the person who comes to the sink. The height of person can be estimated from the image. Furthermore, one makes use of this height value to find the suitable sink height for the user. Finally, the sink is descending or ascending by the lifting columns to adjust it to the different height of people. In this thesis, the author has implemented a method, which estimates the height of person from a single image. This technique is based on the single view metrology. Keywords: Sink, Height Measurement, Vision, Single View Metrology • 307. Lundberg, Lars An Optimal Upper Bound on the Minimal Completion Time in Distributed Supercomputing1994Conference paper (Refereed) We first consider an MIMD multiprocessor configuration with n processors. A parallel program, consisting of n processes, is executed on this system-one process per processor. The program terminates when all processes are completed. Due to synchronizations, processes may be blocked waiting for events in other processes. Associated with the program is a parallel profile vector nu , index i (1<or=i<or=n) in this vector indicates the percentage of the total execution time when i processes are executing. We then consider a distributed MIMD supercomputer with k clusters, containing u processors each. The same parallel program, consisting of n processes, is executed on this system. Each process can only be executed by processors in the same cluster. Finding a schedule with minimal completion time in this case is NP-hard. We are interested in the gain of using n processors compared to using k clusters containing u processors each. The gain is defined by the ratio between the minimal completion time using processor clusters and the completion time using a schedule with one process per processor. We present the optimal upper bound for this ratio in the form of an analytical expression in n, nu , k and u. We also demonstrate how this result can be used when evaluating heuristic scheduling algorithms (12 Refs.) • 308. Lundberg, Lars Bounding the gain of changing the number of memory modules in shared memory multiprocessors1997In: Nordic Journal of Computing, ISSN 1236-6064, Vol. 4, no 3, p. 233-58Article in journal (Refereed) We consider a multiprocessor, with p processors and m memory modules. If more than one processor want to access a memory module simultaneously, these accesses will be serialized due to memory contention. The completion time of a program executing on this system is thus affected by the way addresses are mapped onto memory modules, and finding a mapping which results in minimal completion time is NP-hard. If we change the number of memory modules from m to m’, while keeping the number processors constant, we will generally change the minimal completion time. The gain of changing the number of memory modules from m to m’ for a certain program is defined as the ratio between the minimal completion times, using m and m’ modules respectively. Here, we present an optimal upper bound on the maximum gain of changing the number of memory modules, as a function of m, m’ and p, including the case when m’ is infinitely large. The bound is obtained by investigating a mathematical formulation. The mathematical tools involved are essentially elementary combinatorics. The formula for calculating the bound is mathematically complicated but can be rapidly computed for reasonable m, m’ and p. This bound makes it possible to do price-performance trade-offs and to compare any mapping of addresses to memory modules with the optimal case. The results are applicable to different multiprocessor architectures, e.g. systems with crossbar networks and systems with multiple buses. The results also make it possible to calculate optimal performance bounds for multiprocessors containing cache memories: as well as for multiprocessors with no cache memories. Moreover, we discuss how the results can be used for calculating bounds for programs with as well as without synchronizations. • 309. Lundberg, Lars Comparing the optimal performance of different MIMD multiprocessor architectures1998Conference paper (Refereed) We compare the performance of systems consisting of one large cluster containing q processors with systems where processors are grouped into k clusters containing u processors each. A parallel program, consisting of n processes, is executed on this system. Processes may be relocated between the processors in a cluster. They may,however not be relocated from one cluster to another. The performance criterion is the completion time of the parallel program. We present two functions: g(n,k,u,q) and G(k,u,q). Provided that we can find optimal or near optimal schedules,these functions put optimal upper bounds on the gain of using one cluster containing q processors compared to using k clusters containing u processors each. The function g(n,k,u,q) is valid for programs with n processes, whereas G(k,u,q) only depends on the two multiprocessor architectures. By evaluating g(n,k,u,q) and G(k,u,q) we show that the gain of increasing the cluster size from 1 to 2 and from 2 to 4 is relatively large. However, the gain of using clusters larger than 4 is very limited. • 310. Lundberg, Lars Using Golomb Rulers for Minimizing Collisions in Closed Hashing2004Conference paper (Refereed) We give conditions for hash table probing which minimize the expected number of collisions. A probing algorithm is determined by a sequence of numbers denoting jumps for an item during multiple collisions. In linear probing, this sequence consists of only ones – for each collision we jump to the next location. To minimize the collisions, it turns out that one should use the Golomb ruler conditions: consecutive partial sums of the jump sequence should be distinct. The commonly used quadratic probing scheme fulfils the Golomb condition for some cases. We define a new probing scheme – Golomb probing - that fulfills the Golomb conditions for a much larger set of cases. Simulations show that Golomb probing is always better than quadratic and linear and in some cases the collisions can be reduced with 25% compared to quadratic and with more than 50% compared to linear. • 311. Blekinge Institute of Technology, School of Planning and Media Design. "You can cut sync, you can´t cut feel" Ett djupdyk in i trampets värld2011Independent thesis Basic level (degree of Bachelor)Student thesis I dagens filmbransch blir arbetet med ljud i film allt mer viktigt då publiken inte bara förväntar sig en visuell effekt utan även en helhetsupplevelse. För att filmen skall kunna förmedla rätt känsla till publiken, gäller det att det visuella, musiken och ljudet fungerar så optimalt som möjligt. Det är viktigt att ljudet hjälper filmen att få fram den känslan som regissören vill förmedla. För att ljudet till en film skall kunna hjälpa regissören att förmedla ett budskap eller känsla är det viktigt att arbetet med ljudet också får ta plats i en filmproduktion. Det här arbetet är en skildring mellan arbetet med tramp på ljudföretaget Europa Foley och boken The foley grail. Arbetet beskriver hur processen med tramp till en filmproduktion på Europa Foley kan gå till och vad som skiljer sig med trampet