The use of explicit algorithms and episodic context to teach subtraction to students with learning problems in mathematics /

This research attempted to address the question of the role of explicit algorithms and episodic contexts in the acquisition of computational procedures for regrouping in subtraction. Three groups of students having difficulty learning to subtract with regrouping were taught procedures for doing so through either an explicit algorithm, an episodic content or an examples approach. It was hypothesized that the use of an explicit algorithm represented in a flow chart format would facilitate the acquisition and retention of specific procedural steps relative to the other two conditions. On the other hand, the use of paragraph stories to create episodic content was expected to facilitate the retrieval of algorithms, particularly in a mixed presentation format. The subjects were tested on similar, near, and far transfer questions over a four-day period. Near and far transfer algorithms were also introduced on Day Two. The results suggested that both explicit and episodic context facilitate performance on questions requiring subtraction with regrouping. However, the differential effects of these two approaches on near and far transfer questions were not as easy to identify. Explicit algorithms may facilitate the acquisition of specific procedural steps while at the same time inhibiting the application of such steps to transfer questions. Similarly, the value of episodic context in cuing the retrieval of an algorithm may be limited by the ability of a subject to identify and classify a new question as an exemplar of a particular episodically deflned problem type or category. The implications of these findings in relation to the procedures employed in the teaching of Mathematics to students with learning problems are discussed in detail.

The effect of moisture on decomposition processes in the disturbed peatlands of the Wainfleet bog /

The purpose of this study was to determine the effect of increased soil moisture levels on the decomposition processes in a peat-extracted bog. Field experiments, in which soil moisture levels were manipulated, were conducted using 320 microcosms in the Wainfleet Bog from May 2002 to November 2004. Decomposition was measured using litter bags and monitoring the abundance of macro invertebrate decomposers known as Collembola. Litter bags containing wooden toothpicks (n=2240), filter paper (n=480) and Betula pendula leaves (n=40) were buried in the soil and removed at regular time intervals up to one year. The results of the litter bag studies demonstrated a significant reduction of the decomposition of toothpicks (p<0.001), filter paper (p<0.001), and Betula pendula leaves (pdecomposition can be obtained by restoring the soil moisture levels near those of undisturbed conditions.

The kinetics and induced decomposition on the thermal decomposition of hydroperoxides /

This project is focussed on the thermsLl decomposition of t-butyl hydroperoxide and sec-butyl hydroperoxide at 120°C to 160°C in three alcohol solvents. These are methanol, ethajiol and isopropyl alcohol. The aim of the project was to examine the process of induced decomposition. Thermal decomposition of t-hutyl hydroperoxide and sec-butyl hydroperoxide indicate that these reactions have first-order kinetics with activation energies on the order of 20 to 28 K cal/mole, Styrene was used as a free radical trap to inhibit the induced decomposition. The results permitted calculation of how much induced decomposition occurred in its absence. The experimental resvilts indicate that the induced decomposition is important for t-butyl hydroperoxide in alcohol solvents, as shown by both the reaction rate suid product studies. But sec-butyl hydroperoxide results show that the concerted mechanism for the interaction of two sec-butylperoxy radicals occurs in addition to the induced decomposition. Di-sodium E.D,T.A. was added to reduce possible effects of trace transition metal ion .impurities. The result of this experiment were not as expected. The rate of hydroperoxide decomposition was about the same but was zero-order in hydroperoxide concentration.

A study of the thermal decomposition of allyl t-butyl peroxide and 3-hydroperoxy-1-propene (allyl hydroperoxide) in toluene /|nby Krishnankutty Nair V. G. -- 260 St. Catharines [Ont. : s. n.],

