936 resultados para 010501 Algebraic Structures in Mathematical Physics
Resumo:
Deflection compensation of flexible boom structures in robot positioning is usually done using tables containing the magnitude of the deflection with inverse kinematics solutions of a rigid structure. The number of table values increases greatly if the working area of the boom is large and the required positioning accuracy is high. The inverse kinematics problems are very nonlinear, and if the structure is redundant, in some cases it cannot be solved in a closed form. If the structural flexibility of the manipulator arms is taken into account, the problem is almost impossible to solve using analytical methods. Neural networks offer a possibility to approximate any linear or nonlinear function. This study presents four different methods of using neural networks in the static deflection compensation and inverse kinematics solution of a flexible hydraulically driven manipulator. The training information required for training neural networks is obtained by employing a simulation model that includes elasticity characteristics. The functionality of the presented methods is tested based on the simulated and measured results of positioning accuracy. The simulated positioning accuracy is tested in 25 separate coordinate points. For each point, the positioning is tested with five different mass loads. The mean positioning error of a manipulator decreased from 31.9 mm to 4.1 mm in the test points. This accuracy enables the use of flexible manipulators in the positioning of larger objects. The measured positioning accuracy is tested in 9 separate points using three different mass loads. The mean positioning error decreased from 10.6 mm to 4.7 mm and the maximum error from 27.5 mm to 11.0 mm.
Resumo:
Kokeellinen moodianalyysi on kokeellinen menetelmä, jolla voidaan selvittää rakenteille ominaista värähtelyä. Työssä oli kolme tavoitetta, jotka pyrittiin saavuttamaan. Ensimmäinen tavoite oli ohjeistuksen luominen rakenteiden ominaismuotojen visuaaliseksi tarkastelemiseksi Lappeenrannan teknillisellä yliopistolla käytettävissä olevilla laitteistoilla ja ohjelmilla. Ohjeistuksen perustana on ajatus siitä, että kokeellinen moodianalyysi saataisiin tehokkaampaan käyttöön koneensuunnittelun opetuksessa. Ohjeistus tehtiin pääasiassa kuvien ja kuvia tukevien selitysten avulla. Työn toisena tavoitteena oli verrata rakenteen ominaisvärähtelyä, kun se oli tuettu vapaasti ja kun se oli tuettu kiinteästi sen luonnolliseen ympäristöön. Taajuuksia verrattaessa huomattiin, että eri tavoin tuetut rakenteet käyttäytyvät eri tavalla, mikä on otettava huomioon, kun tutkitaan kriittisiä värähtelyjä. Ominaisvärähtelyjä voidaan selvittää myös matemaattisesti esimerkiksi äärellisten elementtien menetelmällä. Työn kolmantena tavoitteena oli verrata elementtimenetelmällä ja kokeellisesti saatuja ominaisvärähtelyn arvoja. Elementtimallia pyrittiin tarkentamaan eri parametrejä muuttamalla niin, että ominaistaajuuksien arvot vastaavat mahdollisimman hyvin toisiaan. Tavoite saavutettiin.
Resumo:
This study is concerned with 'nature' specifically as the subject-matter of physics, or natural science, as described by Aristotle in his "Physics". It also discusses the definitions of nature, and more specifically physical nature, provided by Avicenna (d. 1037) and Averroes (d. 1198) in their commentaries on Aristotle's "Physics". Avicenna and Averroes share Aristotle's conception of nature as a principle of motion and rest. While according to Aristotle the subject matter of physics appears to be nature, or what exists by nature, Avicenna believes that it is the natural body, and Averroes holds that the subject matter of physics or natural science consists in the natural things, in what constitutes a slight shift in focus.
