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Littérature scientifique sur le sujet « Mathematical Proof and Demonstration »

Auteur : Grafiati
Publié le 4 juin 2021
Mis à jour le 13 février 2022

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Articles de revues sur le sujet "Mathematical Proof and Demonstration"

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Hirschhorn, Daniel B., et Denisse R. Thompson. « Technology and Reasoning in Algebra and Geometry ». Mathematics Teacher 89, no 2 (février 1996) : 138–42. http://dx.doi.org/10.5951/mt.89.2.0138.

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If one topic is likely to be stressed by algebra and geometry teachers, it is reasoning. In algebra classes, students are constantly being asked to show their work and justify their simplifications, often without formal connection to proof concepts or the proof process. In geometry classes, students are expected to learn how to write simple proofs. However, evidence shows that students are not learning these reasoning skills. In the 1985–86 National Assessment of Educational Progress, Silver and Carpenter (1989, 18) found that “many eleventhgrade students are confused about the fundamental distinctions among mathematical demonstrations, assumptions, and proofs.” Most students thought a theorem was a demonstration or an assumption. Senk (1985) found that only about 30 percent of students mastered proof wTiting in geometry, despite being enrolled in a year-long course emphasizing proof. Thompson (1992) found that roughly 60 percent of precalculus students were successful at trigonometric-identity proofs, more than 30 percent could complete number-theory proofs dealing with divisibility, and less than 20 percent could handle indirect arguments or proof by mathematical induction.
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Karunakaran, Shiv, Ben Freeburn, Nursen Konuk et Fran Arbaugh. « Improving Preservice Secondary Mathematics Teachers' Capability With Generic Example Proofs ». Mathematics Teacher Educator 2, no 2 (mars 2014) : 158–70. http://dx.doi.org/10.5951/mathteaceduc.2.2.0158.

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Preservice mathematics teachers are entrusted with developing their future students' interest in and ability to do mathematics effectively. Various policy documents place an importance on being able to reason about and prove mathematical claims. However, it is not enough for these preservice teachers, and their future students, to have a narrow focus on only one type of proof (demonstration proof), as opposed to other forms of proof, such as generic example proofs or pictorial proofs. This article examines the effectiveness of a course on reasoning and proving on preservice teachers' awareness of and abilities to recognize and construct generic example proofs. The findings support assertions that such a course can and does change preservice teachers' capability with generic example proofs.
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Meo, Santolo, et Luisa Toscano. « On the Existence and Uniqueness of the ODE Solution and Its Approximation Using the Means Averaging Approach for the Class of Power Electronic Converters ». Mathematics 9, no 10 (19 mai 2021) : 1146. http://dx.doi.org/10.3390/math9101146.

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Power electronic converters are mathematically represented by a system of ordinary differential equations discontinuous right-hand side that does not verify the conditions of the Cauchy-Lipschitz Theorem. More generally, for the properties that characterize their discontinuous behavior, they represent a particular class of systems on which little has been investigated over the years. The purpose of the paper is to prove the existence of at least one global solution in Filippov’s sense to the Cauchy problem related to the mathematical model of a power converter and also to calculate the error in norm between this solution and the integral of its averaged approximation. The main results are the proof of this theorem and the analytical formulation that provides to calculate the cited error. The demonstration starts by a proof of local existence provided by Filippov himself and already present in the literature for a particular class of systems and this demonstration is generalized to the class of electronic power converters, exploiting the non-chattering property of this class of systems. The obtained results are extremely useful for estimating the accuracy of the averaged model used for analysis or control of the effective system. In the paper, the goodness of the analytical proof is supported by experimental tests carried out on a converter prototype representing the class of power electronics converter.
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Hodds, Mark, Lara Alcock et Matthew Inglis. « Self-Explanation Training Improves Proof Comprehension ». Journal for Research in Mathematics Education 45, no 1 (janvier 2014) : 62–101. http://dx.doi.org/10.5951/jresematheduc.45.1.0062.

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In this article, the authors report 3 experiments demonstrating that a simple booklet containing self-explanation training, designed to focus students' attention on logical relationships within a mathematical proof, can significantly improve their proof comprehension.
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Barbero, M., T. Fritzsch, L. Gonella, F. Hügging, H. Krüger, M. Rothermund et N. Wermes. « A via last TSV process applied to ATLAS pixel detector modules : proof of principle demonstration ». Journal of Instrumentation 7, no 08 (10 août 2012) : P08008. http://dx.doi.org/10.1088/1748-0221/7/08/p08008.

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Arpaia, P., M. Buzio, M. Kazazi et S. Russenschuck. « Proof-of-principle demonstration of a translating coils-based method for measuring the magnetic field of axially-symmetric magnets ». Journal of Instrumentation 10, no 02 (10 février 2015) : P02004. http://dx.doi.org/10.1088/1748-0221/10/02/p02004.

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Anellis, Irving. « Charles Peirce and Bertrand Russell on Euclid ». Revista Brasileira de História da Matemática 19, no 37 (16 octobre 2020) : 79–94. http://dx.doi.org/10.47976/rbhm2019v19n3779-94.

