913 resultados para Materials Analysis Mathematics
Resumo:
Textile manufacture occupies a prominent place in the national economy. Because of its importance researches have been made on the development of new materials, equipment and methods used in the production process. The cutting of textiles starts in the basic stage, to be followed by the process of the making of clothes and other articles. In the hot cutting of fabric, one of the variables of great importance in the control of the process is the contact temperature between the tool and the fabric. This work presents a technique for the measurement of the temperature based on the processing of infrared images. With this purpose, it was developed a system which is composed of an infrared camera, a framegrabber PC board and a software which analyses the punctual temperature in the cut area enabling the operator to achieve the necessary control of other variables involved in the process.
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In 1859, Charles Darwin published his theory of evolution by natural selection, the process occurring based on fitness benefits and fitness costs at the individual level. Traditionally, evolution has been investigated by biologists, but it has induced mathematical approaches, too. For example, adaptive dynamics has proven to be a very applicable framework to the purpose. Its core concept is the invasion fitness, the sign of which tells whether a mutant phenotype can invade the prevalent phenotype. In this thesis, four real-world applications on evolutionary questions are provided. Inspiration for the first two studies arose from a cold-adapted species, American pika. First, it is studied how the global climate change may affect the evolution of dispersal and viability of pika metapopulations. Based on the results gained here, it is shown that the evolution of dispersal can result in extinction and indeed, evolution of dispersalshould be incorporated into the viability analysis of species living in fragmented habitats. The second study is focused on the evolution of densitydependent dispersal in metapopulations with small habitat patches. It resulted a very surprising unintuitive evolutionary phenomenon, how a non-monotone density-dependent dispersal may evolve. Cooperation is surprisingly common in many levels of life, despite of its obvious vulnerability to selfish cheating. This motivated two applications. First, it is shown that density-dependent cooperative investment can evolve to have a qualitatively different, monotone or non-monotone, form depending on modelling details. The last study investigates the evolution of investing into two public-goods resources. The results suggest one general path by which labour division can arise via evolutionary branching. In addition to applications, two novel methodological derivations of fitness measures in structured metapopulations are given.
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This study will concentrate on Product Data Management (PDM) systems, and sheet metal design features and classification. In this thesis, PDM is seen as an individual system which handles all product-related data and information. The meaning of relevant data is to take the manufacturing process further with fewer errors. The features of sheet metals are giving more information and value to the designed models. The possibility of implementing PDM and sheet metal features recognition are the core of this study. Their integration should make the design process faster and manufacturing-friendly products easier to design. The triangulation method is the basis for this research. The sections of this triangle are: scientific literature review, interview using the Delphi method and the author’s experience and observations. The main key findings of this study are: (1) the area of focus in triangle (the triangle of three different point of views: business, information exchange and technical) depends on the person’s background and their role in the company, (2) the classification in the PDM system (and also in the CAD system) should be done using the materials, tools and machines that are in use in the company and (3) the design process has to be more effective because of the increase of industrial production, sheet metal blank production and the designer’s time spent on actual design and (4) because Design For Manufacture (DFM) integration can be done with CAD-programs, DFM integration with the PDM system should also be possible.