som beskrivs i The foley grail. De största skillnaderna är hur studion är uppbyggd och hur teamet jobbar med trampet till en filmproduktion. Dessutom tar reflektionen upp ett liknande fenomen som jag har upplevt under mitt arbete på Europa Foley och som även författaren Ament beskriver i The foley grail. • 312. Blekinge Institute of Technology, Faculty of Engineering, Department of Mathematics and Natural Sciences. Chain conditions for epsilon-strongly graded rings with applications to Leavitt path algebrasManuscript (preprint) (Other academic) Let$G$be a group with neutral element$e$and let$S=\bigoplus_{g \in G}S_g$be a$G$-graded ring. A necessary condition for$S$to be noetherian is that the principal component$S_e$is noetherian. The following partial converse is well-known: If$S$is strongly-graded and$G$is a polycyclic-by-finite group, then$S_e$being noetherian implies that$S$is noetherian. We will generalize the noetherianity result to the recently introduced class of epsilon-strongly graded rings. We will also provide results on the artinianity of epsilon-strongly graded rings. As our main application we obtain characterizations of noetherian and artinian Leavitt path algebras with coefficients in a general unital ring. This extends a recent characterization by Steinberg for Leavitt path algebras with coefficients in a commutative unital ring and previous characterizations by Abrams, Aranda Pino and Siles Molina for Leavitt path algebras with coefficients in a field. Secondly, we obtain characterizations of noetherian and artinian unital partial crossed products. • 313. Blekinge Institute of Technology, Faculty of Engineering, Department of Mathematics and Natural Sciences. Chain Conditions for Epsilon-Strongly Graded Rings with Applications to Leavitt Path Algebras2019In: Algebras and Representation Theory, ISSN 1386-923X, E-ISSN 1572-9079Article in journal (Refereed) Let G be a group with neutral element e and let S=⊕g∈GSg be a G-graded ring. A necessary condition for S to be noetherian is that the principal component Se is noetherian. The following partial converse is well-known: If S is strongly-graded and G is a polycyclic-by-finite group, then Se being noetherian implies that S is noetherian. We will generalize the noetherianity result to the recently introduced class of epsilon-strongly graded rings. We will also provide results on the artinianity of epsilon-strongly graded rings. As our main application we obtain characterizations of noetherian and artinian Leavitt path algebras with coefficients in a general unital ring. This extends a recent characterization by Steinberg for Leavitt path algebras with coefficients in a commutative unital ring and previous characterizations by Abrams, Aranda Pino and Siles Molina for Leavitt path algebras with coefficients in a field. Secondly, we obtain characterizations of noetherian and artinian unital partial crossed products. © 2019, The Author(s). • 314. Blekinge Institute of Technology, Faculty of Engineering, Department of Mathematics and Natural Sciences. Induced quotient group gradings of epsilon-strongly graded ringsManuscript (preprint) (Other academic) Let$G$be a group and let$S=\bigoplus_{g \in G} S_g$be a$G$-graded ring. Given a normal subgroup$N$of$G$, there is a naturally induced$G/N$-grading of$S$. It is well-known that if$S$is strongly$G$-graded, then the induced$G/N$-grading is strong for any$N$. The class of epsilon-strongly graded rings was recently introduced by Nystedt, Ã–inert and Pinedo as a generalization of unital strongly graded rings. We give an example of an epsilon-strongly graded partial skew group ring such that the induced quotient group grading is not epsilon-strong. Moreover, we give necessary and sufficient conditions for the induced$G/N$-grading of an epsilon-strongly$G$-graded ring to be epsilon-strong. Our method involves relating different types of rings equipped with local units (s-unital rings, rings with sets of local units, rings with enough idempotents) with generalized epsilon-strongly graded rings. • 315. Blekinge Institute of Technology, Faculty of Engineering, Department of Mathematics and Natural Sciences. The graded structure of algebraic Cuntz-Pimsner ringsManuscript (preprint) (Other academic) The algebraic Cuntz-Pimsner rings are naturally$\mathbb{Z}$-graded rings that generalize both Leavitt path algebras and unperforated$\mathbb{Z}$-graded Steinberg algebras. We classify strongly, epsilon-strongly and nearly epsilon-strongly graded algebraic Cuntz-Pimsner rings up to graded isomorphism. As an application, we characterize noetherian and artinian fractional skew monoid rings by a single corner automorphism. • 316. Blekinge Institute of Technology, Faculty of Engineering, Department of Mathematics and Natural Sciences. The structure of epsilon-strongly graded rings with applications to Leavitt path algebras and Cuntz-Pimsner rings2019Licentiate thesis, comprehensive summary (Other academic) The research field of graded ring theory is a rich area of mathematics with many connections to e.g. the field of operator algebras. In the last 15 years, algebraists and operator algebraists have defined algebraic analogues of important operator algebras. Some of those analogues are rings that come equipped with a group grading. We want to reach a better understanding of the graded structure of those analogue rings. Among group graded rings, the strongly graded rings stand out as being especially well-behaved. The development of the general theory of strongly graded rings was initiated by Dade in the 1980s and since then numerous structural results have been established for strongly graded rings. In this thesis, we study the class of epsilon-strongly graded rings which was recently introduced by Nystedt, Öinert and Pinedo. This class is a natural generalization of the well-studied class of unital strongly graded rings. Our aim is to lay the foundation for a general theory of epsilon-strongly graded rings generalizing the theory of strongly graded rings. This thesis is based on three articles. The first two articles mainly concern structural properties of epsilon-strongly graded rings. In the first article, we investigate a functorial construction called the induced quotient group grading. In the second article, using results from the first article, we generalize the Hilbert Basis Theorem for strongly graded rings to epsilon-strongly graded rings and apply it to Leavitt path algebras. In the third article, we study the graded structure of algebraic Cuntz-Pimsner rings. In particular, we obtain a partial classification of unital strongly, epsilon-strongly and nearly epsilon-strongly graded Cuntz-Pimsner rings up to graded isomorphism. • 317. Blekinge Institute of Technology, School of Engineering, Department of Telecommunication Systems. Dynamic Channel Allocation in GSM Network2008Independent thesis Advanced level (degree of Master (Two Years))Student thesis The rapid evolution of cellular technology and the more user demand for advanced mobile services leads the industry to develop more efficient network structures. The increasing number of cellular subscribers and the demand for cellular