Karnaugh map analysis and synthesis of threshold functions

A unate function can easily be identified on a Karnaugh map from the well-known property that it cons ist s only ofess en ti al prime implicante which intersect at a common implicant. The additional property that the plot of a unate function F(x, ... XII) on a Karnaugh map should possess in order that F may also be Ivrealizable (n';:; 6) has been found. It has been sh own that the I- realizability of a unate function F corresponds to the ' compac tness' of the plot of F. No resort to tho inequalities is made, and no pre-processing such as positivizing and ordering of the given function is required.

Vähemmistövaltiokirkon synty : Ortodoksisen kirkkokunnan ja valtion suhteiden muotoutuminen Suomessa 1917-1922

The Birth of the Minority State Church Development of the legal relationship between the state of Finland and the Finnish Orthodox Church 1917 1922 Mika Nokelainen, University of Helsinki, Finland. The present research seeks to explain how the legal relationship developed between the state of Finland and the Orthodox Church of Finland. The main focus is on three statutes: 1) the Statute of the Orthodox Church in Finland as stated by Prime Minister J. K. Paasikivi s cabinet in November 1918, 2) The Republican Constitution of July 1919 and 3) The Freedom of Religion Act of 1923. This study examines how different political goals influenced the three statutes mentioned above. Another important factor that is taken into account is the attitude of the Lutheran Church of Finland, the church of the national majority, towards the Orthodox minority and its judicial position in the country. Finland became independent in December 1917, in the aftermath of the November Revolution in Russia. The Orthodox Church already had hundreds of years of history in Finland. In the 19th century, several statutes by emperors of Russia had made the Orthodox Church an official state church of Finland. Due to the long history of the Orthodox Church in Finland, Prime Minister Paasikivi s cabinet made the decision to support the church in the spring of 1918. Furthermore, the cabinet s goal to occupy East Karelia increased its willingness to support the church. The Finnish-national Orthodox Church was needed to educate the East-Karelians. A new statute on the Orthodox Church in Finland came into force in November 1918, reorganising the administration, economy and legal relationship between the church and state in Finland. With this statue, the cabinet gained some authority over the church. Sections of this statute made possible, for example, the cabinet s interference in the internal affairs of the church. The Republican Constitution of 1919 included the principle of freedom of religion. The state, which previously had been Lutheran, now became non-denominational. However, the Republican Constitution explicitly mentioned the Lutheran as well as the Orthodox Church, which indirectly confirmed the position of the Orthodox Church as the second state church of Finland. This position was finally confirmed by the Freedom of Religion Act in 1923. In general, the Lutheran Church of Finland did not resist the judicial position of the Orthodox Church. However, some Lutherans regarded the Orthodox Church with suspicion because of its intimate connection with Russia.

Rakkauden välittäjä vai moraalinvartija : Narratiivinen tutkimus Suomen evankelis-luterilaisen kirkon papeista perhe- ja seksuaalikysymysten äärellä

The research goal was to clarify how ministers in the Evangelical Lutheran Church of Finland construct their identities when they confront family and sexual issues, particularly as seen in their narrations about their work and the factors that influence their ways of working. The approach was a narrative one placing the emphases was on the internal story. The research material consisted of interviews of 19 ministers and the written biographies of 3 ministers who had also been interviewed. The data was analysed narratively (analysis of the narrations and a narrative analysis). The life stories were classified on the basis of the logic in each, and five different internal story types were created: the persons on the road to recovery, those within safe boundaries, those who had learnt to be critical, those with an obligation to help, and those who had grown to be open. In all of the story types was evidented a conflict between the ministry of the Church and the way it was adapted to the lives of individuals experiencing family and sexual issues. On one hand, this was a source of stress at work, but on the other, it offered a chance to create new images of ministers struggling with family and sexual issues. Life experience was found to be important when the study subjects interpreted and dealt with family and sexual issues. Those on the road to recovery felt that becoming a Christian and the personal recovery that faith had made possible had a significant impact on their personal lives. This healing effect of faith was also a strengthening factor for them when they dealt with family and sexual issues. Typically, they approached work situations by taking into account their faith and the type of psychological knowledge that was acceptable within the boundaries set by it. Those within safe boundaries worked within the limits prescribed by the revivalist movement that they had grown up in, from their childhood onwards, and their experiences in adulthood had even strengthened their commitment to the movement. Typically, they were keen to proclaim the views of the movement in public, but they were also prone to stay silent if and when felt those views would cause an uproar. Those who had learnt to be critical had previously been holistically committed to the views expressed by the Church in family and sexual matters. It was their experiences in life that had led them into conflict with the teachings of the Church. Their approach to work was one of ambivalence resulting from a conflict between their current and previous views, which was further exacerbated by their irresolution concerning how a minister should act in these situations. Those with an obligation to help questioned the church teachings marriage as the only family ideal. When they met various kinds of families and sexual identities, and also when they adopted the identity of a helper, the foundation of their ministerial identity was the Two Commandments of Love. Their work was burdened, however, by a fear of how the Church and the parishioners would take their teaching. Those who had grown to be open were more sure of themselves than the other groups. Years in the ministry as well as life-long experience had made them into persons who were following paths of their own. Openly critical of the views on family and sexual issues proclaimed by the Church, they were keen to present their personal convictions and were able to defend these publicly when necessary. Search words: Narrative research, internal story, minister, church, family, sexuality.

