On Arithmetic Progressions and Perfect Powers

In this thesis we will consider the problems that occur at the intersection of arithmetic progressions and perfect powers. In particular we will study the Erd˝os-Selfridge curves, By^l = x(x + d). . .(x + (k − 1)d), and sums of powers of arithmetic progressions, in particular y ^l = (x−d)^3+x^3+ (x+d)^3 . We shall study these curves using aspects of algebraic and analytic number theory. To all the equations studied we shall show that a putative solution gives rise to solutions of (potentially many) Fermat equations. In the case of Erd˝os-Selfridge curves we will use the modular method to understand the prime divisors of d for large `. Then we shall attach Dirichlet characters to such solutions, which allows us to use analytic methods regarding bounds on the value of sums of characters. These bounds will allow us to show that there can’t be too many simultaneous solutions to the Fermat equations we described. This leads to a contradiction for large k, as the number of Fermat equations generated will grow faster than the possible number of simultaneous solutions. We study the arithmetic progression curves by attaching Fermat equations of signature (l, l, 2). We then use the classical modular method to attach Frey-Hellegouarch curves and level lowered modular forms. It is possible to show that the Frey-Hellegouarch curves that associate to modular forms in a non-trivial cuspidal newspace are all quadratic twists of each other. It is then possible to compute if there are modular forms of the right level that could associate to such a twist of an elliptic curve

Multi-list Food Recommender Systems for Healthier Choices

Recipe websites are a popular destination for home cooks to discover new recipes and find what to cook. However, the most popular way of recommending recipes to users is trough similarity and popularity-based recommendations, which previous research has shown tend to be unhealthy. Building upon knowledge on how diverse sets of options increases satisfaction, this thesis investigates whether a multi-list recommender interface can support healthier food choices compared to traditional single-list interfaces, as well as increase choice satisfaction. As diverse set of options may introduce choice overload to users, explanations were investigated in terms of how they affect user evaluation with regards to choice difficulty, perceived diversity and understandability. A developed recommender system was used in a online study (N = 366), where users could select recipes from recommendations, as well as answering short questionnaires regarding their choices. The analysis showed that a multi-list recommender system was not able to support healthier food choices. However, users who interacted with the multi-list interface found it more satisfactory compared to single-list users. No significant evidence was found that explanations could mitigate choice difficulty. This thesis provides novel work on the utilization of multi-list recommender systems with explanations in the food recommender domain, which can further be expanded with considering other factors such including personalized recommendations in the multi-list interface.Masteroppgave i informasjonsvitenskapINFO390MASV-INF

From creationism to economics : how far should analyses of pseudoscience extend?

Both the scientific and philosophical problems with classic pseudosciences such as astrology and creationism are well known, leading to institutions that are not structured to promote cognitive advancement. A focus on institutions, however, also encourages recognition of gray areas, such as parapsychology, which combines scientifically dubious claims with institutions that are comparable to most social sciences in their structure. Furthermore, institutional approaches to pseudoscience also raise questions about some academically mainstream fields such as economics. In such cases, pseudoscientific aspects of practice are harder to identify, highlighting the need to place analyses of pseudoscience in a wider context of institutional pathologies

Importance of using high test voltage for transformer turns ratio test

The transformer turns ratio test is one of the fundamental routine tests for transformer inspection. This test is used as an indicator of various problems with the transformer windings, such as shorted turns. According to international standards, the pass / fail criterion for turns ratio deviations is ± 0.5 %. This places high demands on the accuracy of the test devices. The measurement accuracy depends on the test device accuracy and test voltage applied. A higher test voltage applied to the high voltage (HV) transformer side will induce a higher voltage on the low voltage (LV) side, providing a more accurate measurement. Also, higher test voltage will result in higher transformer saturation, leading to more accurate results. The relation between test voltage and accuracy will be elaborated, and the implications for the turns ratio test will be discussed. Case studies that support the importance of using the higher test voltage when the transformer turns ratio test is performed will be presented as well

Is There A Political Argument For Teaching Evolution?