Resumo:
The steel industry produces, besides steel, also solid mineral by-products or slags, while it emits large quantities of carbon dioxide (CO2). Slags consist of various silicates and oxides which are formed in chemical reactions between the iron ore and the fluxing agents during the high temperature processing at the steel plant. Currently, these materials are recycled in the ironmaking processes, used as aggregates in construction, or landfilled as waste. The utilization rate of the steel slags can be increased by selectively extracting components from the mineral matrix. As an example, aqueous solutions of ammonium salts such as ammonium acetate, chloride and nitrate extract calcium quite selectively already at ambient temperature and pressure conditions. After the residual solids have been separated from the solution, calcium carbonate can be precipitated by feeding a CO2 flow through the solution. Precipitated calcium carbonate (PCC) is used in different applications as a filler material. Its largest consumer is the papermaking industry, which utilizes PCC because it enhances the optical properties of paper at a relatively low cost. Traditionally, PCC is manufactured from limestone, which is first calcined to calcium oxide, then slaked with water to calcium hydroxide and finally carbonated to PCC. This process emits large amounts of CO2, mainly because of the energy-intensive calcination step. This thesis presents research work on the scale-up of the above-mentioned ammonium salt based calcium extraction and carbonation method, named Slag2PCC. Extending the scope of the earlier studies, it is now shown that the parameters which mainly affect the calcium utilization efficiency are the solid-to-liquid ratio of steel slag and the ammonium salt solvent solution during extraction, the mean diameter of the slag particles, and the slag composition, especially the fractions of total calcium, silicon, vanadium and iron as well as the fraction of free calcium oxide. Regarding extraction kinetics, slag particle size, solid-to-liquid ratio and molar concentration of the solvent solution have the largest effect on the reaction rate. Solvent solution concentrations above 1 mol/L NH4Cl cause leaching of other elements besides calcium. Some of these such as iron and manganese result in solution coloring, which can be disadvantageous for the quality of the PCC product. Based on chemical composition analysis of the produced PCC samples, however, the product quality is mainly similar as in commercial products. Increasing the novelty of the work, other important parameters related to assessment of the PCC quality, such as particle size distribution and crystal morphology are studied as well. As in traditional PCC precipitation process, the ratio of calcium and carbonate ions controls the particle shape; a higher value for [Ca2+]/[CO32-] prefers precipitation of calcite polymorph, while vaterite forms when carbon species are present in excess. The third main polymorph, aragonite, is only formed at elevated temperatures, above 40-50 °C. In general, longer precipitation times cause transformation of vaterite to calcite or aragonite, but also result in particle agglomeration. The chemical equilibrium of ammonium and calcium ions and dissolved ammonia controlling the solution pH affects the particle sizes, too. Initial pH of 12-13 during the carbonation favors nonagglomerated particles with a diameter of 1 μm and smaller, while pH values of 9-10 generate more agglomerates of 10-20 μm. As a part of the research work, these findings are implemented in demonstrationscale experimental process setups. For the first time, the Slag2PCC technology is tested in scale of ~70 liters instead of laboratory scale only. Additionally, design of a setup of several hundreds of liters is discussed. For these purposes various process units such as inclined settlers and filters for solids separation, pumps and stirrers for material transfer and mixing as well as gas feeding equipment are dimensioned and developed. Overall emissions reduction of the current industrial processes and good product quality as the main targets, based on the performed partial life cycle assessment (LCA), it is most beneficial to utilize low concentration ammonium salt solutions for the Slag2PCC process. In this manner the post-treatment of the products does not require extensive use of washing and drying equipment, otherwise increasing the CO2 emissions of the process. The low solvent concentration Slag2PCC process causes negative CO2 emissions; thus, it can be seen as a carbon capture and utilization (CCU) method, which actually reduces the anthropogenic CO2 emissions compared to the alternative of not using the technology. Even if the amount of steel slag is too small for any substantial mitigation of global warming, the process can have both financial and environmental significance for individual steel manufacturers as a means to reduce the amounts of emitted CO2 and landfilled steel slag. Alternatively, it is possible to introduce the carbon dioxide directly into the mixture of steel slag and ammonium salt solution. The process would generate a 60-75% pure calcium carbonate mixture, the remaining 25-40% consisting of the residual steel slag. This calcium-rich material could be re-used in ironmaking as a fluxing agent instead of natural limestone. Even though this process option would require less process equipment compared to the Slag2PCC process, it still needs further studies regarding the practical usefulness of the products. Nevertheless, compared to several other CO2 emission reduction methods studied around the world, the within this thesis developed and studied processes have the advantage of existing markets for the produced materials, thus giving also a financial incentive for applying the technology in practice.