networks communication (3rd and 4th generation) drives to the research of the new methodologies for the design of cellular networks and services. This thesis has been generated and complied with the objective of proposing GSM Network Utilizing DYNAMIC CHANNEL ALLOCATION starting with the architecture of GSM Network with system design. In next chapter we define the channels that are transmitted over the Air Interface, leading further towards the Channel Allocation Schemes in GSM. In this chapter we describe the various types of channels are used in GSM Network. Furthermore define the main two strategies for channel assignment, briefly differentiate between the FCA (Fixed Channel Allocation) and (Dynamic Channel Allocation) as well as advantages of both schemes. Then the major is study of (Dynamic Channel Allocation) and the proposed Algorithm for Dynamic Channel Allocation in GSM network is presented and discussed. All channels will placed in a pool and on demand or on request will be assigned to the user for that particular call that will be helpful to maintain the grade of service and increase system capacity. • 318. Blekinge Institute of Technology, School of Engineering. Inexact Programming2012Independent thesis Advanced level (degree of Master (Two Years))Student thesis Two types of fuzzy linear programming i.e. fuzzy number linear programming and interval number linear programming are used for optimization problems. In interval form of linear programming we convert the inequalities from the feasible region, containing intervals as coefficients, to two groups of inequalities characterized by real, exact coefficients values. Then classical programming has been used to achieve an optimal solution in the feasible region. In fuzzy number linear programming, α‐cuts and LR forms of fuzzy numbers as coefficients have been used to find optimal solution in the feasible region. Finally the numerical examples and their solutions are attached to provide explanations of procedures. • 319. University of Science, VNM. Blekinge Institute of Technology, Faculty of Engineering, Department of Mathematics and Natural Sciences. Quasi-duo differential polynomial rings2018In: Journal of Algebra and its Applications, ISSN 0219-4988, E-ISSN 1793-6829, Vol. 17, no 4, article id 1850072Article in journal (Refereed) In this article we give a characterization of left (right) quasi-duo differential polynomial rings. We provide non-trivial examples of such rings and give a complete description of the maximal ideals of an arbitrary quasi-duo differential polynomial ring. Moreover, we show that there is no left (right) quasi-duo differential polynomial ring in several indeterminates. • 320. Blekinge Institute of Technology, School of Engineering. A probabilistic pricing model for a company's projects2012Independent thesis Basic level (degree of Bachelor)Student thesis The company’s pricing is often highly impacted by the estimation of competitors’ project costs, which also is the main scope in this degree project. The purpose is to develop a pricing model dealing with uncertainties, since this is a main issue in the current pricing process. A pre-study has been performed, followed by a model implementation. An analysis of the model was then made, before conclusions were drawn. Project cost estimation foremost, but also probability distribution functions and pricing as a general concept, were investigated in the mainly literary pre-study. Two suitable methods for project cost estimation were identified; Monte Carlo simulation and Hierarchy Probability Cost Analysis. These lead to a theoretical project cost estimation model. A model was implemented in Matlab. It treats project cost estimation, but no other pricing aspects. The model was developed based on the theoretical one to the extent possible. Project costs were broken down in sub costs which were included in a Monte Carlo simulation. Competitors’ project costs were estimated using this technique. To analyse the model’s accuracy was difficult. It differs from the theoretical one in terms of how probability distribution functions and correlations are estimated. These problems depend on projects with shifting characteristics and limited data and time. A solid framework has been created though. Improvement possibilities exist, e.g. more accurate estimates and a model handling other pricing aspects. The major threat is that nobody maintains the model. Anyway, estimates are not more than just estimates. The model should therefore be viewed as a helpful tool, not an answer. • 321. Blekinge Institute of Technology, School of Engineering, Department of Mathematics and Natural Sciences. Mathematical Modelling of The Global Positioning System Tracking Signals2008Independent thesis Advanced level (degree of Master (One Year))Student thesis Recently, there has been increasing interest within the potential user community of Global Positioning System (GPS) for high precision navigation problems such as aircraft non precision approach, river and harbor navigation, real-time or kinematic surveying. In view of more and more GPS applications, the reliability of GPS is at this issue. The Global Positioning System (GPS) is a space-based radio navigation system that provides consistent positioning, navigation, and timing services to civilian users on a continuous worldwide basis. The GPS system receiver provides exact location and time information for an unlimited number of users in all weather, day and night, anywhere in the world. The work in this thesis will mainly focuss on how to model a Mathematical expression for tracking GPS Signal using Phase Locked Loop filter receiver. Mathematical formulation of the filter are of two types: the first order and the second order loops are tested successively in order to find out a compromised on which one best provide a zero steady state error that will likely minimize noise bandwidth to tracks frequency modulated signal and returns the phase comparator characteristic to the null point. Then the Z-transform is used to build a phase-locked loop in software for digitized data. Finally, a Numerical Methods approach is developed using either MATLAB or Mathematica containing the package for Gaussian elimination to provide the exact location or the tracking of a GPS in the space for a given a coarse/acquisition (C/A) code. • 322. Blekinge Institute of Technology, School of Engineering, Department of Mechanical Engineering. Parameter Identification for Mechanical Joints2006Independent thesis Advanced level (degree of Master (One Year))Student thesis All but the simplest physical systems contains mechanical joints. The behavior of these joints is sometimes the dominant factor in over all system behavior. The potential for occurence of microslip and macroslip normally makes the behavior of joints non-linear. Accurate modeling of joints requires a non-linear ramework. As clamping pressures are typically random ad variable, the behavior of the joints becomes random. Joint geometries are random along with other unknowns of the joints. Two different methods for measuring the energy dissipation are explained. In the experimental method, the