Resumo:
Photosynthesis, the process in which carbon dioxide is converted into sugars using the energy of sunlight, is vital for heterotrophic life on Earth. In plants, photosynthesis takes place in specific organelles called chloroplasts. During chloroplast biogenesis, light is a prerequisite for the development of functional photosynthetic structures. In addition to photosynthesis, a number of other metabolic processes such as nitrogen assimilation, the biosynthesis of fatty acids, amino acids, vitamins, and hormones are localized to plant chloroplasts. The biosynthetic pathways in chloroplasts are tightly regulated, and especially the reduction/oxidation (redox) signals play important roles in controlling many developmental and metabolic processes in chloroplasts. Thioredoxins are universal regulatory proteins that mediate redox signals in chloroplasts. They are able to modify the structure and function of their target proteins by reduction of disulfide bonds. Oxidized thioredoxins are restored via the action of thioredoxin reductases. Two thioredoxin reductase systems exist in plant chloroplasts, the NADPHdependent thioredoxin reductase C (NTRC) and ferredoxin-thioredoxin reductase (FTR). The ferredoxin-thioredoxin system that is linked to photosynthetic light reactions is involved in light-activation of chloroplast proteins. NADPH can be produced via both the photosynthetic electron transfer reactions in light, and in darkness via the pentose phosphate pathway. These different pathways of NADPH production enable the regulation of diverse metabolic pathways in chloroplasts by the NADPH-dependent thioredoxin system. In this thesis, the role of NADPH-dependent thioredoxin system in the redox-control of chloroplast development and metabolism was studied by characterization of Arabidopsis thaliana T-DNA insertion lines of NTRC gene (ntrc) and by identification of chloroplast proteins regulated by NTRC. The ntrc plants showed the strongest visible phenotypes when grown under short 8-h photoperiod. This indicates that i) chloroplast NADPH-dependent thioredoxin system is non-redundant to ferredoxinthioredoxin system and that ii) NTRC particularly controls the chloroplast processes that are easily imbalanced in daily light/dark rhythms with short day and long night. I identified four processes and the redox-regulated proteins therein that are potentially regulated by NTRC; i) chloroplast development, ii) starch biosynthesis, iii) aromatic amino acid biosynthesis and iv) detoxification of H2O2. Such regulation can be achieved directly by modulating the redox state of intramolecular or intermolecular disulfide bridges of enzymes, or by protecting enzymes from oxidation in conjunction with 2-cysteine peroxiredoxins. This thesis work also demonstrated that the enzymatic antioxidant systems in chloroplasts, ascorbate peroxidases, superoxide dismutase and NTRC-dependent 2-cysteine peroxiredoxins are tightly linked up to prevent the detrimental accumulation of reactive oxygen species in plants.
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A retrospective study was conducted to identify the occurrence and types of ocular disorders in 57 Amazon parrots admitted to the Ophthalmology Service, Veterinary Teaching Hospital, School of Veterinary Medicine, University of São Paulo, Brazil from 1997 to 2006. The most frequent observed disorder was cataracts, present in 24 of the 114 examined eyes (57 parrots). Uveitis, ulcerative keratitis and keratoconjunctivitis were frequently diagnosed as well. The cornea was the most affected ocular structure, with 28 reported disorders. Uveal disorders also were commonly observed. Conjunctiva and eyelid disorders were diagnosed in lower frequency. Results suggest that cataracts are common and that cornea, lens and uvea are the most affected ocular structures in Amazon parrots.
Resumo:
Technological capabilities are built to support different types of collaboration, and this gives the justification to widely observe, how activity environments are influenced by technology. Technology as an enabler can be addressed from different perspectives, other than merely technological. Dynamic, evolving environment is at the same time interesting but also challenging. As a multinational collaboration environment, the maritime surveillance is an good example of time critical and evolving environment, where technological solutions enable new ways of collaboration. Justification for the inspiration to use maritime environment as the baseline for understanding the challenges in creating and maintaining adequate level of situational awareness, derives from the complexity of the collaboration and information sharing environment elements, needed to be taken into account, when analyzing criticalities related to decision making. Situational awareness is an important element supporting decision making, and challenges related to it can also be observed in the maritime environment. This dissertation describes the structures and factors involved in this complex setting, found from the case studies that should be taken into account when trying to understand, how these elements affect the activities. This dissertation focuses on the gray area that is between a life threatening situation and normal everyday activities. From the multinational experimentation series case studies, MNE5 and MNE6 it was possible to observe situations that were not life threatening for the participants themselves, but not also basic every day activities. These case studies provided a unique possibility to see situations, where gaining of situational awareness and decision making are challenged with time critical crisis situations. Unfortunately organizations do not normally take the benefit from the everyday work to prepare themselves for possible emerging crisis situations. This dissertation focuses on creating a conceptual model and a concept that supports organizations – also outside the maritime community – to improve their ability to support gaining of situational awareness from the individual training level, all the way to changes in