This essay develops my keynote address on the topic of creationism and science education, delivered at the conference Religions, Science and Technology in Cultural Contexts: Dynamics of Change, NTNU, Trondheim (2012). Debates over evolution in science education take place in a political context where liberal and conservative visions about the purpose of education come into conflict. Comparing the history of creationist pressures on science education in the United States and Turkey highlights the broad contours of these competing visions. The current conservative ascendancy in both countries, however, makes it difficult to reach any consensus on the practical benefits of including evolution in mass science education. This paper is one of a collection that originated in the IAHR Special Conference “Religions, Science and Technology in Cultural Contexts:  Dynamics of Change”, held at The Norwegian University of Science and Technology on March 1–2, 2012. For an overall introduction see the article by Ulrika Mårtensson, also published here. &nbsp

Tinjauan hukum ekonomi syariah terhadap jual beli mata uang rupiah kuno di Alun-Alun Bandung

Di zaman dekarang ini terdapat cara yang menarik perhatian masyarakat dalam bisnis, itu untuk sekedar mencari keuntungan hingga hal-hal yang bersifat kepuasan. Salah satu bisnis yang sekarang diminati adalah bisnis jual beli mata uang rupiah kuno, salah satunya di Alun-Alun Bandung. Menariknya dalam transaksi tersebut mata uang rupiah kuno bisa dinilai dengan harga yang mahal. Meskipun demikian, ternyata banyak orang-orang yang mencari barang tersebut baik dari kalangan para pedagang sendiri, hal inilah yang melatar belakangi penelitian ini yakni. Penetapan harga secara tinggi tetapi diminati oleh masyarakat secara umum. Penelitian ini bertujuan untuk mengetahui (1) cara pedagang dalam menentukan harga jual beli mata uang rupiah kuno di Alun-Alun Bandung. (2) dan untuk mengetahui mengenai landasan hukum jual beli mata uang rupiah kuno di Alun-Alun Bandung. Serta (3) mengetahui kedudukan hokum jual beli mata uang rupiah kuno di Alun-Alun Bandung. Penelitian ini dilakukan dengan menggunakan metode deskriptif, Karena hal ini benar-benar terjadi dikalangan masyarakat Alun-Alun Bandung. Pengambilan data dilakukan dengan menggunakan teknik observasi dan data wawancara kepada beberapa narasumber yaitu penjual dan pembeli (kolektor) yang terlibat langsung di dalam proses jual beli mata uang rupiah kuno. Hasil penelitian yang diperoleh dalam penelitian ini dapat diketahui bahwa dalam penentuan harga jual beli mata uang rupiah kuno punya kriteria tersendiri, dilihat dari tingkat kerusakan yang dimiliki uang tersebut, kualitas uang, ketersediaan barang, dari katalog uangnya, tahun cetakan, dan jenis seri uang kuno tersebut. Maka dari itu dari penentuan harga mata uang kuno ini sesuai dengan aturan islam, dilihat dari landasan hokum yang dilakukan oleh penjual dan pembeli adalah dilihat dari objek jual beli, ijab qabulnya terlaksana serta cara membayarnya pun dilakukan dengan kesepakatan antara penjual dan pembeli, begitupun dengan kedudukan hokum pada jual beli mata uang kuno ini dilakukan sesuai dengan rukun dan syarat yang berlaku, begitupun dengan penentuan harga, penentuan harga ini dipandang sah dengan mengacu pada factor yang mempengaruhi penentuan harga yang tercatat dalam fatwa Ibn Taimiyah

Acceleration of LV winding resistance measurement

The winding resistance measurement requires extended time. According to IEC 60076-1 and IEEE C57.12.90 standards, the test should be performed using DC test current on all phases of the high voltage, low voltage, and tertiary sides, and for all tap positions. Speeding up this measurement is very attractive. This paper presents two approaches to transformer saturation: increasing the test current, and a special connection of the windings to increase the number of turns. The presented case study shows the difference between the regular test procedure and a modified one