Kinetics and product studies of the decompositions of allyl-t-butyl peroxide and 3-hydroperoxy- l-propene (allyl hydroperoxide ) in tolune were investigated. Decompositions of allyl-t-butyl peroxide in toluene at 130-1600 followed first order kinetics with an activation energy of 32.8 K.cals/mol and a log A factor of 13.65. The rates of decomposition were lowered in presence of the radical trap~methyl styrene. By the radical trap method, the induced decomposition at 1300 is shown to be 12.5%. From the yield of 4-phenyl-l,2- epoxy butane the major path of induced decomposition is shown to be via an addition mechanism. On the other hand, di-t-butYl peroxyoxalate induced decomposition of this peroxide at 600 proceeded by an abstraction mechanism. Induced decomposition of peroxides and hydroperoxides containing the allyl system is proposed to occur mainly through an addition mechanism at these higher temperatures. Allyl hydroperoxide in toluene at 165-1850 decomposes following 3/2 order kinetics with an Ea of 30.2 K.cals per mole and log A of 10.6. Enormous production of radicals through chain branching may explain these relatively low values of E and log A. The complexity of the reaction is indicated a by the formation of various products of the decomposition. A study of the radical attack of the hydro peroxide at lower temperatures is suggested as a further work to throw more light on the nature of decomposition of this hydroperoxide.

The kinetics and mechanism of the thermal decomposition of sec-Butyl peroxide in liquid phase /|nby Sandor Szilagyi. -- 260 St. Catharines, Ont. : [s. n.],

Re~tes artd pJ~oducts of tllerma]. d,ecom.position of sec-butyl peroxide at 110 - 150°C i.n four solvents h,ave been determined. The d,ecompos i tion vJas sb.o\'\Tn to be tlnlmolecl.llar wi tho energies of activation in toluene, benzene, and cyclohexane of 36 .7-+ 1.0, 33.2 +- 1..0, 33.t~) +.. 1.0 I'(:cal/mol respectively. The activation energy of thermal decomposition for the d,et.1terated peroxide was found to be 37.2 4:- 1.0 KC8:1/1TIol in toluene. A.bo1J.t 70 - 80/~ ol~ tJJ.e' pl~od.1..1CtS could, be explained by kn01rJ11 reactions of free allcoxy raclicals J and very littJ...e, i.f allY, disPl"Opox~tiol'lation of tll10 sec-butoxy radica.ls in t116 solvent cage could be detected. The oth,er 20 - 30% of the peroxide yielded H2 and metb.:'ll etb..yl 1{etol1e. Tl1.e yield. o:f H2 "'lIas unafJ:'ected by the nature or the viscosity of the solvent, but H2 was not formed when s-t1U202 lrJaS phctolyzed. in tolttene at 35°C nor 'tl!Jrl.en the peroxide 1;'JaS tl1.ermally o..ecoJnposed. in the gas p11ase. ~pC-Dideutero-~-butYlperoxide was prepared and decomposed in toluene at 110 - 150°C. The yield of D2 was about ·•e1ne same 248 the yield. of I{2 from s-Bu202, bU.t th.e rate of decomposition (at 135°C) 1iJas only 1/1.55 as fast. Ivlecl1.anisms fOl') J:1ydrogen produ.ction are discussed, but none satisfactorily explains all the evidence.

The kinetics and mechanism of the thermal decomposition of bis diphenyl methyl and related peroxides in liquid phase /|nby C. Thankachan. -- 260 St. Catharines, Ont. : [s. n.],

Rates and products have been determined for the thermal decomposition of bis diphenyl methyl peroxide and diphenyl methyl tert* butyl peroxide at 110@~145@C* The decomposition was uniformly unimolecular with activation energies for the bis diphenyl methyl peroxide in tetrachloroethylene* toluene and nitrobenzene 26,6* 28*3f and 27 Kcals/mole respectively. Diphenyl methyl tert* butyl peroxide showed an activation energy of 38*6 Kcals/mole* About 80-90% of the products in the case of diphenyl methyl peroxide could be explained by the concerted process, this coupled with the negative entropies of activation obtained is a conclusive evidence for the reaction adopting a major concerted path* All the products in the case of diphenyl methyl peroxide could be explained by known reactions of alkoxy radicals* About 80-85% of tert butanol and benzophenone formed suggested far greater cage disproportionation than diffusing apart* Rates of bis triphenyl methyl peroxide have been determined in tetrachloroethylene at 100-120@C* The activation energy was found to be 31 Kcals/mole*

A G. C./M. S. study of the reaction and decomposition products of pentafluorophenyl-grignard and lithium reagents