organizational structures in aiming for better support for decision making from the individual level to the highest decision making level. Quick changes and unpredictability are reality in organizations and organizations do not have the possibility to control all the factors that affect their functioning. Since we cannot be prepared for everything, and predict every crisis, individual activities inside teams and as a part of organizations, need to be supported with guidance, tools and training in order to support acting in challenging situations. In fact the ideology of the conceptual model created, lies especially in the aim of not controlling everything in beforehand, but supporting organizations with concrete procedures to help individuals to react in different, unpredictable situations, instead of focusing on traditional risk prevention and management. Technological capabilities are not automatically solutions for functional challenges; this is why it is justified to broaden the problem area observation from the technological perspective. This dissertation demonstrates that it is possible to support collaboration in a multinational environment with technological solutions, but it requires the recognition of technological limitations and accepting the possible restrictions related to technological innovations. Technology should not be considered value per se, the value of technology should be defined according to the support of activities, including strategic and operational environment evaluation, identification of organizational elements, and taking into account also the social factors and their challenges. Then we are one step closer to providing technological solutions that support the actual activities by taking into account the variables of the activity environment in question. The multidisciplinary view to approach the information sharing and collaboration framework, is derived especially from the complexity of decision making and building of situational awareness, since they are not build or created in vacuity, but in the organizational framework by the people doing it with the technological capabilities, enabled by the organizational structures. Introduced case studies were related to maritime environment, but according to the research results, it is valid to argue, that based on the lessons learned it is possible to create and further develop conceptual model and to create a general concept to support a wider range of organizations in their attempt to gain better level of situational awareness (SA) and to support decision making. To proof the versatile usage of the developed concept, I have introduced the case study findings to the health care environment and reflected the identified elements from the trauma center to the created concept. The main contribution to complete this adventure is the presented situational awareness concept created in the respect to NATO concept structure. This has been done to tackle the challenge of collaboration by focusing on situational awareness in the information sharing context by providing a theoretical ground and understanding, of how these issues should be approached, and how these elements can be generalized and used to support activities in other environments as well. This dissertation research has been a several year evolving process reflecting and affecting presented case studies and this learning experience from the case studies has also affected the goals and research questions of this dissertation. This venture has been written from a retro perspective according to ideology of process modeling and design rationale to present to the reader how this entire journey took place and what where the critical milestones that affected the end result, conceptual model. Support in a challenging information sharing framework can be provided with the right type of combination of tools, procedures and individual effort. This dissertation will provide insights to those with a new approach to war technology for the organizations to gain a better level of awareness and to improve the capabilities in decision making. This dissertation will present, from the war technology starting point, a new approach and possibility for the organizations to create a better level of awareness and support for decision making with the right combination of tools, procedures and individual effort.
Resumo:
In nature, many animals use body coloration to communicate with each other. For example, colorations can be used as signals between individuals of the same species, but also to recognise individuals of other species, and if they may comprise a threat or not. Many animals use protective coloration to avoid predation. The two most common strategies of protective coloration are camouflage and aposematism. Camouflaged animals have coloration that minimises detection, usually by matching colours or structures in the background. Aposematic animals, on the other hand, signal to predators that they are defended. The defence can be physical structures, such as spikes and hairs, or chemical compounds that make the animal distasteful or even deadly toxic. In order for the warning signal to be effective, the predator has to recognise it as such. Studies have shown that birds for example, that are important visual predators on insects, learn to recognise and avoid unpalatable prey faster if they contrast the background or have large internal contrasts. Typical examples of aposematic species have conspicuous colours like yellow, orange or red, often in combination with black. My thesis focuses on the appearance and function of aposematic colour patterns. Even though researchers have studied aposematism for over a century, there is still a lot we do not know about the phenomenon. For example, as it is crucial that the predators recognise a warning signal, aposematic colorations should assumingly evolve homogeneously and be selected for maximal conspicuousness. Instead, there is an extensive variation of colours and patterns among warning colorations, and it is not uncommon to find typical cryptic colours, such as