Awareness on 3R practice: a case study at UTHM Pagoh residential college

Solid waste can be defined as any scrap material; or unwanted surplus substance; or rejected products arising from the application of any process [1]. This also includes any substance required to be disposed of as being broken, worn out, contaminated or otherwise spoiled. Over the years, the problems of solid waste generation are increasing all over the world. In the year 2016, cities around the world generated 2.01 billion tonnes of solid waste, amounting to a footprint of 0.74 kilograms per person per day [2]. With rapid population growth and urbanisation, the annual waste generation is expected to increase to 3.4 billion tonnes by year 2050. The same trend can be seen in Malaysia. The waste generation rate in this country has been steadily increasing from 12.3 million tonnes in year 2013 to 13.9 million tonnes in year 2018 [3]. This amount is expected to increase to 14.4 million tonnes by year 2020

On methods of computing galois groups and their implementations in MAPLE.

by Tang Ko Cheung, Simon.Thesis date on t.p. originally printed as 1997, of which 7 has been overwritten as 8 to become 1998.Thesis (M.Phil.)--Chinese University of Hong Kong, 1998.Includes bibliographical references (leaves 95-97).Chapter 1 --- Introduction --- p.5Chapter 1.1 --- Motivation --- p.5Chapter 1.1.1 --- Calculation of the Galois group --- p.5Chapter 1.1.2 --- Factorization of polynomials in a finite number of steps IS feasible --- p.6Chapter 1.2 --- Table & Diagram of Transitive Groups up to Degree 7 --- p.8Chapter 1.3 --- Background and Notation --- p.13Chapter 1.4 --- Content and Contribution of THIS thesis --- p.17Chapter 2 --- Stauduhar's Method --- p.20Chapter 2.1 --- Overview & Restrictions --- p.20Chapter 2.2 --- Representation of the Galois Group --- p.21Chapter 2.3 --- Groups and Functions --- p.22Chapter 2.4 --- Relative Resolvents --- p.24Chapter 2.4.1 --- Computing Resolvents Numerically --- p.24Chapter 2.4.2 --- Integer Roots of Resolvent Polynomials --- p.25Chapter 2.5 --- The Determination of Galois Groups --- p.26Chapter 2.5.1 --- Searching Procedures --- p.26Chapter 2.5.2 --- "Data: T(x1,x2 ,... ,xn), Coset Rcpresentatives & Searching Diagram" --- p.27Chapter 2.5.3 --- Examples --- p.32Chapter 2.6 --- Quadratic Factors of Resolvents --- p.35Chapter 2.7 --- Comment --- p.35Chapter 3 --- Factoring Polynomials Quickly --- p.37Chapter 3.1 --- History --- p.37Chapter 3.1.1 --- From Feasibility to Fast Algorithms --- p.37Chapter 3.1.2 --- Implementations on Computer Algebra Systems --- p.42Chapter 3.2 --- Squarefree factorization --- p.44Chapter 3.3 --- Factorization over finite fields --- p.47Chapter 3.4 --- Factorization over the integers --- p.50Chapter 3.5 --- Factorization over algebraic extension fields --- p.55Chapter 3.5.1 --- Reduction of the problem to the ground field --- p.55Chapter 3.5.2 --- Computation of primitive elements for multiple field extensions --- p.58Chapter 4 --- Soicher-McKay's Method --- p.60Chapter 4.1 --- "Overview, Restrictions and Background" --- p.60Chapter 4.2 --- Determining cycle types in GalQ(f) --- p.62Chapter 4.3 --- Absolute Resolvents --- p.64Chapter 4.3.1 --- Construction of resolvent --- p.64Chapter 4.3.2 --- Complete Factorization of Resolvent --- p.65Chapter 4.4 --- Linear Resolvent Polynomials --- p.67Chapter 4.4.1 --- r-sets and r-sequences --- p.67Chapter 4.4.2 --- Data: Orbit-length Partitions --- p.68Chapter 4.4.3 --- Constructing Linear Resolvents Symbolically --- p.70Chapter 4.4.4 --- Examples --- p.72Chapter 4.5 --- Further techniques --- p.72Chapter 4.5.1 --- Quadratic Resolvents --- p.73Chapter 4.5.2 --- Factorization over Q(diac(f)) --- p.73Chapter 4.6 --- Application to the Inverse Galois Problem --- p.74Chapter 4.7 --- Comment --- p.77Chapter A --- Demonstration of the MAPLE program --- p.78Chapter B --- Avenues for Further Exploration --- p.84Chapter B.1 --- Computational Galois Theory --- p.84Chapter B.2 --- Notes on SAC´ؤSymbolic and Algebraic Computation --- p.88Bibliography --- p.9