Understanding mathematical proof
Taylor, John
2014-01-01
Introduction The need for proof The language of mathematics Reasoning Deductive reasoning and truth Example proofs Logic and ReasoningIntroduction Propositions, connectives, and truth tables Logical equivalence and logical implication Predicates and quantification Logical reasoning Sets and Functions Introduction Sets and membership Operations on setsThe Cartesian product Functions and composite functions Properties of functions The Structure of Mathematical ProofsIntroduction Some proofs dissected An informal framework for proofs Direct proof A more formal framework Finding Proofs Direct proo
Proof Auditing Formalised Mathematics
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Mark Miles Adams
2016-01-01
Full Text Available The first three formalisations of major mathematical proofs have heralded a new age in formalised mathematics, establishing that informal proofs at the limits of what can be understood by humans can be checked by machine. However, formalisation itself can be subject to error, and yet there is currently no accepted process in checking, or even much concern that such checks have not been performed. In this paper, we motivate why we should be concerned about correctness, and argue the need for proof auditing, to rigorously and independently check a formalisation. We discuss the issues involved in performing an audit, and propose an effective and efficient auditing process. Throughout we use the Flyspeck Project, that formalises the Kepler Conjecture proof, to illustrate our point.
Dickerson, David S.; Doerr, Helen M.
2014-12-01
Proof serves many purposes in mathematics. In this qualitative study of 17 high school mathematics teachers, we found that these teachers perceived that two of the most important purposes for proof in school mathematics were (a) to enhance students' mathematical understanding and (b) to develop generalized thinking skills that were transferable to other fields of endeavor. We found teachers were divided on the characteristics (or features) of proofs that would serve these purposes. Teachers with less experience tended to believe that proofs in the high school should adhere to strict standards of language and reasoning while teachers with more experience tended to believe that proofs based on concrete or visual features were well suited for high school mathematics. This study has implications for teacher preparation because it appears that there is a wide variation in how teachers think about proof. It seems likely that students would experience proof very differently merely because they were seated in different classrooms.
Lakatos and Hersh on Mathematical Proof
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Hossein Bayat
2015-12-01
Full Text Available The concept of Mathematical Proof has been controversial for the past few decades. Different philosophers have offered different theories about the nature of Mathematical Proof, among which theories presented by Lakatos and Hersh have had significant similarities and differences with each other. It seems that a comparison and critical review of these two theories will lead to a better understanding of the concept of mathematical proof and will be a big step towards solving many related problems. Lakatos and Hersh argue that, firstly, “mathematical proof” has two different meanings, formal and informal; and, secondly, informal proofs are affected by human factors, such as individual decisions and collective agreements. I call these two thesis, respectively, “proof dualism” and “humanism”. But on the other hand, their theories have significant dissimilarities and are by no means equivalent. Lakatos is committed to linear proof dualism and methodological humanism, while Hersh’s theory involves some sort of parallel proof dualism and sociological humanism. According to linear proof dualism, the two main types of proofs are provided in order to achieve a common goal: incarnation of mathematical concepts and methods and truth. However, according to the parallel proof dualism, two main types of proofs are provided in order to achieve two different types of purposes: production of a valid sequence of signs (the goal of the formal proof and persuasion of the audience (the goal of the informal proof. Hersh’s humanism is informative and indicates pluralism; whereas, Lakatos’ version of humanism is normative and monistic.
Proof and knowledge in mathematics
Detlefsen, Michael
2005-01-01
These questions arise from any attempt to discover an epistemology for mathematics. This collection of essays considers various questions concerning the nature of justification in mathematics and possible sources of that justification. Among these are the question of whether mathematical justification is a priori or a posteriori in character, whether logical and mathematical differ, and if formalization plays a significant role in mathematical justification,
Introduction to proof in abstract mathematics
Wohlgemuth, Andrew
2011-01-01
The primary purpose of this undergraduate text is to teach students to do mathematical proofs. It enables readers to recognize the elements that constitute an acceptable proof, and it develops their ability to do proofs of routine problems as well as those requiring creative insights. The self-contained treatment features many exercises, problems, and selected answers, including worked-out solutions. Starting with sets and rules of inference, this text covers functions, relations, operation, and the integers. Additional topics include proofs in analysis, cardinality, and groups. Six appendixe
Exploring mathematics problem-solving and proof
Grieser, Daniel
2018-01-01
Have you ever faced a mathematical problem and had no idea how to approach it? Or perhaps you had an idea but got stuck halfway through? This book guides you in developing your creativity, as it takes you on a voyage of discovery into mathematics. Readers will not only learn strategies for solving problems and logical reasoning, but they will also learn about the importance of proofs and various proof techniques. Other topics covered include recursion, mathematical induction, graphs, counting, elementary number theory, and the pigeonhole, extremal and invariance principles. Designed to help students make the transition from secondary school to university level, this book provides readers with a refreshing look at mathematics and deep insights into universal principles that are valuable far beyond the scope of this book. Aimed especially at undergraduate and secondary school students as well as teachers, this book will appeal to anyone interested in mathematics. Only basic secondary school mathematics is requi...
Towards an Intelligent Tutor for Mathematical Proofs
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Serge Autexier
2012-02-01
Full Text Available Computer-supported learning is an increasingly important form of study since it allows for independent learning and individualized instruction. In this paper, we discuss a novel approach to developing an intelligent tutoring system for teaching textbook-style mathematical proofs. We characterize the particularities of the domain and discuss common ITS design models. Our approach is motivated by phenomena found in a corpus of tutorial dialogs that were collected in a Wizard-of-Oz experiment. We show how an intelligent tutor for textbook-style mathematical proofs can be built on top of an adapted assertion-level proof assistant by reusing representations and proof search strategies originally developed for automated and interactive theorem proving. The resulting prototype was successfully evaluated on a corpus of tutorial dialogs and yields good results.
Preservice Mathematics Teachers' Metaphorical Perceptions towards Proof and Proving
Ersen, Zeynep Bahar
2016-01-01
Since mathematical proof and proving are in the center of mathematics; preservice mathematics teachers' perceptions against these concepts have a great importance. Therefore, the study aimed to determine preservice mathematics teachers' perceptions towards proof and proving through metaphors. The participants consisted of 192 preservice…
Proof, rigour and informality : a virtue account of mathematical knowledge
Tanswell, Fenner Stanley
2017-01-01
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...
Skolem and pessimism about proof in mathematics.
Cohen, Paul J
2005-10-15
Attitudes towards formalization and proof have gone through large swings during the last 150 years. We sketch the development from Frege's first formalization, to the debates over intuitionism and other schools, through Hilbert's program and the decisive blow of the Gödel Incompleteness Theorem. A critical role is played by the Skolem-Lowenheim Theorem, which showed that no first-order axiom system can characterize a unique infinite model. Skolem himself regarded this as a body blow to the belief that mathematics can be reliably founded only on formal axiomatic systems. In a remarkably prescient paper, he even sketches the possibility of interesting new models for set theory itself, something later realized by the method of forcing. This is in contrast to Hilbert's belief that mathematics could resolve all its questions. We discuss the role of new axioms for set theory, questions in set theory itself, and their relevance for number theory. We then look in detail at what the methods of the predicate calculus, i.e. mathematical reasoning, really entail. The conclusion is that there is no reasonable basis for Hilbert's assumption. The vast majority of questions even in elementary number theory, of reasonable complexity, are beyond the reach of any such reasoning. Of course this cannot be proved and we present only plausibility arguments. The great success of mathematics comes from considering 'natural problems', those which are related to previous work and offer a good chance of being solved. The great glories of human reasoning, beginning with the Greek discovery of geometry, are in no way diminished by this pessimistic view. We end by wishing good health to present-day mathematics and the mathematics of many centuries to come.
Explanatory Unification by Proofs in School Mathematics
Komatsu, Kotaro; Fujita, Taro; Jones, Keith; Naoki, Sue
2018-01-01
Kitcher's idea of 'explanatory unification', while originally proposed in the philosophy of science, may also be relevant to mathematics education, as a way of enhancing student thinking and achieving classroom activity that is closer to authentic mathematical practice. There is, however, no mathematics education research treating explanatory…
Semantic Contamination and Mathematical Proof: Can a Non-Proof Prove?
Mejia-Ramos, Juan Pablo; Inglis, Matthew
2011-01-01
The way words are used in natural language can influence how the same words are understood by students in formal educational contexts. Here we argue that this so-called semantic contamination effect plays a role in determining how students engage with mathematical proof, a fundamental aspect of learning mathematics. Analyses of responses to…
Proofs of the Cantor-Bernstein theorem a mathematical excursion
Hinkis, Arie
2013-01-01
This book offers an excursion through the developmental area of research mathematics. It presents some 40 papers, published between the 1870s and the 1970s, on proofs of the Cantor-Bernstein theorem and the related Bernstein division theorem. While the emphasis is placed on providing accurate proofs, similar to the originals, the discussion is broadened to include aspects that pertain to the methodology of the development of mathematics and to the philosophy of mathematics. Works of prominent mathematicians and logicians are reviewed, including Cantor, Dedekind, Schröder, Bernstein, Borel, Zermelo, Poincaré, Russell, Peano, the Königs, Hausdorff, Sierpinski, Tarski, Banach, Brouwer and several others mainly of the Polish and the Dutch schools. In its attempt to present a diachronic narrative of one mathematical topic, the book resembles Lakatos’ celebrated book Proofs and Refutations. Indeed, some of the observations made by Lakatos are corroborated herein. The analogy between the two books is clearly an...
Why prove it again? alternative proofs in mathematical practice
Dawson, Jr , John W
2015-01-01
This monograph considers several well-known mathematical theorems and asks the question, “Why prove it again?” while examining alternative proofs. It explores the different rationales mathematicians may have for pursuing and presenting new proofs of previously established results, as well as how they judge whether two proofs of a given result are different. While a number of books have examined alternative proofs of individual theorems, this is the first that presents comparative case studies of other methods for a variety of different theorems. The author begins by laying out the criteria for distinguishing among proofs and enumerates reasons why new proofs have, for so long, played a prominent role in mathematical practice. He then outlines various purposes that alternative proofs may serve. Each chapter that follows provides a detailed case study of alternative proofs for particular theorems, including the Pythagorean Theorem, the Fundamental Theorem of Arithmetic, Desargues’ Theorem, the...
The Development of Proofs in Analytical Mathematics for Undergraduate Students
Ali, Maselan; Sufahani, Suliadi; Hasim, Nurnazifa; Saifullah Rusiman, Mohd; Roslan, Rozaini; Mohamad, Mahathir; Khalid, Kamil
2018-04-01
Proofs in analytical mathematics are essential parts of mathematics, difficult to learn because its underlying concepts are not visible. This research consists of problems involving logic and proofs. In this study, a short overview was provided on how proofs in analytical mathematics were used by university students. From the results obtained, excellent students obtained better scores compared to average and poor students. The research instruments used in this study consisted of two parts: test and interview. In this way, analysis of students’ actual performances can be obtained. The result of this study showed that the less able students have fragile conceptual and cognitive linkages but the more able students use their strong conceptual linkages to produce effective solutions
Visual Considerations in the Presentation of Mathematical Proofs
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Lara Alcock
2010-11-01
Full Text Available This article is about visual issues in the presentation of mathematics within teaching situations. It focuses particularly on the presentation of proofs to undergraduate students. We describe some of the decisions that a lecturer must make when presenting a written proof, from the layout of individual equations to the layout of a whole argument on the page. We consider the way in which these decisions are made explicit for lecturers who construct electronic learning resources termed e-Proofs, and conclude by discussing the constraints and affordances of this technology.
ProofJudge: Automated Proof Judging Tool for Learning Mathematical Logic
DEFF Research Database (Denmark)
Villadsen, Jørgen
2015-01-01
Today we have software in many artefacts, from medical devices to cars and airplanes, and the software must not only be efficient and intelligent but also reliable and secure. Tests can show the presence of bugs but cannot guarantee their absence. A machine-checked proof using mathematical logic...... pen and paper because no adequate tool was available. The learning problem is how to make abstract concepts of logic as concrete as possible. ProofJudge is a computer system and teaching approach for teaching mathematical logic and automated reasoning which augments the e-learning tool NaDeA (Natural...
ProofJudge: Automated Proof Judging Tool for Learning Mathematical Logic
DEFF Research Database (Denmark)
Villadsen, Jørgen
2016-01-01
Today we have software in many artefacts, from medical devices to cars and airplanes, and the software must not only be efficient and intelligent but also reliable and secure. Tests can show the presence of bugs but cannot guarantee their absence. A machine-checked proof using mathematical logic...... using pen and paper because no adequate tool was available. The learning problem is how to make abstract concepts of logic as concrete as possible. ProofJudge is a computer system and teaching approach for teaching mathematical logic and automated reasoning which augments the e-learning tool Na...
The Proof is in the Pudding The Changing Nature of Mathematical Proof
Krantz, Steven G
2011-01-01
This text explores the many transformations that the mathematical proof has undergone from its inception to its versatile, present-day use, considering the advent of high-speed computing machines. Though there are many truths to be discovered in this book, by the end it is clear that there is no formalized approach or standard method of discovery to date. Most of the proofs are discussed in detail with figures and equations accompanying them, allowing both the professional mathematician and those less familiar with mathematics to derive the same joy from reading this book.
Roads to infinity the mathematics of truth and proof
Stillwell, John C
2010-01-01
Winner of a CHOICE Outstanding Academic Title Award for 2011!This book offers an introduction to modern ideas about infinity and their implications for mathematics. It unifies ideas from set theory and mathematical logic, and traces their effects on mainstream mathematical topics of today, such as number theory and combinatorics. The treatment is historical and partly informal, but with due attention to the subtleties of the subject. Ideas are shown to evolve from natural mathematical questions about the nature of infinity and the nature of proof, set against a background of broader questions
Feriyanto
2018-01-01
This research aims to describe the ability of students’ mathematical proof in determining the validity of argument reviewed from gender differences. The subjects of this research were one male and one female student of the fifth semester of Mathematic Education study program. The subjects were selected based on the highest mathematics ability which was assesed from their previous assignments and tests. In addition, the communication ability of the subjects was also considered in order to facilitate the researcher in conducting interviews. Based on the result of the test with direct and indirect proof, it could be concluded that the subjects were able to: 1) mention all facts/premises and write about what should be shown (conclusion) in direct proof and write additional premise in indirect proof; 2) connect facts/premises to concepts which must be mastered; 3) use equivalent concept to manipulate and organize the proof; 4) use the concept of syllogism and tollens mode to obtain the desired conclusion; 5) construct mathematical evidence systematically, and logically; 6) complement the reason for each step appropriately. The difference was that the male subject wrote the final conclusion, while the female subject did not write the final conclusion on the proof.
Philosophy of mathematics an introduction to a world of proofs and pictures
Brown, James Robert
1999-01-01
This text discusses the great philosophers and the importance of mathematics to their thought. It includes topics such as: the mathematical image; platonism; picture-proofs; applied mathematics; Hilbert and Godel; knots and nations; definitions; picture-proofs and Wittgenstein; and computation, proof and conjecture.
Proofs and fundamentals a first course in abstract mathematics
Bloch, Ethan D
2003-01-01
In an effort to make advanced mathematics accessible to a wide variety of students, and to give even the most mathematically inclined students a solid basis upon which to build their continuing study of mathematics, there has been a tendency in recent years to introduce students to the for mulation and writing of rigorous mathematical proofs, and to teach topics such as sets, functions, relations and countability, in a "transition" course, rather than in traditional courses such as linear algebra. A transition course functions as a bridge between computational courses such as Calculus, and more theoretical courses such as linear algebra and abstract algebra. This text contains core topics that I believe any transition course should cover, as well as some optional material intended to give the instructor some flexibility in designing a course. The presentation is straightforward and focuses on the essentials, without being too elementary, too exces sively pedagogical, and too full to distractions. Some of ...
Komatsu, Kotaro
2016-01-01
The process of proofs and refutations described by Lakatos is essential in school mathematics to provide students with an opportunity to experience how mathematical knowledge develops dynamically within the discipline of mathematics. In this paper, a framework for describing student processes of proofs and refutations is constructed using a set of…
Students Thinking Process in Compiling Mathematical Proof with Semantics Strategy
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Abdussakir Abdussakir
2015-03-01
Full Text Available Proses Berpikir Mahasiswa dalam Menyusun Bukti Matematis dengan Strategi Semantik Abstract: This study is aimed to reveal the thinking process in proof construction performed by students with semantic strategy. This study use descriptive-qualitative approach. The thinking process of students will be analyzed using theoretical framework of David Tall about the three worlds of mathematical thinking. The result are three ways of thinking in semantic strategy, namely (1 started from formal world then move into the symbolic or embodied-symbolic world with possibility of more than once and ends within or outside of the formal world, (2 started from symbolic world or embodied-symbolic world then move to the formal world with possibility of more than once and ends within or outside of the formal world, and (3 all thinking processes performed outside of formal world that does not obtain formal proof. Key Words: thinking process, mathematical proof, semantic strategy Abstrak: Penelitian ini bertujuan untuk menjelaskan proses berpikir mahasiswa dalam menyusun bukti matematis dengan strategi semantik. Penelitian ini menggunakan pendekatan deskiptif-kualitatif. Analisis data dilakukan dengan menggunakan kerangka kerja David Tall tentang tiga dunia berpikir matematik. Hasil penelitian menunjukkan bahwa terdapat enam kemungkinan jalur dalam strategi semantik ditinjau dari teori tiga dunia berpikir matematis. Hasil penelitian menunjukkan ada tiga jalur berpikir mahasiswa dalam menyusun bukti matematis dengan strategi semantik, yaitu (1 bermula dari dunia berpikir formal berpindah ke dunia berpikir wujud-simbolik atau dunia berpikir simbolik dengan proses perpindahan dimungkinkan lebih dari satu kali dan berakhir di dalam atau di luar dunia berpikir formal, (2 bermula dari dunia berpikir wujud simbolik atau dunia berpikir simbolik (non RSP lalu pindah ke dunia berpikir formal dengan proses perpindahan dimungkinkan lebih dari satu kali dan berakhir di
Exploring Logical Reasoning and Mathematical Proof in Grade 6 Elementary School Students
Flegas, Konstantinos; Charalampos, Lemonidis
2013-01-01
Research and classroom experience reveal that the construction of mathematical proofs is difficult for all students. While many contemporary mathematics curricula recognize the importance of teaching reasoning and proof, in Greece these concepts are introduced at the secondary education level. In this study, we will attempt to investigate a group…
Ugurel, Isikhan; Morali, H. Sevgi; Karahan, Ozge; Boz, Burcak
2016-01-01
The purpose of this study is to describe the procedure and examples of visual proofs (VP-or proof without words) developed by gifted mathematics secondary school students after their experiences. The participants of this study are three male 9th grade students enrolled in a private science high school. In the first stage of the research a briefing…
Opportunities to Learn Reasoning and Proof in High School Mathematics Textbooks
Thompson, Denisse R.; Senk, Sharon L.; Johnson, Gwendolyn J.
2012-01-01
The nature and extent of reasoning and proof in the written (i.e., intended) curriculum of 20 contemporary high school mathematics textbooks were explored. Both the narrative and exercise sets in lessons dealing with the topics of exponents, logarithms, and polynomials were examined. The extent of proof-related reasoning varied by topic and…
Bergwall, Andreas; Hemmi, Kirsti
2017-01-01
Students' difficulties with proof, scholars' calls for proof to be a consistent part of K-12 mathematics, and the extensive use of textbooks in mathematics classrooms motivate investigations on how proof-related items are addressed in mathematics textbooks. We contribute to textbook research by focusing on opportunities to learn proof-related…
Revisiting the reliability of published mathematical proofs: where do we go next?
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Joachim Frans
2014-08-01
Full Text Available Mathematics seems to have a special status when compared to other areas of human knowledge. This special status is linked with the role of proof. Mathematicians all too often believe that this type of argumentation leaves no room for errors or unclarity. In this paper we take a closer look at mathematical practice, more precisely at the publication process in mathematics. We argue that the apparent view that mathematical literature is also more reliable is too naive. We will discuss several problems in the publication process that threaten this view, and give several suggestions on how this could be countered.
Von Neumann's impossibility proof: Mathematics in the service of rhetorics
Dieks, Dennis
2017-11-01
According to what has become a standard history of quantum mechanics, in 1932 von Neumann persuaded the physics community that hidden variables are impossible as a matter of principle, after which leading proponents of the Copenhagen interpretation put the situation to good use by arguing that the completeness of quantum mechanics was undeniable. This state of affairs lasted, so the story continues, until Bell in 1966 exposed von Neumann's proof as obviously wrong. The realization that von Neumann's proof was fallacious then rehabilitated hidden variables and made serious foundational research possible again. It is often added in recent accounts that von Neumann's error had been spotted almost immediately by Grete Hermann, but that her discovery was of no effect due to the dominant Copenhagen Zeitgeist. We shall attempt to tell a story that is more historically accurate and less ideologically charged. Most importantly, von Neumann never claimed to have shown the impossibility of hidden variables tout court, but argued that hidden-variable theories must possess a structure that deviates fundamentally from that of quantum mechanics. Both Hermann and Bell appear to have missed this point; moreover, both raised unjustified technical objections to the proof. Von Neumann's argument was basically that hidden-variables schemes must violate the ;quantum principle; that physical quantities are to be represented by operators in a Hilbert space. As a consequence, hidden-variables schemes, though possible in principle, necessarily exhibit a certain kind of contextuality. As we shall illustrate, early reactions to Bohm's theory are in agreement with this account. Leading physicists pointed out that Bohm's theory has the strange feature that pre-existing particle properties do not generally reveal themselves in measurements, in accordance with von Neumann's result. They did not conclude that the ;impossible was done; and that von Neumann had been shown wrong.
Abdoli-Eramaki, Mohammad; Stevenson, Joan M; Reid, Susan A; Bryant, Timothy J
2007-01-01
In our laboratory, we have developed a prototype of a personal lift augmentation device (PLAD) that can be worn by workers during manual handling tasks involving lifting or lowering or static holding in symmetric and asymmetric postures. Our concept was to develop a human-speed on-body assistive device that would reduce the required lumbar moment by 20-30% without negative consequences on other joints or lifting kinematics. This paper provides mathematical proof using simplified free body diagrams and two-dimensional moment balance equations. Empirical proof is also provided based on lifting trials with nine male subjects who executed sagittal plane lifts using three lifting styles (stoop, squat, free) and three different loads (5, 15, and 25kg) under two conditions (PLAD, No-PLAD). Nine Fastrak sensors and six in-line strap force sensors were used to estimate the reduction of compressive and shear forces on L4/L5 as well as estimate the forces transferred to the shoulders and knees. Depending on lifting technique, the PLAD applied an added 23-36Nm of torque to assist the back muscles during lifting tasks. The peak pelvic girdle contact forces were estimated and their magnitudes ranged from 221.3+/-11.2N for stoop lifting, 324.3+/-17.2N for freestyle lifts to 468.47+/-23.2N for squat lifting. The PLAD was able to reduce the compression and shear forces about 23-29% and 7.9-8.5%, respectively.
Teaching Proofs and Algorithms in Discrete Mathematics with Online Visual Logic Puzzles
Cigas, John; Hsin, Wen-Jung
2005-01-01
Visual logic puzzles provide a fertile environment for teaching multiple topics in discrete mathematics. Many puzzles can be solved by the repeated application of a small, finite set of strategies. Explicitly reasoning from a strategy to a new puzzle state illustrates theorems, proofs, and logic principles. These provide valuable, concrete…
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Satsope Maoto
2018-03-01
Full Text Available This article focuses mainly on two key mathematical processes (representation, and reasoning and proof. Firstly, we observed how teachers learn these processes and subsequently identify what and how to assess learners on the same processes. Secondly, we reviewed one teacher’s attempt to facilitate the learning of the processes in his classroom. Two interrelated questions were pursued: ‘what are the teachers’ challenges in learning mathematical processes?’ and ‘in what ways are teachers’ approaches to learning mathematical processes influencing how they assess their learners on the same processes?’ A case study was undertaken involving 10 high school mathematics teachers who enrolled for an assessment module towards a Bachelor in Education Honours degree in mathematics education. We present an interpretive analysis of two sets of data. The first set consisted of the teachers’ written responses to a pattern searching activity. The second set consisted of a mathematical discourse on matchstick patterns in a Grade 9 class. The overall finding was that teachers rush through forms of representation and focus more on manipulation of numerical representations with a view to deriving symbolic representation. Subsequently, this unidirectional approach limits the scope of assessment of mathematical processes. Interventions with regard to the enhancement of these complex processes should involve teachers’ actual engagements in and reflections on similar learning.
Joshi, Mark
2015-01-01
This innovative textbook introduces a new pattern-based approach to learning proof methods in the mathematical sciences. Readers will discover techniques that will enable them to learn new proofs across different areas of pure mathematics with ease. The patterns in proofs from diverse fields such as algebra, analysis, topology and number theory are explored. Specific topics examined include game theory, combinatorics, and Euclidean geometry, enabling a broad familiarity. The author, an experienced lecturer and researcher renowned for his innovative view and intuitive style, illuminates a wide range of techniques and examples from duplicating the cube to triangulating polygons to the infinitude of primes to the fundamental theorem of algebra. Intended as a companion for undergraduate students, this text is an essential addition to every aspiring mathematician’s toolkit.
Babb, Jeff
2005-01-01
This paper examines the mathematical work of the French bishop, Nicole Oresme (c. 1323-1382), and his contributions towards the development of the concept of graphing functions and approaches to investigating infinite series. The historical importance and pedagogical value of his work will be considered in the context of an undergraduate course on…
A Coordinate-Based Proof of the Scallop Theorem
Ishimoto, Kenta; Yamada, Michio
2012-01-01
We reconsider fluid dynamics for a self-propulsive swimmer in Stokes flow. With an exact definition of deformation of a swimmer, a coordinate-based proof is first given to Purcell's scallop theorem including the body rotation.
Zengin, Yılmaz
2017-11-01
The purpose of this study is to determine the effect of GeoGebra software on pre-service mathematics teachers' attitudes towards proof and proving and to determine pre-service teachers' pre- and post-views regarding proof. The study lasted nine weeks and the participants of the study consisted of 24 pre-service mathematics teachers. The study used the 'Attitude Scale Towards Proof and Proving' and an open-ended questionnaire that were administered before and after the intervention as data collection tools. Paired samples t-test analysis was used for the analysis of quantitative data and content and descriptive analyses were utilized for the analysis of qualitative data. As a result of the data analysis, it was determined that GeoGebra software was an effective tool in increasing pre-service teachers' attitudes towards proof and proving.
Motivated Forgetting in Early Mathematics: A Proof-of-Concept Study
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Gerardo Ramirez
2017-12-01
Full Text Available Educators assume that students are motivated to retain what they are taught. Yet, students commonly report that they forget most of what they learn, especially in mathematics. In the current study I ask whether students may be motivated to forget mathematics because of academic experiences threaten the self-perceptions they are committed to maintaining. Using a large dataset of 1st and 2nd grade children (N = 812, I hypothesize that math anxiety creates negative experiences in the classroom that threaten children’s positive math self-perceptions, which in turn spurs a motivation to forget mathematics. I argue that this motivation to forget is activated during the winter break, which in turn reduces the extent to which children grow in achievement across the school year. Children were assessed for math self-perceptions, math anxiety and math achievement in the fall before going into winter break. During the spring, children’s math achievement was measured once again. A math achievement growth score was devised from a regression model of fall math achievement predicting spring achievement. Results show that children with higher math self-perceptions showed reduced growth in math achievement across the school year as a function of math anxiety. Children with lower math interest self-perceptions did not show this relationship. Results serve as a proof-of-concept for a scientific account of motivated forgetting within the context of education.
Zengin, Yilmaz
2017-01-01
The purpose of this study is to determine the effect of GeoGebra software on pre-service mathematics teachers' attitudes towards proof and proving and to determine pre-service teachers' pre- and post-views regarding proof. The study lasted nine weeks and the participants of the study consisted of 24 pre-service mathematics teachers. The study used…
Linares, Leanne A.; Smith, Phil R.