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Both Charles Sanders Peirce (1839–1914) and Bertrand Russell (1872–1970) held that Euclid’s proofs in geometry were fundamentally flawed, and based largely on mathematical intuition rather than on sound deductive reasoning. They differed, however, as to the role which diagramming played in Euclid’s emonstrations. Specifically, whereas Russell attributed the failures on Euclid’s proofs to his reasoning from diagrams, Peirce held that diagrammatic reasoning could be rendered as logically rigorous and formal. In 1906, in his manuscript “Phaneroscopy” of 1906, he described his existential graphs, his highly iconic, graphical system of logic, as a moving picture of thought, “rendering literally visible before one’s very eyes the operation of thinking in actu”, and as a “generalized diagram of the Mind” (Peirce 1906; 1933, 4.582). More generally, Peirce personally found it more natural for him to reason diagrammatically, rather than algebraically. Rather, his concern with Euclid’s demonstrations was with its absence of explicit explanations, based upon the laws of logic, of how to proceed from one line of the “proof” to the next. This is the aspect of his criticism of Euclid that he shared with Russell; that Euclid’s demonstrations drew from mathematical intuition, rather than from strict formal deduction.
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Ivliev, Y. « DIAGNOSTICS OF MATHEMATICAL PROOF OF THE BEAL CONJECTURE IN MEDICAL PSYCHOLOGY (REMAKE OF PREVIOUS AUTHOR’S ARTICLES CONCERNING FERMAT’S LAST THEOREM) ». East European Scientific Journal 1, no 5(69) (15 juin 2021) : 28–33. http://dx.doi.org/10.31618/essa.2782-1994.2021.1.69.48.

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In the given work diagnostics of mathematical proof of the Beal Conjecture (Generalized Fermat’s Last Theorem) obtained in the earlier author’s works was conducted and truthfulness of the suggested proof was established. Realizing the process of the Bill Conjecture solution, the mathematical structure defining hypothetical equality of the Fermat theorem was determined. Such a structure turned to be one of Pythagorean theorem with whole numbers. With help of Euclid’s geometrical theorem and Fermat’s method of infinite descent one can manage to set that Pythagorean equation in whole numbers representing Fermat’s Last Theorem cannot exist and then the Fermat theorem is true, that is Fermat’s equality in natural numbers does not exist. Thus mental scheme of “demonstratio mirabile”, which Pierre de Fermat mentioned on the margins of Diophantus’s “Arithmetic”, was reconstructed.
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Casesnoves, Francisco. « Inverse methods and integral-differential model demonstration for optimal mechanical operation of power plants – numerical graphical optimization for second generation of tribology models ». Electrical, Control and Communication Engineering 14, no 1 (1 juillet 2018) : 39–50. http://dx.doi.org/10.2478/ecce-2018-0005.

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Abstract Stepping forward from a previous conference contribution, the article focuses on extension of inverse problem algorithms to integral-differential modelling and formal/strict demonstration of graphical-optimization method. It shows evident-mathematical and 3D-imaging proofs of the graphical optimization method with L1 Norm simulations and algorithms. At present, Linear/Nonlinear Optimization mathematical methods constitute the choice of preference in getting improvements for erosion and corrosion simulations- determinations in general tribology, biotribology and tribocorrosion. The method(s) developed are classical numerical optimization settings for objective functions, programming optimization and simulations, and special software for imaging in 3D. Results are diverse and the range of their applications is wide. First, the article provides a definite formal demonstration of the nonlinear graphical optimization both in numerical results and in imaging. Then, the authors propose the development of programming optimization and mathematical proofs-algorithms of the integral-differential model for various models. Subsequently, an overview of stochastic erosion methods based on Markov Chain is presented in the article. Finally, the second generation of tribology models is defined and conceptually explained. To summarise, the article comprises new findings towards modernization of tribology, biotribology and tribocorrosion models, gathering innovative research branches for future extension of the mathematical modelling progress. The results can be applied to both general techniques and mechanical engineering. The analytical and numerical demonstration of the integral-differential model constitutes a key point and essential result of the research. Extension to electromagnetic and electronic models of these methods is also considered feasible and practical
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Di Liscia, Daniel. « The conclusio pulchra, mirabilis et bona : an ingenious demonstration attributable to Nicole Oresme ». Mediaevalia Textos e estudos 37 (2018) : 139–68. http://dx.doi.org/10.21747/21836884/med37a7.

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Hardly any other concept has occupied the minds of philosophers and scientists as much as the con-cept of infinity. Late medieval philosophy is not an exception. Especially within the context of the so-calledcalculatorestradition a new approach emerged which prioritised the analysis of physical, mathematical, and logical problems over the determination of the essence of infinity and its defini-tion. From the fourteenth century onward, it was not unusual in this context to discuss in detail some special cases of motion which included an augmentationin infinitumof the “degrees of velocity”. This paper focuses on a particular case, the “conclusio mirabilis”, a demonstration to which Oresme could have self-referred in this treatiseDe configurationibusas a “more subtle and more difficult” proof. Whereas this short text has until now been analysed according to only one manuscript, the present contribution involves a research regarding a text conglomerate made up of at least seven manuscripts which are somehow mutually connected. It is argued that an attribution of this demon-stration to Oresme is, with due caution, possible, even if further research is still needed to determine the original shape of the text. In addition, this paper includes a short reference to two later important authors, Biagio Pelacani da Parma and Jacques Almain, whose reception of theconclusio mirabi-lisremained unnoticed in the scholarship until now.
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Thèses sur le sujet "Mathematical Proof and Demonstration"

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Lima, Marcella Luanna da Silva. « Sobre pensamento geomátrico, provas e demonstrações matemáticas de alunos do 2º ano do Ensino Médio nos ambientes Lápis e Papel e Geogebra ». Universidade Estadual da Paraíba, 2015. http://tede.bc.uepb.edu.br/tede/jspui/handle/tede/2336.