Decomposition and side reactions of, and the synthetic use of, pentafluorophenylmagnesium bromide and pentafluorophenyllithium have been investigated using G,C9/M.S, techniques• Their reactions with reagents such as CgF^X (X - H, F, CI, Br, 1), C6F4X2 (X - H, CI)f C6F3C13, C6H6. (CgX5)3P (X = H, F), (C6X5)3P=0 (X = H, F), (CgX5)Si (CH3)3 (X = H, F) and (CH0K SiCl , n = 1,2, in ether or ether/n-hexane were studied• In addition to the principal reaction of synthetic use, namely the replacement of a halogen by a pentafluorophenyl group, two types of side reactions were observed* These were (i) intermolecular loss of LiF via a nucleophilic substitution, and (ii) intramolecular loss of LiF, followed by the addition of either inorganic salts such as lithium or magnesium halides, or organometal compounds such as organolithium or organo-Grigaard* G.C«/M.S. techniques were routinely employed to study complicated reaction mixtures. Although mass spectrometry alone has disadvantages for the identification of isomers, deduction of the most probable pathway often helps overcome this problem.

The kinetics and solvent effects on the thermal decomposition of isopropyl peroxide and 1, 2-dioxane

Rates of H2 formation have been determined for the thermal decomposition of isopropyl peroxide at l30o-l50oC in toluene and methanol and at l400C in isopropyl alcohol and water. Product studies have been carried out at l400C in these solvents. The decomposition of isopropyl peroxide was shown to be unimolecular with energies of activation in toluene, and methanol of 39.1, 23.08 Kcal/mole respectively. It has been shown that the rates of H2 formation in decomposition of isopropyl peroxide are solvent dependent and that the ~ vs "'2';' values (parameters for solvent polarity) givesastraight line. Mechanisms for hydrogen production are discussed which satisfactorily explain the stabilization of the six-centered transition state by the solvent. One possibility is that of conformation stabilization by solvent and the other, a transition state with sufficient ionic character to be stabilized by a polar solvent. Rates of thermal decomposition of 1,2-dioxane in tert-butylbenzene at l40o-l70oC have been determined. The activation energy was found to be 33.4 Kcal/mole. This lower activation energy, compared to that for the decomposition of isopropyl peroxide in toluene (39.1 Kcal/mole) has been explained in terms of ring strain. Decomposition of 1,2 dioxane in MeOH does not follow a first order reaction. Several mechanisms have been suggested for the products observed for decomposition of 1;2-dioxane in toluene and methanol.

Properties and algorithms of the (n, k)-star graphs

The (n, k)-star interconnection network was proposed in 1995 as an attractive alternative to the n-star topology in parallel computation. The (n, k )-star has significant advantages over the n-star which itself was proposed as an attractive alternative to the popular hypercube. The major advantage of the (n, k )-star network is its scalability, which makes it more flexible than the n-star as an interconnection network. In this thesis, we will focus on finding graph theoretical properties of the (n, k )-star as well as developing parallel algorithms that run on this network. The basic topological properties of the (n, k )-star are first studied. These are useful since they can be used to develop efficient algorithms on this network. We then study the (n, k )-star network from algorithmic point of view. Specifically, we will investigate both fundamental and application algorithms for basic communication, prefix computation, and sorting, etc. A literature review of the state-of-the-art in relation to the (n, k )-star network as well as some open problems in this area are also provided.

Decoding algorithms using side-effect machines

Bioinformatics applies computers to problems in molecular biology. Previous research has not addressed edit metric decoders. Decoders for quaternary edit metric codes are finding use in bioinformatics problems with applications to DNA. By using side effect machines we hope to be able to provide efficient decoding algorithms for this open problem. Two ideas for decoding algorithms are presented and examined. Both decoders use Side Effect Machines(SEMs) which are generalizations of finite state automata. Single Classifier Machines(SCMs) use a single side effect machine to classify all words within a code. Locking Side Effect Machines(LSEMs) use multiple side effect machines to create a tree structure of subclassification. The goal is to examine these techniques and provide new decoders for existing codes. Presented are ideas for best practices for the creation of these two types of new edit metric decoders.