2009-01-01
A geometry textbook or mathematics journal that prints all the work that mathematicians use as they generate proofs of mathematical results would be rare indeed. The false starts, the tentative conjectures, and the arguments that led nowhere--these are conveniently omitted; only the final successful product is presented to the world. To students…
Weber, Keith
2010-01-01
Many mathematics educators have noted that mathematicians do not only read proofs to gain conviction but also to obtain insight. The goal of this article is to discuss what this insight is from mathematicians' perspective. Based on interviews with nine research-active mathematicians, two sources of insight are discussed. The first is reading a…
Habsah, Fitria
2017-01-01
This research aims to produce mathematics textbook for grade VII junior high school students based on realistic mathematics and oriented to the mathematical reasoning and mathematical communication. The quality is determined based on Nieveen criteria, including validity, practicality, and effectiveness.This study was a research and development and used Borg & Gall model. The subject of this research were the students of SMPN 2 Pujon-Kabupaten Malang, that is 30 students in an experimental cla...
Accounting for Proof Test Data in a Reliability Based Design Optimization Framework
Ventor, Gerharad; Scotti, Stephen J.
2012-01-01
This paper investigates the use of proof (or acceptance) test data during the reliability based design optimization of structural components. It is assumed that every component will be proof tested and that the component will only enter into service if it passes the proof test. The goal is to reduce the component weight, while maintaining high reliability, by exploiting the proof test results during the design process. The proposed procedure results in the simultaneous design of the structural component and the proof test itself and provides the designer with direct control over the probability of failing the proof test. The procedure is illustrated using two analytical example problems and the results indicate that significant weight savings are possible when exploiting the proof test results during the design process.
Belkić, Dževad; Belkić, Karen
2015-06-01
Magnetic resonance (MR)-based modalities aid breast cancer detection without exposure to ionizing radiation. Magnetic resonance imaging is very sensitive but costly and insufficiently specific. Molecular imaging through magnetic resonance spectroscopy (MRS) can provide information about key metabolites. Here, the measured/encoded time signals cannot be interpreted directly, necessitating mathematics for mapping to the more manageable frequency domain. Conventional applications of MRS are hampered by data analysis via the fast Fourier transform (FFT) and postprocessing by fitting techniques. Most in vivo MRS studies on breast cancer rely upon estimations of total choline (tCHO). These have yielded only incremental improvements in diagnostic accuracy. In vitro studies reveal richer metabolic information for identifying breast cancer, particularly in closely overlapping components of tCHO. Among these are phosphocholine (PC), a marker of malignant transformation of the breast. The FFT cannot assess these congested spectral components. This can be done by the fast Padé transform (FPT), a high-resolution, quantification-equipped method, which we presently apply to noisy MRS time signals consistent with those encoded in breast cancer. The FPT unequivocally and robustly extracted the concentrations of all physical metabolites, including PC. In sharp contrast, the FFT produced a rough envelope spectrum with a few distorted peaks and key metabolites absent altogether. As such, the FFT has poor resolution for these typical MRS time signals from breast cancer. Hence, based on Fourier-estimated envelope spectra, tCHO estimates are unreliable. Using even truncated time signals, the FPT clearly distinguishes noise from true metabolites whose concentrations are accurately extracted. The high resolution of the FPT translates directly into shortened examination time of the patient. These capabilities strongly suggest that by applying the FPT to time signals encoded in vivo from
Proofs of the Kochen–Specker theorem based on a system of three qubits
International Nuclear Information System (INIS)
Waegell, Mordecai; Aravind, P K
2012-01-01
A number of new proofs of the Kochen–Specker theorem are given based on the observables of the three-qubit Pauli group. Each proof is presented in the form of a diagram from which it is obvious by inspection. Each of our observable-based proofs leads to a system of projectors and bases that generally yields a large number of ‘parity proofs’ of the Kochen–Specker theorem. Some examples of such proofs are given and some of their applications are discussed. (paper)
Directory of Open Access Journals (Sweden)
Morten Andersen
Full Text Available The chronic Philadelphia-negative myeloproliferative neoplasms (MPNs are acquired stem cell neoplasms which ultimately may transform to acute myelogenous leukemia. Most recently, chronic inflammation has been described as an important factor for the development and progression of MPNs in the biological continuum from early cancer stage to the advanced myelofibrosis stage, the MPNs being described as "A Human Inflammation Model for Cancer Development". This novel concept has been built upon clinical, experimental, genomic, immunological and not least epidemiological studies. Only a few studies have described the development of MPNs by mathematical models, and none have addressed the role of inflammation for clonal evolution and disease progression. Herein, we aim at using mathematical modelling to substantiate the concept of chronic inflammation as an important trigger and driver of MPNs.The basics of the model describe the proliferation from stem cells to mature cells including mutations of healthy stem cells to become malignant stem cells. We include a simple inflammatory coupling coping with cell death and affecting the basic model beneath. First, we describe the system without feedbacks or regulatory interactions. Next, we introduce inflammatory feedback into the system. Finally, we include other feedbacks and regulatory interactions forming the inflammatory-MPN model. Using mathematical modeling, we add further proof to the concept that chronic inflammation may be both a trigger of clonal evolution and an important driving force for MPN disease progression. Our findings support intervention at the earliest stage of cancer development to target the malignant clone and dampen concomitant inflammation.
DEFF Research Database (Denmark)
Andersen, Morten; Sajid, Zamra; Pedersen, Rasmus K.
2017-01-01
The chronic Philadelphia-negative myeloproliferative neoplasms (MPNs) are acquired stem cell neoplasms which ultimately may transform to acute myelogenous leukemia. Most recently, chronic inflammation has been described as an important factor for the development and progression of MPNs.......The basics of the model describe the proliferation from stem cells to mature cells including mutations of healthy stem cells to become malignant stem cells. We include a simple inflammatory coupling coping with cell death and affecting the basic model beneath. First, we describe the system without feedbacks...... or regulatory interactions. Next, we introduce inflammatory feedback into the system. Finally, we include other feedbacks and regulatory interactions forming the inflammatory-MPN model. Using mathematical modeling, we add further proof to the concept that chronic inflammation may be both a trigger of clonal...
Czech Academy of Sciences Publication Activity Database
Krajíček, Jan
2004-01-01
Roč. 69, č. 2 (2004), s. 387-397 ISSN 0022-4812 R&D Projects: GA AV ČR IAA1019901; GA MŠk LN00A056 Institutional research plan: CEZ:AV0Z1019905 Keywords : propositional proof system s * circuits * polynomial simulation Subject RIV: BA - General Mathematics Impact factor: 0.331, year: 2004
Conceptualising inquiry based education in mathematics
DEFF Research Database (Denmark)
Blomhøj, Morten; Artigue, Michéle
2013-01-01
of inquiry as a pedagogical concept in the work of Dewey (e.g. 1916, 1938) to analyse and discuss its migration to science and mathematics education. For conceptualizing inquiry-based mathematics education (IBME) it is important to analyse how this concept resonates with already well-established theoretical...... frameworks in mathematics education. Six such frameworks are analysed from the perspective of inquiry: the problem-solving tradition, the Theory of Didactical Situations, the Realistic Mathematics Education programme, the mathematical modelling perspective, the Anthropological Theory of Didactics...
Proof of cipher text ownership based on convergence encryption
Zhong, Weiwei; Liu, Zhusong
2017-08-01
Cloud storage systems save disk space and bandwidth through deduplication technology, but with the use of this technology has been targeted security attacks: the attacker can get the original file just use hash value to deceive the server to obtain the file ownership. In order to solve the above security problems and the different security requirements of cloud storage system files, an efficient information theory security proof of ownership scheme is proposed. This scheme protects the data through the convergence encryption method, and uses the improved block-level proof of ownership scheme, and can carry out block-level client deduplication to achieve efficient and secure cloud storage deduplication scheme.
New zero-input overflow stability proofs based on Lyapunov theory
Werter, M.J.; Ritzerfeld, J.H.F.
1989-01-01
The authors demonstrate some proofs of zero-input overflow-oscillation suppression in recursive digital filters. The proofs are based on the second method of Lyapunov. For second-order digital filters with complex conjugated poles, the state describes a trajectory in the phase plane, spiraling
Modifying the ECC-based grouping-proof RFID system to increase inpatient medication safety.
Ko, Wen-Tsai; Chiou, Shin-Yan; Lu, Erl-Huei; Chang, Henry Ker-Chang
2014-09-01
RFID technology is increasingly used in applications that require tracking, identification, and authentication. It attaches RFID-readable tags to objects for identification and execution of specific RFID-enabled applications. Recently, research has focused on the use of grouping-proofs for preserving privacy in RFID applications, wherein a proof of two or more tags must be simultaneously scanned. In 2010, a privacy-preserving grouping proof protocol for RFID based on ECC in public-key cryptosystem was proposed but was shown to be vulnerable to tracking attacks. A proposed enhancement protocol was also shown to have defects which prevented proper execution. In 2012, Lin et al. proposed a more efficient RFID ECC-based grouping proof protocol to promote inpatient medication safety. However, we found this protocol is also vulnerable to tracking and impersonation attacks. We then propose a secure privacy-preserving RFID grouping proof protocol for inpatient medication safety and demonstrate its resistance to such attacks.
Inquiry-based Learning in Mathematics Education
DEFF Research Database (Denmark)
Dreyøe, Jonas; Larsen, Dorte Moeskær; Hjelmborg, Mette Dreier
From a grading list of 28 of the highest ranked mathematics education journals, the six highest ranked journals were chosen, and a systematic search for inquiry-based mathematics education and related keywords was conducted. This led to five important theme/issues for inquiry-based learning...
Computer-Game-Based Tutoring of Mathematics
Ke, Fengfeng
2013-01-01
This in-situ, descriptive case study examined the potential of implementing computer mathematics games as an anchor for tutoring of mathematics. Data were collected from middle school students at a rural pueblo school and an urban Hispanic-serving school, through in-field observation, content analysis of game-based tutoring-learning interactions,…
Directory of Open Access Journals (Sweden)
Fitria Habsah
2017-05-01
Full Text Available This research aims to produce mathematics textbook for grade VII junior high school students based on realistic mathematics and oriented to the mathematical reasoning and mathematical communication. The quality is determined based on Nieveen criteria, including validity, practicality, and effectiveness.This study was a research and development and used Borg & Gall model. The subject of this research were the students of SMPN 2 Pujon-Kabupaten Malang, that is 30 students in an experimental class (using the developed textbook and 29 students in a control class (using BSE book from the government. The teaching material was categorized valid if the expert's judgment at least is categorized as “good”. The teaching material was categorized practical if both of teachers and students assessment at least categorized as “good”. The teaching material was categorized effectively if minimum 75% of student scores at least is categorized as “good” for the mathematical reasoning test and mathematical communication test. This research resulted in a valid, practical, and effective teaching material. The resulted of the validation show that material teaching is valid. The resulted of teachers and students assessment show that the product is practical. The tests scores show that the product is effective. Percentage of students who categorized at least as “good” is 83,33% for the mathematical reasoning and 86,67% for the mathematical communication. The resulted of statistic test shows that the product more effective than the BSE book from the government in terms of mathematical reasoning and mathematical communication.
Proofs without Words: A Visual Application of Reasoning and Proof
Bell, Carol J.
2011-01-01
Reasoning and Proof is one of the Process Standards set forth in National Council of Teachers of Mathematics' (NCTM) "Principles and Standards for School Mathematics." Thus, it is important to give students opportunities to build their reasoning skills and aid their understanding of the proof process. Teaching students how to do proofs is a…
Parity proofs of the Kochen–Specker theorem based on the Lie algebra E8
International Nuclear Information System (INIS)
Waegell, Mordecai; Aravind, P K
2015-01-01
The 240 root vectors of the Lie algebra E8 lead to a system of 120 rays in a real eight-dimensional Hilbert space that contains a large number of parity proofs of the Kochen–Specker (KS) theorem. After introducing the rays in a triacontagonal representation due to Coxeter, we present their KS diagram in the form of a ‘basis table’ showing all 2025 bases (i.e., sets of eight mutually orthogonal rays) formed by the rays. Only a few of the bases are actually listed, but simple rules are given, based on the symmetries of E8, for obtaining all the other bases from the ones shown. The basis table is an object of great interest because all the parity proofs of E8 can be exhibited as subsets of it. We show how the triacontagonal representation of E8 facilitates the identification of substructures that are more easily searched for their parity proofs. We have found hundreds of different types of parity proofs, ranging from 9 bases (or contexts) at the low end to 35 bases at the high end, and involving projectors of various ranks and multiplicities. After giving an overview of the proofs we found, we present a few concrete examples of the proofs that illustrate both their generic features as well as some of their more unusual properties. In particular, we present a proof involving 34 rays and 9 bases that appears to provide the most compact proof of the KS theorem found to date in eight-dimensions. (paper)
The challenge of computer mathematics.
Barendregt, Henk; Wiedijk, Freek
2005-10-15
Progress in the foundations of mathematics has made it possible to formulate all thinkable mathematical concepts, algorithms and proofs in one language and in an impeccable way. This is not in spite of, but partially based on the famous results of Gödel and Turing. In this way statements are about mathematical objects and algorithms, proofs show the correctness of statements and computations, and computations are dealing with objects and proofs. Interactive computer systems for a full integration of defining, computing and proving are based on this. The human defines concepts, constructs algorithms and provides proofs, while the machine checks that the definitions are well formed and the proofs and computations are correct. Results formalized so far demonstrate the feasibility of this 'computer mathematics'. Also there are very good applications. The challenge is to make the systems more mathematician-friendly, by building libraries and tools. The eventual goal is to help humans to learn, develop, communicate, referee and apply mathematics.
Kane, Jonathan M
2016-01-01
This is a textbook on proof writing in the area of analysis, balancing a survey of the core concepts of mathematical proof with a tight, rigorous examination of the specific tools needed for an understanding of analysis. Instead of the standard "transition" approach to teaching proofs, wherein students are taught fundamentals of logic, given some common proof strategies such as mathematical induction, and presented with a series of well-written proofs to mimic, this textbook teaches what a student needs to be thinking about when trying to construct a proof. Covering the fundamentals of analysis sufficient for a typical beginning Real Analysis course, it never loses sight of the fact that its primary focus is about proof writing skills. This book aims to give the student precise training in the writing of proofs by explaining exactly what elements make up a correct proof, how one goes about constructing an acceptable proof, and, by learning to recognize a correct proof, how to avoid writing incorrect proofs. T...
A simple proof of Debreu's Gap Lemma | Ouwehand | ORiON
African Journals Online (AJOL)
Debreu's Gap Lemma is central to the proof of his fundamental result on the existence of continuous utility functions. A short proof based on a standard textbook construction of utility functions on countable linearly ordered sets is presented here. The proof is accessible to students with limited mathematical background, thus ...
Principle-Based Mathematics: An Exploratory Study
Poon, Rebecca Chung-Yan
2014-01-01
Although educators and policymakers are becoming increasingly aware of the need for professional development that is content specific (Kennedy, 1999) and focuses on deepening and broadening teachers' knowledge of content for teaching (American Federation of Teachers, 2002; National Academy of Education, 2009), little attention has been given to supporting teachers' development of content knowledge as defined by Shulman (1986). Principle-Based Mathematics (PBM), a presentation of K-12 mathemat...
A Lightweight RFID Grouping-Proof Protocol Based on Parallel Mode and DHCP Mechanism
Directory of Open Access Journals (Sweden)
Zhicai Shi
2017-07-01
Full Text Available A Radio Frequency Identification (RFID grouping-proof protocol is to generate an evidence of the simultaneous existence of a group of tags and it has been applied to many different fields. For current grouping-proof protocols, there still exist some flaws such as low grouping-proof efficiency, being vulnerable to trace attack and information leakage. To improve the secure performance and efficiency, we propose a lightweight RFID grouping-proof protocol based on parallel mode and DHCP (Dynamic Host Configuration Protocol mechanism. Our protocol involves multiple readers and multiple tag groups. During the grouping-proof period, one reader and one tag group are chosen by the verifier by means of DHCP mechanism. When only a part of the tags of the chosen group exist, the protocol can also give the evidence of their co-existence. Our protocol utilizes parallel communication mode between reader and tags so as to ensure its grouping-proof efficiency. It only uses Hash function to complete the mutual authentication among verifier, readers and tags. It can preserve the privacy of the RFID system and resist the attacks such as eavesdropping, replay, trace and impersonation. Therefore the protocol is secure, flexible and efficient. It only uses some lightweight operations such as Hash function and a pseudorandom number generator. Therefore it is very suitable to some low-cost RFID systems.
Developing Mathematics Problems Based on Pisa Level
Directory of Open Access Journals (Sweden)
Shahibul Ahyan
2014-01-01
Full Text Available This research aims to produce mathematics problems based on PISA level with valid and practical content of change and relationships and has potential effect for Junior High School students. A development research method developed by Akker, Gravemeijer, McKenney and Nieveen is used this research. In the first stage, the researcher analyzed students, algebra material in school-based curricula (KTSP and mathematics problems of PISA 2003 of change and relationships content. The second stage, the researcher designed 13 problems with content of change and relationships. The last, the researcher used formative evaluation design developed by Tessmer which includes self evaluation, one-to-one, expert review, small group, and field test. The data collect by walk through, interview, and questionnaire. The result of this research indicated that 12 mathematical problems based on PISA level of change and relationships content that developed have validity, practically, and potential effects for Junior High School students.
Equihash: Asymmetric Proof-of-Work Based on the Generalized Birthday Problem
Directory of Open Access Journals (Sweden)
Alex Biryukov
2017-04-01
Full Text Available Proof-of-work is a central concept in modern cryptocurrencies and denial-ofservice protection tools, but the requirement for fast verification so far has made it an easy prey for GPU-, ASIC-, and botnet-equipped users. The attempts to rely on memory-intensive computations in order to remedy the disparity between architectures have resulted in slow or broken schemes. In this paper we solve this open problem and show how to construct an asymmetric proof-of-work (PoW based on a computationally-hard problem, which requires a great deal of memory to generate a proof (called a ”memory-hardness” feature but is instant to verify. Our primary proposal, Equihash, is a PoW based on the generalized birthday problem and enhanced Wagner’s algorithm for it. We introduce the new technique of algorithm binding to prevent cost amortization and demonstrate that possible parallel implementations are constrained by memory bandwidth. Our scheme has tunable and steep time-space tradeoffs, which impose large computational penalties if less memory is used. Our solution is practical and ready to deploy: a reference implementation of a proof-of-work requiring 700 MB of RAM runs in 15 seconds on a 2.1 GHz CPU, increases the computations by a factor of 1000 if memory is halved, and presents a proof of just 120 bytes long.
Dog Mathematics: Exploring Base-4
Kurz, Terri L.; Yanik, H. Bahadir; Lee, Mi Yeon
2016-01-01
Using a dog's paw as a basis for numerical representation, sixth grade students explored how to count and regroup using the dog's four digital pads. Teachers can connect these base-4 explorations to the conceptual meaning of place value and regrouping using base-10.
Quantum group based theory for antiferromagnetism and superconductivity: proof and further evidence
Energy Technology Data Exchange (ETDEWEB)
Alam, Sher; Mamun, S.M.; Yanagisawa, T.; Khan, Hayatullah; Rahman, M.O.; Termizi, J.A.S
2003-10-15
Previously one of us presented a conjecture to model antiferromagnetism and high temperature superconductivity and their 'unification' by quantum group symmetry rather than the corresponding classical symmetry in view of the critique by Baskaran and Anderson of Zhang's classical SO(5) model. This conjecture was further sharpened, experimental evidence and the important role of 1-d systems (stripes) was emphasized and moreover the relationship between quantum groups and strings via WZWN models were given in an earlier paper. In this brief note we give and discuss mathematical proof of this conjecture, which completes an important part of this idea, since previously an explicit simple mathematical proof was lacking. It is important to note that in terms of physics that the arbitrariness (freedom) of the d-wave factor g{sup 2}(k) is tied to quantum group symmetry whereas in order to recover classical SO(5) one must set it to unity in an adhoc manner. We comment on the possible connection between this freedom and the pseudogap behaviour in the cuprates.
Proof of the insecurity of quantum secret sharing based on the Smolin bound entangled states
International Nuclear Information System (INIS)
Ya-Fei, Yu; Zhi-Ming, Zhang
2009-01-01
This paper reconsiders carefully the possibility of using the Smolin bound entangled states as the carrier for sharing quantum secret. It finds that the process of quantum secret sharing based on Smolin states has insecurity though the Smolin state was reported to violate maximally the two-setting Bell-inequality. The general proof is given. (general)
Simple security proof of quantum key distribution based on complementarity
International Nuclear Information System (INIS)
Koashi, M
2009-01-01
We present an approach to the unconditional security of quantum key distribution protocols based on a complementarity argument. The approach is applicable to, but not limited to, every case that has been treated via the argument by Shor and Preskill based on entanglement distillation, with a benefit of decoupling of the error correction from the privacy amplification. It can also treat cases with uncharacterized apparatuses. We derive a secure key rate for the Bennett-Brassard-1984 protocol with an arbitrary source characterized only by a single parameter representing the basis dependence.
Geroch, Robert
1985-01-01
Mathematical Physics is an introduction to such basic mathematical structures as groups, vector spaces, topological spaces, measure spaces, and Hilbert space. Geroch uses category theory to emphasize both the interrelationships among different structures and the unity of mathematics. Perhaps the most valuable feature of the book is the illuminating intuitive discussion of the ""whys"" of proofs and of axioms and definitions. This book, based on Geroch's University of Chicago course, will be especially helpful to those working in theoretical physics, including such areas as relativity, particle
Shor-Preskill-type security proof for quantum key distribution without public announcement of bases
International Nuclear Information System (INIS)
Hwang, Won-Young; Wang Xiangbin; Matsumoto, Keiji; Kim, Jaewan; Lee, Hai-Woong
2003-01-01
We give a Shor-Preskill-type security proof to quantum key distribution without public announcement of bases [W.Y. Hwang et al., Phys. Lett. A 244, 489 (1998)]. First, we modify the Lo-Chau protocol once more so that it finally reduces to the quantum key distribution without public announcement of bases. Then we show how we can estimate the error rate in the code bits based on that in the checked bits in the proposed protocol, which is the central point of the proof. We discuss the problem of imperfect sources and that of large deviation in the error rate distributions. We discuss when the bases sequence must be discarded
On Federated and Proof Of Validation Based Consensus Algorithms In Blockchain
Ambili, K. N.; Sindhu, M.; Sethumadhavan, M.
2017-08-01
Almost all real world activities have been digitized and there are various client server architecture based systems in place to handle them. These are all based on trust on third parties. There is an active attempt to successfully implement blockchain based systems which ensures that the IT systems are immutable, double spending is avoided and cryptographic strength is provided to them. A successful implementation of blockchain as backbone of existing information technology systems is bound to eliminate various types of fraud and ensure quicker delivery of the item on trade. To adapt IT systems to blockchain architecture, an efficient consensus algorithm need to be designed. Blockchain based on proof of work first came up as the backbone of cryptocurrency. After this, several other methods with variety of interesting features have come up. In this paper, we conduct a survey on existing attempts to achieve consensus in block chain. A federated consensus method and a proof of validation method are being compared.
Preservice Mathematics Teachers' Perceptions of Drama Based Instruction
Bulut, Neslihan
2016-01-01
The purpose of this study was to determine the perceptions of pre-service mathematics teachers related to drama-based instruction. For this purpose, effects of a drama-based mathematics course on senior class pre-service mathematics teachers' knowledge about drama-based instruction and teacher candidates' competencies for developing and…
Foundational aspects of non standard mathematics
Ballard, David
1994-01-01
This work proposes a major new extension of "non"standard mathematics. Addressed to a general mathematical audience, the book is intended to be philosophically provocative. The model theory on which "non"standard mathematics has been based is first reformulated within point set topology, which facilitates proofs and adds perspective. These topological techniques are then used to give new, uniform conservativity proofs for the various versions of "non"standard mathematics proposed by Nelson, Hrbáček, and Kawai. The proofs allow for sharp comparison. Addressing broader issues, Ballard then argues that what is novel in these forms of "non"standard mathematics is the introduction, however tentative, of relativity in one's mathematical environment. This hints at the possibility of a mathematical environment which is radically relativistic. The work's major and final feature is to present and prove conservative a version of "non"standard mathematics which, for the first time, illustrates this full radical relativ...
PROOF as a service on the cloud: a virtual analysis facility based on the CernVM ecosystem
International Nuclear Information System (INIS)
Berzano, D; Blomer, J; Buncic, P; Charalampidis, I; Ganis, G; Lestaris, G; Meusel, R
2014-01-01
PROOF, the Parallel ROOT Facility, is a ROOT-based framework which enables interactive parallelism for event-based tasks on a cluster of computing nodes. Although PROOF can be used simply from within a ROOT session with no additional requirements, deploying and configuring a PROOF cluster used to be not as straightforward. Recently great efforts have been spent to make the provisioning of generic PROOF analysis facilities with zero configuration, with the added advantages of positively affecting both stability and scalability, making the deployment operations feasible even for the end user. Since a growing amount of large-scale computing resources are nowadays made available by Cloud providers in a virtualized form, we have developed the Virtual PROOF-based Analysis Facility: a cluster appliance combining the solid CernVM ecosystem and PoD (PROOF on Demand), ready to be deployed on the Cloud and leveraging some peculiar Cloud features such as elasticity. We will show how this approach is effective both for sysadmins, who will have little or no configuration to do to run it on their Clouds, and for the end users, who are ultimately in full control of their PROOF cluster and can even easily restart it by themselves in the unfortunate event of a major failure. We will also show how elasticity leads to a more optimal and uniform usage of Cloud resources.
CSIR Research Space (South Africa)
Mthethwa, Sthembile
2016-12-01
Full Text Available Conference on Information Science and Security, Pattaya, Thailand, 19 - 22 December 2016 An improved smartcard for the South African Social Security Agency (SASSA): A proof of life based solution Mthethwa, S. Barbour, G. Thinyane, M...
Mathematical programming solver based on local search
Gardi, Frédéric; Darlay, Julien; Estellon, Bertrand; Megel, Romain
2014-01-01
This book covers local search for combinatorial optimization and its extension to mixed-variable optimization. Although not yet understood from the theoretical point of view, local search is the paradigm of choice for tackling large-scale real-life optimization problems. Today's end-users demand interactivity with decision support systems. For optimization software, this means obtaining good-quality solutions quickly. Fast iterative improvement methods, like local search, are suited to satisfying such needs. Here the authors show local search in a new light, in particular presenting a new kind of mathematical programming solver, namely LocalSolver, based on neighborhood search. First, an iconoclast methodology is presented to design and engineer local search algorithms. The authors' concern about industrializing local search approaches is of particular interest for practitioners. This methodology is applied to solve two industrial problems with high economic stakes. Software based on local search induces ex...
International Nuclear Information System (INIS)
Malzacher, Peter; Manafov, Anar
2010-01-01
PROOF on Demand (PoD) is a set of utilities, which allows starting a PROOF cluster at user request, on any resource management system. It provides a plug-in based system, which allows to use different job submission frontends, such as LSF or gLite WMS. Main components of PoD are the PROOFAgent and the PAConsole. PROOFAgent provides the communication layer between the PROOF master on the local machine and the PROOF workers on the remote resources, possibly behind a firewall. PAConsole provides a user-friendly GUI, which is used to setup, manage, and shutdown the dynamic PROOF cluster. Installation is simple and doesn't require administrator privileges, and all the processes run in user space. PoD gives users, who don't have a centrally-administrated static PROOF cluster at their institute, the possibility to enjoy the full power of interactive analysis with PROOF.
Mathematical modeling of acid-base physiology.