Resumo:
In the framework of the biorefinery concept researchers aspire to optimize the utilization of plant materials, such as agricultural wastes and wood. For most of the known processes, the first steps in the valorisation of biomass are the extraction and purification of the individual components. The obtained raw products by means of a controlled separation can consecutively be modified to result in biofuels or biogas for energy production, but also in value-added products such as additives and important building blocks for the chemical and material industries. Considerable efforts are undertaken in order to substitute the use of oil-based starting materials or at least minimize their processing for the production of everyday goods. Wood is one of the raw materials, which have gained large attention in the last decades and its composition has been studied in detail. Nowadays, the extraction of water-soluble hemicelluloses from wood is well known and so for example xylan can be obtained from hardwoods and O-acetyl galactoglucomannans (GGMs) from softwoods. The aim of this work was to develop water-soluble amphiphilic materials of GGM and to assess their potential use as additives. Furthermore, GGM was also applied as a crosslinker in the synthesis of functional hydrogels for the removal of toxic metals and metalloid ions from aqueous solutions. The distinguished products were obtained by several chemical approaches and analysed by nuclear magnetic resonance spectroscopy (NMR), Fourier transform infrared spectroscopy (FTIR), size exclusion chromatography (SEC), thermal gravimetric analysis (TGA), scanning electron microscope SEM, among others. Bio-based surfactants were produced by applying GGM and different fatty acids as starting materials. On one hand, GGM-grafted-fatty acids were prepared by esterification and on the other hand, well-defined GGM-block-fatty acid derivatives were obtained by linking amino-functional fatty acids to the reducing end of GGM. The reaction conditions for the syntheses were optimized and the resultant amphiphilic GGM derivatives were evaluated concerning their ability to reduce the surface tension of water as surfactants. Furthermore, the block-structured derivatives were tested in respect to their applicability as additives for the surface modification of cellulosic materials. Besides the GGM surfactants with a bio-based hydrophilic and a bio-based hydrophobic part, also GGM block-structured derivatives with a synthetic hydrophobic tail, consisting of a polydimethylsiloxane chain, were prepared and assessed for the hydrophobization of surface of nanofibrillated cellulose films. In order to generate GGM block-structured derivatives containing a synthetic tail with distinguished physical and chemical properties, as well as a tailored chain length, a controlled polymerization method was used. Therefore, firstly an initiator group was introduced at the reducing end of the GGM and consecutively single electron transfer-living radical polymerization (SET-LRP) was performed by applying three different monomers in individual reactions. For the accomplishment of the synthesis and the analysis of the products, challenges related to the solubility of the reactants had to be overcome. Overall, a synthesis route for the production of GGM block-copolymers bearing different synthetic polymer chains was developed and several derivatives were obtained. Moreover, GGM with different molar masses were, after modification, used as a crosslinker in the synthesis of functional hydrogels. Hereby, a cationic monomer was used during the free radical polymerization and the resultant hydrogels were successfully tested for the removal of chromium and arsenic ions from aqueous solutions. The hydrogel synthesis was tailored and materials with distinguished physical properties, such as the swelling rate, were obtained after purification. The results generated in this work underline the potential of bio-based products and the urge to continue carrying out research in order to be able to use more green chemicals for the manufacturing of biorenewable and biodegradable daily products.