energy dissipation of a non-linear joint is calculated from the slope of the envelope of the time response of acceleration. The simulation work is carried out by considering a smooth hysteresis model with the help of Matlab programming. Finally, the parameters are extracted for a specific non-linear system by comparing analytical and experimental results. • 323. Mbiydzenyuy, Gideon Assessment of Telematic Systems for Road Freight Transport2010Licentiate thesis, comprehensive summary (Other academic) The focus of this thesis is the assessment of telematic systems for road freight transport from a planning perspective. The aim is to support strategic decisions related to architectural choices for such systems, with the possibility to achieve synergies by supporting multiple telematic services. The past decade has witnessed enormous growth in cargo volumes resulting in increasing demand for transport capacity. To match this increasing demand only with expansion of infrastructure, e.g. road and vehicles, does not seem to be a sustainable strategy. One of the few approaches with the potential to improve the use of current transport capacity is the integrated use of modern information and communication technology, otherwise known as telematic systems for road transport, an important component within Intelligent Transport Systems (ITS). This type of systems can deliver multiple services that can be used to improve the efficiency and safety of road freight transport. However, attempts to unleash the potential of telematic systems and make maximum possible use of the available transport capacity have been hindered by several challenges ranging from planning and design to development and deployment. Considering the large scope of possible telematic services that can potentially be deployed in road freight transport, this thesis suggests a framework in order to enable structured assessment of telematic systems. Based on the suggested framework, a set of potential transport telematic services are identified and a method for quantifying the value of the services to society is developed. The suggested method takes into account the expected impact on different transportation challenges, such as accidents, fuel consumption, and infrastructure maintenance. Quantitative methods are provided for studying the value of services sharing a common infrastructure. Using quantified benefits of services and costs of various functionalities required by telematic services, the concept of a multi-service architecture is investigated using optimization methods, which handles the multi-dimensional relations between different services that are otherwise difficult to analyze with traditional cost-benefit analysis. The analyses show which telematic services can be achieved with different approaches, such as vehicle-to-vehicle communication, vehicle-to-infrastructure communication, etc. Although multi-service architectures are promising, several challenges need to be overcome, including security, service quality, privacy, and business models. The knowledge gained from the work presented in this thesis can be valuable for different stakeholders, such as governments, service providers, and transport service users, in fostering the planning, design, development, and deployment of telematic systems in transport. • 324. Mbiydzenyuy, Gideon Toward Cost-Efficient Integration of Telematic Systems Using K-Spanning Tree and Clustering Algorithms2011Conference paper (Refereed) This article uses analytical methods to assess reductions in total costs of telematic systems that can result from common infrastructure utilization. Analytical methods based on clustering and K-minimum spanning tree can be adopted for finding clusters or sets which maximize reductions in total system costs due to infrastructure sharing between telematic systems. Efficient integration of telematic systems through infrastructure sharing can positively influence telematic service interoperability while reducing costs. Results show the measure of synergy for each K-value, as well as total cost savings of up to 2%. • 325. Blekinge Institute of Technology, School of Engineering, Department of Signal Processing. Implementing Efficient iterative 3D Deconvolution for Microscopy2009Independent thesis Advanced level (degree of Master (One Year))Student thesis Both Gauss-Seidel Iterative 3D deconvolution and Richardson-Lucy like algorithms are used due to their stability and high quality results in high noise microscopic medical image processing. An approach to determine the difference between these two algorithms is presented in this paper. It is shown that the convergence rate and the quality of these two algorithms are influenced by the size of the point spread function (PSF). Larger PSF sizes causes faster convergence but this effect falls off for larger sizes . It is furthermore shown that the relaxation factor and the number of iterations are influencing the convergence rate of the two algorithms. It has been found that increasing relaxation factor and number of iterations improve convergence and can reduce the error of the deblurred image. It also found that overrelaxation converges faster than underrelaxation for small number of iterations. However, it can be achieved smaller final error with under-relaxation. The choice of underrelaxation factor and overrelaxation factor value are highly problem specific and different from one type of images. In addition, when it comes to 3D iterative deconvolution, the influence of boundary conditions for these two algorithms is discussed. Implementation aspects are discussed and it is concluded that cache memory is vital for achieving a fast implementation of iterative 3D deconvolution. A mix of the two algorithms have been developed and compared with the previously mentioned Gauss-Seidel and the Richardson-Lucy-like algorithms. The experiments indicate that, if the value of the relaxation parameter is optimized, then the Richardson-Lucy-like algorithm has the best performance for 3D iterative deconvolution. • 326. Blekinge Institute of Technology, School of Engineering. Blekinge Institute of Technology, School of Engineering. Performance Analysis of 3-hop using DAF and DF over 2-hop Relaying Protocols2013Independent thesis Advanced level (degree of Master (Two Years))Student thesis In wireless Communication, the need of radio spectrum increases nowadays. But in the system we are losing approximately 82-86% of spectrum most of the time due to the absence of Primary User (PU). To overcome this issue Cognitive Radio (CR) is an admirable approach. The concept of cooperative communication needs to be considering because high data rate is the demand for wireless services. Cooperative diversity in the network realized by 3-hop Decode, Amplify and Forward (DAF) and Decode and Forward (DF) and in 2-hop DF and Amplify and Forward (AF) Protocols implemented in cognitive radio communication network using Orthogonal Space Time Block Coding (OSTBC). The communication between end points is accomplished by using Multiple Input and Multiple Output (MIMO) antenna arrangement. During the Propagation, Alamouti Space Time Block Coding