We consider a finite section (Galerkin) and a collocation method for Cauchy singular integral equations on the interval based on weighted Chebyshev polymoninals, where the coefficients of the operator are piecewise continuous. Stability conditions are derived using Banach algebra techniques, where also the system case is mentioned. With the help of appropriate Sobolev spaces a result on convergence rates is proved. Computational aspects are discussed in order to develop an effective algorithm. Numerical results, also for a class of nonlinear singular integral equations, are presented.

Wide area cellular mobile networks have rapidly evolved over the years. In the beginning achieving wide area coverage was a great achievement – enabling subscribers to call from wherever they were currently located and whenever they wanted. Additionally these systems supported mobility of subscribers, so that calls could continue even while a subscriber moved from one cell to another. Today mobility management is something everyone takes for granted. New functionality is continuously being developed for these networks. An important aspect of this evolution has been to enable new applications and technologies to be introduced while maintaining interoperability with the existing technologies. These mobile networks use new technologies and enable new applications, but they interconnect with existing networks that utilize earlier technologies, such as the existing fixed telephone network. These interconnections enable communication between subscribers connected via all of these networks. In today’s mobile networks there are a variety of technologies working side by side, for example 2G, GPRS, 3G, and so on. The earlier networks used circuit switching technology, but the trend in later networks was to transition exclusively to packet switching. One of the most important network entities is the mobile switch center (MSC). In the earlier circuit switched networks the MSC is the heart of the circuit switching network. The MSC is responsible for management, control, and communication to and from the mobile stations (MSs) in the area managed by the MSC. The MSC stores information about each of the MSs in one or more databases. In the subscriber’s home network the information about their subscription is stored in a home location register (HLR), while when this subscriber is in another network information is stored in a visitor location register (VLR). The MSC together with other elements of the core network handles mobility management, enabling both handover and roaming. A gateway MSC enables MSs to communicate with phones connected to the fixed network. The aim of this thesis is to analyze the traffic situation for Kulyab region in order to configure and install the MSC in Kulyab. For the time being there is no radio network controller (RNC) in Kulyab region, so the MSC in Kulyab will be configured to support 2G traffic. The configuration will be based on the expected mobile traffic load in the Kulyab region, thus the first steps in the process were to collect and analyze data about the existing traffic in this region that is currently served by a MSC located outside of this region. The configuration of the new MSC will be based on this analysis. After installing and configuring the new MSC some question need to be answered, namely: Can the MSC in Kulyab support all the base stations in Kulyab region? If not, how many base stations can it support? To what extent does the addition of this new MSC improve the overall network in terms of increased reliability, capacity, and throughput? How much will the capacity of the existing MSC, that is responsible for traffic outside Dushanbe, be increased due to the introduction of the new MSC? / Den mobila täckningen har utvecklats snabbt under åren. Att uppnå den mobila täckningen var i början en stor prestation – att kunna erbjuda telefontjänster för abonnenterna var än de befann sig och när de ville. Förutom detta så stödde detta system också fri rörlighet för abonnenterna. Under ett samtal kunde de förflytta sig från en cell till ett annan utan att samtalet bröts. Nu är mobilitetshanteringen någonting självklart. Nya funktioner utvecklas ständigt för dessa nätverk. En viktig aspekt för utvecklingen är att möjliggöra så att nya applikationer och teknologier kan introduceras och fortfarande vara kompatibla med de existerande teknikerna. Dessa mobilnätverk använder nya tekniker och möjliggör nya applikationer som är kompatibla med det existerande nätverket. Det existerande nätverket använder sig av tidigare teknologier, så som den fasta telefonnätet. Detta möjliggör kommunikation mellan abonnenterna från olika nätverk. I dagens nätverk finns det ett antal olika nätverk, som t.ex. 2G, GPRS, 3G och så vidare. Det tidigare nätverket använde sig av kretskopplad teknik, men trenden är attuteslutande använda sig av paketkopplad teknik. En av de viktigaste nätverksenheterna är ”Mobile switch center” (MSC). I de tidigare kretskopplade nätverket är MSC hjärtat i det kretskopplade nätverket. MSC är ansvarig för hanteringen, kontrollen och kommunikation till och från demobila enheterna (MS) i området som kontrolleras av MSCn. MSC lagrar information om var och en av MS i ett eller flera databaser. I abonnentens hemnätverk finns information om abonnentens abonnemang i ett hemregister (HLR). När abonnenten befinner sig i ett annat nätverk lagras informationen i ett gästregister (VLR). MSC hanterar mobilitet tillsammans med andra nätverksenheter i ”Core network” (CN) och möjliggör överlämnande (handover) och roaming. ”Gateway MSC” GMSC möjliggör kommunikation mellan MS och det fasta nätverket. Syftet med examensarbetet är att analysera trafiken för Kulyab-regionen för att konfigurera och installera en MSC i Kulyab. För tillfället finns ingen ”Radio network controller” (RNC) i regionen Kulyab, så MSCn i Kulyab kommer att konfigureras för att stödja 2G trafik. Konfigurationen baseras på den förväntade belastningen av mobiltrafiken i Kulyab-regionen, följaktligen är det första steget i processen att samla ihop och analysera information om den existerande trafiken i Kulyab-regionen. Trafiken tillhörande Kulyab-regionen handskas för närvarande av en MSC som befinner sig utanför detta område. Konfigurationen av den nya MSCn kommer att baseras på denna analys. Efter installationen och konfigurationen av den nya MSCn kommer följande frågor att bli besvarade, nämligen: Kan MSCn i Kulyab stödja alla basstationerna i Kulyab regionen? Om inte, hur många basstationer kan MSCn stödja? Till vilken grad kommer den nya MSCn att förbättra nätverket i termer av ökad tillförlitlighet, kapacitet och trafikgenomströmning? Hur mycket kommer kapacitetsökningen för den existerande MSC utanför Dushanbe att öka då MSC i Kulyab installeras?