Resumo:
Environmental issues, including global warming, have been serious challenges realized worldwide, and they have become particularly important for the iron and steel manufacturers during the last decades. Many sites has been shut down in developed countries due to environmental regulation and pollution prevention while a large number of production plants have been established in developing countries which has changed the economy of this business. Sustainable development is a concept, which today affects economic growth, environmental protection, and social progress in setting up the basis for future ecosystem. A sustainable headway may attempt to preserve natural resources, recycle and reuse materials, prevent pollution, enhance yield and increase profitability. To achieve these objectives numerous alternatives should be examined in the sustainable process design. Conventional engineering work cannot address all of these substitutes effectively and efficiently to find an optimal route of processing. A systematic framework is needed as a tool to guide designers to make decisions based on overall concepts of the system, identifying the key bottlenecks and opportunities, which lead to an optimal design and operation of the systems. Since the 1980s, researchers have made big efforts to develop tools for what today is referred to as Process Integration. Advanced mathematics has been used in simulation models to evaluate various available alternatives considering physical, economic and environmental constraints. Improvements on feed material and operation, competitive energy market, environmental restrictions and the role of Nordic steelworks as energy supplier (electricity and district heat) make a great motivation behind integration among industries toward more sustainable operation, which could increase the overall energy efficiency and decrease environmental impacts. In this study, through different steps a model is developed for primary steelmaking, with the Finnish steel sector as a reference, to evaluate future operation concepts of a steelmaking site regarding sustainability. The research started by potential study on increasing energy efficiency and carbon dioxide reduction due to integration of steelworks with chemical plants for possible utilization of available off-gases in the system as chemical products. These off-gases from blast furnace, basic oxygen furnace and coke oven furnace are mainly contained of carbon monoxide, carbon dioxide, hydrogen, nitrogen and partially methane (in coke oven gas) and have proportionally low heating value but are currently used as fuel within these industries. Nonlinear optimization technique is used to assess integration with methanol plant under novel blast furnace technologies and (partially) substitution of coal with other reducing agents and fuels such as heavy oil, natural gas and biomass in the system. Technical aspect of integration and its effect on blast furnace operation regardless of capital expenditure of new operational units are studied to evaluate feasibility of the idea behind the research. Later on the concept of polygeneration system added and a superstructure generated with alternative routes for off-gases pretreatment and further utilization on a polygeneration system producing electricity, district heat and methanol. (Vacuum) pressure swing adsorption, membrane technology and chemical absorption for gas separation; partial oxidation, carbon dioxide and steam methane reforming for methane gasification; gas and liquid phase methanol synthesis are the main alternative process units considered in the superstructure. Due to high degree of integration in process synthesis, and optimization techniques, equation oriented modeling is chosen as an alternative and effective strategy to previous sequential modelling for process analysis to investigate suggested superstructure. A mixed integer nonlinear programming is developed to study behavior of the integrated system under different economic and environmental scenarios. Net present value and specific carbon dioxide emission is taken to compare economic and environmental aspects of integrated system respectively for different fuel systems, alternative blast furnace reductants, implementation of new blast furnace technologies, and carbon dioxide emission penalties. Sensitivity analysis, carbon distribution and the effect of external seasonal energy demand is investigated with different optimization techniques. This tool can provide useful information concerning techno-environmental and economic aspects for decision-making and estimate optimal operational condition of current and future primary steelmaking under alternative scenarios. The results of the work have demonstrated that it is possible in the future to develop steelmaking towards more sustainable operation.
Resumo:
Laser additive manufacturing (LAM), known also as 3D printing, is a powder bed fusion (PBF) type of additive manufacturing (AM) technology used to manufacture metal parts layer by layer by assist of laser beam. The development of the technology from building just prototype parts to functional parts is due to design flexibility. And also possibility to manufacture tailored and optimised components in terms of performance and strength to weight ratio of final parts. The study of energy and raw material consumption in LAM is essential as it might facilitate the adoption and usage of the technique in manufacturing industries. The objective this thesis was find the impact of LAM on environmental and economic aspects and to conduct life cycle inventory of CNC machining and LAM in terms of energy and raw material consumption at production phases. Literature overview in this thesis include sustainability issues in manufacturing industries with focus on environmental and economic aspects. Also life cycle assessment and its applicability in manufacturing industry were studied. UPLCI-CO2PE! Initiative was identified as mostly applied exiting methodology to conduct LCI analysis in discrete manufacturing process like LAM. Many of the reviewed literature had focused to PBF of polymeric material and only few had considered metallic materials. The studies that had included metallic materials had only measured input and output energy or materials of the process and compared to different AM systems without comparing to any competitive process. Neither did any include effect of process variation when building metallic parts with LAM. Experimental testing were carried out to make dissimilar samples with CNC machining and LAM in this thesis. Test samples were designed to include part complexity and weight reductions. PUMA 2500Y lathe machine was used in the CNC machining whereas a modified research machine representing EOSINT M-series was used for the LAM. The raw material used for making the test pieces were stainless steel 316L bar (CNC machined parts) and stainless steel 316L powder (LAM built parts). An analysis of power, time, and the energy consumed in each of the manufacturing processes on production phase showed that LAM utilises more energy than CNC machining. The high energy consumption was as result of duration of production. Energy consumption profiles in CNC machining showed fluctuations with high and low power ranges. LAM energy usage within specific mode (standby, heating, process, sawing) remained relatively constant through the production. CNC machining was limited in terms of manufacturing freedom as it was not possible to manufacture all the designed sample by machining. And the one which was possible was aided with large amount of material removed as waste. Planning phase in LAM was shorter than in CNC machining as the latter required many preparation steps. Specific energy consumption (SEC) were estimated in LAM based on the practical results and assumed platform utilisation. The estimated platform utilisation showed SEC could reduce when more parts were placed in one build than it was in with the empirical results in this thesis (six parts).