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Coordenação de Aperfeiçoamento de Pessoal de Nível Superior - CAPES
Our research work aimed to investigate what type of proof, mathematical demonstration and level of geometrical thinking can occur from a didactic proposal within pencil, paper and GeoGebra environments. As qualitative research and study case, we used as instruments essays with Mathematical Proof and Demonstration themes, a didactic proposal developed by a team of five people who inserted worked collaboratively in the CAPES/OBEDUC/UFMS/UEPB/UFAL Project, field notes, participant observation, audios and photos. We elaborated a didactic proposal with eighteen activities, divided into four parts, which encouraged the students to reflect, justify, prove and demonstrate. The proposal application was carried out in July 2015 with High School 2nd year students of a public school in the town of Areia, Paraíba. For such, the students organized themselves in couples and one trio and the data collection happened in three moments. In the first moment we applied the essay, revised angles, triangles and theorems with the students and worked GeoGebra application with them. In the second moment we applied Parts I and II of the proposal with eight activities on Pythagoras Theorem and three activities on Sum of the Internal Angles of a Triangle Theorem, respectively. In the third moment we applied Part III, with two questions on External Angle Theorem and Part IV, with five question to be worked with the GeoGebra application on Pythagoras Theorem and Sum of the Internal Angles of a Triangle Theorem. In our research work we analyzed the work developed by the trio of students, once they were great in responding all the questions/activities. We analyzed Activity 8 of Part I, Activity 1 and 2 of Part II and all Activities of Part IV, totalizing in eight questions. We used the triangulation method for our study case and, firstly, we traced the profiles of the trio in relation to Mathematical Proof and Demonstration. Then we investigated the geometric thinking and the mathematical proof and demonstration used by the trio of students in the pencil and paper and GeoGebra environments. For such, we used discussions around the level of geometrical thinking proposed by Parzysz (2006) and the type of proofs proposed by Balacheff (2000) and Nasser and Tinoco (2003). From our research results we could conclude that the trio of students could not develop the justifications or proofs, once they did not understand what are mathematical proof and demonstration are, in their essays they understand mathematical proofs as bimestrial evaluations applied by the mathematics teacher. Moreover, the mathematical proofs performed by these students were in accordance with naive empiricism, pragmatic proof (Balacheff, 2000) and graphic justification (Nassar and Tinoco, 2003). In this way, when we observed the students geometrical thinking (Parzysz, 2006) we noted that it fits into two levels of the non-axiomatic Geometry: the Concrete Geomety (G0) and the Spatio-Graphique Geometry (G1), once these students used drawings to justify their affirmations, as the validation of the affirmation was done by the trio. We believe that if in Mathematic classes the teachers contemplate mathematical proof and demonstration, respecting the level of education, the degree of knowledge and maturity of the students, they could strongly contribute to the process of teaching and learning Mathematics and geometrical thinking, once the students would be led to reflect, justify, prove and demonstrate their ideas.
Nossa pesquisa investigou que tipo de provas, demonstrações matemáticas e nível de pensamento geométrico de alunos do 2º Ano do Ensino Médio podem ocorrer a partir de uma proposta didática nos ambientes lápis e papel e GeoGebra. Como pesquisa qualitativa, e estudo de caso, utilizamos como instrumentos redação com o tema Provas e Demonstrações Matemáticas, proposta didática desenvolvida por uma equipe de cinco pessoas que trabalhou de forma colaborativa inserida no Projeto CAPES/OBEDUC/UFMS/UEPB/UFAL Edital 2012, notas de campo, observação participante, gravações em áudio e fotos. Elaboramos uma proposta didática com 18 atividades, dividida em quatro partes, que incentivam alunos a refletirem, justificarem, provarem e demonstrarem. A aplicação dessa proposta se deu em julho de 2015 aos alunos do 2º Ano do Ensino Médio de uma escola pública na cidade de Areia, Paraíba. Para isso, os alunos se agruparam em duplas e um trio e a coleta dos dados se deu em três momentos. No primeiro momento, aplicamos a redação, revisamos com os alunos ângulos, triângulos e teoremas e trabalhamos com eles o aplicativo GeoGebra. No segundo momento, aplicamos as Partes I e II da proposta com 8 atividades sobre Teorema de Pitágoras e 3 atividades sobre Teorema da Soma dos Ângulos Internos de um Triângulo, respectivamente. No terceiro momento, aplicamos a Parte III, com 2 questões sobre o Teorema do Ângulo Externo e a Parte IV, com 5 questões à serem trabalhadas no aplicativo GeoGebra sobre o Teorema de Pitágoras e Teorema da Soma dos Ângulos Internos de um Triângulo. Em nossa pesquisa analisamos o trabalho desenvolvido pelo trio de alunos, uma vez que foram ricos na tentativa de r esponder a todas as perguntas/atividades. Analisamos a Atividade 8 da Parte I, as Atividades 1 e 2 da Parte II e todas as Atividades da Parte IV, totalizando em 8 questões. Utilizamos o método de triangulação de dados para nosso estudo de caso e, primeiramente, traçamos o perfil do trio de alunos com relação às Provas e Demonstrações Matemáticas. Em seguida, investigamos o pensamento geométrico e as provas e demonstrações matemáticas utilizadas pelo trio de alunos nos ambientes lápis e papel e GeoGebra. Para isso, utilizamos as discussões sobre os níveis do pensamento geométrico propostos por Parzysz (2006) e tipos de provas propostos por Balacheff (2000) e Nasser e Tinoco (2003). A partir de nossos resultados pudemos concluir que o trio de alunos não conseguiu desenvolver suas justificativas nem provas, uma vez que não entendem o que vem a ser provas e demonstrações matemáticas, e em suas redações percebemos que estes alunos tratam provas matemáticas como as avaliações aplicadas bimestralmente pelo professor de Matemática. Além disso, as provas matemáticas realizadas por estes alunos se enquadram no empirismo ingênuo, prova pragmática (Balacheff, 2000) e justificativa gráfica (Nasser e Tinoco, 2003). Dessa forma, quando observamos o pensamento geométrico (Parzysz, 2006) destes alunos, notamos que se enquadra nos dois níveis da Geometria não axiomática: a Geometria Concreta (G0) e a Geometria Spatio-Graphique (G1), uma vez que estes alunos se utilizam de desenhos para justificar suas afirmações, como também a validação das afirmações foi feita pela percepção do trio. Acreditamos que se nas aulas de Matemática os professores contemplassem provas e demonstrações matemáticas, respeitando o nível de escolaridade, o grau de conhecimento e a maturidade dos alunos, contribuiriam fortemente para o processo de ensino e aprendizagem da Matemática e do pensamento geométrico, uma vez que os alunos seriam levados a refletir, justificar, provar e demonstrar suas ideias.
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Swanzy, Michael John. « Analysis and demonstration : a proof-of-concept compass star tracker ». Texas A&M University, 2005. http://hdl.handle.net/1969.1/4853.