is used to accomplish spatial diversity and the encoded data is transmitted through Rayleigh fading channel. CR decodes the transmitted signal using Maximum Likelihood (ML) decoding method. Afterward signal broadcast toward the destination. To check the energy level of signal, energy detection technique applies at the Cognitive Controller (CC). Finally, CC will take ultimate decision for the presence of primary user if the energy level of signal is greater than predefined threshold level, it means PU is present otherwise it is absent. The main objective of this thesis is to analyze the performance of 3-hop and 2-hop communication network using relays. The performance is compared on the bases of two parameters i.e. Bit Error Rate (BER) and Probability of Detection (PD). The results are processed and validated by MATLAB simulation. • 327. Blekinge Institute of Technology, School of Engineering. Fuzzy linear programming problems solved with Fuzzy decisive set method2009Independent thesis Advanced level (degree of Master (One Year))Student thesis In the thesis, there are two kinds of fuzzy linear programming problems, one of them is a linear programming problem with fuzzy technological coefficients and the second is linear programming problem in which both the right-hand side and the technological coefficients are fuzzy numbers. I solve the fuzzy linear programming problems with fuzzy decisive set method. • 328. Meleshko, Sergey Symmetries of Integro-Differential Equations2010, XIIIBook (Other academic) This book aims to coherently present applications of group analysis to integro-differential equations in an accessible way. The book will be useful to both physicists and mathematicians interested in general methods to investigate nonlinear problems using symmetries. Differential and integro-differential equations, especially nonlinear, present the most effective way for describing complex processes. Therefore, methods to obtain exact solutions of differential equations play an important role in physics, applied mathematics and mechanics. This book provides an easy to follow, but comprehensive, description of the application of group analysis to integro-differential equations. The book is primarily designed to present both fundamental theoretical and algorithmic aspects of these methods. It introduces new applications and extensions of the group analysis method. The authors have designed a flexible text for postgraduate courses spanning a variety of topics. • 329. Melin, Jan Two types of limit cycles of a resonant converter modelled by a three-dimensional system2008In: Nonlinear Analysis: Hybrid Systems, ISSN 1751-570X, E-ISSN 1878-7460, Vol. 2, no 4, p. 1275-1286Article in journal (Refereed) In this paper, the long-run dynamics of a controlled resonant converter, modelled as a piecewise system, is studied. The modelling of the resonant converter can be done using various approximations and the long-run dynamics of the two dimensional cases were earlier analysed. In this paper, we discuss results that can be extended to the three dimensional case. It seems that limit cycles describe the longrun dynamics in important situations in the three dimensional case, too. Our objective is to relate the limit cycles found previously in the two-dimensional case to those found now in the three dimensional approximation. • 330. Blekinge Institute of Technology, School of Engineering, Department of Mechanical Engineering. Load Calculation and Simulation of an Asphalt Roller2005Independent thesis Advanced level (degree of Master (One Year))Student thesis Free body diagrams of an Asphalt Roller were designed for several load cases and used for an optimisation study. Assumptions for the load calculations for each load case were carried out in MATLAB®. The Roller was built in I-DEAS® and the results were compared with the theoretical results • 331. Blekinge Institute of Technology, School of Engineering. Video Quality Evaluation using NR metric with Detection of Frame Dips and Drops2013Independent thesis Advanced level (degree of Master (Two Years))Student thesis Wireless technology has become the most interesting field in the area of communications and networking. Video transmission plays a major role in this area. Data transmission via wireless communications is a major task, especially to send the data without loss of packets. The digital video decoder produces dropped or repeated frames from the encoded video due to packet loss. Brief frame drops of one frame duration are referred as dips. This research work investigates how to identify these frame dips and drops and also to measure the quality of the video which contain frame dips and frame drops. A dynamic threshold estimator is implemented to identify these frame dips. The qualitative analysis of a video is performed using a No Reference metric. In this metric the quality assessment can be achieved by identification of frame dips and drops and calculating Modified Fraction of Dropped Frames. Dips and abrupt temporal variation occurring at the end of frame freezing event of a video fluidity impairment caused by frame dropping will be taken into account using this metric. The parameters which are generated from Structural Similarity Index Metric (SSIM) analysis are efficient enough to compare the video quality and estimate the metric performance objectively. Our proposed metric has predicted the SSIM with a Pearson correlation coefficient of 0.99 in test1, 0.92 in test2 and 0.99 in test3. Therefore in terms of prediction accuracy the proposed metric has a good correlation with the deployed metric and obtained robustness to our approach. • 332. Mustafa, Wail Fuzzy-based Opportunistic Power Control Strategy in Cognitive Radio Networks2010Conference paper (Refereed) This paper considers the spectrum sharing network consisting of a pair of primary users (PUs) and a pair of cognitive users (CRs) in a fading channel. The pair of PUs establishes a wireless link as the PU link. The pair of CRs establishes a wireless link as the CR link. The PU link and CR link utilize spectrum simultaneously with different priorities. The PU link has a higher priority to utilize spectrum with respect to the CR link. When the PU link utilizes spectrum, a desired quality of service (QoS) is given to be assured and the CR utilizes spectrum with an opportunistic power scale under this constraint, assuring the desired QoS on the PU link. To compute an optimal opportunistic power scale for the CR link, a fuzzy-based opportunistic power control strategy is proposed based on the Mamdani fuzzy control model using two input variables: the PU’s SNR and PU’s interference channel gain. By the proposed fuzzy-based power control strategy, the desired QoS could be assured on the PU link and the bit error rate (BER) is also reduced compared with the spectrum sharing network without power control strategy. • 333. Blekinge Institute of Technology, School of Engineering. Eigen Fuzzy Sets of Fuzzy Relation with Applications2010Independent thesis Advanced level (degree of Master (Two Years))Student thesis Eigen fuzzy sets of fuzzy relation can be used for the estimation of highest and