green and brown in aposematic colour patterns. One hypothesis to this variation is that an aposematic coloration does not have to be maximally signalling in order to be effective, instead it is sufficient to have distinct features that can be easily distinguished from edible prey. To be maximally conspicuous is one way to achieve this, but not the only way. Another hypothesis is that aposematic prey that do not exhibit maximal conspicuousness can exploit both camouflage and aposematism in a distance-dependent fashion, by being signalling when seen close up but camouflaged at a distance. Many prey animals also make use of both strategies by shifting colour at different ecological conditions such as seasonal variations, fluctuations in food resources or between life stages. Yet another explanation for the variation may be that prey animals are usually exposed to several predator species that vary in visual perception and tolerance towards various toxins. The aim with this thesis is, by studying their functions, to understand why aposematic warning signals vary in appearance, specifically in the level of conspicuousness, and if warning coloration can be combined with camouflage. In paper I, I investigated if the colour pattern of the aposematic larva of the Apollo butterfly (Parnassius apollo) can switch function with viewing distance, and be signalling at close range but camouflaged at a distance, by comparing detection time between different colour variants and distances. The results show that the natural coloration has a dual distance-dependent function. Moreover, the study shows that an aposematic coloration does not have to be selected for maximal conspicuousness. A prey animal can optimise its coloration primarily by avoiding detection, but also by investing in a secondary defence, which presence can be signalled if detected. In paper II, I studied how easily detected the coloration of the firebug (Pyrrhocoris apterus), a typical aposematic species, is at different distances against different natural backgrounds, by comparing detection time between different colour variants. Here, I found no distance-dependent switch in function. Instead, the results show that the coloration of the firebug is selected for maximal conspicuousness. One explanation for this is that the firebug is more mobile than the butterfly larva in study I, and movement is often incompatible with efficient camouflage. In paper III, I investigated if a seasonal related colour change in the chemically defended striated shieldbug (Graphosoma lineatum) is an adaptation to optimise a protective coloration by shifting from camouflage to aposematism between two seasons. The results confirm the hypothesis that the coloration expressed in the late summer has a camouflage function, blending in with the background. Further, I investigated if the internal pattern as such increased the effectiveness of the camouflage. Again, the results are in accordance with the hypothesis, as the patterned coloration was more difficult to detect than colorations lacking an internal pattern. This study shows how an aposematic species can optimise its defence by shifting from camouflage to aposematism, but in a different fashion than studied in paper I. The aim with study IV was to study the selection on aposematic signals by identifying characteristics that are common for colorations of aposematic species, and that distinguish them from colorations of other species. I compared contrast, pattern element size and colour proportion between a group of defended species and a group of undefended species. In contrast to my prediction, the results show no significant differences between the two groups in any of the analyses. One explanation for the non-significant results could be that there are no universal characteristics common for aposematic species. Instead, the selection pressures acting on defended species vary, and therefore affect their appearance differently. Another explanation is that all defended species may not have been selected for a conspicuous aposematic warning coloration. Taken together, my thesis shows that having a conspicuous warning coloration is not the only way to be aposematic. Also, aposematism and camouflage is not two mutually exclusive opposites, as there are prey species that exploit both strategies. It is also important to understand that prey animals are exposed to various selection pressures and trade-offs that affect their appearance, and determines what an optimal coloration is for each species or environment. In conclusion, I hold that the variation among warning colorations is larger and coloration properties that have been considered as archetypically aposematic may not be as widespread and representative as previously assumed.
Resumo:
The expression of cytoskeletal proteins was evaluated immunohistochemically in 36 normal ovaries sampled from 18 sows and 44 cystic ovaries sampled from of 22 sows, was evaluated. All sows had history of reproductive problems, such as infertility or subfertility. The immunohistochemically stained area (IHCSA) was quantified through image analysis to evaluate the expression of these proteins in the follicular wall of secondary, tertiary, and cystic follicles. Cytokeratins (CK) immunoreactivity was strong in the granulosa cell layer (GC) and mild in the theca interna (TI) and externa (TE) of the normal follicles. There was severe reduction of the reaction to CK in the GC in the cystic follicles, mainly in the luteinized cysts. The immunoreactivity for vimentin was higher in the GC from normal and cystic follicles in contrast with the other follicular structures. In the luteinized cysts, the IHCSA for vimentin was significantly higher in TI and in both observed cysts, the labeling was more accentuated in TE. Immunohistochemical detection of desmin and α-SMA was restricted to the TE, without differences between the normal and cystic follicles. The results of the current study show that the development of ovarian cysts in sows is associated to changes in the expression of the cytoskeletal proteins CK and vimentin.