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This research analyzes and demonstrates the local position determination problem on Earth using a novel instrument, the Compass Star Tracker. Special focus is given to the theoretical development of the mathematics of local position determination, the design and fabrication of a proof-of-concept instrument, an error source analysis, and the experimental tests used to validate the position determination concepts. Star sensors are typically used as attitude determination instruments on spacecraft orbiting Earth. In this capacity, the star sensor determines the orientation of the spacecraft using digital images of the stars. This research utilizes the basic functionality of the star sensor in a new way; the orientation information from the star image is used to determine a user's latitude and longitude coordinates on Earth. This concept is valuable because it allows users to determine their position autonomously. The fundamental concepts that enable local position determination were originally published in Drs. Samaan, Mortari, and Junkins (AAS 04-007). This research improves upon that work by eliminating the zenith-orientation constraint and providing several crucial theoretical corrections. In addition to the position determination mathematics, this research provides analysis of the theoretical and practical error sources associated with the position determination problem. This research also details the design, fabrication, and experimental test program of a proof-of-concept Compass Star Tracker. Together, the theoretical development, error analysis, instrument design, and test program serve as validation of the the position determination concept. This work is intended as the first of many steps toward eventual deployment of autonomous position determination sensors on the Moon and Mars.
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Pasini, Mirtes Fátima. « Argumentação e prova : explorações a partir da análise de uma coleção didática ». Pontifícia Universidade Católica de São Paulo, 2007. https://tede2.pucsp.br/handle/handle/11282.

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Coordenação de Aperfeiçoamento de Pessoal de Nível Superior
This work is inserted the research project Argumentation and Proof in School Mathematics (AProvaME), which aims to study the teaching and learning of mathematical proofs during compulsory schooling. The main research question of this contribution to the project relates to how proof is treated in particular geometry topics in one collection of mathematics textbooks for secondary school students. More specifically, the study aims to identify how the passage from empiricism to deduction is contemplated in the textbook activities as well as to document the interventions and strategies necessary on the part of the mathematics teacher in order to manage this transition. The types of proofs in the classification of Balacheff (1988) and the functions of proof identified by de Villiers (2001) serve as the principle theoretical tools for these analyses. Following a survey of the activities related to proof and proving in topics related to the theorem of Pythagoras and properties of straight lines and triangles, teaching sequences based on these activities were developed with students from the 8th Grade of a secondary school within the public school system of the municipal of Jacupiranga in the State of São Paulo. The main findings of the study indicate that the teacher has at his or her disposal material that permit a broad approach to proof and proving, although the passage from exercises involving reliance on empirical manipulations for validation to the construction of proofs based on mathematical properties is not very explicitly addressed, with the result that intense teacher intervention is necessary at this point. A particular difficulty faced by the teacher is knowing how to intervene without assuming responsibility for the resolution of the task in question. Finally, a dynamic geometry activity is presented, as an attempt to provide a learning situation which might enable students to engage more spontaneously in the transition from evidence-based arguments to valid mathematical proofs
Nosso trabalho está inserido no Projeto Argumentação e Prova na Matemática Escolar (AProvaME), que tem como objetivo estudar o ensino e aprendizagem de provas matemáticas na Educação Básica. A questão principal da pesquisa consiste em analisar o tratamento deste tema em determinados conteúdos geométricos de uma coleção de livros didáticos do Ensino Fundamental. Mais especificamente, o estudo busca identificar como a passagem do empirismo à dedução é contemplada nas atividades dos livros e quais as intervenções e estratégias necessárias por parte do professor para gerenciar essa passagem. Os tipos de prova na classificação de Balacheff (1988) e as funções de prova identificadas por De Villiers (2001) foram as principais ferramentas teóricas utilizadas para estas análises. Após um levantamento das atividades relacionadas à prova nos conteúdos Teorema de Pitágoras, Retas Paralelas e as propriedades dos Triângulos, seqüências baseadas nessas atividades foram desenvolvidas com alunos de 8.ª Série do Ensino Fundamental de uma escola pública no Município de Jacupiranga, do Estado da São Paulo. Concluímos que o professor tem à sua disposição material consistente para trabalhar com seus alunos, embora exista o problema na passagem brusca de exercícios empíricos em diversos níveis de verificação para as demonstrações formais, sendo necessária intervenção do professor por meio de revisões pertinentes, proporcionando ao aluno esclarecimentos para desenvolver uma atividade. A principal dificuldade para o professor foi interferir sem assumir a responsabilidade de resolver a situação em questão. Por fim, apresenta-se uma atividade no ambiente de geometria dinâmica, visando proporcionar uma transição mais espontânea entre argumentos baseados em evidência e argumentos baseados em propriedades matemáticas
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Macmillan, Emily. « Argumentation and Proof : Investigating the Effect of Teaching Mathematical Proof on Students' Argumentation Skills ». Thesis, University of Oxford, 2009. http://ethos.bl.uk/OrderDetails.do?uin=uk.bl.ethos.517230.