Occhipinti, Rossana; Boron, Walter F
2015-01-01
pH is one of the most important parameters in life, influencing virtually every biological process at the cellular, tissue, and whole-body level. Thus, for cells, it is critical to regulate intracellular pH (pHi) and, for multicellular organisms, to regulate extracellular pH (pHo). pHi regulation depends on the opposing actions of plasma-membrane transporters that tend to increase pHi, and others that tend to decrease pHi. In addition, passive fluxes of uncharged species (e.g., CO2, NH3) and charged species (e.g., HCO3(-), [Formula: see text] ) perturb pHi. These movements not only influence one another, but also perturb the equilibria of a multitude of intracellular and extracellular buffers. Thus, even at the level of a single cell, perturbations in acid-base reactions, diffusion, and transport are so complex that it is impossible to understand them without a quantitative model. Here we summarize some mathematical models developed to shed light onto the complex interconnected events triggered by acids-base movements. We then describe a mathematical model of a spherical cells-which to our knowledge is the first one capable of handling a multitude of buffer reactions-that our team has recently developed to simulate changes in pHi and pHo caused by movements of acid-base equivalents across the plasma membrane of a Xenopus oocyte. Finally, we extend our work to a consideration of the effects of simultaneous CO2 and HCO3(-) influx into a cell, and envision how future models might extend to other cell types (e.g., erythrocytes) or tissues (e.g., renal proximal-tubule epithelium) important for whole-body pH homeostasis. Copyright © 2015 Elsevier Ltd. All rights reserved.
Parity proofs of the Kochen–Specker theorem based on 60 complex rays in four dimensions
International Nuclear Information System (INIS)
Waegell, Mordecai; Aravind, P K
2011-01-01
It is pointed out that the 60 complex rays in four dimensions associated with a system of two qubits yield over 10 9 critical parity proofs of the Kochen–Specker theorem. The geometrical properties of the rays are described, an overview of the parity proofs contained in them is given and examples of some of the proofs are exhibited. (paper)
Zazkis, Dov; Zazkis, Rina
2016-01-01
A significant body of research literature in mathematics education attends to mathematical proofs. However, scant research attends to proof comprehension, which is the focus of this study. We examine perspective secondary teachers' conceptions of what constitutes comprehension of a given proof and their ideas of how students' comprehension can be…
Strahm, Thomas; Studer, Thomas
2016-01-01
The aim of this volume is to collect original contributions by the best specialists from the area of proof theory, constructivity, and computation and discuss recent trends and results in these areas. Some emphasis will be put on ordinal analysis, reductive proof theory, explicit mathematics and type-theoretic formalisms, and abstract computations. The volume is dedicated to the 60th birthday of Professor Gerhard Jäger, who has been instrumental in shaping and promoting logic in Switzerland for the last 25 years. It comprises contributions from the symposium “Advances in Proof Theory”, which was held in Bern in December 2013. Proof theory came into being in the twenties of the last century, when it was inaugurated by David Hilbert in order to secure the foundations of mathematics. It was substantially influenced by Gödel's famous incompleteness theorems of 1930 and Gentzen's new consistency proof for the axiom system of first order number theory in 1936. Today, proof theory is a well-established branch ...
PROOF as a Service on the Cloud: a Virtual Analysis Facility based on the CernVM ecosystem
Berzano, Dario; Buncic, Predrag; Charalampidis, Ioannis; Ganis, Gerardo; Lestaris, Georgios; Meusel, René
2014-01-01
PROOF, the Parallel ROOT Facility, is a ROOT-based framework which enables interactive parallelism for event-based tasks on a cluster of computing nodes. Although PROOF can be used simply from within a ROOT session with no additional requirements, deploying and configuring a PROOF cluster used to be not as straightforward. Recently great efforts have been spent to make the provisioning of generic PROOF analysis facilities with zero configuration, with the added advantages of positively affecting both stability and scalability, making the deployment operations feasible even for the end user. Since a growing amount of large-scale computing resources are nowadays made available by Cloud providers in a virtualized form, we have developed the Virtual PROOF-based Analysis Facility: a cluster appliance combining the solid CernVM ecosystem and PoD (PROOF on Demand), ready to be deployed on the Cloud and leveraging some peculiar Cloud features such as elasticity. We will show how this approach is effective both for sy...
Paterson, Judy; Sneddon, Jamie
2011-01-01
This article reports on the learning conversations between a mathematician and a mathematics educator as they worked together to change the delivery model of a third year discrete mathematics course from a traditional lecture mode to team-based learning (TBL). This change prompted the mathematician to create team tasks which increasingly focused…
Algebraic proofs over noncommutative formulas
Czech Academy of Sciences Publication Activity Database
Tzameret, Iddo
2011-01-01
Roč. 209, č. 10 (2011), s. 1269-1292 ISSN 0890-5401 R&D Projects: GA MŠk LC505 Institutional research plan: CEZ:AV0Z10190503 Keywords : proof complexity * algebraic proof system s * frege proofs Subject RIV: BA - General Mathematics Impact factor: 0.560, year: 2011 http://www.sciencedirect.com/science/article/pii/S089054011100109X
Directory of Open Access Journals (Sweden)
Syarifah Fadillah
2017-03-01
Full Text Available The problem in this research is to know how the process of developing mathematics physics instructional book based on inquiry approach and its supporting documents to improve students' mathematical problem-solving ability. The purpose of this research is to provide mathematical physics instruction based on inquiry approach and its supporting documents (semester learning activity plan, lesson plan and mathematical problem-solving test to improve students' mathematical problem-solving ability. The development of textbook refers to the ADDIE model, including analysis, design, development, implementation, and evaluation. The validation result from the expert team shows that the textbook and its supporting documents are valid. The test results of the mathematical problem-solving skills show that all test questions are valid and reliable. The result of the incorporation of the textbook in teaching and learning process revealed that students' mathematical problem-solving ability using mathematical physics instruction based on inquiry approach book was better than the students who use the regular book.
From Inductive Reasoning to Proof
Yopp, David A.
2009-01-01
Mathematical proof is an expression of deductive reasoning (drawing conclusions from previous assertions). However, it is often inductive reasoning (conclusions drawn on the basis of examples) that helps learners form their deductive arguments, or proof. In addition, not all inductive arguments generate more formal arguments. This article draws a…
Student Perspectives of Web-Based Mathematics
Loong, Esther Yook-Kin; Herbert, Sandra
2012-01-01
This paper presents the results of a survey conducted with students (N = 97) whose teachers have used the Web in their mathematics classes. Their responses to the use of the Internet for learning mathematics are reported here. Factor analyses were used to determine the constructs that underlie the survey. These constructs were found to be…
Web-Based Implementation of Discrete Mathematics
Love, Tanzy; Keinert, Fritz; Shelley, Mack
2006-01-01
The Department of Mathematics at Iowa State University teaches a freshman-level Discrete Mathematics course with total enrollment of about 1,800 students per year. The traditional format includes large lectures, with about 150 students each, taught by faculty and temporary instructors in two class sessions per week and recitation sections, with…
Authentication Based on Non-Interactive Zero-Knowledge Proofs for the Internet of Things.
Martín-Fernández, Francisco; Caballero-Gil, Pino; Caballero-Gil, Cándido
2016-01-07
This paper describes the design and analysis of a new scheme for the authenticated exchange of confidential information in insecure environments within the Internet of Things, which allows a receiver of a message to authenticate the sender and compute a secret key shared with it. The proposal is based on the concept of a non-interactive zero-knowledge proof, so that in a single communication, relevant data may be inferred to verify the legitimacy of the sender. Besides, the new scheme uses the idea under the Diffie-Hellman protocol for the establishment of a shared secret key. The proposal has been fully developed for platforms built on the Android Open Source Project, so it can be used in any device or sensor with this operating system. This work provides a performance study of the implementation and a comparison between its promising results and others obtained with similar schemes.
Authentication Based on Non-Interactive Zero-Knowledge Proofs for the Internet of Things
Directory of Open Access Journals (Sweden)
Francisco Martín-Fernández
2016-01-01
Full Text Available This paper describes the design and analysis of a new scheme for the authenticated exchange of confidential information in insecure environments within the Internet of Things, which allows a receiver of a message to authenticate the sender and compute a secret key shared with it. The proposal is based on the concept of a non-interactive zero-knowledge proof, so that in a single communication, relevant data may be inferred to verify the legitimacy of the sender. Besides, the new scheme uses the idea under the Diffie–Hellman protocol for the establishment of a shared secret key. The proposal has been fully developed for platforms built on the Android Open Source Project, so it can be used in any device or sensor with this operating system. This work provides a performance study of the implementation and a comparison between its promising results and others obtained with similar schemes.
The Failure to Construct Proof Based on Assimilation and Accommodation Framework from Piaget
Netti, Syukma; Nusantara, Toto; Subanji; Abadyo; Anwar, Lathiful
2016-01-01
The purpose of this article is to describe the process of a proof construction. It is more specific on the failure of the process. Piaget's frameworks, assimilation and accommodation, were used to analyze it. Method of this research was qualitative method. Data were collected by asking five students working on problems of proof using think aloud…
Anku, Sitsofe E.
1997-09-01
Using the reform documents of the National Council of Teachers of Mathematics (NCTM) (NCTM, 1989, 1991, 1995), a theory-based multi-dimensional assessment framework (the "SEA" framework) which should help expand the scope of assessment in mathematics is proposed. This framework uses a context based on mathematical reasoning and has components that comprise mathematical concepts, mathematical procedures, mathematical communication, mathematical problem solving, and mathematical disposition.
Proof assistants: History, ideas and future
Indian Academy of Sciences (India)
application is and will be in computer supported modelling and verification of sys- tems. But there is still ... Introduction ... compute with them, but their main focus is on doing proofs. ..... Proof development in a type theory based proof assistant.
Dzierżanowski, J; Szarmach, A; Słoniewski, P; Czapiewski, P; Piskunowicz, M; Bandurski, T; Szmuda, T
2014-08-01
The aim of this study was to investigate the morphometry of the posterior communicating artery (PCoA), on the basis of angio-computed tomography (CT), and to give proof of the mathematical definition of the term "hypopal sia of the PCoA". One hundred 3-dimensional (3D) angio-CT images, performed in adult patients with bilateral reconstruction of the PCoA (200 results) were used tocalculate the morphometry of the vessel. The average length of the vessel on the right side was 14.48 ± 3.47 mm, andon the left side 14.98 ± 4.77 mm (in women 14.75 mm, in men 14.70 mm). The mean of the diameter at the "proximal" point (the junction with P1) on the right side was 1.49 ± 0.51 mm, and on the left 1.46 ± 0.47 mm (in women 1.44 mm and in men 1.51 mm). The mean of the diameter in the "distal" part (the connection with ICA) on the right side was 1.4 ± 0.49 mm, and on the left 1.37 ± 0.41 mm (in women 1.38 mm, and in men 1.39 mm). No statistical correlation between the length and the diameter of the PCoA in relation to the sex and side was shown. On the basis of our measurements, we defined the hypoplasia of the artery as the estimated value less than the average diameter minus the standard deviation. The percentage distribution was as follows: the left artery 15.5%, the right artery 24%, women 11.5%, and the men 9%. Similarly to the above parameters, we have not found any statistical differences. The presence of the foetal origin was noted in 25% of the radiological examinations. The infundibular widening was visualised in 11.5% of cases of 3D reconstructions. The agenesis of PCoA was found in 9% (never bilaterally), and in 1 case the unilateral duplication of the artery was observed. No statistical differences between those parameters in relation to sex and the examined side were revealed. Morphological calculation of the PCoA on the basis of angio-CT from adult patients did not show any statistical differences depending on sex or the investigated side. The presented
Tattoo-based noninvasive glucose monitoring: a proof-of-concept study.
Bandodkar, Amay J; Jia, Wenzhao; Yardımcı, Ceren; Wang, Xuan; Ramirez, Julian; Wang, Joseph
2015-01-06
We present a proof-of-concept demonstration of an all-printed temporary tattoo-based glucose sensor for noninvasive glycemic monitoring. The sensor represents the first example of an easy-to-wear flexible tattoo-based epidermal diagnostic device combining reverse iontophoretic extraction of interstitial glucose and an enzyme-based amperometric biosensor. In-vitro studies reveal the tattoo sensor's linear response toward physiologically relevant glucose levels with negligible interferences from common coexisting electroactive species. The iontophoretic-biosensing tattoo platform is reduced to practice by applying the device on human subjects and monitoring variations in glycemic levels due to food consumption. Correlation of the sensor response with that of a commercial glucose meter underscores the promise of the tattoo sensor to detect glucose levels in a noninvasive fashion. Control on-body experiments demonstrate the importance of the reverse iontophoresis operation and validate the sensor specificity. This preliminary investigation indicates that the tattoo-based iontophoresis-sensor platform holds considerable promise for efficient diabetes management and can be extended toward noninvasive monitoring of other physiologically relevant analytes present in the interstitial fluid.
Mathematical biology modules based on modern molecular biology and modern discrete mathematics.
Robeva, Raina; Davies, Robin; Hodge, Terrell; Enyedi, Alexander
2010-01-01
We describe an ongoing collaborative curriculum materials development project between Sweet Briar College and Western Michigan University, with support from the National Science Foundation. We present a collection of modules under development that can be used in existing mathematics and biology courses, and we address a critical national need to introduce students to mathematical methods beyond the interface of biology with calculus. Based on ongoing research, and designed to use the project-based-learning approach, the modules highlight applications of modern discrete mathematics and algebraic statistics to pressing problems in molecular biology. For the majority of projects, calculus is not a required prerequisite and, due to the modest amount of mathematical background needed for some of the modules, the materials can be used for an early introduction to mathematical modeling. At the same time, most modules are connected with topics in linear and abstract algebra, algebraic geometry, and probability, and they can be used as meaningful applied introductions into the relevant advanced-level mathematics courses. Open-source software is used to facilitate the relevant computations. As a detailed example, we outline a module that focuses on Boolean models of the lac operon network.
Mathematical Biology Modules Based on Modern Molecular Biology and Modern Discrete Mathematics
Davies, Robin; Hodge, Terrell; Enyedi, Alexander
2010-01-01
We describe an ongoing collaborative curriculum materials development project between Sweet Briar College and Western Michigan University, with support from the National Science Foundation. We present a collection of modules under development that can be used in existing mathematics and biology courses, and we address a critical national need to introduce students to mathematical methods beyond the interface of biology with calculus. Based on ongoing research, and designed to use the project-based-learning approach, the modules highlight applications of modern discrete mathematics and algebraic statistics to pressing problems in molecular biology. For the majority of projects, calculus is not a required prerequisite and, due to the modest amount of mathematical background needed for some of the modules, the materials can be used for an early introduction to mathematical modeling. At the same time, most modules are connected with topics in linear and abstract algebra, algebraic geometry, and probability, and they can be used as meaningful applied introductions into the relevant advanced-level mathematics courses. Open-source software is used to facilitate the relevant computations. As a detailed example, we outline a module that focuses on Boolean models of the lac operon network. PMID:20810955
Combinatorial Proofs and Algebraic Proofs
Indian Academy of Sciences (India)
Permanent link: https://www.ias.ac.in/article/fulltext/reso/018/07/0630-0645. Keywords. Combinatorial proof; algebraic proof; binomial identity; recurrence relation; composition; Fibonacci number; Fibonacci identity; Pascal triangle. Author Affiliations. Shailesh A Shirali1. Sahyadri School Tiwai Hill, Rajgurunagar Pune 410 ...
Directory of Open Access Journals (Sweden)
Beatrix Barth
2016-12-01
Full Text Available Neurofeedback is a promising tool for treatment and rehabilitation of several patient groups. In this proof of principle study, near-infrared spectroscopy (NIRS based neurofeedback of frontal cortical areas was investigated in healthy adults. Main aims were the assessment of learning, the effects on performance in a working memory (n-back task and the impact of applied strategies on regulation.13 healthy participants underwent 8 sessions of NIRS based neurofeedback within two weeks to learn to voluntarily up-regulate hemodynamic activity in prefrontal areas. An n-back task in pre-/post measurements was used to monitor neurocognitive changes. Mean oxygenated hemoglobin (O2Hb amplitudes over the course of the sessions as well as during the n-back task were evaluated. 12 out of 13 participants were able to regulate their frontal hemodynamic response via NIRS neurofeedback. However, no systematic learning effects were observed in frontal O2Hb amplitudes over the training course in our healthy sample. We found an impact of applied strategies in only 5 out of 13 subjects. Regarding the n-back task, neurofeedback appeared to induce more focused and specific brain activation compared to pre-training measurement. NIRS based neurofeedback is a feasible and potentially effective method, with an impact on activation patterns in a working memory task. Ceiling effects might explain the lack of a systematic learning pattern in healthy subjects. Clinical studies are needed to show effects in patients exhibiting pathological deviations in prefrontal function.
Vote Counting as Mathematical Proof
DEFF Research Database (Denmark)
Schürmann, Carsten; Pattinson, Dirk
2015-01-01
then consists of a sequence (or tree) of rule applications and provides an independently checkable certificate of the validity of the result. This reduces the need to trust, or otherwise verify, the correctness of the vote counting software once the certificate has been validated. Using a rule...
Billings, Jake
2017-01-01
A new variation of blockchain proof of work algorithm is proposed to incentivize the timely execution of image processing algorithms. A sample image processing algorithm is proposed to determine interesting images using analysis of the entropy of pixel subsets within images. The efficacy of the image processing algorithm is examined using two small sets of training and test data. The interesting image algorithm is then integrated into a simplified blockchain mining proof of work algorithm bas...
Directory of Open Access Journals (Sweden)
Yong-Shin Kang
2018-01-01
Full Text Available Serialized tracing provides the ability to track and trace the lifecycle of the products and parts. Unlike barcodes, Radio frequency identification (RFID, which is an important building block for internet of things (IoT, does not require a line of sight and has the advantages of recognizing many objects simultaneously and rapidly, and storing more information than barcodes. Therefore, RFID has been used in a variety of application domains such as logistics, distributions, and manufacturing, significantly improving traceability and process efficiency. In this study, we applied RFID to improve the just-in-sequence operation of an automotive inbound logistics process. First, we implemented an RFID-based visibility system for real-time traceability and control of part supply from the production lines of suppliers to the assembly line of a car manufacturer. Second, we developed an RFID-based sequence-error proofing system to avoid accidental line stops due to incorrect part sequencing. The whole system has been successfully installed in a rear-axle inbound logistics process of GM Korea. We achieved a significant amount of cost savings, especially due to the prevention of sequencing errors and part shortages, and the reduction of manual operations. Thorough cost-benefit analysis demonstrates the clear economic feasibility of using RFID technologies for the just-in-sequence inbound logistics in an automobile manufacturing environment.
PROOF-based analysis on the ATLAS grid facilities: first experience with the PoD/PanDa plugin
International Nuclear Information System (INIS)
Vilucchi, E; Nardo, R Di; Mancini, G; Pineda, A R Sanchez; Salvo, A De; Donato, C Di; Doria, A; Ganis, G; Manafov, A; Mazza, S; Preltz, F; Rebatto, D; Salvucci, A
2014-01-01
In the ATLAS computing model Grid resources are managed by PanDA, the system designed for production and distributed analysis, and data are stored under various formats in ROOT files. End-user physicists have the choice to use either the ATHENA framework or directly ROOT, that provides users the possibility to use PROOF to exploit the computing power of multi-core machines or to dynamically manage analysis facilities. Since analysis facilities are, in general, not dedicated to PROOF only, PROOF-on-Demand (PoD) is used to enable PROOF on top of an existing resource management system. In a previous work we investigated the usage of PoD to enable PROOF-based analysis on Tier-2 facilities using the PoD/gLite plug-in interface. In this paper we present the status of our investigations using the recently developed PoD/PanDA plug-in to enable PROOF and a real end-user ATLAS physics analysis as payload. For this work, data were accessed using two different protocols: XRootD and file protocol. The former in the site where the SRM interface is Disk Pool Manager (DPM) and the latter where the SRM interface is StoRM with GPFS file system. We will first describe the results of some benchmark tests we run on the ATLAS Italian Tier-1 and Tier-2s sites and at CERN. Then, we will compare the results of different types of analysis, comparing performances accessing data in relation to different types of SRM interfaces and accessing data with XRootD in the LAN and in the WAN using the ATLAS XROOTD storage federation infrastructure.
Stork Color Proofing Technology
Ekman, C. Frederick
1989-04-01
For the past few years, Stork Colorproofing B.V. has been marketing an analog color proofing system in Europe based on electrophoto-graphic technology it pioneered for the purpose of high resolution, high fidelity color imaging in the field of the Graphic Arts. Based in part on this technology, it will make available on a commercial basis a digital color proofing system in 1989. Proofs from both machines will provide an exact reference for the user and will look, feel, and behave in a reproduction sense like the printed press sheet.
Fawcett, Harold P.
This yearbook focuses on the teaching of a geometry course emphasizing critical thinking and methods of proof rather than on learning a body of theorems. In the first chapter the problem is defined, and its origin and background are discussed. Next the organization of the experimental situation is described. Chapter 3 gives numerous illustrations…
Czech Academy of Sciences Publication Activity Database
Jeřábek, Emil
2012-01-01
Roč. 58, č. 3 (2012), s. 177-187 ISSN 0942-5616 R&D Projects: GA AV ČR IAA100190902; GA MŠk(CZ) 1M0545 Institutional support: RVO:67985840 Keywords : proof complexity * monotone sequent calculus Subject RIV: BA - General Mathematics Impact factor: 0.376, year: 2012 http://onlinelibrary.wiley.com/doi/10.1002/malq.201020071/full
Problem of mathematical deduction of the existence of black holes
Directory of Open Access Journals (Sweden)
Yuan-Shun Chin
1990-01-01
Full Text Available The mathematical proof of existence of Black Hole is based on the assumption of mass being independent of speed. Considering the effect of special relativity of the dependence of mass with speed there is no Black hole.
International Nuclear Information System (INIS)
Zhou, Weifeng; Cai, Jian-Feng; Gao, Hao
2013-01-01
A popular approach for medical image reconstruction has been through the sparsity regularization, assuming the targeted image can be well approximated by sparse coefficients under some properly designed system. The wavelet tight frame is such a widely used system due to its capability for sparsely approximating piecewise-smooth functions, such as medical images. However, using a fixed system may not always be optimal for reconstructing a variety of diversified images. Recently, the method based on the adaptive over-complete dictionary that is specific to structures of the targeted images has demonstrated its superiority for image processing. This work is to develop the adaptive wavelet tight frame method image reconstruction. The proposed scheme first constructs the adaptive wavelet tight frame that is task specific, and then reconstructs the image of interest by solving an l 1 -regularized minimization problem using the constructed adaptive tight frame system. The proof-of-concept study is performed for computed tomography (CT), and the simulation results suggest that the adaptive tight frame method improves the reconstructed CT image quality from the traditional tight frame method. (paper)
Test of Einstein-Podolsky-Rosen steering based on the all-versus-nothing proof.
Wu, Chunfeng; Chen, Jing-Ling; Ye, Xiang-Jun; Su, Hong-Yi; Deng, Dong-Ling; Wang, Zhenghan; Oh, C H
2014-03-06
In comparison with entanglement and Bell nonlocality, Einstein-Podolsky-Rosen steering is a newly emerged research topic and in its incipient stage. Although Einstein-Podolsky-Rosen steering has been explored via violations of steering inequalities both theoretically and experimentally, the known inequalities in the literatures are far from well-developed. As a result, it is not yet possible to observe Einstein-Podolsky-Rosen steering for some steerable mixed states. Recently, a simple approach was presented to identify Einstein-Podolsky-Rosen steering based on all-versus-nothing argument, offering a strong condition to witness the steerability of a family of two-qubit (pure or mixed) entangled states. In this work, we show that the all-versus-nothing proof of Einstein-Podolsky-Rosen steering can be tested by measuring the projective probabilities. Through the bound of probabilities imposed by local-hidden-state model, the proposed test shows that steering can be detected by the all-versus-nothing argument experimentally even in the presence of imprecision and errors. Our test can be implemented in many physical systems and we discuss the possible realizations of our scheme with non-Abelian anyons and trapped ions.
Eringen, A Cemal
2013-01-01
Continuum Physics: Volume 1 - Mathematics is a collection of papers that discusses certain selected mathematical methods used in the study of continuum physics. Papers in this collection deal with developments in mathematics in continuum physics and its applications such as, group theory functional analysis, theory of invariants, and stochastic processes. Part I explains tensor analysis, including the geometry of subspaces and the geometry of Finsler. Part II discusses group theory, which also covers lattices, morphisms, and crystallographic groups. Part III reviews the theory of invariants th
Dragalin, A G
1988-01-01
This monograph is intended to present the most important methods of proof theory in intuitionistic logic, assuming the reader to have mastered an introductory course in mathematical logic. The book starts with purely syntactical methods based on Gentzen's cut-elimination theorem, followed by intuitionistic arithmetic where Kleene's realizability method plays a central role. The author then studies algebraic models and completeness theorems for them. After giving a survey on the principles of intuitionistic analysis, the last part of the book presents the cut-elimination theorem in intuitionistic simple theory of types with an extensionality rule.
How Mathematicians Determine if an Argument Is a Valid Proof
Weber, Keith
2008-01-01
The purpose of this article is to investigate the mathematical practice of proof validation--that is, the act of determining whether an argument constitutes a valid proof. The results of a study with 8 mathematicians are reported. The mathematicians were observed as they read purported mathematical proofs and made judgments about their validity;…
Proof Problems with Diagrams: An Opportunity for Experiencing Proofs and Refutations
Komatsu, Kotaro; Tsujiyama, Yosuke; Sakamaki, Aruta; Koike, Norio
2014-01-01
It has become gradually accepted that proof and proving are essential at all grades of mathematical learning. Among the various aspects of proof and proving, this study addresses proofs and refutations described by Lakatos, in particular a part of increasing content by deductive guessing, to introduce an authentic process into mathematics…
Directory of Open Access Journals (Sweden)
Andreas J. Stylianides
2011-08-01
Full Text Available The concept of proof is central to meaningful learning of mathematics, but is hard for students to learn. A serious misconception dominant amongst students at all levels of schooling is that empirical arguments are proofs. An important question, then, is the following: What knowledge might enable teachers to help students overcome this misconception? Earlier research led to construction of a significant but rather incomplete ‘knowledge package’ for teaching in this area. Major elements of this knowledge package are summarised and its further development is contributed to by discussing a research-based instructional intervention found to be effective in helping secondary students begin to overcome the misconception that empirical arguments are proofs. Implications for mathematics teacher education are considered.
Boogaard, Floris; Tipping, Jonathan; Muthanna, T.; Duffy, A.; Bendall, Barry; Kluck, Jeroen
There is a wide diversity of projects undertaken to address urban resillience and climate proofing in the world. International knowledge exchange tools are evaluated with result: stakeholders demand tools that are interactive, open source and provide more detailed information (location, free photo
Stein, Sherman K
2010-01-01
Anyone can appreciate the beauty, depth, and vitality of mathematics with the help of this highly readable text, specially developed from a college course designed to appeal to students in a variety of fields. Readers with little mathematical background are exposed to a broad range of subjects chosen from number theory, topology, set theory, geometry, algebra, and analysis. Starting with a survey of questions on weight, the text discusses the primes, the fundamental theorem of arithmetic, rationals and irrationals, tiling, tiling and electricity, probability, infinite sets, and many other topi
A mathematical model for camera calibration based on straight lines
Directory of Open Access Journals (Sweden)
Antonio M. G. Tommaselli
2005-12-01
Full Text Available In other to facilitate the automation of camera calibration process, a mathematical model using straight lines was developed, which is based on the equivalent planes mathematical model. Parameter estimation of the developed model is achieved by the Least Squares Method with Conditions and Observations. The same method of adjustment was used to implement camera calibration with bundles, which is based on points. Experiments using simulated and real data have shown that the developed model based on straight lines gives results comparable to the conventional method with points. Details concerning the mathematical development of the model and experiments with simulated and real data will be presented and the results with both methods of camera calibration, with straight lines and with points, will be compared.
