This thesis consists of six papers. In Paper I, we give an algorithm for merging sorted lists of monomials and together with a projection technique, we obtain a new complexity bound for the Buchberger-Möller algorithm and the FGLM algorithm. In Paper II, we discuss four different constructions of vector space bases associated to vanishing ideals of points. We show how to compute normal forms with respect to these bases and give complexity bounds. As an application we drastically improve the computational algebra approach to the reverse engineering of gene regulatory networks. In Paper III, we introduce the concept of multiplication matrices for ideals of projective dimension zero. We discuss various applications and, in particular, we give a new algorithm to compute the variety of an ideal of projective dimension zero. In Paper IV, we consider a subset of projective space over a finite field and give a geometric description of the minimal degree of a non-vanishing form with respect to this subset. We also give bounds on the minimal degree in terms of the cardinality of the subset. In Paper V, we study an associative version of an algorithm constructed to compute the Hilbert series for graded Lie algebras. In the commutative case we use Gotzmann's persistence theorem to show that the algorithm terminates in finite time. In Paper VI, we connect the commutative version of the algorithm in Paper V with the Buchberger algorithm. / At the time of doctoral defence, the following papers were unpublished and had a status as follows: Paper 3: Manuscript. Paper 4: Manuscript. Paper 5: Manuscript. Paper 6: Manuscript

Arbetets art: Examensarbete i lärarutbildningen, Avancerad nivå, 15 hp Högskolan i Skövde Titel: Nolltolerans i skolan om hot och våld - En studie om rektorers tolkning av begreppet nolltolerans Sidantal: 41 Författare: David Löfving och Joakim Petersson Handledare: Kennert Orlenius Datum: januari, 2009 Nyckelord: nolltolerans, hot och våld, åtgärder, gränsdragning, agerande I USA på 1990-talet infördes en lag gällande nolltolerans mot vapen i skolan. Denna lag har fått en vidare tolkning vilket har gjort att många elever har blivit exkluderade från undervisningen av märkliga skäl. Uppsatsen handlar om rektorers syn på begreppet nolltolerans i frågor om hot och våld mot skolpersonal. Vidare redogör studien för hur rektorer arbetar förebyggande och hur deras efterarbete ser ut. Dessutom berör studien rektorers erfarenheter kring hot och våld mot skolpersonal. För att nå fram till studiens syfte så intervjuades rektorer på högstadieskolor. De intervjuade rektorerna hade inga större erfarenheter kring hot och våld mot skolpersonal. Rektorerna är positivt inställda till nolltoleransbegreppet dock så ser de en viss svårighet till att införa ett sådant begrepp. Allting handlar om gränsdragningar, var går gränsen för hot och våld? Rektorerna ger också uttryck för det förebyggande arbetet i undervisningen. Det finns handlingsplaner på samtliga av de intervjuade rektorernas arbetsplatser som både tar upp förebyggande och efterföljande arbete kring hot och våld.

The optimum ordering strategies for the coded V-BLAST system with capacity achieving temporal codes on each stream are studied in this thesis. Mathematical representations of the optimum detection ordering strategies for the coded V-BLAST under instantaneous rate allocation (IRA), uniform power/rate allocation (URA), instantaneous power allocation(IPA) and instantaneous power/rate allocation (IPRA) are derived. For two transmit antennas, it is shown that the optimum detection strategies are based on the per-stream before-processing channel gains. Based on approximations of the per-stream capacity equation, closed-form expressions of the optimal ordering strategy under the IRA at low and high signal to noise ratio (SNR) are derived. Necessary optimality conditions under the IRA are given. Thresholds for the low, intermediate and high SNR regimes in the 2-Tx-antenna system under the IPRA are determined, and the SNR gain of the ordering is studied for each regime. Performances of simple suboptimal ordering strategies are analysed, some of which perform very close to the optimum one.