lowest levels of involved variables when applying max-min composition on fuzzy relations. By the greatest eigen fuzzy sets (set which can be greater anymore) maximum membership degrees of any fuzzy set can be found, with the help of least eigen fuzzy set (set which can be less anymore) minimum membership degrees of any fuzzy sets can be found as well.The lowest and highest level, impact or e ffect of anything can be found by applying eigen fuzzy set theory. The implicational aspect of this research study is medical and customer satisfaction level measurement. By applying methods of eigen fuzzy set theory the e ffectiveness of medical cure and customer satisfaction can be found with high precision. • 334. Moscow MV Lomonosov State Univ, RUS. Blekinge Institute of Technology, Faculty of Engineering, Department of Mechanical Engineering. On Front Motion in a Burgers-Type Equation with Quadratic and Modular Nonlinearity and Nonlinear Amplification2018In: Doklady. Mathematics, ISSN 1064-5624, E-ISSN 1531-8362, Vol. 97, no 1, p. 99-103Article in journal (Refereed) A singularly perturbed initial-boundary value problem for a parabolic equation known in applications as a Burgers-type or reaction-diffusion-advection equation is considered. An asymptotic approximation of solutions with a moving front is constructed in the case of modular and quadratic nonlinearity and nonlinear amplification. The influence exerted by nonlinear amplification on front propagation and blowing- up is determined. The front localization and the blowing-up time are estimated. • 335. Blekinge Institute of Technology, School of Engineering. Investigation of the Equations Modelling Chemical Waves Using Lie Group Analysis2012Independent thesis Advanced level (degree of Master (Two Years))Student thesis A system of nonlinear di fferential equations, namely, the Belousov-Zhabotinskii reaction model has been investigated for nonlinear self-adjointness using the recent work of Professor N.H.Ibragimov. It is shown that the model is not nonlinearly self-adjoint. The symmetries of the system and nonlinear conservation laws are calculated. The modi fied system, which is nonlinearly self-adjoint, is also analysed. Its symmetries and conservation laws are presented. • 336. Blekinge Institute of Technology, School of Management. Blekinge Institute of Technology, School of Management. Lågkonjunktur, En studie i vilka skillnader som finns för variationen i antal anställda inom IT- respektive industribranschen2009Independent thesis Basic level (degree of Bachelor)Student thesis Sammanfattning Titel: Lågkonjunktur – En studie i vilka skillnader som finns för variationen i antal anställda inom IT- respektive industribranschen Författare: Emilio Nilsson, Oscar Kacprzak Handledare: Emil Numminen Institution: Blekinge Tekniska Högskola Kurs: Kandidatarbete i Företagsekonomi Syfte: Syftet med uppsatsen är att undersöka och analysera för hur företagets ekonomiska data för den relativt unga IT-sektorn förklarar antal anställda gentemot hur företagets ekonomiska data förklarar nyckeltalet för en äldre mer erfaren bransch som industrisektorn. Metod: Vi har samlat ihop kvartalsrapporter från 1999 års första kvartal till 2009 års första kvartal för totalt 10 stycken företag som vi bedömt lämpliga för studien, 5 företag från IT-branschen samt 5 företag från industribranschen. Vi har därefter fört regressionsanalyser med antal anställda som Y-variabel och totala intäkter, aktienivå, rörelsekostnader samt rörelseresultat som X-variabler för att finna korrelationen däremellan. Slutsats: De framkomna resultaten från regressionsanalyserna pekar på att det finns skillnader branscherna emellan. Dessa var mest påtagliga i variablerna totala intäkter och rörelsekostnader. För båda variablerna hade industriföretagen större korrelation med Y-variabeln än vad IT-företagen hade. Korrelationen mellan antal anställda och rörelseresultatet kunde vi inte urskilja några tendenser branscherna emellan. Aktienivån hade en något större korrelation i variationen av antalet anställda för industriföretagen än för IT-företagen, där korrelationen var låg rakt igenom. Abstract Title: Recession - A study of the differences that exist for the variation in the number of employees in the IT and industrial sector Author: Emilio Nilsson, Oscar Kacprzak Supervisor: Emil Numminen Institution: Blekinge Institute of Technology Course: Bachelor thesis in Economics Purpose: The aim of the paper is to examine and analyze how a company's financial data for the relatively young IT sector explains the number of employees compared to how the financial data explains it for an older more experienced branch like the industry sector. Method: We have collected quarterly reports from the first quarter of 1999 to the first quarter of 2009 for a total of 10 different companies that we determined appropriate for the study, 5 companies from the IT sector and 5 companies from the industrial sector. We have subsequently conducted a regression analysis with number of employees as the Y-variable and total income, stock level, operating expenses and operating income as the X-variables to find the correlation between them. Conclusion: The results of the regression analysis indicate that there are differences between the industries. These were most visible in the variables of total income and operating expenses. For both variables, the industrial companies’ had a greater correlation with the Y-variable than IT companies had. In the correlation between the number of employees and operating profit, we could not find any differences between the sectors. Stock levels had a slightly higher correlation in the variance of the number of employees for manufacturing companies than for the IT companies, where the correlation was low right through. • 337. Blekinge Institute of Technology, Department of Telecommunications and Mathematics. Blekinge Institute of Technology, Department of Telecommunications and Mathematics. Tight Bounds on the Minimum Euclidean Distance for Block Coded Phase Shift Keying1996Report (Refereed) We present upper and lower bounds on the minimum Euclidean distance$d_{Emin}(C)$for block coded PSK. The upper bound is an analytic expression depending on the alphabet size$q$, the block length$n$and the number of codewords$|C|$of the code$C$. This bound is valid for all block codes with$q\geq4$and with medium or high rate - codes where$|C|>(q/3)^n$. The lower bound is valid for Gray coded binary codes only. This bound is a function of$q$and of the minimum Hamming distance$d_{Hmin}(B)$of the corresponding binary code$B$. We apply the results on two main classes of block codes for PSK; Gray coded binary codes and multilevel codes. There are several known codes in both classes which satisfy the upper bound on$d_{Emin}(C)$with equality. These codes are therefore best possible, given$q,n$and$|C|$. We can deduce that the upper bound for many parameters$q,n$and$|C|$is optimal or near optimal. In the case of Gray coded binary codes, both bounds can be applied. It follows for many binary codes that the upper and the lower bounds on$d_{Emin}(C)$coincide. Hence, for these codes$d_{Emin}(C)\$ is maximal.