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Hemmi, Kirsti. « Approaching Proof in a Community of Mathematical Practice ». Doctoral thesis, Stockholm : Department of Mathematics, Stockholm University, 2006. http://urn.kb.se/resolve?urn=urn:nbn:se:su:diva-1217.

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Owen, Stephen G. « Finding and using analogies to guide mathematical proof ». Thesis, University of Edinburgh, 1988. http://hdl.handle.net/1842/27156.

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This thesis is concerned with reasoning by analogy within the context of auto-mated problem solving. In particular, we consider the provision of an analogical reasoning component to a resolution theorem proving system. The framework for reasoning by analogy which we use (called Basic APS) contains three major components -the finding of analogies (analogy matching), the construction of analogical plans, and the application of the plans to guide the search of a theorem prover. We first discuss the relationship of analogy to other machine learning techniques. We then develop programs for each of the component processes of Basic APS. First we consider analogy matching. We reconstruct, analyse and crticise two previous analogy matchers. We introduce the notion of analogy heuristics in order to understand the matchers. We find that we can explain the short-comings of the matchers in terms of analogy heuristics. We then develop a new analogy matching algorithm, based on flexible application of analogy heuristics, and demonstrate its superiority to the previous matchers. We go on to consider analogical plan construction. We describe procedures for constructing a plan for the solution of a problem, given the solution of a different problem and an analogy match between the two problems. Again, we compare our procedures with corresponding ones from previous systems. We then describe procedures for the execution of analogical plans. We demon-strate the procedures on a number of example analogies. The analogies involved are straightforward for a human, but the problems themselves involve.huge search spaees, if tackled directly using resolution. By comparison with unguided search, we demonstrate the dramatic reductfon in search entaile_d by the use of an ana-logical plan. We then consider some directions for development of our analogy systems, which have not yet been implemented. Firstly, towards more flexible and power-ful execution of analogical plans. Secondly, towards an analogy system which can improve its own ability to find and apply analogies over the course of experience.
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Almeida, Julio Cesar Porfirio de. « Argumentação e prova na matemática escolar do ensino básico : a soma das medidas dos ângulos internos de um triângulo ». Pontifícia Universidade Católica de São Paulo, 2007. https://tede2.pucsp.br/handle/handle/11502.

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This study is about the demonstration of amount of measure the internal angles of triangles made by 8th grade from Fundamental School and the First year of High School, from of resolution of two specified questions. This work intends to contribute with the Argumentation and Proof in School Mathematics project (AprovaME), that has as one of objectives the mapping of conceptions about teenager s argumentation and proofs in public and private schools of São Paulo (state) For this was made a questionnaire in two books, five questions of Algebra and with five questions of Geometry. They were given to 1998 pupils aged between 14 and 16 years. The two analyzed questions are in the Geometry notebook. After checking the given information, took out 50 pupils as sample, that answers were classified in four progressive levels according their form of argument used in evolution of the Pragmatic proof (first principles methods of verification) to the Intellectual proof (elaborations of reasoning from logical-deduction nature and the production of explanation characterized as mathematics demonstration). In the following phase these pupils were put in groups according with the types of answers presented, to do the individual interviews aiming explanations about their choose. Finish the work a conclusive survey based in the results of the analysis, where are suggested forms of approach of subject Proofs and Demonstrations in the classroom, contemplating the execution of dynamic activities that give privilege the construction of mathematically consistent argument based in the expression of generalized reasoning
Este estudo trata da demonstração da soma da medida dos ângulos internos de um triângulo por alunos da oitava série do Ensino Fundamental e da primeira série do Ensino Médio, a partir da resolução de duas questões específicas. Procura contribuir com o Projeto Argumentação e Prova na Matemática Escolar (AprovaME), que tem como um de seus objetivos o mapeamento das concepções sobre argumentação e prova de alunos adolescentes em escolas públicas e particulares do Estado de São Paulo. Para esse levantamento foi elaborado um questionário contendo, em dois cadernos, cinco questões de Álgebra e cinco de Geometria, aplicados a 1998 alunos na faixa etária entre 14 e 16 anos. As duas questões analisadas estão inseridas no caderno de Geometria. Após a tabulação das informações coletadas, extraiu-se dessa população uma amostra de 50 alunos, cujas respostas foram classificadas em quatro níveis progressivos quanto às formas de validação dos argumentos empregados numa evolução da categoria Prova Pragmática (métodos rudimentares de verificação) à Prova Intelectual (elaboração de raciocínios de natureza lógico-dedutiva e produção de explicações caracterizadas como demonstrações matemáticas). Na etapa seguinte, esses alunos foram agrupados de acordo com os tipos de resposta apresentados para a realização de entrevistas individuais visando à obtenção de esclarecimentos adicionais sobre suas escolhas. Encerra o trabalho um panorama conclusivo baseado no resultado da análise em que são sugeridas formas de abordagem do tema Provas e Demonstrações em sala de aula, contemplando a realização de atividades dinâmicas que privilegiem a construção de argumentos matematicamente consistentes, fundamentados na expressão de raciocínios generalizadores
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Van, de Merwe Chelsey Lynn. « Student Use of Mathematical Content Knowledge During Proof Production ». BYU ScholarsArchive, 2020. https://scholarsarchive.byu.edu/etd/8474.