The main part of the thesis is applications of the Strong Artin conjecture to number theory. We have two applications. One is generating number fields with extreme class numbers. The other is generating extreme positive and negative values of Euler-Kronecker constants. For a given number field $K$ of degree $n$, let $\widehat{K}$ be the normal closure of $K$ with $Gal(\widehat{K}/\Bbb Q)=G.$ Let $Gal(\widehat{K}/K)=H$ for some subgroup $H$ of $G$. Then, $$ L(s,\rho,\widehat{K}/\Bbb Q)=\frac{\zeta_K(s)}{\zeta(s)} $$ where $Ind_H^G1_H = 1_G + \rho$. When $L(s,\rho)$ is an entire function and has a zero-free region $[\alpha,1] \times [-(\log N)^2, (\log N)^2]$ where $N$ is the conductor of $L(s,\rho)$, we can estimate $\log L(1,\rho)$ and $\frac{L'}{L}(1,\rho)$ as a sum over small primes: $$ \log L(1,\rho) = \sum_{p\leq(\log N)^{k}}\lambda(p)p^{-1} + O_{l,k,\alpha}(1)$$ $$ \frac{L'}{L}(1,\rho)=-\sum_{p\leq x} \frac{\lambda(p) \log{p}}{p} +O_{l,x,\alpha}(1). $$ where $0 < k < \frac{16}{1-\alpha}$ and $(\log N)^{\frac{16}{1-\alpha}} \leq x \leq N^{\frac{1}{4}}$. With these approximations, we can study extreme values of class numbers and Euler-Kronecker constants. Let $\frak{K}$ $(n,G,r_1,r_2)$ be the set of number fields of degree $n$ with signature $(r_1,r_2)$ whose normal closures are Galois $G$ extension over $\Bbb Q$. Let $f(x,t) \in \Bbb Z[t][x]$ be a parametric polynomial whose splitting field over $\Bbb Q (t)$ is a regular $G$ extension. By Cohen's theorem, most specialization $t\in \Bbb Z$ corresponds to a number field $K_t$ in $\frak{K}$ $(n,G,r_1,r_2)$ with signature $(r_1,r_2)$ and hence we have a family of Artin L-functions $L(s,\rho,t)$. By counting zeros of L-functions over this family, we can obtain L-functions with the zero-free region above. In Chapter 1, we collect the known cases for the Strong Artin conjecture and prove it for the cases of $G=A_4$ and $S_4$. We explain how to obtain the approximations of $\log (1,\rho)$ and $\frac{L'}{L}(1,\rho)$ as a sum over small primes in detail. We review the theorem of Kowalski-Michel on counting zeros of automorphic L-functions in a family. In Chapter 2, we exhibit many parametric polynomials giving rise to regular extensions. They contain the cases when $G=C_n,$ $3\leq n \leq 6$, $D_n$, $3\leq n \leq 5$, $A_4, A_5, S_4, S_5$ and $S_n$, $n \geq 2$. In Chapter 3, we construct number fields with extreme class numbers using the parametric polynomials in Chapter 2. In Chapter 4, We construct number fields with extreme Euler-Kronecker constants also using the parametric polynomials in Chapter 2. In Chapter 5, we state the refinement of Weil's theorem on rational points of algebraic curves and prove it. The second topic in the thesis is about simple zeros of Maass L-functions. We consider a Hecke Maass form $f$ for $SL(2,\Bbb Z)$. In Chapter 6, we show that if the L-function $L(s,f)$ has a non-trivial simple zero, it has infinitely many simple zeros. This result is an extension of the result of Conrey and Ghosh.

The main part of the thesis is applications of the Strong Artin conjecture to number theory. We have two applications. One is generating number fields with extreme class numbers. The other is generating extreme positive and negative values of Euler-Kronecker constants. For a given number field $K$ of degree $n$, let $\widehat{K}$ be the normal closure of $K$ with $Gal(\widehat{K}/\Bbb Q)=G.$ Let $Gal(\widehat{K}/K)=H$ for some subgroup $H$ of $G$. Then, $$ L(s,\rho,\widehat{K}/\Bbb Q)=\frac{\zeta_K(s)}{\zeta(s)} $$ where $Ind_H^G1_H = 1_G + \rho$. When $L(s,\rho)$ is an entire function and has a zero-free region $[\alpha,1] \times [-(\log N)^2, (\log N)^2]$ where $N$ is the conductor of $L(s,\rho)$, we can estimate $\log L(1,\rho)$ and $\frac{L'}{L}(1,\rho)$ as a sum over small primes: $$ \log L(1,\rho) = \sum_{p\leq(\log N)^{k}}\lambda(p)p^{-1} + O_{l,k,\alpha}(1)$$ $$ \frac{L'}{L}(1,\rho)=-\sum_{p\leq x} \frac{\lambda(p) \log{p}}{p} +O_{l,x,\alpha}(1). $$ where $0 < k < \frac{16}{1-\alpha}$ and $(\log N)^{\frac{16}{1-\alpha}} \leq x \leq N^{\frac{1}{4}}$. With these approximations, we can study extreme values of class numbers and Euler-Kronecker constants. Let $\frak{K}$ $(n,G,r_1,r_2)$ be the set of number fields of degree $n$ with signature $(r_1,r_2)$ whose normal closures are Galois $G$ extension over $\Bbb Q$. Let $f(x,t) \in \Bbb Z[t][x]$ be a parametric polynomial whose splitting field over $\Bbb Q (t)$ is a regular $G$ extension. By Cohen's theorem, most specialization $t\in \Bbb Z$ corresponds to a number field $K_t$ in $\frak{K}$ $(n,G,r_1,r_2)$ with signature $(r_1,r_2)$ and hence we have a family of Artin L-functions $L(s,\rho,t)$. By counting zeros of L-functions over this family, we can obtain L-functions with the zero-free region above. In Chapter 1, we collect the known cases for the Strong Artin conjecture and prove it for the cases of $G=A_4$ and $S_4$. We explain how to obtain the approximations of $\log (1,\rho)$ and $\frac{L'}{L}(1,\rho)$ as a sum over small primes in detail. We review the theorem of Kowalski-Michel on counting zeros of automorphic L-functions in a family. In Chapter 2, we exhibit many parametric polynomials giving rise to regular extensions. They contain the cases when $G=C_n,$ $3\leq n \leq 6$, $D_n$, $3\leq n \leq 5$, $A_4, A_5, S_4, S_5$ and $S_n$, $n \geq 2$. In Chapter 3, we construct number fields with extreme class numbers using the parametric polynomials in Chapter 2. In Chapter 4, We construct number fields with extreme Euler-Kronecker constants also using the parametric polynomials in Chapter 2. In Chapter 5, we state the refinement of Weil's theorem on rational points of algebraic curves and prove it. The second topic in the thesis is about simple zeros of Maass L-functions. We consider a Hecke Maass form $f$ for $SL(2,\Bbb Z)$. In Chapter 6, we show that if the L-function $L(s,f)$ has a non-trivial simple zero, it has infinitely many simple zeros. This result is an extension of the result of Conrey and Ghosh.