Mathematical foundations of epistemology based on experiments
Directory of Open Access Journals (Sweden)
Sergey M. Krylov
2015-09-01
Full Text Available The paper deals with basic prerequisites for the development of epistemology, which uses information concerning real experiments in the real world (with real objects. Such experiments are conducted by “formal-technological” analogs of Turing Machines. These analogs are called “universal synthesizers-analyzers”. They can perform syntheses and analyses of various objects or constructions (obtained by conjunctions of finite number of smaller objects called basic elements with the help of various algorithmic systems having some restrictions. Such algorithmic systems are called Formal Technologies. They have formal structures that are very similar to the formal structure of Maltsev's algebraic systems. This formal closeness allows us, first, to set up a hypothesis concerning algorithmic basis of almost all surrounding physical processes, as understandable as well as till non-understandable ones, that partially explains the wide applicability of mathematics to the outer world; second, this closeness allows one to formulate and prove some theorems (called assertions concerning features and peculiar properties of cognitive algorithms in one-, two- or three-dimensional surroundings for various formal technological systems, including a so called “acquired knowledge effectiveness theorem”. The theorem (assertion can be applied to a very wide class of formal technologies which use an equality predicate for objects analyses. In the paper various cognitive algorithms are listed and proved. These algorithms have different sets of technological operations resembling syntheses and decompositions, as well as different sets of analytical operations including equality predicates, “random stationary mapping” operations (which use unknown algorithms to obtain stationary results, therefore these operations are very similar to oracles in Turing Machines, operations that define object shapes, and so on. The structure of automatic cognitive devices called
International Nuclear Information System (INIS)
Demazure, M.
1988-01-01
The 1988 progress report of the Mathematics center (Polytechnic School, France), is presented. The Center is composed of different research teams: analysis, Riemann geometry, group theory, formal calculus and algorithm geometry, dynamical systems, topology and singularity. For each team, the members, the research topics, the national and international cooperations, are given. The papers concerning the investigations carried out in 1988, are listed [fr
Feferman on foundations logic, mathematics, philosophy
Sieg, Wilfried
2017-01-01
This volume honours the life and work of Solomon Feferman, one of the most prominent mathematical logicians of the latter half of the 20th century. In the collection of essays presented here, researchers examine Feferman’s work on mathematical as well as specific methodological and philosophical issues that tie into mathematics. Feferman’s work was largely based in mathematical logic (namely model theory, set theory, proof theory and computability theory), but also branched out into methodological and philosophical issues, making it well known beyond the borders of the mathematics community. With regard to methodological issues, Feferman supported concrete projects. On the one hand, these projects calibrate the proof theoretic strength of subsystems of analysis and set theory and provide ways of overcoming the limitations imposed by Gödel’s incompleteness theorems through appropriate conceptual expansions. On the other, they seek to identify novel axiomatic foundations for mathematical practice, truth ...
Doing Mathematics with Purpose: Mathematical Text Types
Dostal, Hannah M.; Robinson, Richard
2018-01-01
Mathematical literacy includes learning to read and write different types of mathematical texts as part of purposeful mathematical meaning making. Thus in this article, we describe how learning to read and write mathematical texts (proof text, algorithmic text, algebraic/symbolic text, and visual text) supports the development of students'…
Proof of Concept: Model Based Bionic Muscle with Hyperbolic Force-Velocity Relation
Directory of Open Access Journals (Sweden)
D. F. B. Haeufle
2012-01-01
Full Text Available Recently, the hyperbolic Hill-type force-velocity relation was derived from basic physical components. It was shown that a contractile element CE consisting of a mechanical energy source (active element AE, a parallel damper element (PDE, and a serial element (SE exhibits operating points with hyperbolic force-velocity dependency. In this paper, a technical proof of this concept was presented. AE and PDE were implemented as electric motors, SE as a mechanical spring. The force-velocity relation of this artificial CE was determined in quick release experiments. The CE exhibited hyperbolic force-velocity dependency. This proof of concept can be seen as a well-founded starting point for the development of Hill-type artificial muscles.
Proof mass effects on spiral electrode d33 mode piezoelectric diaphragm-based energy harvester
Shen, Zhiyuan; Liu, Shuwei; Miao, Jianmin; Woh, Lye Sun; Wang, Zhihong
2013-01-01
This paper presents the characterization of an energy harvester using a piezoelectric diaphragm as the vibration energy conversion microstructure. The diaphragm containing the spiral electrode operates in the d33 mode. The energy harvesting performance of the diaphragm was characterized. The optimal resistance load and the working frequency were characterized. The resonance tuning and the energy harvesting enhancement due to a proof mass were verified. © 2013 IEEE.
Prospective Mathematics Teachers' Understanding of the Base Concept
Horzum, Tugba; Ertekin, Erhan
2018-01-01
The purpose of this study is to analyze what kind of conceptions prospective mathematics teachers (PMTs) have about the base concept (BC). One-hundred and thirty-nine PMTs participated in the study. In this qualitative research, data were obtained through open-ended questions, the semi-structured interviews and pictures of geometric figures drawn…
Mathematics creative thinking levels based on interpersonal intelligence
Kuncorowati, R. H.; Mardiyana; Saputro, D. R. S.
2017-12-01
Creative thinking ability was one of student’s ability to determine various alternative solutions toward mathematics problem. One of indicators related to creative thinking ability was interpersonal intelligence. Student’s interpersonal intelligence would influence to student’s creativity. This research aimed to analyze creative thinking ability level of junior high school students in Karanganyar using descriptive method. Data was collected by test, questionnaire, interview, and documentation. The result showed that students with high interpersonal intelligence achieved third and fourth level in creative thinking ability. Students with moderate interpersonal intelligence achieved second level in creative thinking ability and students with low interpersonal intelligence achieved first and zero level in creative thinking ability. Hence, students with high, moderate, and low interpersonal intelligence could solve mathematics problem based on their mathematics creative thinking ability.
Brain based learning with contextual approach to mathematics achievement
Directory of Open Access Journals (Sweden)
V Kartikaningtyas
2017-12-01
Full Text Available The aim of this study was to know the effect of Brain Based Learning (BBL with a contextual approach to mathematics achievement. BBL-contextual is the learning model that designed to develop and optimize the brain ability for getting a new concept and solving the real life problem. This study method was a quasi-experiment. The population was the junior high school students. The sample chosen by using stratified cluster random sampling. The sample was 109 students. The data collected through a mathematics achievement test that was given after the treatment. The data analyzed by using one way ANOVA. The results of the study showed that BBL-contextual is better than direct learning on mathematics achievement. It means BBL-contextual could be an effective and innovative model.
Aberdein, Andrew
2014-01-01
This book presents a comprehensive investigation into the relationship between argumentation theory and the philosophy of mathematical practice. It offers large array of examples ranging from the history of mathematics to formal proof verification.
Factors Influencing Elementary Mathematics Teachers' Beliefs in Reform-Based Teaching
Sawyer, Amanda Gantt
2017-01-01
I investigated a reform based teachers' beliefs about the nature of mathematics, teaching mathematics, and learning mathematics, and the factors leading to their formation. I interviewed and observed a reform-based elementary mathematics teacher with 13 years' experience teaching first grade. She held a Platonist/problem solver view of…
Computerized Proof Techniques for Undergraduates
Smith, Christopher J.; Tefera, Akalu; Zeleke, Aklilu
2012-01-01
The use of computer algebra systems such as Maple and Mathematica is becoming increasingly important and widespread in mathematics learning, teaching and research. In this article, we present computerized proof techniques of Gosper, Wilf-Zeilberger and Zeilberger that can be used for enhancing the teaching and learning of topics in discrete…
Proof-of-Concept Experiments on a Gallium-Based Ignitron for Pulsed Power Applications
Ali, H. K.; Hanson, V. S.; Polzin, K. A.; Pearson, J. B.
2015-01-01
ignitron designs have used mercury as the liquid metal cathode, owing to its presence as a liquid at room temperatures and a vapor pressure of 10 Pa (75 mtorr) at room temperature. While these are favorable properties, there are obvious environmental and personal safety concerns with the storage, handling, and use of mercury and its compounds. The purpose of the present work was to fabricate and test an ignitron that used as its cathode an alternate liquid metal that was safe to handle and store. To that end, an ignitron test article that used liquid gallium as the cathode material was developed and tested. Gallium is a metal that has a melting temperature of 29.76 C, which is slightly above room temperature, and a boiling point of over 2,300 C at atmospheric pressure. This property makes gallium the element with the largest relative difference between melting and boiling points. Gallium has a limited role in biology, and when ingested, it will be subsequently processed by the body and expelled rather than accumulating to toxic levels. The next section of this Technical Memorandum (TM) provides background information on the development of mercury-based ignitrons, which serves as the starting point for the development of the gallium-based variant. Afterwards, the experimental hardware and setup used in proof-of-concept testing of a basic gallium ignitron are presented. Experimental data, consisting of discharge voltage and current waveforms as well as high-speed imaging of the gallium arc discharge in the gallium ignitron test article, are presented to demonstrate the efficacy of the concept. Discussion of the data and suggestions on improvements for future iterations of the design are presented in the final two sections of this TM.
Threshold Decryption and Zero-Knowledge Proofs for Lattice-Based Cryptosystems
DEFF Research Database (Denmark)
Bendlin, Rikke; Damgård, Ivan Bjerre
2010-01-01
generation protocol. In the final part of the paper we show how one can, in zero-knowledge - prove knowledge of the plaintext contained in a given ciphertext from Regev's original cryptosystem or our variant. The proof is of size only a constant times the size of the public key....... a very efficient and non-interactive decryption protocol. We prove the threshold cryptosystem secure against passive adversaries corrupting all but one of the players, and againts active adversaries corrupting less than one third of the players. We also describe how one can build a distributed key...
Supply Chain Based Solution to Prevent Fuel Tax Evasion: Proof of Concept Final Report
Energy Technology Data Exchange (ETDEWEB)
Capps, Gary J [ORNL; Lascurain, Mary Beth [ORNL; Franzese, Oscar [ORNL; Earl, Dennis Duncan [ORNL; West, David L [ORNL; McIntyre, Timothy J [ORNL; Chin, Shih-Miao [ORNL; Hwang, Ho-Ling [ORNL; Connatser, Raynella M [ORNL; Lewis Sr, Samuel Arthur [ORNL; Moore, Sheila A [ORNL
2011-12-01
The goal of this research was to provide a proof-of-concept (POC) system for preventing non-taxable (non-highway diesel use) or low-taxable (jet fuel) petrochemical products from being blended with taxable fuel products and preventing taxable fuel products from cross-jurisdiction evasion. The research worked to fill the need to validate the legitimacy of individual loads, offloads, and movements by integrating and validating, on a near-real-time basis, information from global positioning system (GPS), valve sensors, level sensors, and fuel-marker sensors.
The Computer Student Worksheet Based Mathematical Literacy for Statistics
Manoy, J. T.; Indarasati, N. A.
2018-01-01
The student worksheet is one of media teaching which is able to improve teaching an activity in the classroom. Indicators in mathematical literacy were included in a student worksheet is able to help the students for applying the concept in daily life. Then, the use of computers in learning can create learning with environment-friendly. This research used developmental research which was Thiagarajan (Four-D) development design. There are 4 stages in the Four-D, define, design, develop, and disseminate. However, this research was finish until the third stage, develop stage. The computer student worksheet based mathematical literacy for statistics executed good quality. This student worksheet is achieving the criteria if able to achieve three aspects, validity, practicality, and effectiveness. The subject in this research was the students at The 1st State Senior High School of Driyorejo, Gresik, grade eleven of The 5th Mathematics and Natural Sciences. The computer student worksheet products based mathematical literacy for statistics executed good quality, while it achieved the aspects for validity, practical, and effectiveness. This student worksheet achieved the validity aspects with an average of 3.79 (94.72%), and practical aspects with an average of 2.85 (71.43%). Besides, it achieved the effectiveness aspects with a percentage of the classical complete students of 94.74% and a percentage of the student positive response of 75%.
International Nuclear Information System (INIS)
Behrenhoff, W; Ehrenfeld, W; Samson, J; Stadie, H
2011-01-01
The 'parallel ROOT facility' (PROOF) from the ROOT framework provides a mechanism to distribute the load of interactive and non-interactive ROOT sessions on a set of worker nodes optimising the overall execution time. While PROOF is designed to work on a dedicated PROOF cluster, the benefits of PROOF can also be used on top of another batch scheduling system with the help of temporary per user PROOF clusters. We will present a lightweight tool which starts a temporary PROOF cluster on a SGE based batch cluster or, via a plugin mechanism, e.g. on a set of bare desktops via ssh. Further, we will present the result of benchmarks which compare the data throughput for different data storage back ends available at the German National Analysis Facility (NAF) at DESY.
Palinussa, Anderson L.
2013-01-01
This paper presents the findings of a quasi-experimental with pre-test-post-test design and control group that aims to assess students' critical mathematical thinking skills and character through realistic mathematics education (RME) culture-based. Subjects of this study were 106 junior high school students from two low and medium schools level in…
Two Project-Based Strategies in an Interdisciplinary Mathematical Modeling in Biology Course
Ludwig, Patrice; Tongen, Anthony; Walton, Brian
2018-01-01
James Madison University faculty team-teach an interdisciplinary mathematical modeling course for mathematics and biology students. We have used two different project-based approaches to emphasize the mathematical concepts taught in class, while also exposing students to new areas of mathematics not formally covered in class. The first method…
Algebraic Reasoning in Solving Mathematical Problem Based on Learning Style
Indraswari, N. F.; Budayasa, I. K.; Ekawati, R.
2018-01-01
This study aimed to describe algebraic reasoning of secondary school’s pupils with different learning styles in solving mathematical problem. This study begins by giving the questionnaire to find out the learning styles and followed by mathematical ability test to get three subjects of 8th-grade whereas the learning styles of each pupil is visual, auditory, kinesthetic and had similar mathematical abilities. Then it continued with given algebraic problems and interviews. The data is validated using triangulation of time. The result showed that in the pattern of seeking indicator, subjects identified the things that were known and asked based on them observations. The visual and kinesthetic learners represented the known information in a chart, whereas the auditory learner in a table. In addition, they found the elements which makes the pattern and made a relationship between two quantities. In the pattern recognition indicator, they created conjectures on the relationship between two quantities and proved it. In the generalization indicator, they were determining the general rule of pattern found on each element of pattern using algebraic symbols and created a mathematical model. Visual and kinesthetic learners determined the general rule of equations which was used to solve problems using algebraic symbols, but auditory learner in a sentence.
Mathematical Modeling of Column-Base Connections under Monotonic Loading
Directory of Open Access Journals (Sweden)
Gholamreza Abdollahzadeh
2014-12-01
Full Text Available Some considerable damage to steel structures during the Hyogo-ken Nanbu Earthquake occurred. Among them, many exposed-type column bases failed in several consistent patterns, such as brittle base plate fracture, excessive bolt elongation, unexpected early bolt failure, and inferior construction work, etc. The lessons from these phenomena led to the need for improved understanding of column base behavior. Joint behavior must be modeled when analyzing semi-rigid frames, which is associated with a mathematical model of the moment–rotation curve. The most accurate model uses continuous nonlinear functions. This article presents three areas of steel joint research: (1 analysis methods of semi-rigid joints; (2 prediction methods for the mechanical behavior of joints; (3 mathematical representations of the moment–rotation curve. In the current study, a new exponential model to depict the moment–rotation relationship of column base connection is proposed. The proposed nonlinear model represents an approach to the prediction of M–θ curves, taking into account the possible failure modes and the deformation characteristics of the connection elements. The new model has three physical parameters, along with two curve-fitted factors. These physical parameters are generated from dimensional details of the connection, as well as the material properties. The M–θ curves obtained by the model are compared with published connection tests and 3D FEM research. The proposed mathematical model adequately comes close to characterizing M–θ behavior through the full range of loading/rotations. As a result, modeling of column base connections using the proposed mathematical model can give crucial beforehand information, and overcome the disadvantages of time consuming workmanship and cost of experimental studies.
Vivaldi, Franco
2014-01-01
This book teaches the art of writing mathematics, an essential -and difficult- skill for any mathematics student. The book begins with an informal introduction on basic writing principles and a review of the essential dictionary for mathematics. Writing techniques are developed gradually, from the small to the large: words, phrases, sentences, paragraphs, to end with short compositions. These may represent the introduction of a concept, the abstract of a presentation or the proof of a theorem. Along the way the student will learn how to establish a coherent notation, mix words and symbols effectively, write neat formulae, and structure a definition. Some elements of logic and all common methods of proofs are featured, including various versions of induction and existence proofs. The book concludes with advice on specific aspects of thesis writing (choosing of a title, composing an abstract, compiling a bibliography) illustrated by large number of real-life examples. Many exercises are included; over 150...
Cardiac output-based fluid optimization for kidney transplant recipients: a proof-of-concept trial.
Corbella, Davide; Toppin, Patrick Jason; Ghanekar, Anand; Ayach, Nour; Schiff, Jeffery; Van Rensburg, Adrian; McCluskey, Stuart A
2018-04-10
Intravenous fluid management for deceased donor kidney transplantation is an important, modifiable risk factor for delayed graft function (DGF). The primary objective of this study was to determine if goal-directed fluid therapy using esophageal Doppler monitoring (EDM) to optimize stroke volume (SV) would alter the amount of fluid given. This randomized, proof-of-concept trial enrolled 50 deceased donor renal transplant recipients. Data collected included patient characteristics, fluid administration, hemodynamics, and complications. The EDM was used to optimize SV in the EDM group. In the control group, fluid management followed the current standard of practice. The groups were compared for the primary outcome of total intraoperative fluid administered. There was no difference in the mean (standard deviation) volume of intraoperative fluid administered to the 24 control and 26 EDM patients [2,307 (750) mL vs 2,675 (842) mL, respectively; mean difference, 368 mL; 95% confidence interval (CI), - 87 to + 823; P = 0.11]. The incidence of complications in the control and EDM groups was similar (15/24 vs 17/26, respectively; P = 0.99), as was the incidence of delayed graft failure (8/24 vs 11/26, respectively; P = 0.36). Goal-directed fluid therapy did not alter the volume of fluid administered or the incidence of complications. This proof-of-concept trial provides needed data for conducting a larger trial to determine the influence of fluid therapy on the incidence in DGF in deceased donor kidney transplantation. www.clinicaltrials.gov (NCT02512731). Registered 31 July 2015.
Conrad, Karen S.; Tracy, Dyanne M.
Research has shown that elementary teachers are mathematics anxious, and that this anxiousness can be transmitted to their students. Therefore, many students are not afforded the opportunity to participate in a comfortable mathematics environment. Preservice elementary teachers (n=63) reported their pre- and posttest mathematics anxiety using the…
Andriani, Ade; Dewi, Izwita; Halomoan, Budi
2018-03-01
In general, this research is conducted to improve the quality of lectures on mathematics learning strategy in Mathematics Department. The specific objective of this research is to develop learning instrument of mathematics learning strategy based on Higher Order Thinking Skill (HOTS) that can be used to improve mathematical communication and self efficacy of mathematics education students. The type of research is development research (Research & Development), where this research aims to develop a new product or improve the product that has been made. This development research refers to the four-D Model, which consists of four stages: defining, designing, developing, and disseminating. The instrument of this research is the validation sheet and the student response sheet of the instrument.
Proofs and generalizations of the pythagorean theorem
Directory of Open Access Journals (Sweden)
Lialda B. Cavalcanti
2011-01-01
Full Text Available This article explores a topic developed by a group of researchers of the Science and Technology Teaching School of Instituto Federal de Pernambuco, Brazil (IFPE, in assistance to the development of the Mathematics Practical and Teaching Laboratory of the distance learning Teaching Licensure, financed by the Universidad Abierta de Brasil. In this article, we describe the peculiarities present in the proofs of the Pythagorean theorem with the purpose of illustrating some of these methods. The selection of these peculiarities was founded and based on the comparison of areas by means of the superimposition of geometrical shapes and used several different class resources. Some generalizations of this important theorem in mathematical problem-solving are also shown.
Mathematicians' Perspectives on Features of a Good Pedagogical Proof
Lai, Yvonne; Weber, Keith; Mejia-Ramos, Juan Pablo
2012-01-01
In this article, we report two studies investigating what mathematicians value in a pedagogical proof. Study 1 is a qualitative study of how eight mathematicians revised two proofs that would be presented in a course for mathematics majors. These mathematicians thought that introductory and concluding sentences should be included in the proofs,…
Wardono; Waluya, S. B.; Mariani, Scolastika; Candra D, S.
2016-02-01
This study aims to find out that there are differences in mathematical literacy ability in content Change and Relationship class VII Junior High School 19, Semarang by Problem Based Learning (PBL) model with an Indonesian Realistic Mathematics Education (called Pendidikan Matematika Realistik Indonesia or PMRI in Indonesia) approach assisted Elearning Edmodo, PBL with a PMRI approach, and expository; to know whether the group of students with learning PBL models with PMRI approach and assisted E-learning Edmodo can improve mathematics literacy; to know that the quality of learning PBL models with a PMRI approach assisted E-learning Edmodo has a good category; to describe the difficulties of students in working the problems of mathematical literacy ability oriented PISA. This research is a mixed methods study. The population was seventh grade students of Junior High School 19, Semarang Indonesia. Sample selection is done by random sampling so that the selected experimental class 1, class 2 and the control experiment. Data collected by the methods of documentation, tests and interviews. From the results of this study showed average mathematics literacy ability of students in the group PBL models with a PMRI approach assisted E-learning Edmodo better than average mathematics literacy ability of students in the group PBL models with a PMRI approach and better than average mathematics literacy ability of students in the expository models; Mathematics literacy ability in the class using the PBL model with a PMRI approach assisted E-learning Edmodo have increased and the improvement of mathematics literacy ability is higher than the improvement of mathematics literacy ability of class that uses the model of PBL learning with PMRI approach and is higher than the improvement of mathematics literacy ability of class that uses the expository models; The quality of learning using PBL models with a PMRI approach assisted E-learning Edmodo have very good category.
Stöltzner, Michael
Answering to the double-faced influence of string theory on mathematical practice and rigour, the mathematical physicists Arthur Jaffe and Frank Quinn have contemplated the idea that there exists a `theoretical' mathematics (alongside `theoretical' physics) whose basic structures and results still require independent corroboration by mathematical proof. In this paper, I shall take the Jaffe-Quinn debate mainly as a problem of mathematical ontology and analyse it against the backdrop of two philosophical views that are appreciative towards informal mathematical development and conjectural results: Lakatos's methodology of proofs and refutations and John von Neumann's opportunistic reading of Hilbert's axiomatic method. The comparison of both approaches shows that mitigating Lakatos's falsificationism makes his insights about mathematical quasi-ontology more relevant to 20th century mathematics in which new structures are introduced by axiomatisation and not necessarily motivated by informal ancestors. The final section discusses the consequences of string theorists' claim to finality for the theory's mathematical make-up. I argue that ontological reductionism as advocated by particle physicists and the quest for mathematically deeper axioms do not necessarily lead to identical results.
Filler segmentation of SEM paper images based on mathematical morphology.
Ait Kbir, M; Benslimane, Rachid; Princi, Elisabetta; Vicini, Silvia; Pedemonte, Enrico
2007-07-01
Recent developments in microscopy and image processing have made digital measurements on high-resolution images of fibrous materials possible. This helps to gain a better understanding of the structure and other properties of the material at micro level. In this paper SEM image segmentation based on mathematical morphology is proposed. In fact, paper models images (Whatman, Murillo, Watercolor, Newsprint paper) selected in the context of the Euro Mediterranean PaperTech Project have different distributions of fibers and fillers, caused by the presence of SiAl and CaCO3 particles. It is a microscopy challenge to make filler particles in the sheet distinguishable from the other components of the paper surface. This objectif is reached here by using switable strutural elements and mathematical morphology operators.
The internal radiation dose calculations based on Chinese mathematical phantom
International Nuclear Information System (INIS)
Wang Haiyan; Li Junli; Cheng Jianping; Fan Jiajin
2006-01-01
The internal radiation dose calculations built on Chinese facts become more and more important according to the development of nuclear medicine. the MIRD method developed and consummated by the society of Nuclear Medicine (America) is based on the European and American mathematical phantom and can't fit Chinese well. The transport of γ-ray in the Chinese mathematical phantom was simulated with Monte Carlo method in programs as MCNP4C. the specific absorbed fraction (Φ) of Chinese were calculated and the Chinese Φ database was created. The results were compared with the recommended values by ORNL. the method was proved correct by the coherence when the target organ was the same with the source organ. Else, the difference was due to the different phantom and the choice of different physical model. (authors)
Edwin Musdi
2016-01-01
This research aims to develop a mathematics instructional model based realistic mathematics education (RME) to promote students' problem-solving abilities. The design research used Plomp models, which consists of preliminary phase, development or proto-typing phase and assessment phase. At this study, only the first two phases conducted. The first phase, a preliminary investigation, carried out with a literature study to examine the theory-based instructional learning RME model, characterist...
Proof complexity of intuitionistic implicational formulas
Czech Academy of Sciences Publication Activity Database
Jeřábek, Emil
2017-01-01
Roč. 168, č. 1 (2017), s. 150-190 ISSN 0168-0072 EU Projects: European Commission(XE) 339691 - FEALORA Institutional support: RVO:67985840 Keywords : proof complexity * intuitionistic logic * implicational fragment Subject RIV: BA - General Mathematics OBOR OECD: Pure mathematics Impact factor: 0.647, year: 2016 http://www.sciencedirect.com/science/article/pii/S0168007216301154
Computer-Assisted Discovery and Proof
Energy Technology Data Exchange (ETDEWEB)
Bailey, David H.; Borwein, Jonathan M.
2007-12-10
With the advent of powerful, widely-available mathematical software, combined with ever-faster computer hardware, we are approaching a day when both the discovery and proof of mathematical facts can be done in a computer-assisted manner. his article presents several specific examples of this new paradigm in action.
What is the problem in problem-based learning in higher education mathematics
Dahl, Bettina
2018-01-01
Problem and Project-Based Learning (PBL) emphasise collaborate work on problems relevant to society and emphases the relation between theory and practice. PBL fits engineering students as preparation for their future professions but what about mathematics? Mathematics is not just applied mathematics, but it is also a body of abstract knowledge where the application in society is not always obvious. Does mathematics, including pure mathematics, fit into a PBL curriculum? This paper argues that it does for two reasons: (1) PBL resembles the working methods of research mathematicians. (2) The concept of society includes the society of researchers to whom theoretical mathematics is relevant. The paper describes two cases of university PBL projects in mathematics; one in pure mathematics and the other in applied mathematics. The paper also discusses that future engineers need to understand the world of mathematics as well as how engineers fit into a process of fundamental-research-turned-into-applied-science.
Values and Norms of Proof for Mathematicians and Students
Dawkins, Paul Christian; Weber, Keith
2017-01-01
In this theoretical paper, we present a framework for conceptualizing proof in terms of mathematical values, as well as the norms that uphold those values. In particular, proofs adhere to the values of establishing a priori truth, employing decontextualized reasoning, increasing mathematical understanding, and maintaining consistent standards for…
Three Styles Characterising Mathematicians' Pedagogical Perspectives on Proof
Hemmi, Kirsti
2010-01-01
The article describes mathematicians' pedagogical perspectives on proof in the teaching of first year university students at a mathematics department in Sweden. A conceptual frame that was used in the data analysis combines theories about proof from earlier mathematics education research with a social practice approach of Lave and Wenger. A…
Ottmar, Erin R.; Rimm-Kaufman, Sara E.; Larsen, Ross A.; Berry, Robert Q.
