Peg Solitaire on Graphs In Which We Allow Merging and Jumping

Peg solitaire is a game in which pegs are placed in every hole but one and the player jumps over pegs along rows or columns to remove them. Usually, the goal of the player is to leave only one peg. In a 2011 paper, this game is generalized to graphs. In this thesis, we consider a variation of peg solitaire on graphs in which pegs can be removed either by jumping them or merging them together. To motivate this, we survey some of the previous papers in the literature. We then determine the solvability of several classes of graphs including stars and double stars, caterpillars, trees of small diameter, particularly four and five, and articulated caterpillars. We conclude this thesis with several open problems related to this study

Winnability of The Group Labeling Lights Out Game on Complete Bipartite Graphs

For an arbitrary graph, we can play Lights Out on it if we assign a number label to each of the vertices of a graph G, representing states of on/off in the original Lights Out game, with the edges connecting those vertices representing the buttons that are adjacent to each other. This project is focused on a slightly modifed version of the game\u27s original rules, with the labels for the vertices coming from the group Zn. It is not always possible to win the game. We will be investigating the values of n for which this group labeling Lights Out! game is always winnable when played on complete bipartite graphs

2006 Annual Research Symposium Abstract Book

2006 annual volume of abstracts for science research projects conducted by students at Trinity College

Assessment for Learning in EBE/CLIL : a learning-oriented approach to assessing English language skills and curriculum content at early primary level

Assessment is usually viewed as an inevitable event in teachers' and learners’ lives resulting from an imposition from education systems. However, if done well, assessment can provide learners, teachers and other stakeholders with sound information about learner performance and progress which will ultimately boost learning and feed into school success. This project work discusses ways of assessing both English language and curriculum content at early primary level and aims to provide learning-oriented guidelines and a principled framework for such assessment. It is meant for learners and teachers involved in Early Bilingual Education/Content and Language Integrated Learning at early primary level.A avaliação é comummente vista como um acontecimento inevitável na vida dos alunos e dos professores, resultante de uma imposição dos sistemas de ensino. No entanto, se bem conduzida, a avaliação pode, de forma eficaz, informar alunos, professores e outros atores, sobre o desempenho e o progresso do aluno, o que acabará por promover a aprendizagem e contribuir para o sucesso escolar. O presente trabalho de projeto discute formas de avaliar a língua inglesa e os conteúdos curriculares no 1.º ciclo do ensino básico e tem como objetivo fornecer recomendações orientadas para a aprendizagem, bem como um referencial para essa avaliação. Este trabalho tem como destinatários alunos e professores envolvidos num contexto de ensino bilingue precoce/aprendizagem integrada de conteúdos curriculares e língua no 1.º ciclo do ensino básico

An appraisal of the physical environmental quality of the Selebi Phikwe Ni-Cu mine area, South-Eastern

ThesisThis research project focused on the environmental impact of mining and smelting nickel-copper (Ni-Cu) at the Selebi Phikwe area, south-eastern Botswana. Physico-chemical properties, mineralogical identification and characterisation, and heavy metals concentrations of elements for samples of tailings dump, soils, particulate air matter (PAM), Colophospermum mopane (mopane plant), and Imbrasia belina (phane caterpillar) were investigated. Physico-chemical properties studied on tailings dump and soil samples included soil texture and colour, particle size distribution (PSD), pH, electrical conductivity (EC), cation exchange capacity (CEC) and descriptive petrography. Identification and characterisation of minerals contained in tailings dump, soil, and PAM samples were performed employing X-ray powder diffraction (XRPD) techniques which included clay size and heavy minerals fractionation. Chemical analyses for heavy metals (cadmium, Cd; cobalt, Co; chromium, Cr; nickel, Ni and selenium, Se) concentrations in tail ings dump, soils, PAM, mopane leaves and phane caterpillar were measured with a graphite furnace atomic absorption spectrometer (GFAAS) whereas the flame atomic absorption spectrometer (FAAS) measured copper, Cu; iron, Fe and zinc, Zn concentration levels. The clay and silt soil components made up to 50 wt % of soil. Very acidic soils were located close to the smelter/concentrator plant, and both soil EC and CEC va lues were significantly low. Physical tests revealed albite, NaAISi30 s; cristobalite, a- Si02; chalcopyrite, CuFeS2; pyrrhotite, Fe1_xS; tremolite, Ca2MgsSis022(OHh; and pentlandite, (Fe,Ni)9Ss; to be contained in tailings dump. Soil colour varied from pale yellow, reddish yellow to dark reddish brown. The tailings dump comprised of nickelbloedite, Na2(Ni(S04h.4H20; pyrrhotite; quartz, Si02; pentlandite; malachite,Cu2C03(OHh; chalcopyrite; actinolite, Ca2(Mg,Fe)sSis022(OHh; cristobalite; tremolite; kaolinite, AI2SbOs(OH)4; mica and albite. The PAM consisted of quartz, Si02; pyrrhotite; chalcopyrite, CuFeS2; albite, and djurleite, CU31 S16. Bulk soil samples consisted of actinolite, albite, quartz, microciine, KAISi30 s; pyrrhotite, silicon sulphide, SiS; and cobalt oxide, CoO whereas the < 2 f.In fraction was made of kaolinite, smectite, Nao.3(AI,MghSi4010(OH)2.xH20; anorthite, CaAI2Si20 s; illite, KAI2(Si~1010)(OH)2 and quartz. Ojurleite polymorphs (CU31S16 and CU193S) were formed from secondary mineralisation of chalcopyrite and the S02 released from concentration/smelting processes. Ambient temperature and an acidic milieu created favourable conditions for the formation of nickelblodite and malachite from the primary ore minerals: pentlandite, chalcopyrite and pyrrhotite in tailings dump. Cobalt oxide and silicon sulphide identified in surface soils were indicative of environmental chemical alteration of mining waste deposited on surface soils. High concentrations of heavy metals recorded in different environmental media had affected the physical environmental quality at Selebi Phikwe. Heavy metals including Cd, Co, Cr, Cu, Fe, Ni, Se and Zn, which are deleterious to the environment, and pose as health hazards to humanbeings, were associated with these minerals. Contamination of waterbodies around Selebi Phikwe might have been possible by the heavy ions in solution. Consumption of stunted phane might pose as health hazard. In overcoming pollution problems at Selebi Phikwe, aspects of pollution management such as phytoremediation and phytomining, environmental desulphurisation, phytostabilisation, and biotechnology could be introduced as pollution control measures

Town of Peterborough, New Hampshire 2017 annual reports of the officials, departments, and committees of the town for the calendar year ending December 31, 2017.

This is an annual report containing vital statistics for a town/city in the state of New Hampshire