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Proof is an important component of advanced mathematical activity. Nevertheless, undergraduates struggle to write valid proofs. Research identifies many of the struggles students experience with the logical nature and structure of proofs. Little research examines the role mathematical content knowledge plays in proof production. This study begins to fill this gap in the research by analyzing what role mathematical content knowledge plays in the success of a proof and how undergraduates use mathematical content knowledge during proofs. Four undergraduates participated in a series of task-based interviews wherein they completed several proofs. The interviews were analyzed to determine how the students used mathematical content knowledge and how mathematical content knowledge affected a proof’s validity. The results show that using mathematical content knowledge during a proof is nontrivial for students. Several of the proofs attempted by the students were unsuccessful due to issues with mathematical content knowledge. The data also show that students use mathematical content knowledge in a variety of ways. Some student use of mathematical content is productive and efficient, while other student practices are less efficient in formal proofs.
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Cramer, Marcos [Verfasser]. « Proof-checking mathematical texts in controlled natural language / Marcos Cramer ». Bonn : Universitäts- und Landesbibliothek Bonn, 2013. http://d-nb.info/1045276626/34.

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Tanswell, Fenner Stanley. « Proof, rigour and informality : a virtue account of mathematical knowledge ». Thesis, University of St Andrews, 2017. http://hdl.handle.net/10023/10249.

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This thesis is about the nature of proofs in mathematics as it is practiced, contrasting the informal proofs found in practice with formal proofs in formal systems. In the first chapter I present a new argument against the Formalist-Reductionist view that informal proofs are justified as rigorous and correct by corresponding to formal counterparts. The second chapter builds on this to reject arguments from Gödel's paradox and incompleteness theorems to the claim that mathematics is inherently inconsistent, basing my objections on the complexities of the process of formalisation. Chapter 3 looks into the relationship between proofs and the development of the mathematical concepts that feature in them. I deploy Waismann's notion of open texture in the case of mathematical concepts, and discuss both Lakatos and Kneebone's dialectical philosophies of mathematics. I then argue that we can apply work from conceptual engineering to the relationship between formal and informal mathematics. The fourth chapter argues for the importance of mathematical knowledge-how and emphasises the primary role of the activity of proving in securing mathematical knowledge. In the final chapter I develop an account of mathematical knowledge based on virtue epistemology, which I argue provides a better view of proofs and mathematical rigour.
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Livres sur le sujet "Mathematical Proof and Demonstration"

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G, Dhombres Jean, dir. Une histoire de l'imaginaire mathématique : Vers le théorème fondamental de l'algèbre et sa demonstration par Laplace en 1795. Paris : Hermann, 2011.

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1957-, Taylor John, dir. 100% mathematical proof. Chichester : Wiley, 1996.

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Rowan, Garnier, dir. Understanding mathematical proof. Boca Raton : Taylor & Francis, 2014.

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Stirling, David S. G. Mathematical analysis and proof. 2e éd. Chichester, UK : Horwood Pub., 2009.

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Stirling, David S. G. Mathematical analysis and proof. 2e éd. Chichester, UK : Horwood Pub., 2009.

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Mathematical reasoning : Writing and proof. 2e éd. Upper Saddle River, N.J : Pearson Prentice Hall, 2007.

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Mathematical reasoning : Writing and proof. Upper Saddle River, N.J : Prentice Hall, 2003.

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Norman, E. Logic and proof. Needham Heights, MA : Ginn Press, 1991.

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Dragalin, Alʹbert Grigorʹevich. Mathematical intuitionism : Introduction to proof theory. Providence, R.I : American Mathematical Society, 1988.

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Havil, Julian. Nonplussed ! : Mathematical proof of implausible ideas. Princeton, N.J : Princeton University Press, 2011.

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Chapitres de livres sur le sujet "Mathematical Proof and Demonstration"

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Hebborn, J. E., et C. Plumpton. « Mathematical proof ». Dans Methods of Algebra, 42–53. London : Macmillan Education UK, 1985. http://dx.doi.org/10.1007/978-1-349-07670-3_4.

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Schroeder, Severin. « Mathematical Proof ». Dans Wittgenstein on Mathematics, 141–88. New York, NY : Routledge, 2021. | Series : Wittgenstein’s thought and legacy : Routledge, 2020. http://dx.doi.org/10.4324/9781003056904-12.

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Hanna, Gila. « Mathematical Proof ». Dans Advanced Mathematical Thinking, 54–61. Dordrecht : Springer Netherlands, 2002. http://dx.doi.org/10.1007/0-306-47203-1_4.

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Inglis, Matthew, et Andrew Aberdein. « Diversity in Proof Appraisal ». Dans Mathematical Cultures, 163–79. Cham : Springer International Publishing, 2016. http://dx.doi.org/10.1007/978-3-319-28582-5_10.