The purpose of this study was to examine whether the degree of discipline in social services may be the reason why more children are evicted in one municipality in Stockholm, compared to another. Since our purpose was to study the degree of discipline in social services work with eviction cases where children are concerned, discipline is therefore a central part of the study. The interest in the subject arose from our prior understanding that social services approach to discipline may affect the extent of evictions. In order to answer the study’s question at issue, a qualitative interview was conducted to create an understanding of the discipline and a vignette study was conducted to compare the social workers assessments in two municipalities in Stockholm, Högstad and Lågby. The study's interviews and vignette study was complemented with previous research related to the topic. The theoretical perspective was the basis for the analysis of the empirical study and consisted interconnection of theory by Michel Foucaults as well as Greta Marie Skaus and Erich Fromms perspective which helped us create a better understanding of the discipline in social services. In conclusion, we discussed thoughts and ideas that arose during the study and the results show, among other things, obvious elements of discipline in social services. Additional knowledge from the study contributed to increased understanding was in which way the social services approach to discipline affects their assessments in eviction cases where children are concerned.

A 4 bit, Rom-Less Direct Digital Frequency Synthesizer (DDFS) is designed in 65nm CMOS technology. Interleaving with Return-to-Zero (RTZ) technique is used to increase the output bandwidth and synthesized frequencies. The performance of the designed synthesizer is evaluated using Cadence Virtuoso design tool. With 3.2 GHz sampling frequency, the DDFS achieves the spurious-free dynamic range (SFDR) of 60 dB to 58 dB for synthesized frequencies between 200 MHz to 1.6 GHz. With 6.4 GHz sampling frequency, the synthesizer achieves the SFDR of 46 dB to 40 dB for synthesized frequencies between 400 MHz to 3.2 GHz. The power consumption is 80 mW for the designed mixed-signal blocks.

The smart dust concept is a fairly recent phenomenon to engineering. It assumes monitoring of a real natural environment in which motes or smart dust machines swarm in collective and coordinate information among themselves and/or to a backend control platform. In analog mixed signal field work on such devices is gaining momentum such that it is conceived to be one of the emerging fields in technology, and work was only possible once the technology for fabrication touched the nanoscale regions. Smart dust network involves remote devices connected in a hive sensing burst type datum signals from the environment and relaying information amongst themselves in an energy efficient manner to coordinate an appropriate response to a detected stimulus. The project presumed a RF based communication strategy for coordination amongst the devices through a wireless medium. That is less susceptible to stringent requirements of LOS and a base band processing system that comprised of an environment sensor, an AFE module, an ADC, a DSP and a DAC. Essentially a 10 bit, 2 Mega Hertz MHz pipelined ADC implemented in a STM 65nm technology. The ADC benefits the smart dust device in allowing it to process data in an energy efficient way and also focusing on reduced complexity as itsdesign feature. While it differs in the other ADC of the system by operating at a higher frequency and assuming a different design philosophy assuming a coherent system sensitive to a clock. The thesis work assumes that various features ofenergy harvesting, regulation and power management present in the smart dustmote would enable the system to contain such a diverse ADC. The ADCs output digital datum would be compatible to the rest of the design modules consisting mainly of DSP sections. The ADC novelty is based on the fact that it removes the necessity of employing a high power consuming OpAmp whose design parameters become more complex as technology scales to the nanoscale era and further down. A systematic, bottom up, test driven approach to design is utilized and various behaviours of the system are captured in Cadence design environment with verilogto layout models and MATLAB and Simulink models.

