Doctor of Philosophy / Department of Mathematics / Christopher G. Pinner / For a fixed integer n ≥ 2, we show that a permutation of the least residues mod p of the form f(x) = Ax[superscript k] mod p cannot map a residue class mod n to just one residue class mod n once p is sufficiently large, other than the maps f(x) = ±x mod p when n is even and f(x) = ±x or ±x [superscript (p+1)/2] mod p when n is odd. We also show that for fixed n the image of each residue class mod n contains every residue class mod n, except for a bounded number of maps for each p, namely those with (k −1, p−1) > (p−1)/1.6n⁴ and A from a readily described set of size less than 1.6n⁴. For n > 2 we give O(n²) examples of f(x) where the image of one of the residue classes mod n does miss at least one residue class mod n.

Pits and mounds in pebble: A study of archaeological remains in ancient pebble beaches inthe county of Västerbotten. Pits (Sw. boplatsgropar) and mounds (Sw. boplatsvallar) in ancient pebble beaches are two types of archaeological remains that are common under the highest coastline in the county of Västerbotten, Sweden. Although common, knowledge of these archaeological remains is limited. Organic materials left in pebble formations rapidly break down and degrade due to high exposure to moisture and weather, making dating by traditional archaeological methods such as 14C or dendrochronology impossible. The data for this study consists of two parts. One part has been collected through field surveys by the author and the other part is collected from National Heritage Board´s database of archaeological sites (Sw. Riksantikvarieämbetets kulturmiljöregister). The result of this study suggests that the majority of smaller pits and mounds in ancient pebble beaches have been used for storage and that larger pits and mounds are big enough to have functioned as foundations for simple dwellings. It also suggests there is some spatial coherence between the type of archaeological remains known as hut foundations (Sw.tomtningar) and pits in ancient pebble beaches. Albeit this coherence is slight and may be a coincidence. Furthermore, the study suggests there is a spatial coherence between quartz and quartzite handled by humans and pits in ancient pebble beaches that is not a coincidence. Suggestively, some pits in ancient pebble beaches that can be found today have been made and used in prehistoric times, by people who used quartz and quartzite in their daily lives.

This thesis is the study of televangelism contextualized within the country of Romania. It seeks to answer six main questions: I} When the Lord Jesus gave Christendom the global, Gospel mandate, he forced his disciples into a two thousand year struggle with, not only the message, but how to spread this message. Is the Gospel message so powerful that it will penetrate through any method of delivery? Can a former communist country be evangelized through television? 2) The next question asked in this thesis: is the message in and of itself, when conveyed through this media, sufficient to accomplish its goals? Does the media encourage the recipient to fulfill the desires of the message? What about Mass Communication Theory which espouses that television is more likely to reinforce then transform a viewer's belief? 3) The third question wrestled with: would the former communistic country of Romania, when turning to the ideals of the West, receive the Gospel message with greater or lesser significance through the media of television, or would other forms of communication be more desirable? Would television, in comparison to Crusade or Film Evangelism, be a more ideal media for the Gospel at this juncture in Romania's history? 4) Television allows large audiences to be reached with staggering efficiency, but does the medium itself impose limits on the kind of evangelism that can be done? What type of church grows out of an electronic medium? Would television gather a church "unto itself?" 5) In fulfilling the great commission, many organizations and mission groups have arisen with the desire to carry the Gospel message to the ends of the earth with whatever means available, including CBN, who uses television. Can television reach the masses, including the poor, in Eastern block countries? 6) The final question addressed in this research: what are the long term effects of televangelism in this former communistic country? Would a one time television program, given in one week, yield results that can be determined two years later? These questions were not only wrestled with, but conclusions were drawn to make evangelism and particularly televangelism more efficacious. / Philosophy, Practical & Systematic Theology / Th. D. (Practical Theology)

This thesis is the study of televangelism contextualized within the country of Romania. It seeks to answer six main questions: I} When the Lord Jesus gave Christendom the global, Gospel mandate, he forced his disciples into a two thousand year struggle with, not only the message, but how to spread this message. Is the Gospel message so powerful that it will penetrate through any method of delivery? Can a former communist country be evangelized through television? 2) The next question asked in this thesis: is the message in and of itself, when conveyed through this media, sufficient to accomplish its goals? Does the media encourage the recipient to fulfill the desires of the message? What about Mass Communication Theory which espouses that television is more likely to reinforce then transform a viewer's belief? 3) The third question wrestled with: would the former communistic country of Romania, when turning to the ideals of the West, receive the Gospel message with greater or lesser significance through the media of television, or would other forms of communication be more desirable? Would television, in comparison to Crusade or Film Evangelism, be a more ideal media for the Gospel at this juncture in Romania's history? 4) Television allows large audiences to be reached with staggering efficiency, but does the medium itself impose limits on the kind of evangelism that can be done? What type of church grows out of an electronic medium? Would television gather a church "unto itself?" 5) In fulfilling the great commission, many organizations and mission groups have arisen with the desire to carry the Gospel message to the ends of the earth with whatever means available, including CBN, who uses television. Can television reach the masses, including the poor, in Eastern block countries? 6) The final question addressed in this research: what are the long term effects of televangelism in this former communistic country? Would a one time television program, given in one week, yield results that can be determined two years later? These questions were not only wrestled with, but conclusions were drawn to make evangelism and particularly televangelism more efficacious. / Philosophy, Practical and Systematic Theology / Th. D. (Practical Theology)