Resumo:
This thesis develops a method for identifying students struggling in their mathematical studies at an early stage. It helps in directing support to students needing and benefiting from it the most. Thus, frustration felt by weaker students may decrease and therefore, hopefully, also drop outs of potential engineering students. The research concentrates on a combination of personality and intelligence aspects. Personality aspects gave information on conation and motivation for learning. This part was studied from the perspective of motivation and self-regulation. Intelligence aspects gave information on declarative and procedural knowledge: what had been taught and what was actually mastered. Students answered surveys on motivation and self-regulation in 2010 and 2011. Based on their answers, background information, results in the proficiency test, and grades in the first mathematics course, profiles describing the students were formed. In the following years, the profiles were updated with new information obtained each year. The profiles used to identify struggling students combine personality (motivation, selfregulation, and self-efficacy) and intelligence (declarative and procedural knowledge) aspects at the beginning of their studies. Identifying students in need of extra support is a good start, but methods for providing support must be found. This thesis also studies how this support could be taken into account in course arrangements. The methods used include, for example, languaging and scaffolding, and continuous feedback. The analysis revealed that allocating resources based on the predicted progress does not increase costs or lower the results of better students. Instead, it will help weaker students obtain passing grades.
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The recent rapid development of biotechnological approaches has enabled the production of large whole genome level biological data sets. In order to handle thesedata sets, reliable and efficient automated tools and methods for data processingand result interpretation are required. Bioinformatics, as the field of studying andprocessing biological data, tries to answer this need by combining methods and approaches across computer science, statistics, mathematics and engineering to studyand process biological data. The need is also increasing for tools that can be used by the biological researchers themselves who may not have a strong statistical or computational background, which requires creating tools and pipelines with intuitive user interfaces, robust analysis workflows and strong emphasis on result reportingand visualization. Within this thesis, several data analysis tools and methods have been developed for analyzing high-throughput biological data sets. These approaches, coveringseveral aspects of high-throughput data analysis, are specifically aimed for gene expression and genotyping data although in principle they are suitable for analyzing other data types as well. Coherent handling of the data across the various data analysis steps is highly important in order to ensure robust and reliable results. Thus,robust data analysis workflows are also described, putting the developed tools andmethods into a wider context. The choice of the correct analysis method may also depend on the properties of the specific data setandthereforeguidelinesforchoosing an optimal method are given. The data analysis tools, methods and workflows developed within this thesis have been applied to several research studies, of which two representative examplesare included in the thesis. The first study focuses on spermatogenesis in murinetestis and the second one examines cell lineage specification in mouse embryonicstem cells.