• 338. Nilsson, Magnus
A two-metric approach to improve bounds on the minimum Euclidean distance for block codes2008Conference paper (Refereed)

We consider block coded PSK, and improve a previously established upper bound on the minimum Euclidean distance d_E(C) that is valid for any block code C. The bound is an explicit function of the alphabet size, block length and the number of code words. The improvement involves choosing an inner metric to give the best possible bound for the outer metric, which is Euclidean. we describe this approach and its problems, and present empiric results.

• 339.
Blekinge Institute of Technology, School of Engineering, Department of Signal Processing.
First Order Hidden Markov Model: Theory and Implementation Issues2005Report (Refereed)

This report explains the theory of Hidden Markov Models (HMMs). The emphasis is on the theory aspects in conjunction with the implementation issues that are encountered in a floating point processor. The main theory and implementation issues are based on the use of a Gaussian Mixture Model (GMM) as the state density in the HMM, and a Continuous Density Hidden Markov Model (CDHMM) is assumed. Suggestions and advice related to the implementation are given for a typical pattern recognition task.

• 340. Nilsson, Mikael
The Successive Mean Quantization Transform2005Conference paper (Refereed)

This paper presents the Successive Mean Quantization Transform (SMQT). The transform reveals the organization or structure of the data and removes properties such as gain and bias. The transform is described and applied in speech processing and image processing. The SMQT is considered as an extra processing step for the mel frequency cepstral coefficients commonly used in speech recognition. In image processing the transform is applied in automatic image enhancement and dynamic range compression.

• 341.
Blekinge Institute of Technology, Faculty of Engineering, Department of Mechanical Engineering.
Mekaniska beräkningar av armeringstråd vid förläggning på högspänningskablar2014Student thesis

Detta examensarbete har tagit plats på ABB High Voltage Cables i Karlskrona och fokuserar på deras armeringsprocess (AR50) som förstärker kabeln genom påläggning av armeringstrådar. Arbetet är starkt begränsat till enbart den korta perioden för själva påläggningen av tråden och undersöker spänningsskillnader i en armeringstråd beroende på olika kabel – och tråddimensioner samt bromskrafter som används i produktionen. Studien följer en modell – och teoriutvecklande forskningsprocess kombinerat med ett utprövande resultatbildande. Studiens syfte är att tillsammans med en beräkningsmodell öka och fördjupa ABBs kunskaper kring armeringstråden som idag används för att stärka och skydda ABBs alla olika högspänningskablar. Beräkningsmodellen tas fram i FEA (Finita Element Analys) prorammet ABAQUS genom en dynamisk explicit modell. En förklaring till hur beräkningsmodellen har byggts upp och vilka parametrar som används beskrivs i rapporten. Dessa delar bidrar sedan till resultatet i studien som ger en bild av att bromskraften som används i AR50s armeringsprocessen inte behöver kontrolleras med en hög precision så länge den är tillräckligt stor för att hålla armeringstråden sträckt vid påläggningen. Studien visar också att olika kabel – och tråddimensioner inte påverkar spänningsnivåerna något markant vid armeringsprocessen och att nippeln som används i armeringsprocesen för att trycka ner armeringstråden mot kabeln bestämmer hur spänningsbilden ser ut.

• 342. Nyqvist, Robert
Algebraic Dynamical Systems, Analytical Results and Numerical Simulations2007Book (Other academic)

In this thesis we study discrete dynamical system, given by a polynomial, over both finite extension of the fields of p-adic numbers and over finite fields. Especially in the p-adic case, we study fixed points of dynamical systems, and which elements that are attracted to them. We show with different examples how complex these dynamics are. For certain polynomial dynamical systems over finite fields we prove that the normalized average of the numbers of linear factors modulo prime numbers exists. We also show how to calculate the average, by using Chebotarev's Density Theorem. The non-normalized version of the average of the number of linear factors of linearized polynomials modulo prime numbers, tends to infinity, so in that case we find an asymptotic formula instead. We have also used a computer to study different behaviors, such as iterations of polynomials over the p-adic fields and the asymptotic relation mention above. In the last chapter we present the computer programs used in different part of the thesis.

• 343.
Blekinge Institute of Technology, School of Engineering, Department of Mathematics and Science.
Asymptotic behaviour of numbers of cycles of dynamical systems in finite fields2007In: Proceedings of the Jangjeon Mathematical Society, ISSN 1598-7264, Vol. 10, no 1, p. 1-6Article in journal (Refereed)
• 344. Nyqvist, Robert
On the Number of Equivalence Classes of Attracting Dynamical Systems2009In: P-Adic Numbers, Ultrametric Analysis, and Applications, ISSN 2070-0466, E-ISSN 2070-0474, Vol. 1, no 3, p. 264-270Article in journal (Refereed)

We study discrete dynamical systems of the kind h(x) = x + g(x), where g(x) is a monic irreducible polynomial with coefficients in the ring of integers of a p-adic field K. The dynamical systems of this kind, having attracting fixed points, can in a natural way be divided into equivalence classes, and we investigate whether something can be said about the number of those equivalence classes, for a certain degree of the polynomial g(x).

• 345.
Högskolan Väst, SWE.
Blekinge Institute of Technology, Faculty of Engineering, Department of Mathematics and Natural Sciences.
Group gradations on Leavitt path algebras2019In: Journal of Algebra and its Applications, ISSN 0219-4988, E-ISSN 1793-6829Article in journal (Refereed)

Given a directed graph E and an associative unital ring R one may define the Leavitt path algebra with coefficients in R, denoted by LR(E). For an arbitrary group G, LR(E) can be viewed as a G-graded ring. In this paper, we show that LR(E) is always nearly epsilon-strongly G-graded. We also show that if E is finite, then LR(E) is epsilon-strongly G-graded. We present a new proof of Hazrat's characterization of strongly g-graded Leavitt path algebras, when E is finite. Moreover, if E is row-finite and has no source, then we show that LR(E) is strongly-graded if and only if E has no sink. We also use a result concerning Frobenius epsilon-strongly G-graded rings, where G is finite, to obtain criteria which ensure that LR(E) is Frobenius over its identity component. © 2020 World Scientific Publishing Company.

• 346.
University West, Sweden.
Blekinge Institute of Technology, Faculty of Engineering, Department of Mathematics and Natural Sciences.
Simple graded rings, non-associative crossed products and Cayley-Dickson doublings2019In: Journal of Algebra and its Applications, ISSN 0219-4988, E-ISSN 1793-6829, article id 2050231Article in journal (Refereed)

We show that if a non-associative unital ring is graded by a hypercentral group, then the ring is simple if and only if it is graded simple and the center of the ring is a field. Thereby, we extend a result by Jespers from the associative case to the non-associative situation. By applying this result to non-associative crossed products, we obtain non-associative analogues of results by Bell, Jordan and Voskoglou. We also apply this result to Cayley-Dickson doublings, thereby obtaining a new proof of a classical result by McCrimmon.