Computing least common subsumers (lcs) and most specific concepts (msc) are inference tasks that can be used to support the „bottom up” construction of knowledge bases for KR systems based on description logic. For the description logic ALN, the msc need not always exist if one restricts the attention to acyclic concept descriptions. In this paper, we extend the notions lcs and msc to cyclic descriptions, and show how they can be computed. Our approach is based on the automata-theoretic characterizations of fixed-point semantics for cyclic terminologies developed in previous papers. / An abridged version of this technical report has been published at KI'98.

In this paper, we study ill-posedness concepts of nonlinear and linear inverse problems in a Hilbert space setting. We define local ill-posedness of a nonlinear operator equation $F(x) = y_0$ in a solution point $x_0$ and the interplay between the nonlinear problem and its linearization using the Frechet derivative $F\acent(x_0)$ . To find an appropriate ill-posedness concept for the linarized equation we define intrinsic ill-posedness for linear operator equations $Ax = y$ and compare this approach with the ill-posedness definitions due to Hadamard and Nashed.

In this paper we deal with the `strength' of ill-posedness for ill-posed linear operator equations Ax = y in Hilbert spaces, where we distinguish according_to_M. Z. Nashed [15] the ill-posedness of type I if A is not compact, but we have R(A) 6= R(A) for the range R(A) of A; and the ill-posedness of type II for compact operators A: From our considerations it seems to follow that the problems with noncompact operators A are not in general `less' ill-posed than the problems with compact operators. We motivate this statement by comparing the approximation and stability behaviour of discrete least-squares solutions and the growth rate of Galerkin matrices in both cases. Ill-posedness measures for compact operators A as discussed in [10] are derived from the decay rate of the nonincreasing sequence of singular values of A. Since singular values do not exist for noncompact operators A; we introduce stability rates in order to have a common measure for the compact and noncompact cases. Properties of these rates are illustrated by means of convolution equations in the compact case and by means of equations with multiplication operators in the noncompact case. Moreover using increasing rearrangements of the multiplier functions specific measures of ill-posedness called ill-posedness rates are considered for the multiplication operators. In this context, the character of sufficient conditions providing convergence rates of Tikhonov regularization are compared for compact operators and multiplication operators.

This paper is concerned with mesh refinement techniques for treating elliptic boundary value problems in domains with re- entrant edges and corners, and focuses on numerical experiments. After a section about the model problem and discretization strategies, their realization in the experimental code FEMPS3D is described. For two representative examples the numerically determined error norms are recorded, and various mesh refinement strategies are compared.

In this paper we deal with the `strength' of ill-posedness for ill-posed linear operator equations Ax = y in Hilbert spaces, where we distinguish according_to_M. Z. Nashed [15] the ill-posedness of type I if A is not compact, but we have R(A) 6= R(A) for the range R(A) of A; and the ill-posedness of type II for compact operators A: From our considerations it seems to follow that the problems with noncompact operators A are not in general `less' ill-posed than the problems with compact operators. We motivate this statement by comparing the approximation and stability behaviour of discrete least-squares solutions and the growth rate of Galerkin matrices in both cases. Ill-posedness measures for compact operators A as discussed in [10] are derived from the decay rate of the nonincreasing sequence of singular values of A. Since singular values do not exist for noncompact operators A; we introduce stability rates in order to have a common measure for the compact and noncompact cases. Properties of these rates are illustrated by means of convolution equations in the compact case and by means of equations with multiplication operators in the noncompact case. Moreover using increasing rearrangements of the multiplier functions specific measures of ill-posedness called ill-posedness rates are considered for the multiplication operators. In this context, the character of sufficient conditions providing convergence rates of Tikhonov regularization are compared for compact operators and multiplication operators.

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