2015-01-01
This study investigates the effectiveness of the Responsive Classroom (RC) approach, a social and emotional learning intervention, on changing the relations between mathematics teacher and classroom inputs (mathematical knowledge for teaching [MKT] and standards-based mathematics teaching practices) and student mathematics achievement. Work was…
Focus in High School Mathematics: Reasoning and Sense Making in Geometry
National Council of Teachers of Mathematics, 2010
2010-01-01
Classically, geometry has been the subject in which students encounter mathematical proof based on formal deduction. Attention to proof in the geometry curriculum is strengthened by a focus on reasoning and sense making. This book examines the four key elements (conjecturing about geometric objects, construction and evaluation of geometric…
Najafi, Shahriar; Flintsch, Gerardo W; Khaleghian, Seyedmeysam
2016-05-01
Minimizing roadway crashes and fatalities is one of the primary objectives of highway engineers, and can be achieved in part through appropriate maintenance practices. Maintaining an appropriate level of friction is a crucial maintenance practice, due to the effect it has on roadway safety. This paper presents a fuzzy logic inference system that predicts the rate of vehicle crashes based on traffic level, speed limit, and surface friction. Mamdani and Sugeno fuzzy controllers were used to develop the model. The application of the proposed fuzzy control system in a real-time slippery road warning system is demonstrated as a proof of concept. The results of this study provide a decision support model for highway agencies to monitor their network's friction and make appropriate judgments to correct deficiencies based on crash risk. Furthermore, this model can be implemented in the connected vehicle environment to warn drivers of potentially slippery locations. Published by Elsevier Ltd.
Mathematics and Astronomy: Inquire Based Scientific Education at School
de Castro, Ana I. Gómez
2010-10-01
Mathematics is the language of science however, in secondary and high school education students are not made aware of the strong implications behind this statement. This is partially caused because mathematical training and the modelling of nature are not taught together. Astronomy provides firm scientific grounds for this joint training; the mathematics needed is simple, the data can be acquired with simple instrumentation in any place on the planet and the physics is rich with a broad range of levels. In addition, astronomy and space exploration are extremely appealing to young (14-17 years old) students helping to motivate them to study science doing science, i.e. to introduce Inquiry Based Scientific Education (IBSE). Since 1997 a global consortium is being developed to introduce IBSE techniques in secondary/high school education on a global scale: the Global Hands-On Universe association (www.globalhou.org) making use of the astronomical universe as a training lab. This contribution is a brief update on the current activities of the HOU consortium. Relevant URLS: www.globalhou.org, www.euhou.net, www.houspain.com.
Walters, Charles David
Quantitative reasoning (P. W. Thompson, 1990, 1994) is a powerful mathematical tool that enables students to engage in rich problem solving across the curriculum. One way to support students' quantitative reasoning is to develop prospective secondary teachers' (PSTs) mathematical knowledge for teaching (MKT; Ball, Thames, & Phelps, 2008) related to quantitative reasoning. However, this may prove challenging, as prior to entering the classroom, PSTs often have few opportunities to develop MKT by examining and reflecting on students' thinking. Videos offer one avenue through which such opportunities are possible. In this study, I report on the design of a mini-course for PSTs that featured a series of videos created as part of a proof-of-concept NSF-funded project. These MathTalk videos highlight the ways in which the quantitative reasoning of two high school students developed over time. Using a mixed approach to grounded theory, I analyzed pre- and postinterviews using an extant coding scheme based on the Silverman and Thompson (2008) framework for the development of MKT. This analysis revealed a shift in participants' affect as well as three distinct shifts in their MKT around quantitative reasoning with distances, including shifts in: (a) quantitative reasoning; (b) point of view (decentering); and (c) orientation toward problem solving. Using the four-part focusing framework (Lobato, Hohensee, & Rhodehamel, 2013), I analyzed classroom data to account for how participants' noticing was linked with the shifts in MKT. Notably, their increased noticing of aspects of MKT around quantitative reasoning with distances, which features prominently in the MathTalk videos, seemed to contribute to the emergence of the shifts in MKT. Results from this study link elements of the learning environment to the development of specific facets of MKT around quantitative reasoning with distances. These connections suggest that vicarious experiences with two students' quantitative
Experiences of Student Mathematics-Teachers in Computer-Based Mathematics Learning Environment
Karatas, Ilhan
2011-01-01
Computer technology in mathematics education enabled the students find many opportunities for investigating mathematical relationships, hypothesizing, and making generalizations. These opportunities were provided to pre-service teachers through a faculty course. At the end of the course, the teachers were assigned project tasks involving…
Analogy, explanation, and proof
Hummel, John E.; Licato, John; Bringsjord, Selmer
2014-01-01
People are habitual explanation generators. At its most mundane, our propensity to explain allows us to infer that we should not drink milk that smells sour; at the other extreme, it allows us to establish facts (e.g., theorems in mathematical logic) whose truth was not even known prior to the existence of the explanation (proof). What do the cognitive operations underlying the inference that the milk is sour have in common with the proof that, say, the square root of two is irrational? Our ability to generate explanations bears striking similarities to our ability to make analogies. Both reflect a capacity to generate inferences and generalizations that go beyond the featural similarities between a novel problem and familiar problems in terms of which the novel problem may be understood. However, a notable difference between analogy-making and explanation-generation is that the former is a process in which a single source situation is used to reason about a single target, whereas the latter often requires the reasoner to integrate multiple sources of knowledge. This seemingly small difference poses a challenge to the task of marshaling our understanding of analogical reasoning to understanding explanation. We describe a model of explanation, derived from a model of analogy, adapted to permit systematic violations of this one-to-one mapping constraint. Simulation results demonstrate that the resulting model can generate explanations for novel explananda and that, like the explanations generated by human reasoners, these explanations vary in their coherence. PMID:25414655
Aigner, Martin
2014-01-01
This revised and enlarged fifth edition features four new chapters, which contain highly original and delightful proofs for classics such as the spectral theorem from linear algebra, some more recent jewels like the non-existence of the Borromean rings and other surprises. From the Reviews "... Inside PFTB (Proofs from The Book) is indeed a glimpse of mathematical heaven, where clever insights and beautiful ideas combine in astonishing and glorious ways. There is vast wealth within its pages, one gem after another. ... Aigner and Ziegler... write: "... all we offer is the examples that we have selected, hoping that our readers will share our enthusiasm about brilliant ideas, clever insights and wonderful observations." I do. ... " Notices of the AMS, August 1999 "... This book is a pleasure to hold and to look at: ample margins, nice photos, instructive pictures, and beautiful drawings ... It is a pleasure to read as well: the style is clear and entertaining, the level is close to elementary, the necessary b...
Marti, E; Wang, X; Jambari, N N; Rhyner, C; Olzhausen, J; Pérez-Barea, J J; Figueredo, G P; Alcocer, M J C
2015-10-15
Insect bite hypersensitivity (IBH) is a seasonal recurrent skin allergy of horses caused by IgE-mediated reactions to allergens present in the saliva of biting insects of the genus Culicoides, and possibly also Simulium and Stomoxys species. In this work we show that protein microarrays containing complex extracts and pure proteins, including recombinant Culicoides allergens, can be used as a powerful technique for the diagnosis of IBH. Besides the obvious advantages such as general profiling and use of few microliters of samples, this microarray technique permits automation and allows the generation of mathematical models with the calculation of individual risk profiles that can support the clinical diagnosis of allergic diseases. After selection of variables on influence on the projection (VIP), the observed values of sensitivity and specificity were 1.0 and 0.967, respectively. This confirms the highly discriminatory power of this approach for IBH and made it possible to attain a robust predictive mathematical model for this disease. It also further demonstrates the specificity of the protein array method on identifying a particular IgE-mediated disease when the sensitising allergen group is known. Copyright © 2015 Elsevier B.V. All rights reserved.
Yang, Ri-Long; Zhu, Ying-Jie; Chen, Fei-Fei; Dong, Li-Ying; Xiong, Zhi-Chao
2017-08-02
Counterfeiting of valuable certificates, documents, and banknotes is a serious issue worldwide. As a result, the need for developing novel anticounterfeiting materials is greatly increasing. Herein, we report a new kind of ultralong hydroxyapatite nanowire (HAPNW)-based paper with luminescence, fire resistance, and waterproofness properties that may be exploited for anticounterfeiting applications. In this work, lanthanide-ion-doped HAPNWs (HAPNW:Ln 3+ ) with lengths over 100 μm have been synthesized and used as a raw material to fabricating a free-standing luminescent, fire-resistant, water-proof paper through a simple vacuum filtration process. It is interesting to find that the luminescence intensity, structure, and morphology of HAPNW:Ln 3+ highly depend on the experimental conditions. The as-prepared HAPNW:Ln 3+ paper has a unique combination of properties, such as high flexibility, good processability, writing and printing abilities, luminescence, tunable emission color, waterproofness, and fire resistance. In addition, a well-designed pattern can be embedded in the paper that is invisible under ambient light but viewable as a luminescent color under ultraviolet light. Moreover, the HAPNW:Ln 3+ paper can be well-preserved without any damage after being burned by fire or soaked in water. The unique combination of luminescence, fire resistance, and waterproofness properties and the nanowire structure of the as-prepared HAPNW:Ln 3+ paper may be exploited toward developing a new kind of multimode anticounterfeiting technology for various high-level security antiforgery applications, such as in making forgery-proof documents, certificates, labels, and tags and in packaging.
Wang, Shuang; Yin, Zhen-Qiang; Chau, H. F.; Chen, Wei; Wang, Chao; Guo, Guang-Can; Han, Zheng-Fu
2018-04-01
In comparison to qubit-based protocols, qudit-based quantum key distribution ones generally allow two cooperative parties to share unconditionally secure keys under a higher channel noise. However, it is very hard to prepare and measure the required quantum states in qudit-based protocols in general. One exception is the recently proposed highly error tolerant qudit-based protocol known as the Chau15 (Chau 2015 Phys. Rev. A 92 062324). Remarkably, the state preparation and measurement in this protocol can be done relatively easily since the required states are phase encoded almost like the diagonal basis states of a qubit. Here we report the first proof-of-principle demonstration of the Chau15 protocol. One highlight of our experiment is that its post-processing is based on practical one-way manner, while the original proposal in Chau (2015 Phys. Rev. A 92 062324) relies on complicated two-way post-processing, which is a great challenge in experiment. In addition, by manipulating time-bin qudit and measurement with a variable delay interferometer, our realization is extensible to qudit with high-dimensionality and confirms the experimental feasibility of the Chau15 protocol.
Unraveling the Culture of the Mathematics Classroom: A Video-Based Study in Sixth Grade
Depaepe, Fien; De Corte, Erik; Verschaffel, Lieven
2007-01-01
Changing perspectives on mathematics teaching and learning resulted in a new generation of mathematics textbooks, stressing among others the importance of mathematical reasoning and problem-solving skills and their application to real-life situations. The article reports a study that investigates to what extent the reform-based ideas underlying…
A MATLAB-Aided Method for Teaching Calculus-Based Business Mathematics
Liang, Jiajuan; Pan, William S. Y.
2009-01-01
MATLAB is a powerful package for numerical computation. MATLAB contains a rich pool of mathematical functions and provides flexible plotting functions for illustrating mathematical solutions. The course of calculus-based business mathematics consists of two major topics: 1) derivative and its applications in business; and 2) integration and its…
What Is the Problem in Problem-Based Learning in Higher Education Mathematics
Dahl, Bettina
2018-01-01
Problem and Project-Based Learning (PBL) emphasise collaborate work on problems relevant to society and emphases the relation between theory and practice. PBL fits engineering students as preparation for their future professions but what about mathematics? Mathematics is not just applied mathematics, but it is also a body of abstract knowledge…
Project-Based Learning and Design-Focused Projects to Motivate Secondary Mathematics Students
Remijan, Kelly W.
2017-01-01
This article illustrates how mathematics teachers can develop design-focused projects, related to project-based learning, to motivate secondary mathematics students. With first-hand experience as a secondary mathematics teacher, I provide a series of steps related to the engineering design process, which are helpful to teachers in developing…
Mathematical Representation Ability by Using Project Based Learning on the Topic of Statistics
Widakdo, W. A.
2017-09-01
Seeing the importance of the role of mathematics in everyday life, mastery of the subject areas of mathematics is a must. Representation ability is one of the fundamental ability that used in mathematics to make connection between abstract idea with logical thinking to understanding mathematics. Researcher see the lack of mathematical representation and try to find alternative solution to dolve it by using project based learning. This research use literature study from some books and articles in journals to see the importance of mathematical representation abiliy in mathemtics learning and how project based learning able to increase this mathematical representation ability on the topic of Statistics. The indicators for mathematical representation ability in this research classifies namely visual representation (picture, diagram, graph, or table); symbolize representation (mathematical statement. Mathematical notation, numerical/algebra symbol) and verbal representation (written text). This article explain about why project based learning able to influence student’s mathematical representation by using some theories in cognitive psychology, also showing the example of project based learning that able to use in teaching statistics, one of mathematics topic that very useful to analyze data.
Problems and proofs in numbers and algebra
Millman, Richard S; Kahn, Eric Brendan
2015-01-01
Designed to facilitate the transition from undergraduate calculus and differential equations to learning about proofs, this book helps students develop the rigorous mathematical reasoning needed for advanced courses in analysis, abstract algebra, and more. Students will focus on both how to prove theorems and solve problem sets in-depth; that is, where multiple steps are needed to prove or solve. This proof technique is developed by examining two specific content themes and their applications in-depth: number theory and algebra. This choice of content themes enables students to develop an understanding of proof technique in the context of topics with which they are already familiar, as well as reinforcing natural and conceptual understandings of mathematical methods and styles. The key to the text is its interesting and intriguing problems, exercises, theorems, and proofs, showing how students will transition from the usual, more routine calculus to abstraction while also learning how to “prove” or “sol...
Affecting the Flow of a Proof by Creating Presence--A Case Study in Number Theory
Gabel, Mika; Dreyfus, Tommy
2017-01-01
The notion of flow of a proof encapsulates mathematical, didactical, and contextual aspects of proof presentation. A proof may have different flows, depending on the lecturer's choices regarding its presentation. Adopting Perelman's New Rhetoric (PNR) as a theoretical framework, we designed methods to assess aspects of the flow of a proof. We…
Using Assessment for Learning Mathematics with Mobile Tablet Based Solutions
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Ghislain Maurice Norbert Isabwe
2014-03-01
Full Text Available This article discusses assessment for learning in mathematics subjects. Teachers of large classes face the challenge of regularly assessing studentsཿ ongoing mathematical learning achievements. Taking the complexity of assessment and feedback for learning as a background, we have developed a new approach to the assessment for learning mathematics at university level. We devised mobile tablet technology supported assessment processes, and we carried out user studies in both Rwanda and Norway. Results of our study indicated that students found it fruitful to be involved in assessing other studentsཿ mathematics work, i.e. assessing fellow studentsཿ answers to mathematical tasks. By being involved in the assessment process, the students expected mathematical learning gains. Their providing and obtaining of feedback to/from their fellow students using technology supported tools were highly appreciated as regards their own mathematical learning process.
Mathematics a minimal introduction
Buium, Alexandru
2013-01-01
Pre-Mathematical Logic Languages Metalanguage Syntax Semantics Tautologies Witnesses Theories Proofs Argot Strategies Examples Mathematics ZFC Sets Maps Relations Operations Integers Induction Rationals Combinatorics Sequences Reals Topology Imaginaries Residues p-adics Groups Orders Vectors Matrices Determinants Polynomials Congruences Lines Conics Cubics Limits Series Trigonometry Integrality Reciprocity Calculus Metamodels Categories Functors Objectives Mathematical Logic Models Incompleteness Bibliography Index
PREFACE: Physics-Based Mathematical Models for Nanotechnology
Voon, Lok C. Lew Yan; Melnik, Roderick; Willatzen, Morten
2008-03-01
stain-resistant clothing, but with thousands more anticipated. The focus of this interdisciplinary workshop was on determining what kind of new theoretical and computational tools will be needed to advance the science and engineering of nanomaterials and nanostructures. Thanks to the stimulating environment of the BIRS, participants of the workshop had plenty of opportunity to exchange new ideas on one of the main topics of this workshop—physics-based mathematical models for the description of low-dimensional semiconductor nanostructures (LDSNs) that are becoming increasingly important in technological innovations. The main objective of the workshop was to bring together some of the world leading experts in the field from each of the key research communities working on different aspects of LDSNs in order to (a) summarize the state-of-the-art models and computational techniques for modeling LDSNs, (b) identify critical problems of major importance that require solution and prioritize them, (c) analyze feasibility of existing mathematical and computational methodologies for the solution of some such problems, and (d) use some of the workshop working sessions to explore promising approaches in addressing identified challenges. With the possibility of growing practically any shape and size of heterostructures, it becomes essential to understand the mathematical properties of quantum-confined structures including properties of bulk states, interface states, and surface states as a function of shape, size, and internal strain. This workshop put strong emphasis on discussions of the new mathematics needed in nanotechnology especially in relation to geometry and material-combination optimization of device properties such as electronic, optical, and magnetic properties. The problems that were addressed at this meeting are of immense importance in determining such quantum-mechanical properties and the group of invited participants covered very well all the relevant disciplines
Rigorous proof of fuzzy error propagation with matrix-based LCI
Heijungs, Reinout; Tan, Raymond R.
2010-01-01
Background, aim, and scope: Propagation of parametric uncertainty in life cycle inventory (LCI) models is usually performed based on probabilistic Monte Carlo techniques. However, alternative approaches using interval or fuzzy numbers have been proposed based on the argument that these provide a
Hybrid modelling framework by using mathematics-based and information-based methods
International Nuclear Information System (INIS)
Ghaboussi, J; Kim, J; Elnashai, A
2010-01-01
Mathematics-based computational mechanics involves idealization in going from the observed behaviour of a system into mathematical equations representing the underlying mechanics of that behaviour. Idealization may lead mathematical models that exclude certain aspects of the complex behaviour that may be significant. An alternative approach is data-centric modelling that constitutes a fundamental shift from mathematical equations to data that contain the required information about the underlying mechanics. However, purely data-centric methods often fail for infrequent events and large state changes. In this article, a new hybrid modelling framework is proposed to improve accuracy in simulation of real-world systems. In the hybrid framework, a mathematical model is complemented by information-based components. The role of informational components is to model aspects which the mathematical model leaves out. The missing aspects are extracted and identified through Autoprogressive Algorithms. The proposed hybrid modelling framework has a wide range of potential applications for natural and engineered systems. The potential of the hybrid methodology is illustrated through modelling highly pinched hysteretic behaviour of beam-to-column connections in steel frames.
Imbs, Diane-Charlotte; El Cheikh, Raouf; Boyer, Arnaud; Ciccolini, Joseph; Mascaux, Céline; Lacarelle, Bruno; Barlesi, Fabrice; Barbolosi, Dominique; Benzekry, Sébastien
2018-01-01
Concomitant administration of bevacizumab and pemetrexed-cisplatin is a common treatment for advanced nonsquamous non-small cell lung cancer (NSCLC). Vascular normalization following bevacizumab administration may transiently enhance drug delivery, suggesting improved efficacy with sequential administration. To investigate optimal scheduling, we conducted a study in NSCLC-bearing mice. First, experiments demonstrated improved efficacy when using sequential vs. concomitant scheduling of bevacizumab and chemotherapy. Combining this data with a mathematical model of tumor growth under therapy accounting for the normalization effect, we predicted an optimal delay of 2.8 days between bevacizumab and chemotherapy. This prediction was confirmed experimentally, with reduced tumor growth of 38% as compared to concomitant scheduling, and prolonged survival (74 vs. 70 days). Alternate sequencing of 8 days failed in achieving a similar increase in efficacy, thus emphasizing the utility of modeling support to identify optimal scheduling. The model could also be a useful tool in the clinic to personally tailor regimen sequences. © 2017 The Authors CPT: Pharmacometrics & Systems Pharmacology published by Wiley Periodicals, Inc. on behalf of American Society for Clinical Pharmacology and Therapeutics.
Flexibility in Mathematics Problem Solving Based on Adversity Quotient
Dina, N. A.; Amin, S. M.; Masriyah
2018-01-01
Flexibility is an ability which is needed in problem solving. One of the ways in problem solving is influenced by Adversity Quotient (AQ). AQ is the power of facing difficulties. There are three categories of AQ namely climber, camper, and quitter. This research is a descriptive research using qualitative approach. The aim of this research is to describe flexibility in mathematics problem solving based on Adversity Quotient. The subjects of this research are climber student, camper student, and quitter student. This research was started by giving Adversity Response Profile (ARP) questioner continued by giving problem solving task and interviews. The validity of data measurement was using time triangulation. The results of this research shows that climber student uses two strategies in solving problem and doesn’t have difficulty. The camper student uses two strategies in solving problem but has difficulty to finish the second strategies. The quitter student uses one strategy in solving problem and has difficulty to finish it.
Marques, J.P.; Sodickson, D.K.; Ipek, O.; Collins, C.M.; Gruetter, R.
2015-01-01
PurposeAll methods presented to date to map both conductivity and permittivity rely on multiple acquisitions to compute quantitatively the magnitude of radiofrequency transmit fields, B-1(+). In this work, we propose a method to compute both conductivity and permittivity based solely on relative
Prospective mathematics teachers' understanding of the base concept
Horzum, Tuğba; Ertekin, Erhan
2018-02-01
The purpose of this study is to analyze what kind of conceptions prospective mathematics teachers(PMTs) have about the base concept(BC). One-hundred and thirty-nine PMTs participated in the study. In this qualitative research, data were obtained through open-ended questions, the semi-structured interviews and pictures of geometric figures drawn by PMTs. As a result, it was determined that PMTs dealt with the BC in a broad range of seven different images. It was also determined that the base perception of PMTs was limited mostly to their usage in daily life and in this context, they have position-dependent and word-dependent images. It was also determined that PMTs named the base to explain the BC or paid attention to the naming of three-dimensional geometric figures through the statement: 'objects are named according to their bases'. At the same time, it was also determined that PMTs had more than one concept imageswhich were contradicting with each other. According to these findings, potential explanations and advices were given.
Do manual and voxel-based morphometry measure the same? – A proof of concept study
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Niels K. Focke
2014-04-01
Full Text Available Voxel-based morphometry (VBM is a commonly used method to study volumetric variations on a whole brain basis. However it is often criticised for potential confounds, mainly based on imperfect spatial registration. We therefore aimed to evaluate if VBM and gold-standard manual volumetry are measuring the same effects with respect to subcortical grey matter volumes. Manual regions-of-interest (ROIs were drawn in the hippocampus, amygdala, nucleus accumbens, thalamus, putamen, pallidum and caudate nucleus bilaterally. Resulting volumes were used for a whole brain VBM correlation analysis with SPM8. The hippocampus, amygdala, putamen and caudate nucleus were correctly identified by SPM using the contemporary high-dimensional normalization (DARTEL toolbox. This strongly suggests that VBM and manual volumetry both are indeed measuring the same effects with regard to subcortical brain structures.
Friedrich, D T; Sommer, F; Scheithauer, M O; Greve, J; Hoffmann, T K; Schuler, P J
2017-12-01
Objective Advanced transnasal sinus and skull base surgery remains a challenging discipline for head and neck surgeons. Restricted access and space for instrumentation can impede advanced interventions. Thus, we present the combination of an innovative robotic endoscope guidance system and a specific endoscope with adjustable viewing angle to facilitate transnasal surgery in a human cadaver model. Materials and Methods The applicability of the robotic endoscope guidance system with custom foot pedal controller was tested for advanced transnasal surgery on a fresh frozen human cadaver head. Visualization was enabled using a commercially available endoscope with adjustable viewing angle (15-90 degrees). Results Visualization and instrumentation of all paranasal sinuses, including the anterior and middle skull base, were feasible with the presented setup. Controlling the robotic endoscope guidance system was effectively precise, and the adjustable endoscope lens extended the view in the surgical field without the common change of fixed viewing angle endoscopes. Conclusion The combination of a robotic endoscope guidance system and an advanced endoscope with adjustable viewing angle enables bimanual surgery in transnasal interventions of the paranasal sinuses and the anterior skull base in a human cadaver model. The adjustable lens allows for the abandonment of fixed-angle endoscopes, saving time and resources, without reducing the quality of imaging.
Pugh, Charles C
2015-01-01
Based on an honors course taught by the author at UC Berkeley, this introduction to undergraduate real analysis gives a different emphasis by stressing the importance of pictures and hard problems. Topics include: a natural construction of the real numbers, four-dimensional visualization, basic point-set topology, function spaces, multivariable calculus via differential forms (leading to a simple proof of the Brouwer Fixed Point Theorem), and a pictorial treatment of Lebesgue theory. Over 150 detailed illustrations elucidate abstract concepts and salient points in proofs. The exposition is informal and relaxed, with many helpful asides, examples, some jokes, and occasional comments from mathematicians, such as Littlewood, Dieudonné, and Osserman. This book thus succeeds in being more comprehensive, more comprehensible, and more enjoyable, than standard introductions to analysis. New to the second edition of Real Mathematical Analysis is a presentation of Lebesgue integration done almost entirely using the un...
Design and test of a biosensor-based multisensorial system: a proof of concept study.
Santonico, Marco; Pennazza, Giorgio; Grasso, Simone; D'Amico, Arnaldo; Bizzarri, Mariano
2013-12-04
Sensors are often organized in multidimensional systems or networks for particular applications. This is facilitated by the large improvements in the miniaturization process, power consumption reduction and data analysis techniques nowadays possible. Such sensors are frequently organized in multidimensional arrays oriented to the realization of artificial sensorial systems mimicking the mechanisms of human senses. Instruments that make use of these sensors are frequently employed in the fields of medicine and food science. Among them, the so-called electronic nose and tongue are becoming more and more popular. In this paper an innovative multisensorial system based on sensing materials of biological origin is illustrated. Anthocyanins are exploited here as chemical interactive materials for both quartz microbalance (QMB) transducers used as gas sensors and for electrodes used as liquid electrochemical sensors. The optical properties of anthocyanins are well established and widely used, but they have never been exploited as sensing materials for both gas and liquid sensors in non-optical applications. By using the same set of selected anthocyanins an integrated system has been realized, which includes a gas sensor array based on QMB and a sensor array for liquids made up of suitable Ion Sensitive Electrodes (ISEs). The arrays are also monitored from an optical point of view. This embedded system, is intended to mimic the working principles of the nose, tongue and eyes. We call this setup BIONOTE (for BIOsensor-based multisensorial system for mimicking NOse, Tongue and Eyes). The complete design, fabrication and calibration processes of the BIONOTE system are described herein, and a number of preliminary results are discussed. These results are relative to: (a) the characterization of the optical properties of the tested materials; (b) the performance of the whole system as gas sensor array with respect to ethanol, hexane and isopropyl alcohol detection
Design and Test of a Biosensor-Based Multisensorial System: A Proof of Concept Study
Directory of Open Access Journals (Sweden)
Marco Santonico
2013-12-01
Full Text Available Sensors are often organized in multidimensional systems or networks for particular applications. This is facilitated by the large improvements in the miniaturization process, power consumption reduction and data analysis techniques nowadays possible. Such sensors are frequently organized in multidimensional arrays oriented to the realization of artificial sensorial systems mimicking the mechanisms of human senses. Instruments that make use of these sensors are frequently employed in the fields of medicine and food science. Among them, the so-called electronic nose and tongue are becoming more and more popular. In this paper an innovative multisensorial system based on sensing materials of biological origin is illustrated. Anthocyanins are exploited here as chemical interactive materials for both quartz microbalance (QMB transducers used as gas sensors and for electrodes used as liquid electrochemical sensors. The optical properties of anthocyanins are well established and widely used, but they have never been exploited as sensing materials for both gas and liquid sensors in non-optical applications. By using the same set of selected anthocyanins an integrated system has been realized, which includes a gas sensor array based on QMB and a sensor array for liquids made up of suitable Ion Sensitive Electrodes (ISEs. The arrays are also monitored from an optical point of view. This embedded system, is intended to mimic the working principles of the nose, tongue and eyes. We call this setup BIONOTE (for BIOsensor-based multisensorial system for mimicking NOse, Tongue and Eyes. The complete design, fabrication and calibration processes of the BIONOTE system are described herein, and a number of preliminary results are discussed. These results are relative to: (a the characterization of the optical properties of the tested materials; (b the performance of the whole system as gas sensor array with respect to ethanol, hexane and isopropyl alcohol
Inquiry based learning: a student centered learning to develop mathematical habits of mind
Handayani, A. D.; Herman, T.; Fatimah, S.; Setyowidodo, I.; Katminingsih, Y.