Resumo:
The aim of this work is to study the results of tensile tests for austenitic stainless steel type 304 and make accurate FE-models according to the results of the tests. Tensile tests were made at Central Research Institute of Structural Material, Prometey at Saint Petersburg and Mariyenburg in Russia. The test specimens for the tensile tests were produced at Lappeenranta University of Technology in a Laboratory of Steel Structures. In total 4 different tests were made, two with base material specimens and two with transverse butt weld specimens. Each kind of a specimen was tested at room temperature and at low temperature. By comparing the results of room and low temperature tests of similar test specimen we get to study the results of work hardening that affect the austenitic steels at below room temperature. The produced specimens are to be modeled accurately and then imported for nonlinear FEM- analyzing. Using the data gained from the tensile tests the aim is to get the models work like the specimens did during the tests. By using the analyzed results of the FE-models the aim is to calculate and get the stress-strain curves that correspond to the results acquired from the tensile tests.
Resumo:
Nowadays advanced simulation technologies of semiconductor devices occupies an important place in microelectronics production process. Simulation helps to understand devices internal processes physics, detect new effects and find directions for optimization. Computer calculation reduces manufacturing costs and time. Modern simulation suits such as Silcaco TCAD allow simulating not only individual semiconductor structures, but also these structures in the circuit. For that purpose TCAD include MixedMode tool. That tool can simulate circuits using compact circuit models including semiconductor structures with their physical models. In this work, MixedMode is used for simulating transient current technique setup, which include detector and supporting electrical circuit. This technique was developed by RD39 collaboration project for investigation radiation detectors radiation hard properties.
Resumo:
To understand the growth and reproduction of the palm Geonoma schottiana in the gallery forest of Central Brazil, two hypotheses were raised: (i) production of leaves and reproductive structures are concentrated in the period of the year with high light availability; (ii) leaf production and reproductive activity are related to plant length. However, it is expected that senility effects will cause fast reduction in growth and reproduction activities in higher plants. Growth and reproduction were concentrated in the dry season, when insolation is higher than in the wet season, suggesting that leaf and inflorescence production on G. schottiana in the gallery forest understory is more limited by light than by soil humidity. As the individual grows, leaf number and blade area increase, but reproduction activity is independent of plant length. Resources stored in the stem are important to growth, but exogenous factors, as canopy openness, should be more important to reproduction. Plant senescence seems to have a lesser effect on the production of vegetative and reproductive structures in G. schottiana than has been detected in congeneric species with greater clonal activity.
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Dahlstedtia pentaphylla (Taub.) Burkart and D. pinnata (Benth.) Malme belong to the Millettieae tribe and are tropical leguminous trees that produce a strong and unpleasant odour. In the present work, we investigated the distribution, development and histochemistry of foliar and floral secretory cavities that could potentially be related to this odour. The ultrastructure of foliar secretory cavities were also studied and compared with histochemical data. These data were compared with observations recorded for other species of Millettieae in order to gain a phylogenetic and taxonomic perspective. Foliar secretory cavities were only recorded for D. pentaphylla. Floral secretory cavities were present in the calyx, wings and keels in both species; in D. pinnata they also were found in bracteoles and vexillum. Such structures were found to originate through a schizogenous process. Epithelial cells revealed a large amount of flattened smooth endoplasmic reticula, well-developed dictyosomes and vacuoles containing myelin-like structures. Cavity lumen secretion stains strongly for lipids. Features of the secretory cavities studied through ultrastructural and histochemical procedures identify these structures as oil glands. Thus, if the odour produced by such plants has any connection with the accumulation of rotenone, as other species belonging to the "timbó" complex, the lipophilic contents of the secretory cavities of Dahlstedtia species take no part in such odour production. The presence, distribution patterns and frequencies of secretory structures in Dahlstedtia are taxonomically significant and may be utilized as a diagnostic character which justifies the separation of this genus into two species.