Educating to secure the national interest

In this paper I examine how one political actor–former Prime Minister Kevin Rudd–proposes to use education for the purpose of securing national productivity and foreign policy. I work with Foucault’s suggestion that the apparatus of security is the essential technical instrument of governmentality and that the production of milieu, made up of human, spatial, temporal and cultural objects, and the government of risk are key strategies in the bio-politicisation of security. The discourse analysis also draws on Bacchi to problematise statements that (a) represent both the nation and regional neighbours as governable milieu within the ambit of a whole of government approach, and (b) locate literacy and education as both risk and solution in a security apparatus. My examination of the emergence of literacy and education as security technologies, takes account of the discursive effects of Rudd’s representation of the spaces and scale of national, geopolitical and global policy problems. I argue that in these examples of policy texts, education is used as a discursive tool to secure education workers and youth as subjects of economic interest and sovereign rule.

Reed-Muller Canonical Forms in Multivalued Logic

Canonical forms for m-valued functions referred to as m-Reed-Muller canonical (m-RMC) forms that are a generalization of RMC forms of two-valued functions are proposed. m-RMC forms are based on the operations ?m (addition mod m) and .m (multiplication mod m) and do not, as in the cases of the generalizations proposed in the literature, require an m-valued function for m not a power of a prime, to be expressed by a canonical form for M-valued functions, where M > m is a power of a prime. Methods of obtaining the m-RMC forms from the truth vector or the sum of products representation of an m-valued function are discussed. Using a generalization of the Boolean difference to m-valued logic, series expansions for m-valued functions are derived.

Digital revolution or digital divide: Will rural teachers get a piece of the professional development pie?

In order to sustain the rural education community, access to high quality professional development opportunities must become a priority. Teachers in rural areas face many challenges in order to access professional learning equitable to their city counterparts. In the current climate, the Federal government of Australia is committed to initiatives that support the use of ICT in education. These include initiatives such as the Digital Education Revolution, including the National Broadband Network. This "revolution" includes the committal of $2.2 billion funding over six years from 2008 - 2013 which purports to bring substantial and meaningful change to teaching and learning in Australian schools. Of this funding, the Prime Minister (former Minister for Education), Julia Gillard, has committed $40 million of the total budget to ICT related professional development for teachers. But how will rural teachers ensure they get a piece of the PD pie? Access to professional learning is critical and isolation from colleagues, professional associations and support structures can affect the retention of teachers and in turn affect the sustainability of rural communities. This research paper describes the findings of the first phase of a study that investigates access to professional learning from rural and remote areas of Western Australia, the efficiencies of this approach including teacher perceptions and possible opportunities for improvement through the application of technologies. A survey instrument was administered and the results from104 principals and teachers within the Remote Teaching Service and the Country Teaching Program of the Department of Education and Training (WA) are discussed. Qualitative data was collected by semi-structured interviews and emailed questionnaires. Phase One findings highlight the principals and teachers? perceptions of their access to professional development opportunities, professional learning communities and their use of information and communication technologies (ICT) to bridge the gap