2018-05-01
Inquiry based learning is learning that based on understanding constructivist mathematics learning. Learning based on constructivism is the Student centered learning. In constructivism, students are trained and guided to be able to construct their own knowledge on the basis of the initial knowledge that they have before. This paper explained that inquiry based learning can be used to developing student’s Mathematical habits of mind. There are sixteen criteria Mathematical Habits of mind, among which are diligent, able to manage time well, have metacognition ability, meticulous, etc. This research method is qualitative descriptive. The result of this research is that the instruments that have been developed to measure mathematical habits of mind are validated by the expert. The conclusion is the instrument of mathematical habits of mind are valid and it can be used to measure student’s mathematical habits of mind.
Analogy, Explanation, and Proof
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John eHummel
2014-11-01
Full Text Available People are habitual explanation generators. At its most mundane, our propensity to explain allows us to infer that we should not drink milk that smells sour; at the other extreme, it allows us to establish facts (e.g., theorems in mathematical logic whose truth was not even known prior to the existence of the explanation (proof. What do the cognitive operations underlying the (inductive inference that the milk is sour have in common with the (deductive proof that, say, the square root of two is irrational? Our ability to generate explanations bears striking similarities to our ability to make analogies. Both reflect a capacity to generate inferences and generalizations that go beyond the featural similarities between a novel problem and familiar problems in terms of which the novel problem may be understood. However, a notable difference between analogy-making and explanation-generation is that the former is a process in which a single source situation is used to reason about a single target, whereas the latter often requires the reasoner to integrate multiple sources of knowledge. This small-seeming difference poses a challenge to the task of marshaling our understanding of analogical reasoning in the service of understanding explanation. We describe a model of explanation, derived from a model of analogy, adapted to permit systematic violations of this one-to-one mapping constraint. Simulation results demonstrate that the resulting model can generate explanations for novel explananda and that, like the explanations generated by human reasoners, these explanations vary in their coherence.
Learning to Leverage Children's Multiple Mathematical Knowledge Bases in Mathematics Instruction
Turner, Erin E.; Foote, Mary Q.; Stoehr, Kathleen Jablon; McDuffie, Amy Roth; Aguirre, Julia Maria; Bartell, Tonya Gau; Drake, Corey
2016-01-01
In this article, the authors explore prospective elementary teachers' engagement with and reflection on activities they conducted to learn about a single child from their practicum classroom. Through these activities, prospective teachers learned about their child's mathematical thinking and the interests, competencies, and resources she or he…
Mathematical Biology Modules Based on Modern Molecular Biology and Modern Discrete Mathematics
Robeva, Raina; Davies, Robin; Hodge, Terrell; Enyedi, Alexander
2010-01-01
We describe an ongoing collaborative curriculum materials development project between Sweet Briar College and Western Michigan University, with support from the National Science Foundation. We present a collection of modules under development that can be used in existing mathematics and biology courses, and we address a critical national need to…
Cicora, Federico; Mos, Fernando; Petroni, Jorgelina; Casanova, Matías; Reniero, Liliana; Roberti, Javier
2015-01-01
Belatacept provides effective immunosuppression while avoiding the nephrotoxicities associated with calcineurin inhibitors (CNIs). However, existing belatacept-based regimens still have high rates of acute rejection. We hypothesized that therapy with belatacept, mycophenolic acid (MMA), steroids and induction therapy with rabbit anti-thymocyte globulin Fresenius (ATGF), rejection rate could be reduced. Prospective, single center, proof-of-concept study including males and females aged ≥18years, Epstein-Barr virus (EBV)-seropositive recipients of a first, HLA non-identical, live or deceased donor kidney allograft. Only patients with a calculated panel reactive antibody score of 0% were included. Three donors were positive for Chagas disease. Six of twelve patients had at least one infection and five were readmitted to the hospital for treatment. One patient had a Trypanosoma cruzi infection via the graft treated successfully. Median cold ischemia time for the transplant patients with a deceased donor was 21.5h. Mean serum creatinine levels at 1, 3 and 6months were 1.76±0.59, 1.55±0.60 and 1.49±0.60mg/dl, respectively. Two of twelve patients experienced clinical, biopsy-proven rejection, successfully treated with methylprednisolone. No patient developed post-transplant lymphoproliferative disorder (PTLD) or any other malignancy and no patient lost their graft or died during follow-up. The potential of this approach makes it worthy of further investigation. Copyright © 2014 Elsevier B.V. All rights reserved.
Urech, Antoine; Krieger, Tobias; Chesham, Alvin; Mast, Fred W; Berger, Thomas
2015-01-01
Attention bias modification (ABM) programs have been considered as a promising new approach for the treatment of various disorders, including social anxiety disorder (SAD). However, previous studies yielded ambiguous results regarding the efficacy of ABM in SAD. The present proof-of-concept study investigates the feasibility of a newly developed virtual reality (VR)-based dot-probe training paradigm. It was designed to facilitate attentional disengagement from threatening stimuli in socially anxious individuals (N = 15). The following outcomes were examined: (a) self-reports of enjoyment, motivation, flow, and presence; (b) attentional bias for social stimuli; and (c) social anxiety symptoms. Results showed that ABM training is associated with high scores in enjoyment, motivation, flow, and presence. Furthermore, significant improvements in terms of attention bias and social anxiety symptoms were observed from pre- to follow-up assessment. The study suggests that VR is a feasible and presumably a promising new medium for ABM trainings. Controlled studies will need to be carried out.
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Antoine eUrech
2015-10-01
Full Text Available Attention bias modification (ABM programs have been considered as a promising new approach for the treatment of various disorders, including social anxiety disorder (SAD. However, previous studies yielded ambiguous results regarding the efficacy of ABM in SAD. The present proof-of-concept study investigates the feasibility of a newly developed virtual reality (VR-based dot-probe training paradigm. It was designed to facilitate attentional disengagement from threatening stimuli in socially anxious individuals (N=15. The following outcomes were examined: (a self-reports of enjoyment, motivation, flow and presence, (b attentional bias for social stimuli, and (c social anxiety symptoms. Results showed that ABM training is associated with high scores in enjoyment, motivation, flow and presence. Furthermore, significant improvements in terms of attention bias and social anxiety symptoms were observed from pre- to follow-up assessment. The study suggests that VR is a feasible and presumably a promising new medium for ABM trainings. Controlled studies will need to be carried out.
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Thorsten Roland Doeppner
2014-10-01
Full Text Available Ischemic stroke remains a heavy burden for industrialized countries. The only causal therapy is the recanalization of occluded vessels via thrombolysis, which due to a narrow time window still can be offered only to a minority of patients. Since the majority of patients continues to exhibit neurological deficits even following successful thrombolysis, restorative therapies are urgently needed that promote brain remodeling and repair once stroke injury has occurred. Due to their unique properties of action, stem cell-based strategies gained increasing interest during recent years. Using various stroke models in both rodents and primates, the transplantation of stem cells, namely of bone marrow derived mesenchymal stem cells (MSCs or neural progenitor cells (NPCs, has been shown to promote neurological recovery most likely via indirect bystander actions. In view of promising observations, clinical proof-of-concept studies are currently under way, in which effects of stem and precursor cells are evaluated in human stroke patients. In this review we summarize already published studies, which due to the broad experience in other medical contexts mostly employed bone marrow-derived MSCs by means of intravenous transplantation. With the overall number of clinical trials limited in number, only a fraction of these studies used non-treated control groups, and only single studies were adequately blinded. Despite these limitations, first promising results justify the need for more elaborate clinical trials in order to make stem cell transplantation a success for stroke treatment in the future.
Roine, Antti; Saviauk, Taavi; Kumpulainen, Pekka; Karjalainen, Markus; Tuokko, Antti; Aittoniemi, Janne; Vuento, Risto; Lekkala, Jukka; Lehtimäki, Terho; Tammela, Teuvo L; Oksala, Niku K J
2014-01-01
Urinary tract infection (UTI) is a common disease with significant morbidity and economic burden, accounting for a significant part of the workload in clinical microbiology laboratories. Current clinical chemisty point-of-care diagnostics rely on imperfect dipstick analysis which only provides indirect and insensitive evidence of urinary bacterial pathogens. An electronic nose (eNose) is a handheld device mimicking mammalian olfaction that potentially offers affordable and rapid analysis of samples without preparation at athmospheric pressure. In this study we demonstrate the applicability of ion mobility spectrometry (IMS) -based eNose to discriminate the most common UTI pathogens from gaseous headspace of culture plates rapidly and without sample preparation. We gathered a total of 101 culture samples containing four most common UTI bacteries: E. coli, S. saprophyticus, E. faecalis, Klebsiella spp and sterile culture plates. The samples were analyzed using ChemPro 100i device, consisting of IMS cell and six semiconductor sensors. Data analysis was conducted by linear discriminant analysis (LDA) and logistic regression (LR). The results were validated by leave-one-out and 5-fold cross validation analysis. In discrimination of sterile and bacterial samples sensitivity of 95% and specificity of 97% were achieved. The bacterial species were identified with sensitivity of 95% and specificity of 96% using eNose as compared to urine bacterial cultures. These findings strongly demonstrate the ability of our eNose to discriminate bacterial cultures and provides a proof of principle to use this method in urinanalysis of UTI.
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Antti Roine
Full Text Available Urinary tract infection (UTI is a common disease with significant morbidity and economic burden, accounting for a significant part of the workload in clinical microbiology laboratories. Current clinical chemisty point-of-care diagnostics rely on imperfect dipstick analysis which only provides indirect and insensitive evidence of urinary bacterial pathogens. An electronic nose (eNose is a handheld device mimicking mammalian olfaction that potentially offers affordable and rapid analysis of samples without preparation at athmospheric pressure. In this study we demonstrate the applicability of ion mobility spectrometry (IMS -based eNose to discriminate the most common UTI pathogens from gaseous headspace of culture plates rapidly and without sample preparation. We gathered a total of 101 culture samples containing four most common UTI bacteries: E. coli, S. saprophyticus, E. faecalis, Klebsiella spp and sterile culture plates. The samples were analyzed using ChemPro 100i device, consisting of IMS cell and six semiconductor sensors. Data analysis was conducted by linear discriminant analysis (LDA and logistic regression (LR. The results were validated by leave-one-out and 5-fold cross validation analysis. In discrimination of sterile and bacterial samples sensitivity of 95% and specificity of 97% were achieved. The bacterial species were identified with sensitivity of 95% and specificity of 96% using eNose as compared to urine bacterial cultures.These findings strongly demonstrate the ability of our eNose to discriminate bacterial cultures and provides a proof of principle to use this method in urinanalysis of UTI.
Surprising conformers of the biologically important A·T DNA base pairs: QM/QTAIM proofs
Brovarets', Ol'ha O.; Tsiupa, Kostiantyn S.; Hovorun, Dmytro M.
2018-02-01
For the first time novel high-energy conformers – A·T(wWC) (5.36), A·T(wrWC) (5.97), A·T(wH) (5.78) and A·T(wrH) (ΔG=5.82 kcal•mol-1) were revealed for each of the four biologically important A·T(WC) DNA base pairs – Watson-Crick A·T(WC), reverse Watson-Crick A·T(rWC), Hoogsteen A·T(H) and reverse Hoogsteen A·T(rH) at the MP2/aug-cc-pVDZ//B3LYP/6-311++G(d,p) level of quantum-mechanical theory in the continuum with ɛ=4 under normal conditions. Each of these conformers possesses substantially non-planar wobble (w) structure and is stabilized by the participation of the two anti-parallel N6H/N6H'…O4/O2 and N3H…N6 H-bonds, involving the pyramidalized amino group of the A DNA base as an acceptor and a donor of the H-bonding. The transition states – TSA·T(WC)↔A·T(wWC), TSA·T(rWC)↔A·T(wrWC), TSA·T(H)↔A·T(wH) and TSA·T(rH)↔A·T(wrH), controlling the dipole-active transformations of the conformers from the main plane-symmetric state into the high-energy, significantly non-planar state and vice versa, were localized. They also possess wobble structures similarly to the high-energy conformers and are stabilized by the participation of the N6H/N6H'…O4/O2 and N3H…N6 H-bonds. Discovered conformers of the A·T DNA base pairs are dynamically stable short-lived structures (lifetime τ = (1.4-3.9) ps). Their possible biological significance and future perspectives have been briefly discussed.
Surprising Conformers of the Biologically Important A·T DNA Base Pairs: QM/QTAIM Proofs
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Ol'ha O. Brovarets'
2018-02-01
Full Text Available For the first time novel high-energy conformers–A·T(wWC (5.36, A·T(wrWC (5.97, A·T(wH (5.78, and A·T(wrH (ΔG = 5.82 kcal·mol−1 (See Graphical Abstract were revealed for each of the four biologically important A·T DNA base pairs – Watson-Crick A·T(WC, reverse Watson-Crick A·T(rWC, Hoogsteen A·T(H and reverse Hoogsteen A·T(rH at the MP2/aug-cc-pVDZ//B3LYP/6-311++G(d,p level of quantum-mechanical theory in the continuum with ε = 4 under normal conditions. Each of these conformers possesses substantially non-planar wobble (w structure and is stabilized by the participation of the two anti-parallel N6H/N6H′…O4/O2 and N3H…N6 H-bonds, involving the pyramidalized amino group of the A DNA base as an acceptor and a donor of the H-bonding. The transition states – TSA·T(WC↔A·T(wWC, TSA·T(rWC↔A·T(wrWC, TSA·T(H↔A·T(wH, and TSA·T(rH↔A·T(wrH, controlling the dipole-active transformations of the conformers from the main plane-symmetric state into the high-energy, significantly non-planar state and vice versa, were localized. They also possess wobble structures similarly to the high-energy conformers and are stabilized by the participation of the N6H/N6H′…O4/O2 and N3H…N6 H-bonds. Discovered conformers of the A·T DNA base pairs are dynamically stable short-lived structures [lifetime τ = (1.4–3.9 ps]. Their possible biological significance and future perspectives have been briefly discussed.
Teaching Primary School Mathematics and Statistics: Evidence-Based Practice
Averill, Robin; Harvey, Roger
2010-01-01
Here is the only reference book you will ever need for teaching primary school mathematics and statistics. It is full of exciting and engaging snapshots of excellent classroom practice relevant to "The New Zealand Curriculum" and national mathematics standards. There are many fascinating examples of investigative learning experiences,…
Reference dosimetry of proton pencil beams based on dose-area product: a proof of concept.
Gomà, Carles; Safai, Sairos; Vörös, Sándor
2017-06-21
This paper describes a novel approach to the reference dosimetry of proton pencil beams based on dose-area product ([Formula: see text]). It depicts the calibration of a large-diameter plane-parallel ionization chamber in terms of dose-area product in a 60 Co beam, the Monte Carlo calculation of beam quality correction factors-in terms of dose-area product-in proton beams, the Monte Carlo calculation of nuclear halo correction factors, and the experimental determination of [Formula: see text] of a single proton pencil beam. This new approach to reference dosimetry proves to be feasible, as it yields [Formula: see text] values in agreement with the standard and well-established approach of determining the absorbed dose to water at the centre of a broad homogeneous field generated by the superposition of regularly-spaced proton pencil beams.
Informal Content and Student Note-Taking in Advanced Mathematics Classes
Fukawa-Connelly, Timothy; Weber, Keith; Mejía-Ramos, Juan Pablo
2017-01-01
This study investigates 3 hypotheses about proof-based mathematics instruction: (a) that lectures include informal content (ways of thinking and reasoning about advanced mathematics that are not captured by formal symbolic statements), (b) that informal content is usually presented orally but not written on the board, and (c) that students do not…
Computer-Based Mathematics Instructions for Engineering Students
Khan, Mustaq A.; Wall, Curtiss E.
1996-01-01
Almost every engineering course involves mathematics in one form or another. The analytical process of developing mathematical models is very important for engineering students. However, the computational process involved in the solution of some mathematical problems may be very tedious and time consuming. There is a significant amount of mathematical software such as Mathematica, Mathcad, and Maple designed to aid in the solution of these instructional problems. The use of these packages in classroom teaching can greatly enhance understanding, and save time. Integration of computer technology in mathematics classes, without de-emphasizing the traditional analytical aspects of teaching, has proven very successful and is becoming almost essential. Sample computer laboratory modules are developed for presentation in the classroom setting. This is accomplished through the use of overhead projectors linked to graphing calculators and computers. Model problems are carefully selected from different areas.
Proof and Pedagogy in Ancient China: Examples from Liu Hui's Commentary on "JIU ZHANG SUAN SHU".
Siu, Man-Keung
1993-01-01
Illustrates the pedagogical implications embodied in Liu Hui's discussion on the ancient Chinese mathematical classic "JIU ZHANG SUAN SHU" (Nine Chapters on the Mathematical Art) with respect to aspects of proof and, more generally, the role of proof in mathematics. Provides examples involving area and volume. (Contains 25 references.)…
Grating-based phase contrast tomosynthesis imaging: Proof-of-concept experimental studies
International Nuclear Information System (INIS)
Li, Ke; Ge, Yongshuai; Garrett, John; Bevins, Nicholas; Zambelli, Joseph; Chen, Guang-Hong
2014-01-01
Purpose: This paper concerns the feasibility of x-ray differential phase contrast (DPC) tomosynthesis imaging using a grating-based DPC benchtop experimental system, which is equipped with a commercial digital flat-panel detector and a medical-grade rotating-anode x-ray tube. An extensive system characterization was performed to quantify its imaging performance. Methods: The major components of the benchtop system include a diagnostic x-ray tube with a 1.0 mm nominal focal spot size, a flat-panel detector with 96 μm pixel pitch, a sample stage that rotates within a limited angular span of ±30°, and a Talbot-Lau interferometer with three x-ray gratings. A total of 21 projection views acquired with 3° increments were used to reconstruct three sets of tomosynthetic image volumes, including the conventional absorption contrast tomosynthesis image volume (AC-tomo) reconstructed using the filtered-backprojection (FBP) algorithm with the ramp kernel, the phase contrast tomosynthesis image volume (PC-tomo) reconstructed using FBP with a Hilbert kernel, and the differential phase contrast tomosynthesis image volume (DPC-tomo) reconstructed using the shift-and-add algorithm. Three inhouse physical phantoms containing tissue-surrogate materials were used to characterize the signal linearity, the signal difference-to-noise ratio (SDNR), the three-dimensional noise power spectrum (3D NPS), and the through-plane artifact spread function (ASF). Results: While DPC-tomo highlights edges and interfaces in the image object, PC-tomo removes the differential nature of the DPC projection data and its pixel values are linearly related to the decrement of the real part of the x-ray refractive index. The SDNR values of polyoxymethylene in water and polystyrene in oil are 1.5 and 1.0, respectively, in AC-tomo, and the values were improved to 3.0 and 2.0, respectively, in PC-tomo. PC-tomo and AC-tomo demonstrate equivalent ASF, but their noise characteristics quantified by the 3D NPS
Grating-based phase contrast tomosynthesis imaging: Proof-of-concept experimental studies
Li, Ke; Ge, Yongshuai; Garrett, John; Bevins, Nicholas; Zambelli, Joseph; Chen, Guang-Hong
2014-01-01
Purpose: This paper concerns the feasibility of x-ray differential phase contrast (DPC) tomosynthesis imaging using a grating-based DPC benchtop experimental system, which is equipped with a commercial digital flat-panel detector and a medical-grade rotating-anode x-ray tube. An extensive system characterization was performed to quantify its imaging performance. Methods: The major components of the benchtop system include a diagnostic x-ray tube with a 1.0 mm nominal focal spot size, a flat-panel detector with 96 μm pixel pitch, a sample stage that rotates within a limited angular span of ±30°, and a Talbot-Lau interferometer with three x-ray gratings. A total of 21 projection views acquired with 3° increments were used to reconstruct three sets of tomosynthetic image volumes, including the conventional absorption contrast tomosynthesis image volume (AC-tomo) reconstructed using the filtered-backprojection (FBP) algorithm with the ramp kernel, the phase contrast tomosynthesis image volume (PC-tomo) reconstructed using FBP with a Hilbert kernel, and the differential phase contrast tomosynthesis image volume (DPC-tomo) reconstructed using the shift-and-add algorithm. Three inhouse physical phantoms containing tissue-surrogate materials were used to characterize the signal linearity, the signal difference-to-noise ratio (SDNR), the three-dimensional noise power spectrum (3D NPS), and the through-plane artifact spread function (ASF). Results: While DPC-tomo highlights edges and interfaces in the image object, PC-tomo removes the differential nature of the DPC projection data and its pixel values are linearly related to the decrement of the real part of the x-ray refractive index. The SDNR values of polyoxymethylene in water and polystyrene in oil are 1.5 and 1.0, respectively, in AC-tomo, and the values were improved to 3.0 and 2.0, respectively, in PC-tomo. PC-tomo and AC-tomo demonstrate equivalent ASF, but their noise characteristics quantified by the 3D NPS
Online 3D EPID-based dose verification: Proof of concept
Energy Technology Data Exchange (ETDEWEB)
Spreeuw, Hanno; Rozendaal, Roel, E-mail: r.rozendaal@nki.nl; Olaciregui-Ruiz, Igor; González, Patrick; Mans, Anton; Mijnheer, Ben [Department of Radiation Oncology, The Netherlands Cancer Institute, Amsterdam 1066 CX (Netherlands); Herk, Marcel van [University of Manchester, Manchester Academic Health Science Centre, The Christie NHS Foundation Trust, Manchester M20 4BX (United Kingdom)
2016-07-15
Purpose: Delivery errors during radiotherapy may lead to medical harm and reduced life expectancy for patients. Such serious incidents can be avoided by performing dose verification online, i.e., while the patient is being irradiated, creating the possibility of halting the linac in case of a large overdosage or underdosage. The offline EPID-based 3D in vivo dosimetry system clinically employed at our institute is in principle suited for online treatment verification, provided the system is able to complete 3D dose reconstruction and verification within 420 ms, the present acquisition time of a single EPID frame. It is the aim of this study to show that our EPID-based dosimetry system can be made fast enough to achieve online 3D in vivo dose verification. Methods: The current dose verification system was sped up in two ways. First, a new software package was developed to perform all computations that are not dependent on portal image acquisition separately, thus removing the need for doing these calculations in real time. Second, the 3D dose reconstruction algorithm was sped up via a new, multithreaded implementation. Dose verification was implemented by comparing planned with reconstructed 3D dose distributions delivered to two regions in a patient: the target volume and the nontarget volume receiving at least 10 cGy. In both volumes, the mean dose is compared, while in the nontarget volume, the near-maximum dose (D2) is compared as well. The real-time dosimetry system was tested by irradiating an anthropomorphic phantom with three VMAT plans: a 6 MV head-and-neck treatment plan, a 10 MV rectum treatment plan, and a 10 MV prostate treatment plan. In all plans, two types of serious delivery errors were introduced. The functionality of automatically halting the linac was also implemented and tested. Results: The precomputation time per treatment was ∼180 s/treatment arc, depending on gantry angle resolution. The complete processing of a single portal frame
Online 3D EPID-based dose verification: Proof of concept
International Nuclear Information System (INIS)
Spreeuw, Hanno; Rozendaal, Roel; Olaciregui-Ruiz, Igor; González, Patrick; Mans, Anton; Mijnheer, Ben; Herk, Marcel van
2016-01-01
Purpose: Delivery errors during radiotherapy may lead to medical harm and reduced life expectancy for patients. Such serious incidents can be avoided by performing dose verification online, i.e., while the patient is being irradiated, creating the possibility of halting the linac in case of a large overdosage or underdosage. The offline EPID-based 3D in vivo dosimetry system clinically employed at our institute is in principle suited for online treatment verification, provided the system is able to complete 3D dose reconstruction and verification within 420 ms, the present acquisition time of a single EPID frame. It is the aim of this study to show that our EPID-based dosimetry system can be made fast enough to achieve online 3D in vivo dose verification. Methods: The current dose verification system was sped up in two ways. First, a new software package was developed to perform all computations that are not dependent on portal image acquisition separately, thus removing the need for doing these calculations in real time. Second, the 3D dose reconstruction algorithm was sped up via a new, multithreaded implementation. Dose verification was implemented by comparing planned with reconstructed 3D dose distributions delivered to two regions in a patient: the target volume and the nontarget volume receiving at least 10 cGy. In both volumes, the mean dose is compared, while in the nontarget volume, the near-maximum dose (D2) is compared as well. The real-time dosimetry system was tested by irradiating an anthropomorphic phantom with three VMAT plans: a 6 MV head-and-neck treatment plan, a 10 MV rectum treatment plan, and a 10 MV prostate treatment plan. In all plans, two types of serious delivery errors were introduced. The functionality of automatically halting the linac was also implemented and tested. Results: The precomputation time per treatment was ∼180 s/treatment arc, depending on gantry angle resolution. The complete processing of a single portal frame
Online 3D EPID-based dose verification: Proof of concept.
Spreeuw, Hanno; Rozendaal, Roel; Olaciregui-Ruiz, Igor; González, Patrick; Mans, Anton; Mijnheer, Ben; van Herk, Marcel
2016-07-01
Delivery errors during radiotherapy may lead to medical harm and reduced life expectancy for patients. Such serious incidents can be avoided by performing dose verification online, i.e., while the patient is being irradiated, creating the possibility of halting the linac in case of a large overdosage or underdosage. The offline EPID-based 3D in vivo dosimetry system clinically employed at our institute is in principle suited for online treatment verification, provided the system is able to complete 3D dose reconstruction and verification within 420 ms, the present acquisition time of a single EPID frame. It is the aim of this study to show that our EPID-based dosimetry system can be made fast enough to achieve online 3D in vivo dose verification. The current dose verification system was sped up in two ways. First, a new software package was developed to perform all computations that are not dependent on portal image acquisition separately, thus removing the need for doing these calculations in real time. Second, the 3D dose reconstruction algorithm was sped up via a new, multithreaded implementation. Dose verification was implemented by comparing planned with reconstructed 3D dose distributions delivered to two regions in a patient: the target volume and the nontarget volume receiving at least 10 cGy. In both volumes, the mean dose is compared, while in the nontarget volume, the near-maximum dose (D2) is compared as well. The real-time dosimetry system was tested by irradiating an anthropomorphic phantom with three VMAT plans: a 6 MV head-and-neck treatment plan, a 10 MV rectum treatment plan, and a 10 MV prostate treatment plan. In all plans, two types of serious delivery errors were introduced. The functionality of automatically halting the linac was also implemented and tested. The precomputation time per treatment was ∼180 s/treatment arc, depending on gantry angle resolution. The complete processing of a single portal frame, including dose verification, took
Proof-of-principle measurements for an NDA-based core discharge monitor
International Nuclear Information System (INIS)
Halbig, J.K.; Monticone, A.C.
1990-01-01
The feasibility of using nondestructive assay instruments as a core discharge monitor for CANDU reactors was investigated at the Ontario Hydro Bruce Nuclear Generating Station A, Unit 3, in Ontario, Canada. The measurements were made to determine if radiation signatures from discharged irradiated fuel could be measured unambiguously and used to count the number of fuel pushes from a reactor face. Detectors using the (γ,n) reaction thresholds of beryllium and deuterium collected the data, but data from shielded and unshielded ion chambers were collected as well. The detectors were placed on a fueling trolley that carried the fueling machine between the reactors and the central service area. A microprocessor-based electronics system (the GRAND-I, which also resided on the trolley) provided detector biases and preamplifier power and acquired and transferred the data. It was connected by an RS-232 serial link to a lap-top computer adjacent to the fueling control console in the main-reactor control room. The lap-top computer collected and archived the data on a 3.5-in. floppy disk. The results clearly showed such an approach to be a adaptable as a core discharge monitor. 4 refs., 8 figs
Augmented Reality Based Navigation for Computer Assisted Hip Resurfacing: A Proof of Concept Study.