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Nicholson, Neil R. « Mathematical Induction ». Dans A Transition to Proof, 171–220. Boca Raton : CRC Press, Taylor & Francis Group, 2018. : Chapman and Hall/CRC, 2019. http://dx.doi.org/10.1201/9780429259838-4.

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Lopez-Escobar, E. G. K. « Proof functional connectives ». Dans Methods in Mathematical Logic, 208–21. Berlin, Heidelberg : Springer Berlin Heidelberg, 1985. http://dx.doi.org/10.1007/bfb0075313.

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Gorenstein, Daniel, Richard Lyons et Ronald Solomon. « Outline of proof ». Dans Mathematical Surveys and Monographs, 79–139. Providence, Rhode Island : American Mathematical Society, 1994. http://dx.doi.org/10.1090/surv/040.1/02.

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Mason, John, et Gila Hanna. « Values in Caring for Proof ». Dans Mathematical Cultures, 235–57. Cham : Springer International Publishing, 2016. http://dx.doi.org/10.1007/978-3-319-28582-5_14.

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Alibert, Daniel, et Michael Thomas. « Research on Mathematical Proof ». Dans Advanced Mathematical Thinking, 215–30. Dordrecht : Springer Netherlands, 2002. http://dx.doi.org/10.1007/0-306-47203-1_13.

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Zambrana Castañeda, Guillermo. « Wittgenstein On Mathematical Proof ». Dans Mexican Studies in the History and Philosophy of Science, 235–48. Dordrecht : Springer Netherlands, 1995. http://dx.doi.org/10.1007/978-94-009-0109-4_15.

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Actes de conférences sur le sujet "Mathematical Proof and Demonstration"

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Kawai, Toshio, Yoshiro Mihira, Makoto Sato et Maki Hayashi. « Basis of universal existence of 1/f fluctuation— Mathematical proof and numerical demonstrations ». Dans Noise in physical systems and 1/. AIP, 1993. http://dx.doi.org/10.1063/1.44625.

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Gulen, S. Can, et Raub W. Smith. « A Simple Mathematical Approach to Data Reconciliation in a Single-Shaft Combined-Cycle System ». Dans ASME Turbo Expo 2006 : Power for Land, Sea, and Air. ASMEDC, 2006. http://dx.doi.org/10.1115/gt2006-90145.

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The ultimate proof of the soundness and viability of a novel technology is a full-scale demonstration test in which actual components are run successfully over the entire operating envelope. Consequently, collection of accurate and meaningful test data is of utmost importance to the success of the test. Analysis of such data will validate the original design concepts and lead to paths of further improvement for the next generations thereof. Statistical fundamentals to determine accuracy and precision of measured data are amply documented and readily available in well-established standards. The yardstick that should be used for the “meaningfulness” of measured test data is the satisfaction of the fundamental laws of conservation. While it is known that the “true” values of the sensor data when inserted into the governing equations for the tested component will result in perfect balances, “actual” measured values will always result in “imbalances”. Therefore, reconciliation of the individual measurements with the governing conservation equations is a must prior to actual analysis of the data. Reconciliation in this context is estimation of the “true” values of the sensor data from “actual” sensor data by using statistical concepts. This paper describes the development of a data reconciliation concept that is universally applicable to any process or power plant system where sensor data is used. The usefulness and power of the technique is demonstrated by its application to a single-shaft combined cycle with both gas turbine and steam turbine driving a common generator. In the absence of a reliable and accurate measuring system to individually determine gas and steam turbine shaft outputs, data reconciliation is vital to the accurate analysis of data.
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Sundaresan, Vishnu Baba, et Donald J. Leo. « Experimental Investigation for Chemo-Mechanical Actuation Using Biological Transport Mechanisms ». Dans ASME 2005 International Mechanical Engineering Congress and Exposition. ASMEDC, 2005. http://dx.doi.org/10.1115/imece2005-81366.

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Plants have the ability to develop large mechanical force from chemical energy available with bio-fuels. The energy released by the cleavage of a terminal phosphate ion during the hydrolysis of bio-fuel assists the transport of ions and fluids in cellular homeostasis. Materials that develop pressure and hence strain similar to the response of plants to an external stimuli are classified as nastic materials. Calculations for controlled actuation of an active material inspired by biological transport mechanism demonstrated the feasibility of developing such a material with actuation energy densities on the order of 100kJ/m3 by Sundaresan et. al [2004]. The mathematical model for a simplified proof of concept actuator referred to as micro hydraulic actuator uses ion transporters extracted from plants reconstituted on a synthetic bilayer lipid membrane (BLM). Thermodynamic model of the concept actuator discussed in Sundaresan et. al [2005] predicted the ability to develop 5% normalized deformation in thickness of the micro-hydraulic actuator. Our experimental demonstration of controlled fluid transport through AtSUT4 reconstituted on a 1-Palmitoyl-2-Oleoyl-sn-Glycero-3-[Phospho-L-Serine] (Sodium Salt) (POPS), 1-Palmitoyl-2-Oleoyl-sn-Glycero-3-Phosphoethanolamine (POPE) BLM on lead silicate glass plate having an array of 50 μm holes driven by proton gradient is discussed here.
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Malak, Richard J., Lina Tucker et Christiaan J. J. Paredis. « Composing Tradeoff Models for Multi-Attribute System-Level Decision Making ». Dans ASME 2008 International Design Engineering Technical Conferences and Computers and Information in Engineering Conference. ASMEDC, 2008. http://dx.doi.org/10.1115/detc2008-49970.