Resumo:
Project scope is to utilize Six Sigma DMAIC approach and lean principles to improve production quality of the case company. Six Sigma tools and techniques are explored through a literature review and later used in the quality control phase. The focus is set on the Pareto analysis to demonstrate the most evident development areas in the production. Materials that are not delivered to the customer or materials that damaged during transportation comprise the biggest share of all feedbacks. The goal is set to reduce these feedbacks by 50 %. Production observation pointed out that not only material shortages but also over-production is a daily situation. As a result, an initial picking list where the purchased and own production components can be seen, is created, reduction of over- and underproduction and material marking improvement are seen the most competitive options so that the goal can be reached. The picking list development should still continue to make sure that the list can be used not only in the case study but also in the industrial scale. The reduction of material missing category can be evaluated reliably not sooner than in few years because it takes time to gather the needed statistical information.
Resumo:
The purpose of this study was to determine the effect that calculators have on the attitudes and numerical problem-solving skills of primary students. The sample used for this research was one of convenience. The sample consisted of two grade 3 classes within the York Region District School Board. The students in the experimental group used calculators for this problem-solving unit. The students in the control group completed the same numerical problem-solving unit without the use of calculators. The pretest-posttest control group design was used for this study. All students involved in this study completed a computational pretest and an attitude pretest. At the end of the study, the students completed a computational posttest. Five students from the experimental group and five students from the control group received their posttests in the form of a taped interview. At the end of the unit, all students completed the attitude scale that they had received before the numerical problem-solving unit once again. Data for qualitative analysis included anecdotal observations, journal entries, and transcribed interviews. The constant comparative method was used to analyze the qualitative data. A t test was also performed on the data to determine whether there were changes in test and attitude scores between the control and experimental group. Overall, the findings of this study support the hypothesis that calculators improve the attitudes of primary students toward mathematics. Also, there is some evidence to suggest that calculators improve the computational skills of grade 3 students.
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This study is a secondary data analysis of the Trends in Mathematics and Science Study 2003 (TIMSS) to determine if there is a gender bias, unbalanced number of items suited to the cognitive skill of one gender, and to compare performance by location. Results of the Grade 8, math portion of the test were examined. Items were coded as verbal, spatial, verbal /spatial or neither and as conventional or unconventional. A Kruskal- Wallis was completed for each category, comparing performance of students from Ontario, Quebec, and Singapore. A Factor Analysis was completed to determine if there were item categories with similar characteristics. Gender differences favouring males were found in the verbal conventional category for Canadian students and in the spatial conventional category for students in Quebec. The greatest differences were by location, as students in Singapore outperformed students from Canada in all areas except for the spatial unconventional category. Finally, whether an item is conventional or unconventional is more important than whether the item is verbal or spatial. Results show the importance of fair assessment for the genders in both the classroom and on standardized tests.
Resumo:
Two new families of building blocks have been prepared and fully characterized and their coordination chemistry exploited for the preparation of molecule-based magnetic materials. The first class of compounds were prepared by exploiting the chemistry of 3,3'-diamino-2,2'-bipyridine together with 2-pyridine carbonyl chloride or 2-pyridine aldehyde. Two new ligands, 2,2'-bipyridine-3,3'-[2-pyridinecarboxamide] (Li, 2.3) and N'-6/s(2-pyridylmethyl) [2,2'bipyridine]-3,3'-diimine (L2, 2.7), were prepared and characterized. For ligand L4, two copper(II) coordination compounds were isolated with stoichiometrics [Cu2(Li)(hfac)2] (2.4) and [Cu(Li)Cl2] (2.5). The molecular structures of both complexes were determined by X-ray crystallography. In both complexes the ligand is in the dianionic form and coordinates the divalent Cu(II) ions via one amido and two pyridine nitrogen donor atoms. In (2.4), the coordination geometry around both Cu11 ions is best described as distorted trigonal bipyramidal where the remaining two coordination sites are satisfied by hfac counterions. In (2.5), both Cu(II) ions adopt a (4+1) distorted square pyramidal geometry. One copper forms a longer apical