Resumo:
Speed, uncertainty and complexity are increasing in the business world all the time. When knowledge and skills become quickly irrelevant, new challenges are set for information technology (IT) education. Meta-learning skills – learning how to learn rapidly - and innovation skills have become more essential than single technologies or other specific issues. The drastic changes in the information and communications technology (ICT) sector have caused a need to reconsider how IT Bachelor education in Universities of Applied Sciences should be organized and employed to cope with the change. The objective of the study was to evaluate how a new approach to IT Bachelor education, the ICT entrepreneurship study path (ICT-ESP) fits IT Bachelor education in a Finnish University of Applied Sciences. This kind of educational arrangement has not been employed elsewhere in the context of IT Bachelor education. The study presents the results of a four-year period during which IT Bachelor education was renewed in a Finnish University of Applied Sciences. The learning environment was organized into an ICT-ESP based on Nonaka’s knowledge theory and Kolb’s experiental learning. The IT students who studied in the ICT-ESP established a cooperative and learned ICT by running their cooperative at the University of Applied Sciences. The students (called team entrepreneurs) studied by reading theory in books and other sources of explicit information, doing projects for their customers, and reflecting in training sessions on what was learnt by doing and by studying the literature. Action research was used as the research strategy in this study. Empirical data was collected via theme-based interviews, direct observation, and participative observation. Grounded theory method was utilized in the data analysis and the theoretical sampling was used to guide the data collection. The context of the University of Applied Sciences provided a good basis for fostering team entrepreneurship. However, the results showed that the employment of the ICT-ESP did not fit into the IT Bachelor education well enough. The ICT-ESP was cognitively too tough for the team entrepreneurs because they had two different set of rules to follow in their studies. The conventional courses engaged lot of energy which should have been spent for professional development in the ICT-ESP. The amount of competencies needed in the ICT-ESP for professional development was greater than those needed for any other ways of studying. The team entrepreneurs needed to develop skills in ICT, leadership and self-leadership, team development and entrepreneurship skills. The entrepreneurship skills included skills on marketing and sales, brand development, productization, and business administration. Considering the three-year time the team entrepreneurs spent in the ICT-ESP, the challenges were remarkable. Changes to the organization of IT Bachelor education are also suggested in the study. At first, it should be admitted that the ICT-ESP produces IT Bachelors with a different set of competencies compared to the conventional way of educating IT Bachelors. Secondly, the number of courses on general topics in mathematics, physics, and languages for team entrepreneurs studying in the ICTESP should be reconsidered and the conventional course-based teaching of the topics should be reorganized to support the team coaching process of the team entrepreneurs with their practiceoriented projects. Third, the upcoming team entrepreneurs should be equipped with relevant information about the ICT-ESP and what it would require in practice to study as a team entrepreneur. Finally, the upcoming team entrepreneurs should be carefully selected before they start in the ICT-ESP to have a possibility to eliminate solo players and those who have a too romantic view of being a team entrepreneur. The results gained in the study provided answers to the original research questions and the objectives of the study were met. Even though the IT degree programme was terminated during the research process, the amount of qualitative data gathered made it possible to justify the interpretations done.
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Previous genetic association studies have overlooked the potential for biased results when analyzing different population structures in ethnically diverse populations. The purpose of the present study was to quantify this bias in two-locus association studies conducted on an admixtured urban population. We studied the genetic structure distribution of angiotensin-converting enzyme insertion/deletion (ACE I/D) and angiotensinogen methionine/threonine (M/T) polymorphisms in 382 subjects from three subgroups in a highly admixtured urban population. Group I included 150 white subjects; group II, 142 mulatto subjects, and group III, 90 black subjects. We conducted sample size simulation studies using these data in different genetic models of gene action and interaction and used genetic distance calculation algorithms to help determine the population structure for the studied loci. Our results showed a statistically different population structure distribution of both ACE I/D (P = 0.02, OR = 1.56, 95% CI = 1.05-2.33 for the D allele, white versus black subgroup) and angiotensinogen M/T polymorphism (P = 0.007, OR = 1.71, 95% CI = 1.14-2.58 for the T allele, white versus black subgroup). Different sample sizes are predicted to be determinant of the power to detect a given genotypic association with a particular phenotype when conducting two-locus association studies in admixtured populations. In addition, the postulated genetic model is also a major determinant of the power to detect any association in a given sample size. The present simulation study helped to demonstrate the complex interrelation among ethnicity, power of the association, and the postulated genetic model of action of a particular allele in the context of clustering studies. This information is essential for the correct planning and interpretation of future association studies conducted on this population.
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This research work addresses the problem of building a mathematical model for the given system of heat exchangers and to determine the temperatures, pressures and velocities at the intermediate positions. Such model could be used in nding an optimal design for such a superstructure. To limit the size and computing time a reduced network model was used. The method can be generalized to larger network structures. A mathematical model which includes a system of non-linear equations has been built and solved according to the Newton-Raphson algorithm. The results obtained by the proposed mathematical model were compared with the results obtained by the Paterson approximation and Chen's Approximation. Results of this research work in collaboration with a current ongoing research at the department will optimize the valve positions and hence, minimize the pumping cost and maximize the heat transfer of the system of heat exchangers.