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In this paper, we study the prospects for modeling a system by composing tradeoff models of its components. A tradeoff model is an abstract representation of a system in terms of a predictive relationship between its top-level attributes. Designers can use this to predict the attributes they would achieve if they implemented the system. Prior approaches to generating tradeoff information are incompatible with model composition due to their reliance on classical Pareto dominance. We show that by using a generalization of this, called parameterized Pareto dominance, designers can produce tradeoff models that they can compose validly. The focus of this paper is on analyzing the modeling approach mathematically. The main result is proof that, under mild assumptions about how component-level attributes relate to system-level attributes, the approach is mathematically sound from a decision-theoretic perspective. The paper also includes a demonstration of the approach on the design of a hydraulic log splitter system using hydraulic component tradeoff models based on data about commercially-available components.
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Amirudin, Mochammad, Yusuf Fuad et Pradnyo Wijayanti. « Studentsr Proof Schemes for Disproving Mathematical Proposition ». Dans Mathematics, Informatics, Science, and Education International Conference (MISEIC 2018). Paris, France : Atlantis Press, 2018. http://dx.doi.org/10.2991/miseic-18.2018.25.

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MacKenzie, Donald W. « Computers and the Sociology of Mathematical Proof ». Dans 3rd BCS-FACS Northern Formal Methods Workshop. BCS Learning & Development, 1998. http://dx.doi.org/10.14236/ewic/nfm1998.13.

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Gurevich, Shagmar. « Proof of the Kurlberg-Rudnick Rate Conjecture ». Dans p-ADIC MATHEMATICAL PHYSICS : 2nd International Conference. AIP, 2006. http://dx.doi.org/10.1063/1.2193112.

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Spadaccini, Louis, Gregory Tillman, James Gentry, Alexander Chen et Tim Edwards. « Fuel Stabilization Unit Proof of Concept Engine Demonstration ». Dans 44th AIAA/ASME/SAE/ASEE Joint Propulsion Conference & Exhibit. Reston, Virigina : American Institute of Aeronautics and Astronautics, 2008. http://dx.doi.org/10.2514/6.2008-5157.

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Cahit, I. « A Victorian Age Proof of the Four Color Theorem ». Dans ICMS INTERNATIONAL CONFERENCE ON MATHEMATICAL SCIENCE. American Institute of Physics, 2010. http://dx.doi.org/10.1063/1.3525112.

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Mueller, Juergen, Stephen Vargo, David Bame, Dennis Fitzgerald et William Tang. « Proof-of-concept demonstration of a micro-isolation valve ». Dans 35th Joint Propulsion Conference and Exhibit. Reston, Virigina : American Institute of Aeronautics and Astronautics, 1999. http://dx.doi.org/10.2514/6.1999-2726.

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Rapports d'organisations sur le sujet "Mathematical Proof and Demonstration"

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Farmer, W. M., J. D. Guttman et F. J. Thayer. IMPS : An Interactive Mathematical Proof System. Fort Belvoir, VA : Defense Technical Information Center, juillet 1991. http://dx.doi.org/10.21236/ada243162.

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Casagranda, A., D. S. Stafford, G. Pastore, R. L. Williamson, B. W. Spencer et J. D. Hales. UFD Proof-of-Concept Demonstration. Office of Scientific and Technical Information (OSTI), juin 2017. http://dx.doi.org/10.2172/1408525.

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Fletcher, B. E. Underwater Security Vehicle Proof of Concept Demonstration. Fort Belvoir, VA : Defense Technical Information Center, mars 1993. http://dx.doi.org/10.21236/ada264713.

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Chawda, P. V. Proof-of-Concept Demonstration Results for Robotic Visual Servo Controllers. Office of Scientific and Technical Information (OSTI), septembre 2004. http://dx.doi.org/10.2172/885667.

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Rhodes, E. A., D. L. Bowers, R. E. Boyar et C. E. Dickerman. Advanced concept proof-of-principle demonstration : Switchable radioactive neutron source. Office of Scientific and Technical Information (OSTI), octobre 1995. http://dx.doi.org/10.2172/197135.

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Hablanian, David A., Michael Bryant, Nelson Carbonell, Allan Chertok et Paul McTaggart. Modular Aircraft Support System (MASS) Proof-of-Concept Demonstrator Field Demonstration. Fort Belvoir, VA : Defense Technical Information Center, octobre 2001. http://dx.doi.org/10.21236/ada413306.

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Mosallaei, Hossein. Realization of Metamaterial-Based Devices : Mathematical Theory and Physical Demonstration. Fort Belvoir, VA : Defense Technical Information Center, février 2010. http://dx.doi.org/10.21236/ada515521.

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BAIDE, D. G. TANK 241-U-107 SALTCAKE DISSOLUTION PROOF OF CONCEPT RETRIEVAL DEMONSTRATION OPERATIONAL RESULTS. Office of Scientific and Technical Information (OSTI), juin 2003. http://dx.doi.org/10.2172/812316.

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Peter, F. J., et G. R. Laguna. Autonomous gas chromatograph system for Thermal Enhanced Vapor Extraction System (TEVES) proof of concept demonstration. Office of Scientific and Technical Information (OSTI), septembre 1996. http://dx.doi.org/10.2172/383609.

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Hu, P. S. Proof of Concept of ITS as An Alternative Data Resource : A Demonstration Project of Florida and New York Data. Office of Scientific and Technical Information (OSTI), décembre 2001. http://dx.doi.org/10.2172/814552.

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