Liu, He; Auvinet, Edouard; Giles, Joshua; Rodriguez Y Baena, Ferdinando
2018-05-23
Implantation accuracy has a great impact on the outcomes of hip resurfacing such as recovery of hip function. Computer assisted orthopedic surgery has demonstrated clear advantages for the patients, with improved placement accuracy and fewer outliers, but the intrusiveness, cost, and added complexity have limited its widespread adoption. To provide seamless computer assistance with improved immersion and a more natural surgical workflow, we propose an augmented-reality (AR) based navigation system for hip resurfacing. The operative femur is registered by processing depth information from the surgical site with a commercial depth camera. By coupling depth data with robotic assistance, obstacles that may obstruct the femur can be tracked and avoided automatically to reduce the chance of disruption to the surgical workflow. Using the registration result and the pre-operative plan, intra-operative surgical guidance is provided through a commercial AR headset so that the user can perform the operation without additional physical guides. To assess the accuracy of the navigation system, experiments of guide hole drilling were performed on femur phantoms. The position and orientation of the drilled holes were compared with the pre-operative plan, and the mean errors were found to be approximately 2 mm and 2°, results which are in line with commercial computer assisted orthopedic systems today.
Li, Xiling; Luo, Jinghai; Guo, Gang; Mackey, Hamish R; Hao, Tianwei; Chen, Guanghao
2017-05-15
This study aimed to develop an aerobic granular sludge process for the efficient treatment of highly saline wastewater and understand the granulation process in a seawater-based multi-ion matrix. Five identical sequencing batch airlift reactors (SBARs) are used to treat synthetic saline sewage with different proportions of real seawater (0%-100%). The results confirm that aerobic granular sludge can be successfully developed with various proportions of seawater up to 100% and show that seawater not only significantly accelerates granulation but also generates stronger granular structures than does freshwater. The increased presence of gel-forming alginate-like exopolysaccharides in the granules explains why a greater proportion of seawater leads to higher density and improves the cohesive strength of the granules. SEM-EDX analysis further revealed substantial presence of both Ca 2+ and Mg 2+ phosphate in the granule core as well as in the outer layers providing extra bridging forces in addition to alginate-like exopolysaccharides for accelerating the granule formation and maintaining the structure. It is hoped that this work could explore another approach for saline sewage treatment and bring some clues for the mystery of granulation mechanism. Copyright © 2017 Elsevier Ltd. All rights reserved.
Higher-level fusion for military operations based on abductive inference: proof of principle
Pantaleev, Aleksandar V.; Josephson, John
2006-04-01
The ability of contemporary military commanders to estimate and understand complicated situations already suffers from information overload, and the situation can only grow worse. We describe a prototype application that uses abductive inferencing to fuse information from multiple sensors to evaluate the evidence for higher-level hypotheses that are close to the levels of abstraction needed for decision making (approximately JDL levels 2 and 3). Abductive inference (abduction, inference to the best explanation) is a pattern of reasoning that occurs naturally in diverse settings such as medical diagnosis, criminal investigations, scientific theory formation, and military intelligence analysis. Because abduction is part of common-sense reasoning, implementations of it can produce reasoning traces that are very human understandable. Automated abductive inferencing can be deployed to augment human reasoning, taking advantage of computation to process large amounts of information, and to bypass limits to human attention and short-term memory. We illustrate the workings of the prototype system by describing an example of its use for small-unit military operations in an urban setting. Knowledge was encoded as it might be captured prior to engagement from a standard military decision making process (MDMP) and analysis of commander's priority intelligence requirements (PIR). The system is able to reasonably estimate the evidence for higher-level hypotheses based on information from multiple sensors. Its inference processes can be examined closely to verify correctness. Decision makers can override conclusions at any level and changes will propagate appropriately.
A discrete transition to advanced mathematics
Richmond, Bettina
2009-01-01
As the title indicates, this book is intended for courses aimed at bridging the gap between lower-level mathematics and advanced mathematics. The text provides a careful introduction to techniques for writing proofs and a logical development of topics based on intuitive understanding of concepts. The authors utilize a clear writing style and a wealth of examples to develop an understanding of discrete mathematics and critical thinking skills. While including many traditional topics, the text offers innovative material throughout. Surprising results are used to motivate the reader. The last thr
Experimental proof of quantum non-separability based on the transition of the atom in beta-decay
International Nuclear Information System (INIS)
Vatai, E.
1988-01-01
The basic non-local character of the quantum processes is a continuously discussed and doubted problem of quantum theory. Recent experimental proofs of the Bell inequalities are questioned in the literature, using local theories of hidden variables. Present paper shows a simple and direct proof of non-locality of quantum processes, analyzing the case of the beta decay. The hypothetical energy transfer between shell electrons and beta electron-neutrino system is proved to be superluminal but necessary for the energy balance of the process. This argumentation proves the nonseparability and nonlocality of quantum processes. (D.G.) 8 refs
Epistemological bases OF THE RELATIONSHIP between culture and mathematics education
Directory of Open Access Journals (Sweden)
Neivaldo Oliveira Silva
2011-06-01
Full Text Available Our main intention with this theoretical construct is to understand the mathematics education embedded in the social context to which it belongs and where different groups are present with their beliefs, knowledge, practices that, in turn, are the result of a historical process, in which changes occur and affect most of the different fields ofIcnowledge.In the theoretical construction, we start from a more general picture of the world and society, focusing on the historical and social changes and, at the same time, in changes in the scope of mathematical knowledge. We do this through a historical analysis and, along the way, we seek to understand culture, Mathematics and Mathematics Education, as fields or dimensions present in this broader context of historical changes, and seek to establish relationships between thesefields or areas of knowledge, in the context of their productions. ln seeking to understand "culture", we try not to lose sight of the social dynamics that are established in the contacts between different groups, each with characteristics that involve traditions, artistic manifestations, culinary language, but surrounded by a society that results from a globalization process getting stronger. It is in this broader context that we seek to understand mathematics, as a field of knowledge, making an analysis that goes from its origin as well as its implications with reality and society, so that to the end, we present and discuss the Ethnomathematics as a possible alternative to do or to understand the articulation pointed out. Finally, we extend the discussion to understand the mathematics education, in view of its social integration, and the socialization perspective of the mathematical knowledge. We realized that mathematics education, seen as a field of knowledge and considering the need for socialization of this knowledge, is also the result of practices developed and a comprehensive process of change that has been occurring in
Energy Technology Data Exchange (ETDEWEB)
Yamamoto, Tokihiro, E-mail: toyamamoto@ucdavis.edu [Department of Radiation Oncology, University of California Davis School of Medicine, Sacramento, California 95817 (United States); Kent, Michael S.; Wisner, Erik R. [Department of Surgical and Radiological Sciences, University of California Davis School of Veterinary Medicine, Davis, California 95616 (United States); Johnson, Lynelle R.; Stern, Joshua A. [Department of Medicine and Epidemiology, University of California Davis School of Veterinary Medicine, Davis, California 95616 (United States); Qi, Lihong [Department of Public Health Sciences, University of California Davis, Davis, California 95616 (United States); Fujita, Yukio [Department of Radiation Oncology, Tokai University, Isehara, Kanagawa 259-1193 (Japan); Boone, John M. [Department of Radiology, University of California Davis School of Medicine, Sacramento, California 95817 (United States)
2016-07-15
Purpose: Radiotherapy (RT) that selectively avoids irradiating highly functional lung regions may reduce pulmonary toxicity, which is substantial in lung cancer RT. Single-energy computed tomography (CT) pulmonary perfusion imaging has several advantages (e.g., higher resolution) over other modalities and has great potential for widespread clinical implementation, particularly in RT. The purpose of this study was to establish proof-of-principle for single-energy CT perfusion imaging. Methods: Single-energy CT perfusion imaging is based on the following: (1) acquisition of end-inspiratory breath-hold CT scans before and after intravenous injection of iodinated contrast agents, (2) deformable image registration (DIR) for spatial mapping of those two CT image data sets, and (3) subtraction of the precontrast image data set from the postcontrast image data set, yielding a map of regional Hounsfield unit (HU) enhancement, a surrogate for regional perfusion. In a protocol approved by the institutional animal care and use committee, the authors acquired CT scans in the prone position for a total of 14 anesthetized canines (seven canines with normal lungs and seven canines with diseased lungs). The elastix algorithm was used for DIR. The accuracy of DIR was evaluated based on the target registration error (TRE) of 50 anatomic pulmonary landmarks per subject for 10 randomly selected subjects as well as on singularities (i.e., regions where the displacement vector field is not bijective). Prior to perfusion computation, HUs of the precontrast end-inspiratory image were corrected for variation in the lung inflation level between the precontrast and postcontrast end-inspiratory CT scans, using a model built from two additional precontrast CT scans at end-expiration and midinspiration. The authors also assessed spatial heterogeneity and gravitationally directed gradients of regional perfusion for normal lung subjects and diseased lung subjects using a two-sample two-tailed t
Yamamoto, Tokihiro; Kent, Michael S; Wisner, Erik R; Johnson, Lynelle R; Stern, Joshua A; Qi, Lihong; Fujita, Yukio; Boone, John M
2016-07-01
Radiotherapy (RT) that selectively avoids irradiating highly functional lung regions may reduce pulmonary toxicity, which is substantial in lung cancer RT. Single-energy computed tomography (CT) pulmonary perfusion imaging has several advantages (e.g., higher resolution) over other modalities and has great potential for widespread clinical implementation, particularly in RT. The purpose of this study was to establish proof-of-principle for single-energy CT perfusion imaging. Single-energy CT perfusion imaging is based on the following: (1) acquisition of end-inspiratory breath-hold CT scans before and after intravenous injection of iodinated contrast agents, (2) deformable image registration (DIR) for spatial mapping of those two CT image data sets, and (3) subtraction of the precontrast image data set from the postcontrast image data set, yielding a map of regional Hounsfield unit (HU) enhancement, a surrogate for regional perfusion. In a protocol approved by the institutional animal care and use committee, the authors acquired CT scans in the prone position for a total of 14 anesthetized canines (seven canines with normal lungs and seven canines with diseased lungs). The elastix algorithm was used for DIR. The accuracy of DIR was evaluated based on the target registration error (TRE) of 50 anatomic pulmonary landmarks per subject for 10 randomly selected subjects as well as on singularities (i.e., regions where the displacement vector field is not bijective). Prior to perfusion computation, HUs of the precontrast end-inspiratory image were corrected for variation in the lung inflation level between the precontrast and postcontrast end-inspiratory CT scans, using a model built from two additional precontrast CT scans at end-expiration and midinspiration. The authors also assessed spatial heterogeneity and gravitationally directed gradients of regional perfusion for normal lung subjects and diseased lung subjects using a two-sample two-tailed t-test. The mean TRE
International Nuclear Information System (INIS)
Yamamoto, Tokihiro; Kent, Michael S.; Wisner, Erik R.; Johnson, Lynelle R.; Stern, Joshua A.; Qi, Lihong; Fujita, Yukio; Boone, John M.
2016-01-01
Purpose: Radiotherapy (RT) that selectively avoids irradiating highly functional lung regions may reduce pulmonary toxicity, which is substantial in lung cancer RT. Single-energy computed tomography (CT) pulmonary perfusion imaging has several advantages (e.g., higher resolution) over other modalities and has great potential for widespread clinical implementation, particularly in RT. The purpose of this study was to establish proof-of-principle for single-energy CT perfusion imaging. Methods: Single-energy CT perfusion imaging is based on the following: (1) acquisition of end-inspiratory breath-hold CT scans before and after intravenous injection of iodinated contrast agents, (2) deformable image registration (DIR) for spatial mapping of those two CT image data sets, and (3) subtraction of the precontrast image data set from the postcontrast image data set, yielding a map of regional Hounsfield unit (HU) enhancement, a surrogate for regional perfusion. In a protocol approved by the institutional animal care and use committee, the authors acquired CT scans in the prone position for a total of 14 anesthetized canines (seven canines with normal lungs and seven canines with diseased lungs). The elastix algorithm was used for DIR. The accuracy of DIR was evaluated based on the target registration error (TRE) of 50 anatomic pulmonary landmarks per subject for 10 randomly selected subjects as well as on singularities (i.e., regions where the displacement vector field is not bijective). Prior to perfusion computation, HUs of the precontrast end-inspiratory image were corrected for variation in the lung inflation level between the precontrast and postcontrast end-inspiratory CT scans, using a model built from two additional precontrast CT scans at end-expiration and midinspiration. The authors also assessed spatial heterogeneity and gravitationally directed gradients of regional perfusion for normal lung subjects and diseased lung subjects using a two-sample two-tailed t
Context-based mathematics tasks in Indonesia : Toward better practice and achievement
Wijaya, A.
2015-01-01
The Indonesian national curriculum mandates that mathematics education must be relevant to the needs of life and should offer students opportunities to develop the ability to apply their knowledge in society. Furthermore, there are educational movements in Indonesia that promote the application of mathematics and place a premium on using context-based tasks; see the projects Pendidikan MatematikaRealistik Indonesia (Indonesian Realistic Mathematics Education) and Pembelajaran Kontekstual (Con...
Complexity of Propositional Proofs Under a Promise
Czech Academy of Sciences Publication Activity Database
Dershowitz, N.; Tzameret, Iddo
2010-01-01
Roč. 11, č. 3 (2010), s. 1-29 ISSN 1529-3785 Institutional research plan: CEZ:AV0Z10190503 Keywords : theory * promise problems * propositional proof complexity * random 3CNF * resolution Subject RIV: BA - General Mathematics Impact factor: 1.391, year: 2010 http://dl.acm.org/ citation .cfm?doid=1740582.1740586
Complexity of Propositional Proofs Under a Promise
Czech Academy of Sciences Publication Activity Database
Dershowitz, N.; Tzameret, Iddo
2010-01-01
Roč. 11, č. 3 (2010), s. 1-29 ISSN 1529-3785 Institutional research plan: CEZ:AV0Z10190503 Keywords : theory * promise problems * propositional proof complexity * random 3CNF * resolution Subject RIV: BA - General Mathematics Impact factor: 1.391, year: 2010 http://dl.acm.org/citation.cfm?doid=1740582.1740586
Short proofs for the determinant identities
Czech Academy of Sciences Publication Activity Database
Hrubeš, Pavel; Tzameret, I.
2015-01-01
Roč. 44, č. 2 (2015), s. 340-383 ISSN 0097-5397 EU Projects: European Commission(XE) 339691 - FEALORA Program:FP7 Institutional support: RVO:67985840 Keywords : proof complexity * arithmetic circuits Subject RIV: BA - General Mathematics Impact factor: 0.841, year: 2015 http://epubs.siam.org/doi/abs/10.1137/130917788
Gary Chastagner; Marianne Elliott
2017-01-01
The primary purpose of this program was to demonstrate proof of concept of certain mitigation approaches at a repeat P. ramorum-positive nursery site in Washington. Approaches included steam treatment of infested soil areas; creating a gravel âsandwichâ above steam-treated and potentially infested soil surfaces; improving drainage systems; required...
A New Small Emendation of Gödel's Ontological Proof
Czech Academy of Sciences Publication Activity Database
Hájek, Petr
2002-01-01
Roč. 71, č. 2 (2002), s. 149-164 ISSN 0039-3215 R&D Projects: GA MŠk LN00A056 Keywords : ontological proof * Gödel proof * modal logic * comprehension * positive properties Subject RIV: BA - General Mathematics
Kowiyah; Mulyawati, I.
2018-01-01
Mathematic representation is one of the basic mathematic skills that allows students to communicate their mathematic ideas through visual realities such as pictures, tables, mathematic expressions and mathematic equities. The present research aims at: 1) analysing students’ mathematic representation ability in solving mathematic problems and 2) examining the difference of students’ mathematic ability based on their gender. A total of sixty primary school students participated in this study comprising of thirty males and thirty females. Data required in this study were collected through mathematic representation tests, interviews and test evaluation rubric. Findings of this study showed that students’ mathematic representation of visual realities (image and tables) was reported higher at 62.3% than at in the form of description (or statement) at 8.6%. From gender perspective, male students performed better than the females at action planning stage. The percentage of males was reported at 68% (the highest), 33% (medium) and 21.3% (the lowest) while the females were at 36% (the highest), 37.7% (medium) and 32.6% (the lowest).
Directory of Open Access Journals (Sweden)
Edwin Musdi
2016-02-01
Full Text Available This research aims to develop a mathematics instructional model based realistic mathematics education (RME to promote students' problem-solving abilities. The design research used Plomp models, which consists of preliminary phase, development or proto-typing phase and assessment phase. At this study, only the first two phases conducted. The first phase, a preliminary investigation, carried out with a literature study to examine the theory-based instructional learning RME model, characteristics of learners, learning management descriptions by junior high school mathematics teacher and relevant research. The development phase is done by developing a draft model (an early prototype model that consists of the syntax, the social system, the principle of reaction, support systems, and the impact and effects of instructional support. Early prototype model contain a draft model, lesson plans, worksheets, and assessments. Tesssmer formative evaluation model used to revise the model. In this study only phase of one to one evaluation conducted. In the ppreliminary phase has produced a theory-based learning RME model, a description of the characteristics of learners in grade VIII Junior High School Padang and the description of teacher teaching in the classroom. The result showed that most students were still not be able to solve the non-routine problem. Teachers did not optimally facilitate students to develop problem-solving skills of students. It was recommended that the model can be applied in the classroom.
Marshall, Neil; Buteau, Chantal
2014-01-01
As part of their undergraduate mathematics curriculum, students at Brock University learn to create and use computer-based tools with dynamic, visual interfaces, called Exploratory Objects, developed for the purpose of conducting pure or applied mathematical investigations. A student's Development Process Model of creating and using an Exploratory…
Piloting a Web-Based Homework System in Developmental Mathematics Classrooms
Dass, Wendi E.
2012-01-01
This Capstone project studied a pilot of the web-based homework system "Hawkes" in developmental mathematics classes at a mid-sized community college. The purpose of the study was to investigate how three instructors of developmental mathematics courses incorporated "Hawkes" in their classes, what obstacles they encountered,…
An Excel-Aided Method for Teaching Calculus-Based Business Mathematics
Liang, Jiajuan; Martin, Linda
2008-01-01
Calculus-based business mathematics is a required quantitative course for undergraduate business students in most AACSB accredited schools or colleges of business. Many business students, however, have relatively weak mathematical background or even display math-phobia when presented with calculus problems. Because of the popularity of Excel, its…
Effect of Digital Game Based Learning on Ninth Grade Students' Mathematics Achievement
Swearingen, Dixie K.
2011-01-01
This experimental study examined the effect of an educational massive multiplayer online game (MMOG) on achievement on a standards-based mathematics exam. It also examined the interaction of student characteristics (gender and socioeconomic status) with digital game play on mathematics achievement. Two hundred eighty ninth grade students from a…
Huda, Nizlel; Subanji; Nusantar, Toto; Susiswo; Sutawidjaja, Akbar; Rahardjo, Swasono
2016-01-01
This study aimed to determine students' metacognitive failure in Mathematics Education Program of FKIP in Jambi University investigated based on assimilation and accommodation Mathematical framework. There were 35 students, five students did not answer the question, three students completed the questions correctly and 27 students tried to solve…
Examining Teaching Based on Errors in Mathematics Amongst Pupils with Learning Disabilities
Magen-Nagar, Noga
2016-01-01
Teaching mathematics while learning from students' mistakes, errors and misconceptions, is most important for meaningful learning. This study was based on intervention programs prepared by preservice teachers. It aimed to examine their knowledge of assessment of errors in mathematics amongst pupils with learning disabilities, and their use as a…
Directory of Open Access Journals (Sweden)
Melike TURAL SÖNMEZ
2017-12-01
Full Text Available The purpose of this study is to examine the construction of mathematical modelling problems process in the content of financial literacy. It is also aimed to create design proposals for construction of mathematical modelling problems. A design based research method was used in this study. The participants were three seventh grade students, six finance experts and nine mathematics education experts. Data collection tools were transcription of video and tapes group discussions, presentations and worksheets during mathematical modelling activities, and participant experts’ feedback form about mathematical modelling problems. There were three stages in this study. First stage was application of preliminary study. This stage gave information about convenience of problems to grade level, students’ timing for solution of problems, clarity of problems and students’ background about content. In second stage, finance experts commented on convenience of mathematical modelling problems to financial literacy standards. In third stage, mathematics education experts commented on convenience of problems to students’ grade level, mathematical modelling principles and seventh grade mathematics lesson objectives. They also gave suggestion on progress. The frequency value of theme in feedback forms was calculated and experts’ expressions were given as citation. It was given suggestion about stages and application of the design guide
Gender-Based Differential Item Performance in Mathematics Achievement Items.
Doolittle, Allen E.; Cleary, T. Anne
1987-01-01
Eight randomly equivalent samples of high school seniors were each given a unique form of the ACT Assessment Mathematics Usage Test (ACTM). Signed measures of differential item performance (DIP) were obtained for each item in the eight ACTM forms. DIP estimates were analyzed and a significant item category effect was found. (Author/LMO)
Mathematical foundation of the optimization-based fluid animation method
DEFF Research Database (Denmark)
Erleben, Kenny; Misztal, Marek Krzysztof; Bærentzen, Jakob Andreas
2011-01-01
We present the mathematical foundation of a fluid animation method for unstructured meshes. Key contributions not previously treated are the extension to include diffusion forces and higher order terms of non-linear force approximations. In our discretization we apply a fractional step method to ...
Calculus-Based Mathematics: An Australian Endangered Species?
Maltas, Dimitrios; Prescott, Anne
2014-01-01
Many people are discussing the issues surrounding mathematics at all levels of education. Politicians, parents, students, universities, education departments all have a view about what the problem is and all have ideas about what should happen. This article represents a synthesis of the issues and implications of one of the problems evident in…
Great Problems of Mathematics: A Course Based on Original Sources.
Laubenbacher, Reinhard C.; Pengelley, David J.
1992-01-01
Describes the history of five selected problems from mathematics that are included in an undergraduate honors course designed to utilize original sources for demonstrating the evolution of ideas developed in solving these problems: area and the definite integral, the beginnings of set theory, solutions of algebraic equations, Fermat's last…
Problem Solving Abilities and Perceptions in Alternative Certification Mathematics Teachers
Evans, Brian R.
2012-01-01
It is important for teacher educators to understand new alternative certification middle and high school teachers' mathematical problem solving abilities and perceptions. Teachers in an alternative certification program in New York were enrolled in a proof-based algebra course. At the beginning and end of a semester participants were given a…
Proof Rules for Recursive Procedures
Hesselink, Wim H.
1993-01-01
Four proof rules for recursive procedures in a Pascal-like language are presented. The main rule deals with total correctness and is based on results of Gries and Martin. The rule is easier to apply than Martin's. It is introduced as an extension of a specification format for Pascal-procedures, with
On Callan's proof of the BPHZ theorem
International Nuclear Information System (INIS)
Lesniewski, A.
1984-01-01
The author gives an elementary proof of the BPHZ theorem in the case of the Euclidean lambdaphi 4 theory. The method of proof relies on a detailed analysis of the skeleton structure of graphs and estimates based on the Callan-Symanzik equations. (Auth.)
Proof Mining in L1-Approximation
DEFF Research Database (Denmark)
Oliva, Paulo Borges; Kohlenbach, Ulrich
2001-01-01
In this paper, we present another case study in the general project of proof mining which means the logical analysis of prima facie non-effective proofs with the aim of extracting new computationally relevant data. We use techniques based on monotone functional interpretation developed...
Proof Mining in L1-Approximation
DEFF Research Database (Denmark)
Kohlenbach, Ulrich; Oliva, Paulo Borges
2003-01-01
n this paper, we present another case study in the general project of proof mining which means the logical analysis of prima facie non-effective proofs with the aim of extracting new computationally relevant data. We use techniques based on monotone functional interpretation developed in Kohlenbach...
Student’s rigorous mathematical thinking based on cognitive style
Fitriyani, H.; Khasanah, U.
2017-12-01
The purpose of this research was to determine the rigorous mathematical thinking (RMT) of mathematics education students in solving math problems in terms of reflective and impulsive cognitive styles. The research used descriptive qualitative approach. Subjects in this research were 4 students of the reflective and impulsive cognitive style which was each consisting male and female subjects. Data collection techniques used problem-solving test and interview. Analysis of research data used Miles and Huberman model that was reduction of data, presentation of data, and conclusion. The results showed that impulsive male subjects used three levels of the cognitive function required for RMT that were qualitative thinking, quantitative thinking with precision, and relational thinking completely while the other three subjects were only able to use cognitive function at qualitative thinking level of RMT. Therefore the subject of impulsive male has a better RMT ability than the other three research subjects.
The materiality of mathematics: presenting mathematics at the blackboard.
Greiffenhagen, Christian
2014-09-01
Sociology has been accused of neglecting the importance of material things in human life and the material aspects of social practices. Efforts to correct this have recently been made, with a growing concern to demonstrate the materiality of social organization, not least through attention to objects and the body. As a result, there have been a plethora of studies reporting the social construction and effects of a variety of material objects as well as studies that have explored the material dimensions of a diversity of practices. In different ways these studies have questioned the Cartesian dualism of a strict separation of 'mind' and 'body'. However, it could be argued that the idea of the mind as immaterial has not been entirely banished and lingers when it comes to discussing abstract thinking and reasoning. The aim of this article is to extend the material turn to abstract thought, using mathematics as a paradigmatic example. This paper explores how writing mathematics (on paper, blackboards, or even in the air) is indispensable for doing and thinking mathematics. The paper is based on video recordings of lectures in formal logic and investigates how mathematics is presented at the blackboard. The paper discusses the iconic character of blackboards in mathematics and describes in detail a number of inscription practices of presenting mathematics at the blackboard (such as the use of lines and boxes, the designation of particular regions for specific mathematical purposes, as well as creating an 'architecture' visualizing the overall structure of the proof). The paper argues that doing mathematics really is 'thinking with eyes and hands' (Latour 1986). Thinking in mathematics is inextricably interwoven with writing mathematics. © London School of Economics and Political Science 2014.
MATHEMATICAL BASES DECISION OF OLYMPIAD TASKS FROM INFORMATICS ON SITE E-OLIMP
Directory of Open Access Journals (Sweden)
T.A. Vakalyuk
2010-08-01
Full Text Available In the article a new section is examined on a portal from the sporting programming of e-olimp, namely mathematical bases during uniting of olympiads them tasks from an informatics.
Directory of Open Access Journals (Sweden)
Anderson L. Palinussa
2013-01-01
Full Text Available This paper presents the findings of a quasi-experimental with pre-test-post-test design and control group that aims to assess students’ critical mathematical thinking skills and character through realistic mathematics education (RME culture-based. Subjects of this study were 106 junior high school students from two low and medium schools level in Ambon. The instruments of the study are: students’ early math skills test, critical thinking skills mathematical test and perception scale of students’character. Data was analyzed by using t-test and Anova. The study found that: 1 Achievements and enhancement of students’ critical mathematical thinking skills who were treated with by realistic mathematics education is better then students’ skills were treated by conventional mathematics education. The differences are considered to: a overall students, b the level of early math skills, and c schools’ level; 2 Quality of students’ character who were treated by realistic mathematics education is better then students’ character who were treated by conventional mathematics education The differences are considered to: a overall students, b the level of early math skills, and c schools’ level Keywords: Critical Thinking, Students’ Character, Realistic Mathematics Education Culture-Based DOI: http://dx.doi.org/10.22342/jme.4.1.566.75-94
The tools of mathematical reasoning
Lakins, Tamara J
2016-01-01
This accessible textbook gives beginning undergraduate mathematics students a first exposure to introductory logic, proofs, sets, functions, number theory, relations, finite and infinite sets, and the foundations of analysis. The book provides students with a quick path to writing proofs and a practical collection of tools that they can use in later mathematics courses such as abstract algebra and analysis. The importance of the logical structure of a mathematical statement as a framework for finding a proof of that statement, and the proper use of variables, is an early and consistent theme used throughout the book.