There have been proposals of many parity inducing techniques like Forward ErrorCorrection (FEC) which try to cope the problem of channel induced errors to alarge extent if not completely eradicate. The convolutional codes have been widelyidentified to be very efficient among the known channel coding techniques. Theprocess of decoding the convolutionally encoded data stream at the receiving nodecan be quite complex, time consuming and memory inefficient.This thesis outlines the implementation of multistandard soft decision viterbidecoder and word length effects on it. Classic Viterbi algorithm and its variantsoft decision viterbi algorithm, Zero-tail termination and Tail-Biting terminationfor the trellis are discussed. For the final implementation in C language, the "Zero-Tail Termination" approach with soft decision Viterbi decoding is adopted. Thismemory efficient implementation approach is flexible for any code rate and anyconstraint length.The results obtained are compared with MATLAB reference decoder. Simulationresults have been provided which show the performance of the decoderand reveal the interesting trade-off of finite word length with system performance.Such investigation can be very beneficial for the hardware design of communicationsystems. This is of high interest for Viterbi algorithm as convolutional codes havebeen selected in several famous standards like WiMAX, EDGE, IEEE 802.11a,GPRS, WCDMA, GSM, CDMA 2000 and 3GPP-LTE.

Studiens syfte är att undersöka hur det nationella målet för trafiksäkerhet går att följa upp på länsnivå via befintlig statistik från polis och sjukvård. Ger de två källorna en likartad bild av förändringen av antalet vägtrafikskadade under den gångna tjugoårsperioden? Undersök- ningen omfattar personer som skadats och överlevt vägtrafikolyckor i Västmanlands län. Data från 1989/1990 respektive 2008/2009 jämförs. De två statistikkällorna ger en likartad bild av förändringen av antalet vägtrafikskadade bilister, motorcyklister och mopedister. Skillnaderna är däremot stora beträffande gång- trafikanter och cyklister. Antalet skadade personer registrerade av sjukvården i länet har minskat under den studerade tidsperioden. Det beror på att antalet skadade gångtrafikanter och cyklister har blivit färre. På grund av förändringar inom sjukvården kan minskningen inte kvantifieras. Det lägre antalet frakturer, främst hos gångtrafikanter men även hos cyklister, visar att det varit en minskning. Antalet skadade bilister har däremot blivit fler, men de skadas lindrigare än 1989/1990. Gruppen allvarligt skadade bilister (ISS &gt; 8) har dock ökat. För perioden 1997 – 2009 har det inte funnits något nationellt definierat trafiksäkerhetsmål för allvarligt skadade. Enligt polisens statistik är antalet svårt skadade vägtrafikanter i länet oförändrat under perioden. Om allvarligt skadad i sjukvårdens mätning definieras som inlagd på sjukhus har antalet allvarligt skadade under perioden minskat med 27 %. Antalet allvarligt skadade definierat som ISS &gt; 8 är oförändrat. / The purpose of the study is to investigate the extent to which it is possible to make a follow- up on the regional level of the national road safety target by using existing police and hospital statistics. Do the two sources provide a similar picture of the changes of the number of persons injured in road traffic accidents during the past twenty years? The survey covers persons injured but survived in road accidents in the county of Västmanland. 2008/2009 figures are compared with 1989/1990 figures. Both sets of statistics provide a similar picture of the changes with regard to the number of injured motorists, motorcyclists and moped drivers. However, concerning pedestrians and cyclists there are significant differences. During the time period being studied, the number of injured persons registered by the hospitals of the county has decreased. This is due to the fact that the number of pedestrians and cyclists injured has decreased. However, it is due to structural changes of the health care difficult to quantify the reduction. The lower number fractures, primarily of pedestrians but also of cyclists, shows that there has been a decrease. On the contrary, the number of injured motorists has increased, but their injuries are less serious than in 1989/1990. However, the number of those motorists with serious injuries (ISS &gt; 8) has increased. For the period 1997 – 2009 there has not had an established national target for the number of seriously injured. According to police statistics, the number of severely injured road users in the county has remained unchanged during the time period being studied. If those being hospitalized in the medical statistics are defined as seriously injured, the number of seriously injured has decreased with 27 %. However, if seriously injured is defined as those with ISS &gt; 8, the number has remained unchanged.