The document provides an analytical summary of Cambodia's solar energy policy for NRG Solutions. It finds that while political barriers exist, the potential for distributed solar growth in coming years provides an opportunity if public and private stakeholders cooperate. It outlines Cambodia's solar goals and policy actors like the Ministry of Mines and Energy. Recommendations include NRG Solutions working with other solar companies to promote shared goals and establish scheduled policy reviews to assess impacts and opportunities.
Chessboard Puzzles Part 4 - Other Surfaces and VariationsDan Freeman
This document summarizes Dan Freeman's presentation on chessboard puzzles involving surfaces other than the standard chessboard. It discusses knight's tours, domination numbers, and other concepts on toroidal, cylindrical, Klein bottle, and Mobius strip surfaces. Key results include every rectangular board having a closed knight's tour on a torus, formulas for domination numbers of various pieces on these surfaces, and examples of puzzles on different board geometries.
Chessboard Puzzles Part 2 - IndependenceDan Freeman
This document is part 2 of a 4-part series on the mathematics of chessboard puzzles. It examines the concept of independence among different chess pieces on a chessboard, which is defined as the maximum number of pieces that can be placed without any attacking each other. Formulas for the independence number are derived for rooks, bishops, kings, and knights on both square and rectangular boards. The 8-queens problem and its generalization to n-queens are also discussed. Proofs are provided for many of the independence numbers and permutation counts.
This document discusses domination numbers in chessboard puzzles. It defines domination as a set of pieces covering every square or attacking every square. Formulas are given for the domination numbers of rooks, bishops, and kings on an nxn board. For queens and knights, only specific values and bounds have been determined due to greater complexity. The movement rules for each piece are also outlined.
Chessboard Puzzles Part 2 - IndependenceDan Freeman
This document summarizes key concepts related to independence in chessboard puzzles. It defines independence as pieces not attacking each other and introduces independence numbers to represent the maximum independent pieces on a board. Formulas are provided for the independence numbers of different chess pieces, including rooks (n), bishops (2n-2), kings (└1⁄2(n+1)┘), and queens (n). The document also discusses permutations of independent pieces and solutions to the n-queens problem.
The document provides an analytical summary of Cambodia's solar energy policy for NRG Solutions. It finds that while political barriers exist, the potential for distributed solar growth in coming years provides an opportunity if public and private stakeholders cooperate. It outlines Cambodia's solar goals and policy actors like the Ministry of Mines and Energy. Recommendations include NRG Solutions working with other solar companies to promote shared goals and establish scheduled policy reviews to assess impacts and opportunities.
Chessboard Puzzles Part 4 - Other Surfaces and VariationsDan Freeman
This document summarizes Dan Freeman's presentation on chessboard puzzles involving surfaces other than the standard chessboard. It discusses knight's tours, domination numbers, and other concepts on toroidal, cylindrical, Klein bottle, and Mobius strip surfaces. Key results include every rectangular board having a closed knight's tour on a torus, formulas for domination numbers of various pieces on these surfaces, and examples of puzzles on different board geometries.
Chessboard Puzzles Part 2 - IndependenceDan Freeman
This document is part 2 of a 4-part series on the mathematics of chessboard puzzles. It examines the concept of independence among different chess pieces on a chessboard, which is defined as the maximum number of pieces that can be placed without any attacking each other. Formulas for the independence number are derived for rooks, bishops, kings, and knights on both square and rectangular boards. The 8-queens problem and its generalization to n-queens are also discussed. Proofs are provided for many of the independence numbers and permutation counts.
This document discusses domination numbers in chessboard puzzles. It defines domination as a set of pieces covering every square or attacking every square. Formulas are given for the domination numbers of rooks, bishops, and kings on an nxn board. For queens and knights, only specific values and bounds have been determined due to greater complexity. The movement rules for each piece are also outlined.
Chessboard Puzzles Part 2 - IndependenceDan Freeman
This document summarizes key concepts related to independence in chessboard puzzles. It defines independence as pieces not attacking each other and introduces independence numbers to represent the maximum independent pieces on a board. Formulas are provided for the independence numbers of different chess pieces, including rooks (n), bishops (2n-2), kings (└1⁄2(n+1)┘), and queens (n). The document also discusses permutations of independent pieces and solutions to the n-queens problem.
This document describes a chess variant called Hex Chess that is played on a board with an hexagonal shape containing 96 equilateral triangles. It summarizes the movements of the different pieces, which generally follow standard chess movements but adapted to the triangular geometry. It also discusses the development of distance formulas specific to this variant to calculate distances traveled by kings, queens, and potentially other pieces. Finally, it outlines some open problems for further developing and analyzing the geometry and rules of Hex Chess.
This document is the first part of a 4-part series on the mathematics of chessboard domination. It introduces the concept of domination and covers domination numbers for various chess pieces including rooks, bishops, kings, knights, and queens on square and rectangular chessboards. For rooks and bishops, the domination number on an nxn board is simply n. For kings, the number increases as the square of the number of rows/columns needed to cover the board. Knights and queens domination numbers are more complex with no known closed-form formulas.