• 347.
Univ West, SWE.
Blekinge Institute of Technology, Faculty of Engineering, Department of Mathematics and Natural Sciences. Univ Ind Santander, COL.
EPSILON-STRONGLY GROUPOID-GRADED RINGS, THE PICARD INVERSE CATEGORY AND COHOMOLOGY2020In: Glasgow Mathematical Journal, ISSN 0017-0895, E-ISSN 1469-509X, Vol. 62, no 1, p. 233-259, article id PII S0017089519000065Article in journal (Refereed)

We introduce the class of partially invertible modules and show that it is an inverse category which we call the Picard inverse category. We use this category to generalize the classical construction of crossed products to, what we call, generalized epsilon-crossed products and show that these coincide with the class of epsilon-strongly groupoid-graded rings. We then use generalized epsilon-crossed groupoid products to obtain a generalization, from the group-graded situation to the groupoid-graded case, of the bijection from a certain second cohomology group, defined by the grading and the functor from the groupoid in question to the Picard inverse category, to the collection of equivalence classes of rings epsilon-strongly graded by the groupoid.

• 348.
University West, SWE.
Blekinge Institute of Technology, Faculty of Engineering, Department of Mathematics and Natural Sciences. Industrial University of Santander, COL.
Artinian and noetherian partial skew groupoid rings2018In: Journal of Algebra, ISSN 0021-8693, E-ISSN 1090-266X, Vol. 503, p. 433-452Article in journal (Refereed)

Let α={α_g : R_{g^{−1}}→R_g}_{g∈mor(G)} be a partial action of a groupoid G on a (not necessarily associative) ring R and let S=R⋆G be the associated partial skew groupoid ring. We show that if α is global and unital, then S is left (right) artinian if and only if R is left (right) artinian and R_g={0}, for all but finitely many g∈mor(G). We use this result to prove that if α is unital and R is alternative, then S is left (right) artinian if and only if R is left (right) artinian and R_g={0}, for all but finitely many g∈mor(G). This result applies to partial skew group rings, in particular. Both of the above results generalize a theorem by J. K. Park for classical skew group rings, i.e. the case when R is unital and associative, and G is a group which acts globally on R. We provide two additional applications of our main results. Firstly, we generalize I. G. Connell's classical result for group rings by giving a characterization of artinian (not necessarily associative) groupoid rings. This result is in turn applied to partial group algebras. Secondly, we give a characterization of artinian Leavitt path algebras. At the end of the article, we relate noetherian and artinian properties of partial skew groupoid rings to those of global skew groupoid rings, as well as establish two Maschke-type results, thereby generalizing results by M. Ferrero and J. Lazzarin for partial skew group rings to the case of partial skew groupoid rings.

• 349.
University West, SWE.
Blekinge Institute of Technology, Faculty of Engineering, Department of Mathematics and Natural Sciences. Industrial University of Santander, COL.
Epsilon-strongly graded rings, separability and semisimplicity2018In: Journal of Algebra, ISSN 0021-8693, E-ISSN 1090-266X, Vol. 514, no Nov., p. 1-24Article in journal (Refereed)

We introduce the class of epsilon-strongly graded rings and show that it properly contains both the collection of strongly graded rings and the family of unital partial crossed products. We determine when epsilon-strongly graded rings are separable over their principal components. Thereby, we simultaneously generalize a result for strongly group-graded rings by Nastasescu, Van den Bergh and Van Oystaeyen, and a result for unital partial crossed products by Bagio, Lazzarin and Paques. We also show that the family of unital partial crossed products appear in the class of epsilon-strongly graded rings in a fashion similar to how the classical crossed products present themselves in the family of strongly graded rings. Thereby, we obtain, in the special case of unital partial crossed products, a short proof of a general result by Dokuchaev, Exel and Simon concerning when graded rings can be presented as partial crossed products.

• 350.
Högskolan Väst, SWE.
Blekinge Institute of Technology, Faculty of Engineering, Department of Mathematics and Natural Sciences. Blekinge Inst Technol, Dept Math & Nat Sci, SE-37179 Karlskrona, Sweden.. Mälardalens högskola, SWE.
NON-ASSOCIATIVE ORE EXTENSIONS2018In: Israel Journal of Mathematics, ISSN 0021-2172, E-ISSN 1565-8511, Vol. 224, no 1, p. 263-292Article in journal (Refereed)

We introduce non-associative Ore extensions, S = R[X; sigma, delta], for any non-ssociative unital ring R and any additive maps sigma, delta : R -> R satisfying sigma(1) = 1 and delta(1) = 0. In the special case when delta is either left or right R-delta-linear, where R-delta = ker(delta), and R is delta-simple, i.e. {0} and R are the only delta-invariant ideals of R, we determine the ideal structure of the non-associative differential polynomial ring D = R[X; id(R),delta]. Namely, in that case, we show that all non-zero ideals of D are generated by monic polynomials in the center Z(D) of D. We also show that Z(D) = R-delta[p] for a monic p is an element of R-delta [X], unique up to addition of elements from Z(R)(delta) . Thereby, we generalize classical results by Amitsur on differential polynomial rings defined by derivations on associative and simple rings. Furthermore, we use the ideal structure of D to show that D is simple if and only if R is delta-simple and Z(D) equals the field R-delta boolean AND Z(R). This provides us with a non-associative generalization of a result by Oinert, Richter and Silve-strov. This result is in turn used to show a non-associative version of a classical result by Jordan concerning simplicity of D in the cases when the characteristic of the field R-delta boolean AND Z(R) is either zero or a prime. We use our findings to show simplicity results for both non-associative versions of Weyl algebras and non-associative differential polynomial rings defined by monoid/group actions on compact Hausdorff spaces.

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