Properties and algorithms of the (n, k)-arrangement graphs

The (n, k)-arrangement interconnection topology was first introduced in 1992. The (n, k )-arrangement graph is a class of generalized star graphs. Compared with the well known n-star, the (n, k )-arrangement graph is more flexible in degree and diameter. However, there are few algorithms designed for the (n, k)-arrangement graph up to present. In this thesis, we will focus on finding graph theoretical properties of the (n, k)- arrangement graph and developing parallel algorithms that run on this network. The topological properties of the arrangement graph are first studied. They include the cyclic properties. We then study the problems of communication: broadcasting and routing. Embedding problems are also studied later on. These are very useful to develop efficient algorithms on this network. We then study the (n, k )-arrangement network from the algorithmic point of view. Specifically, we will investigate both fundamental and application algorithms such as prefix sums computation, sorting, merging and basic geometry computation: finding convex hull on the (n, k )-arrangement graph. A literature review of the state-of-the-art in relation to the (n, k)-arrangement network is also provided, as well as some open problems in this area.

Properties and algorithms of the hyper-star graph and its related graphs

The hyper-star interconnection network was proposed in 2002 to overcome the drawbacks of the hypercube and its variations concerning the network cost, which is defined by the product of the degree and the diameter. Some properties of the graph such as connectivity, symmetry properties, embedding properties have been studied by other researchers, routing and broadcasting algorithms have also been designed. This thesis studies the hyper-star graph from both the topological and algorithmic point of view. For the topological properties, we try to establish relationships between hyper-star graphs with other known graphs. We also give a formal equation for the surface area of the graph. Another topological property we are interested in is the Hamiltonicity problem of this graph. For the algorithms, we design an all-port broadcasting algorithm and a single-port neighbourhood broadcasting algorithm for the regular form of the hyper-star graphs. These algorithms are both optimal time-wise. Furthermore, we prove that the folded hyper-star, a variation of the hyper-star, to be maixmally fault-tolerant.

Quadtree representation and compression of spatial data

Spatial data representation and compression has become a focus issue in computer graphics and image processing applications. Quadtrees, as one of hierarchical data structures, basing on the principle of recursive decomposition of space, always offer a compact and efficient representation of an image. For a given image, the choice of quadtree root node plays an important role in its quadtree representation and final data compression. The goal of this thesis is to present a heuristic algorithm for finding a root node of a region quadtree, which is able to reduce the number of leaf nodes when compared with the standard quadtree decomposition. The empirical results indicate that, this proposed algorithm has quadtree representation and data compression improvement when in comparison with the traditional method.

Using genetic algorithms for the single allocation hub location problem

Hub location problem is an NP-hard problem that frequently arises in the design of transportation and distribution systems, postal delivery networks, and airline passenger flow. This work focuses on the Single Allocation Hub Location Problem (SAHLP). Genetic Algorithms (GAs) for the capacitated and uncapacitated variants of the SAHLP based on new chromosome representations and crossover operators are explored. The GAs is tested on two well-known sets of real-world problems with up to 200 nodes. The obtained results are very promising. For most of the test problems the GA obtains improved or best-known solutions and the computational time remains low. The proposed GAs can easily be extended to other variants of location problems arising in network design planning in transportation systems.

Comparison of classification ability of hyperball algorithms to neural network and k-nearest neighbour algorithms

The main focus of this thesis is to evaluate and compare Hyperbalilearning algorithm (HBL) to other learning algorithms. In this work HBL is compared to feed forward artificial neural networks using back propagation learning, K-nearest neighbor and 103 algorithms. In order to evaluate the similarity of these algorithms, we carried out three experiments using nine benchmark data sets from UCI machine learning repository. The first experiment compares HBL to other algorithms when sample size of dataset is changing. The second experiment compares HBL to other algorithms when dimensionality of data changes. The last experiment compares HBL to other algorithms according to the level of agreement to data target values. Our observations in general showed, considering classification accuracy as a measure, HBL is performing as good as most ANn variants. Additionally, we also deduced that HBL.:s classification accuracy outperforms 103's and K-nearest neighbour's for the selected data sets.