Chessboard Puzzles Part 3 - Knight's TourDan Freeman
This document summarizes research on knight's tours on chessboards. It defines closed and open knight's tours, provides examples of tours on boards of different sizes, and discusses some related topics like magic squares, Latin squares, and the mathematical proofs investigating the existence of tours on certain board sizes. It also cites several sources for further information on knight's tour puzzles and combinatorics.
Chessboard Puzzles Part 3 - Knight's TourDan Freeman
This document discusses knight's tours on chessboards. It defines closed and open knight's tours, and provides examples of each on various board sizes. Closed tours end where they start, while open tours can end anywhere. The document also discusses theorems about knight's tours and how they can be used to construct magic squares and Latin squares, showing relationships between knight's tours and other mathematical structures.
This document summarizes the dewatering and aquifer modeling for the Barrick Cortez Hills Underground Mine. It describes the complex geology of the area including multiple aquifers. Piezometer data from 2009-2015 was used to create contour maps of the potentiometric surfaces over time, showing up to an 11 foot per month drop in the cones of depression around production wells. Mining within the cone of depression risks rebound of water levels. Additional underground pumping wells are proposed to better dewater areas and mitigate this risk, allowing more flexible mining.
This document discusses creativity in teaching. It suggests that traditional education should be changed to focus on thinking, ideas, critical capacity and creativity. This can be achieved through didactic games, creative games, art, culture and technology. These methods can help improve the organization of teaching, motivate students, and encourage interest and love of learning. Specifically, it recommends exposing students to other cultures, using technology to engage them, and providing art and workshops, as well as educational excursions and visits.
Future of Financial Services - Banking on Innovation - Final PaperJohn Fearn
This document discusses the political barriers to innovative financial services. It argues that while radical change in any sector poses challenges for politicians and regulators, the pace of financial innovation is leaving policymakers behind. It analyzes the political reputations of alternative finance providers, payments services, and high street banks to identify the challenges these firms face in influencing regulation. The document predicts that in the near future, most transactions will be digital, mobile payments will increase, and banking services will fragment across new providers, with 20% of lending from alternative sources. It argues that widespread mobile adoption and the 2007-2009 financial crisis have enabled this radical change by shifting consumer habits and eroding trust in large banks.
This document describes a chess variant called Hex Chess that is played on a board with an hexagonal shape containing 96 equilateral triangles. It summarizes the movements of the different pieces, which generally follow standard chess movements but adapted to the triangular geometry. It also discusses the development of distance formulas specific to this variant to calculate distances traveled by kings, queens, and potentially other pieces. Finally, it outlines some open problems for further developing and analyzing the geometry and rules of Hex Chess.
This document is the first part of a 4-part series on the mathematics of chessboard domination. It introduces the concept of domination and covers domination numbers for various chess pieces including rooks, bishops, kings, knights, and queens on square and rectangular chessboards. For rooks and bishops, the domination number on an nxn board is simply n. For kings, the number increases as the square of the number of rows/columns needed to cover the board. Knights and queens domination numbers are more complex with no known closed-form formulas.
Chessboard Puzzles Part 3 - Knight's TourDan Freeman
This document summarizes research on knight's tours on chessboards. It defines closed and open knight's tours, provides examples of tours on boards of different sizes, and discusses some related topics like magic squares, Latin squares, and the mathematical proofs investigating the existence of tours on certain board sizes. It also cites several sources for further information on knight's tour puzzles and combinatorics.
Chessboard Puzzles Part 3 - Knight's TourDan Freeman
This document discusses knight's tours on chessboards. It defines closed and open knight's tours, and provides examples of each on various board sizes. Closed tours end where they start, while open tours can end anywhere. The document also discusses theorems about knight's tours and how they can be used to construct magic squares and Latin squares, showing relationships between knight's tours and other mathematical structures.
This document summarizes the dewatering and aquifer modeling for the Barrick Cortez Hills Underground Mine. It describes the complex geology of the area including multiple aquifers. Piezometer data from 2009-2015 was used to create contour maps of the potentiometric surfaces over time, showing up to an 11 foot per month drop in the cones of depression around production wells. Mining within the cone of depression risks rebound of water levels. Additional underground pumping wells are proposed to better dewater areas and mitigate this risk, allowing more flexible mining.
This document discusses creativity in teaching. It suggests that traditional education should be changed to focus on thinking, ideas, critical capacity and creativity. This can be achieved through didactic games, creative games, art, culture and technology. These methods can help improve the organization of teaching, motivate students, and encourage interest and love of learning. Specifically, it recommends exposing students to other cultures, using technology to engage them, and providing art and workshops, as well as educational excursions and visits.
Future of Financial Services - Banking on Innovation - Final PaperJohn Fearn
This document discusses the political barriers to innovative financial services. It argues that while radical change in any sector poses challenges for politicians and regulators, the pace of financial innovation is leaving policymakers behind. It analyzes the political reputations of alternative finance providers, payments services, and high street banks to identify the challenges these firms face in influencing regulation. The document predicts that in the near future, most transactions will be digital, mobile payments will increase, and banking services will fragment across new providers, with 20% of lending from alternative sources. It argues that widespread mobile adoption and the 2007-2009 financial crisis have enabled this radical change by shifting consumer habits and eroding trust in large banks.