bond to an adjacent carbonyl oxygen atom, whereas the second copper is chelated to a neighboring Cu-Cl chloride ion to afford chloride bridged linear [Cu2(Li)Cl2]2 tetramers that run along the c-axis of the unit cell. The magnetic susceptibility data for (2.4) reveal the occurrence of weak antiferromagnetic interactions between the copper(II) ions. In contrast, variable temperature magnetic susceptibility measurements for (2.5) reveal more complex magnetic properties with the presence of ferromagnetic exchange between the central dimeric pair of copper atoms and weak antiferromagnetic exchange between the outer pairs of copper atoms. The Schiff-base bis-imine ligand (L2, 2.7) was found to be highly reactive; single crystals grown from dry methanol afforded compound (2.14) for which two methanol molecules had added across the imine double bond. The susceptibility of this ligand to nucleophilic attack at its imine functionality assisted via chelation to Lewis acidic metal ions adds an interesting dimension to its coordination chemistry. In this respect, a Co(II) quaterpyridine-type complex was prepared via a one-pot transformation of ligand L2 in the presence of a Lewis acidic metal salt. The rearranged complex was characterized by X-ray crystallography and a reaction mechanism for its formation has been proposed. Three additional rearranged complexes (2.13), (2.17) and (2.19) were also isolated when ligand (L2, 2.7) was reacted with transition metal ions. The molecular structures of all three complexes have been determined by X-ray crystallography. The second class of compounds that are reported in this thesis, are the two diacetyl pyridine derivatives, 4-pyridyl-2,6-diacetylpyridine (5.5) and 2,2'-6,6'-tetraacetyl-4,4'-bipyridine (5.15). Both of these compounds have been designed as intermediates for the metal templated assembly of a Schiff-base N3O2 macrocycle. From compound (5.15), a covalently tethered dimeric Mn(II) macrocyclic compound of general formula {[Mn^C^XJCl-FkO^Cl-lO.SFbO (5.16) was prepared and characterized. The X-ray analysis of (5.16) reveals that the two manganese ions assume a pentagonal-bipyramidal geometry with the macrocycle occupying the pentagonal plane and the axial positions being filled by a halide ion and a H2O molecule. Magnetic susceptibility data reveal the occurrence of antiferromagnetic interactions between covalently tethered Mn(II)-Mn(II) dimeric units. Following this methodology a Co(II) analogue (5.17) has also been prepared which is isostructural with (5.16).
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Three grade three mathematics textbooks were selected arbitrarily (every other) from a total of six currently used in the schools of Ontario. These textbooks were examined through content analysis in order to determine the extent (i. e., the frequency of occurrence) to which problem solving strategies appear in the problems and exercises of grade three mathematics textbooks, and how well they carry through the Ministry's educational goals set out in The Formative Years. Based on Polya's heuristic model, a checklist was developed by the researcher. The checklist had two main categories, textbook problems and process problems and a finer classification according to the difficulty level of a textbook problem; also six commonly used problem solving strategies for the analysis of a process problem. Topics to be analyzed were selected from the subject guideline The Formative Years, and the same topics were selected from each textbook. Frequencies of analyzed problems and exercises were compiled and tabulated textbook by textbook and topic by topic. In making comparisons, simple frequency count and percentage were used in the absence of any known criteria available for judging highor low frequency. Each textbook was coded by three coders trained to use the checklist. The results of analysis showed that while there were large numbers of exercises in each textbook, not very many were framed as problems according to Polya' s model and that process problems form a small fraction of the number of analyzed problems and exercises. There was no pattern observed as to the systematic placement of problems in the textbooks.
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Forty grade 9 students were selected from a small rural board in southern Ontario. The students were in two classes and were treated as two groups. The treatment group received instruction in the Logical Numerical Problem Solving Strategy every day for 37 minutes over a 6 week period. The control group received instruction in problem solving without this strategy over the same time period. Then the control group received the treat~ent and the treatment group received the instruction without the strategy. Quite a large variance was found in the problem solving ability of students in grade 9. It was also found that the growth of the problem solving ability achievement of students could be measured using growth strands based upon the results of the pilot study. The analysis of the results of the study using t-tests and a MANOVA demonstrated that the teaching of the strategy did not significaritly (at p s 0.05) increase the problem solving achievement of the students. However, there was an encouraging trend seen in the data.