Mathematical Practices and Arts Integration in an Activity-Based Projective Geometry Course
Ernest, Jessica Brooke
It is a general assumption that the mathematical activity of students in school should, at least to some degree, parallel the practices of professional mathematicians (Brown, Collins, Duguid, 1989; Moschkovich, 2013). This assumption is reflected in the Common Core State Standards (CCSSI, 2010) and National Council of Teachers of Mathematics (NCTM, 2000) standards documents. However, the practices included in these standards documents, while developed to reflect the practices of professional mathematicians, may be idealized versions of what mathematicians actually do (Moschkovich, 2013). This might lead us to question then: "What is it that mathematicians do, and what practices are not being represented in the standards documents?" In general, the creative work of mathematicians is absent from the standards and, in turn, from school mathematics curricula, much to the dismay of some mathematicians and researchers (Lockhart, 2009; Rogers, 1999). As a result, creativity is not typically being fostered in mathematics students. As a response to this lack of focus on fostering creativity (in each of the science, technology, engineering, and mathematics disciplines--the STEM disciplines), a movement to integrate the arts emerged. This movement, called the STEAM movement--introducing the letter A into the acronym STEM to signify incorporating the arts--has been gaining momentum, yet limited research has been carried out on the efficacy of integrating the arts into mathematics courses. My experiences as the co-instructor for an activity-based course focused on projective geometry led me to consider the course as a setting for investigating both mathematical practices and arts integration. In this work, I explored the mathematical practices in which students engaged while working to develop an understanding of projective geometry through group activities. Furthermore, I explored the way in which students' learning experiences were enriched through artistic engagement in the
Mathematical logic foundations for information science
Li, Wei
2010-01-01
This book presents the basic principles and formal calculus of mathematical logic. It covers core contents, extensions and developments of classical mathematical logic, and it offers formal proofs and concrete examples for all theoretical results.
Klein, Cornel; Rumpe, Bernhard; Broy, Manfred
2014-01-01
In the SysLab project we develop a software engineering method based on a mathematical foundation. The SysLab system model serves as an abstract mathematical model for information systems and their components. It is used to formalize the semantics of all used description techniques such as object diagrams state automata sequence charts or data-flow diagrams. Based on the requirements for such a reference model, we define the system model including its different views and their relationships.
Using Mathematical Modeling and Set-Based Design Principles to Recommend an Existing CVL Design
2017-09-01
MATHEMATICAL MODELING AND SET-BASED DESIGN PRINCIPLES TO RECOMMEND AN EXISTING CVL DESIGN by William H. Ehlies September 2017 Thesis Advisor...Office of Management and Budget, Paperwork Reduction Project (0704-0188) Washington, DC 20503. 1. AGENCY USE ONLY (Leave blank) 2. REPORT DATE...September 2017 3. REPORT TYPE AND DATES COVERED Master’s thesis 4. TITLE AND SUBTITLE USING MATHEMATICAL MODELING AND SET-BASED DESIGN PRINCIPLES
STEM Gives Meaning to Mathematics
Hefty, Lukas J.
2015-01-01
The National Council of Teachers of Mathematics' (NCTM's) "Principles and Standards for School Mathematics" (2000) outlines fi ve Process Standards that are essential for developing deep understanding of mathematics: (1) Problem Solving; (2) Reasoning and Proof; (3) Communication; (4) Connections; and (5) Representation. The Common Core…
Nasution, M. L.; Yerizon, Y.; Gusmiyanti, R.
2018-04-01
One of the purpose mathematic learning is to develop problem solving abilities. Problem solving is obtained through experience in questioning non-routine. Improving students’ mathematical problem-solving abilities required an appropriate strategy in learning activities one of them is models problem based learning (PBL). Thus, the purpose of this research is to determine whether the problem solving abilities of mathematical students’ who learn to use PBL better than on the ability of students’ mathematical problem solving by applying conventional learning. This research included quasi experiment with static group design and population is students class XI MIA SMAN 1 Lubuk Alung. Class experiment in the class XI MIA 5 and class control in the class XI MIA 6. The instrument of final test students’ mathematical problem solving used essay form. The result of data final test in analyzed with t-test. The result is students’ mathematical problem solving abilities with PBL better then on the ability of students’ mathematical problem solving by applying conventional learning. It’s seen from the high percentage achieved by the group of students who learn to use PBL for each indicator of students’ mathematical problem solving.
International Nuclear Information System (INIS)
González Caballero, I; Cuesta Noriega, A; Rodríguez Marrero, A; Fernández del Castillo, E
2012-01-01
The analysis of the complex LHC data usually follows a standard path that aims at minimizing not only the amount of data but also the number of observables used. After a number of steps of slimming and skimming the data, the remaining few terabytes of ROOT files hold a selection of the events and a flat structure for the variables needed that can be more easily inspected and traversed in the final stages of the analysis. PROOF arises at this point as an efficient mechanism to distribute the analysis load by taking advantage of all the cores in modern CPUs through PROOF Lite, or by using PROOF Cluster or PROOF on Demand tools to build dynamic PROOF cluster on computing facilities with spare CPUs. However using PROOF at the level required for a serious analysis introduces some difficulties that may scare new adopters. We have developed the PROOF Analysis Framework (PAF) to facilitate the development of new analysis by uniformly exposing the PROOF related configurations across technologies and by taking care of the routine tasks as much as possible. We describe the details of the PAF implementation as well as how we succeeded in engaging a group of CMS physicists to use PAF as their daily analysis framework.
Didactic trajectory of research in mathematics education using research-based learning
Charitas Indra Prahmana, Rully; Kusumah, Yaya S.; Darhim
2017-10-01
This study aims to describe the role of research-based learning in design a learning trajectory of research in mathematics education to enhance research and academic writing skills for pre-service mathematics teachers. The method used is a design research with three stages, namely the preliminary design, teaching experiment, and retrospective analysis. The research subjects are pre-service mathematics teacher class of 2012 from one higher education institution in Tangerang - Indonesia. The use of research-based learning in designing learning trajectory of research in mathematics education plays a crucial role as a trigger to enhancing math department preservice teachers research and academic writing skills. Also, this study also describes the design principles and characteristics of the learning trajectory namely didactic trajectory generated by the role of research-based learning syntax.
Lakatos' Proofs and Refutations Comes Alive in an Elementary Classroom.
Atkins, Sandra L.
1997-01-01
Presents an alternative pedagogy implicit in Imre Lakatos's "Proofs and Refutations: The Logic of Mathematical Discovery." Lakatos reveals that learning mathematics is a discourse-laden activity in which it is acceptable, if not preferable, to refute conjecture. Provides examples of using a Lakatosian approach in an elementary classroom.…
Secondary Teachers' Knowledge of Elementary Number Theory Proofs: The Case of General-Cover Proofs
Tabach, Michal; Levenson, Esther; Barkai, Ruthi; Tsamir, Pessia; Tirosh, Dina; Dreyfus, Tommy
2011-01-01
In light of recent reform recommendations, teachers are expected to turn proofs and proving into an ongoing component of their classroom practice. Two questions emerging from this requirement are: Is the mathematical knowledge of high school teachers sufficient to prove various kinds of statements? Does teachers' knowledge allow them to determine…
Combinatorial Proofs and Algebraic Proofs – I
Indian Academy of Sciences (India)
IAS Admin
Shailesh A Shirali is. Director of Sahyadri School. (KFI), Pune, and also Head of the Community Mathematics. Centre in Rishi Valley School. (AP). He has been in the field of mathematics education for three decades, and has been closely involved with the Math. Olympiad movement in India. He is the author of many.
DEFF Research Database (Denmark)
Høyrup, Jens
Plato, so the story goes, held mathematics in high esteem, and those philosopher-kings that ought to rule his republic should have a thorough foundation in mathematics. This may well be true - but an observation made by Aristotle suggests that the mathematics which Plato intends is not the one...... based on theorems and proofs which we normally identify with "Greek mathematics". Most other ancient writers who speak of mathematics as a road towardWisdom also appear to be blissfully ignorant of the mathematics of Euclid, Archimedes, Apollonios, etc. The aim of the paper is to identify the kinds...... of mathematics which were available as external sources for this current (on the whole leaving out of consideration Liberal-Arts mathematics as not properly external). A number of borrowings can be traced to various practitioners' traditions - but always as bits borrowed out of context....
Analysis of mathematical problem-solving ability based on metacognition on problem-based learning
Mulyono; Hadiyanti, R.
2018-03-01
Problem-solving is the primary purpose of the mathematics curriculum. Problem-solving abilities influenced beliefs and metacognition. Metacognition as superordinate capabilities can direct, regulate cognition and motivation and then problem-solving processes. This study aims to (1) test and analyzes the quality of problem-based learning and (2) investigate the problem-solving capabilities based on metacognition. This research uses mixed method study with The subject research are class XI students of Mathematics and Science at High School Kesatrian 2 Semarang which divided into tacit use, aware use, strategic use and reflective use level. The collecting data using scale, interviews, and tests. The data processed with the proportion of test, t-test, and paired samples t-test. The result shows that the students with levels tacit use were able to complete the whole matter given, but do not understand what and why a strategy is used. Students with aware use level were able to solve the problem, be able to build new knowledge through problem-solving to the indicators, understand the problem, determine the strategies used, although not right. Students on the Strategic ladder Use can be applied and adopt a wide variety of appropriate strategies to solve the issues and achieved re-examine indicators of process and outcome. The student with reflective use level is not found in this study. Based on the results suggested that study about the identification of metacognition in problem-solving so that the characteristics of each level of metacognition more clearly in a more significant sampling. Teachers need to know in depth about the student metacognitive activity and its relationship with mathematical problem solving and another problem resolution.
Directory of Open Access Journals (Sweden)
Helmiah Suryani
2017-06-01
Full Text Available This study was aimed to develop and produce an assessment instrument of mathematical learning results based on multiple intelligence. The methods in this study used Borg & Gall-Research and Development approach (Research & Development. The subject of research was 289 students. The results of research: (1 Result of Aiken Analysis showed 58 valid items were between 0,714 to 0,952. (2 Result of the Exploratory on factor analysis indicated the instrument consist of three factors i.e. mathematical logical intelligence-spatial intelligence-and linguistic intelligence. KMO value was 0.661 df 0.780 sig. 0.000 with valid category. This research succeeded to developing the assessment instrument of mathematical learning results based on multiple intelligence of second grade in elementary school with characteristics of logical intelligence of mathematics, spatial intelligence, and linguistic intelligence.
Analytical derivation: An epistemic game for solving mathematically based physics problems
Bajracharya, Rabindra R.; Thompson, John R.
2016-06-01
Problem solving, which often involves multiple steps, is an integral part of physics learning and teaching. Using the perspective of the epistemic game, we documented a specific game that is commonly pursued by students while solving mathematically based physics problems: the analytical derivation game. This game involves deriving an equation through symbolic manipulations and routine mathematical operations, usually without any physical interpretation of the processes. This game often creates cognitive obstacles in students, preventing them from using alternative resources or better approaches during problem solving. We conducted hour-long, semi-structured, individual interviews with fourteen introductory physics students. Students were asked to solve four "pseudophysics" problems containing algebraic and graphical representations. The problems required the application of the fundamental theorem of calculus (FTC), which is one of the most frequently used mathematical concepts in physics problem solving. We show that the analytical derivation game is necessary, but not sufficient, to solve mathematically based physics problems, specifically those involving graphical representations.
Mathematical modeling based on ordinary differential equations: A promising approach to vaccinology.
Bonin, Carla Rezende Barbosa; Fernandes, Guilherme Cortes; Dos Santos, Rodrigo Weber; Lobosco, Marcelo
2017-02-01
New contributions that aim to accelerate the development or to improve the efficacy and safety of vaccines arise from many different areas of research and technology. One of these areas is computational science, which traditionally participates in the initial steps, such as the pre-screening of active substances that have the potential to become a vaccine antigen. In this work, we present another promising way to use computational science in vaccinology: mathematical and computational models of important cell and protein dynamics of the immune system. A system of Ordinary Differential Equations represents different immune system populations, such as B cells and T cells, antigen presenting cells and antibodies. In this way, it is possible to simulate, in silico, the immune response to vaccines under development or under study. Distinct scenarios can be simulated by varying parameters of the mathematical model. As a proof of concept, we developed a model of the immune response to vaccination against the yellow fever. Our simulations have shown consistent results when compared with experimental data available in the literature. The model is generic enough to represent the action of other diseases or vaccines in the human immune system, such as dengue and Zika virus.
Directory of Open Access Journals (Sweden)
Johann Engelbrecht
2009-09-01
Full Text Available Following the political changes of 1994 in South Africa, the decision was taken to replace the traditional skills-based education system at primary and secondary school level (Grades 1 - 12 with an outcomes-based education system (OBE. The OBE approach, referred to as Curriculum 2005, was introduced into schools in 1998. The implementation of the OBE system did not occur without problems, giving rise to revised initiatives and a fair amount of criticism. The 2009 intake of students at universities is the ﬁrst group of students that had been subjected to the OBE approach for their entire school career. This is also the ﬁrst group of students for whom some form of mathematics was compulsory up to Grade 12 level in the form of mathematics or mathematical literacy. These students were characterised by the fact that their mathematics marks for Grade 12 were exceptionally high and that many more students qualiﬁed for university entrance. This article reports on the impact of this new education system on the mathematics prepared-ness of students entering university. The study involves an empirical analysis of the students in the ﬁrst-year mathematics course for engineering students at the University of Pretoria as well as an analysis of a questionnaire completed by experienced lecturers at this university. The question addressed in this article is how the 2009 intake of students cope with mathematics at university level with regard to Performance General attributes Mathematical attributes Content-related attributesResults indicate a decrease in mathematics performance of these students at university level and that the inﬂated matric marks result in unjustiﬁed expectations. However, it is not unusual for marks to decrease from school to university and there is still too little evidence for serious concern. The study also indicates that these students seem to be better equipped with regard to personal attributes such as self-conﬁdence and
Evaluating the Use of Problem-Based Video Podcasts to Teach Mathematics in Higher Education
Kay, Robin; Kletskin, Ilona
2012-01-01
Problem-based video podcasts provide short, web-based, audio-visual explanations of how to solve specific procedural problems in subject areas such as mathematics or science. A series of 59 problem-based video podcasts covering five key areas (operations with functions, solving equations, linear functions, exponential and logarithmic functions,…
Ortiz, Andrés
2017-01-01
The National Strategy for Global Supply Chain Security published in 2012 by the White House identifies two primary goals for strengthening global supply chains: first, to promote the efficient and secure movement of goods, and second to foster a resilient supply chain. The Internet of Things (IoT), and in particular Radio Frequency Identification (RFID) technology, can be used to realize these goals. For product identification, tracking and real-time awareness, RFID tags are attached to goods. As tagged goods move along the supply chain from the suppliers to the manufacturers, and then on to the retailers until eventually they reach the customers, two major security challenges can be identified: (I) to protect the shipment of goods that are controlled by potentially untrusted carriers; and (II) to secure the transfer of ownership at each stage of the chain. For the former, grouping proofs in which the tags of the scanned goods generate a proof of “simulatenous” presence can be employed, while for the latter, ownership transfer protocols (OTP) are used. This paper describes enhanced security solutions for both challenges. We first extend earlier work on grouping proofs and group codes to capture resilient group scanning with untrusted readers; then, we describe a modified version of a recently published OTP based on channels with positive secrecy capacity adapted to be implemented on common RFID systems in the supply chain. The proposed solutions take into account the limitations of low cost tags employed in the supply chain, which are only required to generate pseudorandom numbers and compute one-way hash functions. PMID:28677637
Directory of Open Access Journals (Sweden)
Mike Burmester
2017-07-01
Full Text Available The National Strategy for Global Supply Chain Security published in 2012 by the White House identifies two primary goals for strengthening global supply chains: first, to promote the efficient and secure movement of goods, and second to foster a resilient supply chain. The Internet of Things (IoT, and in particular Radio Frequency Identification (RFID technology, can be used to realize these goals. For product identification, tracking and real-time awareness, RFID tags are attached to goods. As tagged goods move along the supply chain from the suppliers to the manufacturers, and then on to the retailers until eventually they reach the customers, two major security challenges can be identified: (I to protect the shipment of goods that are controlled by potentially untrusted carriers; and (II to secure the transfer of ownership at each stage of the chain. For the former, grouping proofs in which the tags of the scanned goods generate a proof of “simulatenous” presence can be employed, while for the latter, ownership transfer protocols (OTP are used. This paper describes enhanced security solutions for both challenges. We first extend earlier work on grouping proofs and group codes to capture resilient group scanning with untrusted readers; then, we describe a modified version of a recently published OTP based on channels with positive secrecy capacity adapted to be implemented on common RFID systems in the supply chain. The proposed solutions take into account the limitations of low cost tags employed in the supply chain, which are only required to generate pseudorandom numbers and compute one-way hash functions.
Burmester, Mike; Munilla, Jorge; Ortiz, Andrés; Caballero-Gil, Pino
2017-07-04
The National Strategy for Global Supply Chain Security published in 2012 by the White House identifies two primary goals for strengthening global supply chains: first, to promote the efficient and secure movement of goods, and second to foster a resilient supply chain. The Internet of Things (IoT), and in particular Radio Frequency Identification (RFID) technology, can be used to realize these goals. For product identification, tracking and real-time awareness, RFID tags are attached to goods. As tagged goods move along the supply chain from the suppliers to the manufacturers, and then on to the retailers until eventually they reach the customers, two major security challenges can be identified: (I) to protect the shipment of goods that are controlled by potentially untrusted carriers; and (II) to secure the transfer of ownership at each stage of the chain. For the former, grouping proofs in which the tags of the scanned goods generate a proof of "simulatenous" presence can be employed, while for the latter, ownership transfer protocols (OTP) are used. This paper describes enhanced security solutions for both challenges. We first extend earlier work on grouping proofs and group codes to capture resilient group scanning with untrusted readers; then, we describe a modified version of a recently published OTP based on channels with positive secrecy capacity adapted to be implemented on common RFID systems in the supply chain. The proposed solutions take into account the limitations of low cost tags employed in the supply chain, which are only required to generate pseudorandom numbers and compute one-way hash functions.
Ku, Oskar; Chen, Sherry Y.; Wu, Denise H.; Lao, Andrew C. C.; Chan, Tak-Wai
2014-01-01
Many students possess low confidence toward learning mathematics, which, in turn, may lead them to give up pursuing more mathematics knowledge. Recently, game-based learning (GBL) is regarded as a potential means in improving students' confidence. Thus, this study tried to promote students' confidence toward mathematics by using GBL. In addition,…
DEFF Research Database (Denmark)
Puech, Matthias
2013-01-01
this correspondence by applying a series of off-the-shelf program transformations à la Danvy et al. on a type checker for the bidirectional λ-calculus, and get a type checker for the λ¯ -calculus, the proof term assignment of LJT. This functional correspondence revisits the relationship between natural deduction......It is well known in proof theory that sequent-calculus proofs differ from natural deduction proofs by “reversing” elimination rules upside down into left introduction rules. It is also well known that to each recursive, functional program corresponds an equivalent iterative, accumulator......-passing program, where the accumulator stores the continuation of the iteration, in “reversed” order. Here, we compose these remarks and show that a restriction of the intuitionistic sequent calculus, LJT, is exactly an accumulator-passing version of intuitionistic natural deduction NJ. More precisely, we obtain...
Mathematical Modeling in the Undergraduate Curriculum
Toews, Carl
2012-01-01
Mathematical modeling occupies an unusual space in the undergraduate mathematics curriculum: typically an "advanced" course, it nonetheless has little to do with formal proof, the usual hallmark of advanced mathematics. Mathematics departments are thus forced to decide what role they want the modeling course to play, both as a component of the…
The Transition to Formal Thinking in Mathematics
Tall, David
2008-01-01
This paper focuses on the changes in thinking involved in the transition from school mathematics to formal proof in pure mathematics at university. School mathematics is seen as a combination of visual representations, including geometry and graphs, together with symbolic calculations and manipulations. Pure mathematics in university shifts…
[Mathematical exploration of essence of herbal properties based on "Three-Elements" theory].
Jin, Rui; Zhao, Qian; Zhang, Bing
2014-10-01
Herbal property theory of traditional Chinese medicines is the theoretical guidance on authentication of medicinal plants, herborization, preparation of herbal medicines for decoction and clinical application, with important theoretical value and prac- tical significance. Our research team proposed the "three-element" theory for herbal properties for the first time, conducted a study by using combined methods of philology, chemistry, pharmacology and mathematics, and then drew the research conclusion that herbal properties are defined as the chemical compositions-based comprehensive expression with complex and multi-level (positive/negative) biological effects in specific organism state. In this paper, researchers made a systematic mathematical analysis in four aspects--the correlation between herbal properties and chemical component factors, the correlation between herbal properties and organism state fac- tor, the correlation between herbal properties and biological effect factor and the integration study of the three elements, proposed future outlook, and provided reference to mathematical studies and mathematical analysis of herbal properties.
Jost, Jürgen
2015-01-01
The main intention of this book is to describe and develop the conceptual, structural and abstract thinking of mathematics. Specific mathematical structures are used to illustrate the conceptual approach; providing a deeper insight into mutual relationships and abstract common features. These ideas are carefully motivated, explained and illustrated by examples so that many of the more technical proofs can be omitted. The book can therefore be used: · simply as an overview of the panorama of mathematical structures and the relations between them, to be supplemented by more detailed texts whenever you want to acquire a working knowledge of some structure · by itself as a first introduction to abstract mathematics · together with existing textbooks, to put their results into a more general perspective · to gain a new and hopefully deeper perspective after having studied such textbooks Mathematical Concepts has a broader scope and is less detaile...
Fasni, Nurli; Fatimah, Siti; Yulanda, Syerli
2017-05-01
This research aims to achieve some purposes such as: to know whether mathematical problem solving ability of students who have learned mathematics using Multiple Intelligences based teaching model is higher than the student who have learned mathematics using cooperative learning; to know the improvement of the mathematical problem solving ability of the student who have learned mathematics using Multiple Intelligences based teaching model., to know the improvement of the mathematical problem solving ability of the student who have learned mathematics using cooperative learning; to know the attitude of the students to Multiple Intelligences based teaching model. The method employed here is quasi-experiment which is controlled by pre-test and post-test. The population of this research is all of VII grade in SMP Negeri 14 Bandung even-term 2013/2014, later on two classes of it were taken for the samples of this research. A class was taught using Multiple Intelligences based teaching model and the other one was taught using cooperative learning. The data of this research were gotten from the test in mathematical problem solving, scale questionnaire of the student attitudes, and observation. The results show the mathematical problem solving of the students who have learned mathematics using Multiple Intelligences based teaching model learning is higher than the student who have learned mathematics using cooperative learning, the mathematical problem solving ability of the student who have learned mathematics using cooperative learning and Multiple Intelligences based teaching model are in intermediate level, and the students showed the positive attitude in learning mathematics using Multiple Intelligences based teaching model. As for the recommendation for next author, Multiple Intelligences based teaching model can be tested on other subject and other ability.
The written mathematical communication profile of prospective math teacher in mathematical proving
Pantaleon, K. V.; Juniati, D.; Lukito, A.; Mandur, K.
2018-01-01
Written mathematical communication is the process of expressing mathematical ideas and understanding in writing. It is one of the important aspects that must be mastered by the prospective math teacher as tool of knowledge transfer. This research was a qualitative research that aimed to describe the mathematical communication profile of the prospective mathematics teacher in mathematical proving. This research involved 48 students of Mathematics Education Study Program; one of them with moderate math skills was chosen as the main subject. Data were collected through tests, assignments, and task-based interviews. The results of this study point out that in the proof of geometry, the subject explains what is understood, presents the idea in the form of drawing and symbols, and explains the content/meaning of a representation accurately and clearly, but the subject can not convey the argument systematically and logically. Whereas in the proof of algebra, the subject describes what is understood, explains the method used, and describes the content/meaning of a symbolic representation accurately, systematically, logically, but the argument presented is not clear because it is insufficient detailed and complete.
Arnellis, A.; Jamaan, E. Z.; Amalita, N.
2018-04-01
The goal to analyse a improvement of teacher competence after being trained in preparing high-order math olympicad based on high order thinking skills in junior high school teachers in Pesisir Selatan Regency. The sample of these activities are teachers at the MGMP junior high school in Pesisir Selatan District. Evaluation of the implementation is done by giving a pre test and post test, which will measure the success rate of the implementation of this activities. The existence of the devotion activities is expected to understand the enrichment of mathematics olympiad material and training in the preparation of math olympiad questions for the teachers of South Pesisir district junior high school, motivating and raising the interest of the participants in order to follow the mathematics olympiad with the enrichment of mathematics materials and the training of problem solving about mathematics olympiad for junior high school teachers, the participants gain experience and gain insight, as well as the ins and outs of junior mathematics olympiad and implement to teachers and students in olympic competitions. The result of that the post-test is better than the result of pretest in the training of mathematics teacher competence improvement in composing the mathematics olympiad problem based on high order thinking skills of junior high school (SMP) in Pesisir Selatan District, West Sumatra, Indonesia.
Mathematical Based Calculation of Drug Penetration Depth in Solid Tumors
Directory of Open Access Journals (Sweden)
Hamidreza Namazi
2016-01-01
Full Text Available Cancer is a class of diseases characterized by out-of-control cells’ growth which affect cells and make them damaged. Many treatment options for cancer exist. Chemotherapy as an important treatment option is the use of drugs to treat cancer. The anticancer drug travels to the tumor and then diffuses in it through capillaries. The diffusion of drugs in the solid tumor is limited by penetration depth which is different in case of different drugs and cancers. The computation of this depth is important as it helps physicians to investigate about treatment of infected tissue. Although many efforts have been made on studying and measuring drug penetration depth, less works have been done on computing this length from a mathematical point of view. In this paper, first we propose phase lagging model for diffusion of drug in the tumor. Then, using this model on one side and considering the classic diffusion on the other side, we compute the drug penetration depth in the solid tumor. This computed value of drug penetration depth is corroborated by comparison with the values measured by experiments.
Mathematical thinking of maintenance. Problem setting and solving bases
International Nuclear Information System (INIS)
2007-01-01
Plant or mechanical facility for maintenance became more complicated than before and consisted of many subsystems made of various equipments or facilities with parts, which were a system having complicated and hierarchical structure. Maintenance was required to be properly implemented to assure reliability of a system for a long period so as for each equipment to play a specified role for a stable operation of plant. Mathematical thinking using probability theory was rational to optimize maintenance action with failure rate function of system or part of equipment. Reliability function, maintainability function and availability of plant and equipment were defined. Unreliability function was called failure time distribution function (F(t)) and failure rate function (λ(t)) was defined as the ratio of failure time density distribution function (dF(t)/dt) to reliability function (1-F(t)). λ(t) could be expressed as a simple equation with Weibull parameter. Availability at steady state was attributed to ratio of average operating time to sum of operating time and maintenance time, i.e. MTBF/(MTBF+MTTR) where MTBF was mean time between failures and MTTR was mean time to repair. Optimization of system risk and maintenance action was encouraged using computational science simulating material degradation. (T. Tanaka)
Priatna, Nanang
2017-08-01
The use of Information and Communication Technology (ICT) in mathematics instruction will help students in building conceptual understanding. One of the software products used in mathematics instruction is GeoGebra. The program enables simple visualization of complex geometric concepts and helps improve students' understanding of geometric concepts. Instruction applying brain-based learning principles is one oriented at the efforts of naturally empowering the brain potentials which enable students to build their own knowledge. One of the goals of mathematics instruction in school is to develop mathematical communication ability. Mathematical representation is regarded as a part of mathematical communication. It is a description, expression, symbolization, or modeling of mathematical ideas/concepts as an attempt of clarifying meanings or seeking for solutions to the problems encountered by students. The research aims to develop a learning model and teaching materials by applying the principles of brain-based learning aided by GeoGebra to improve junior high school students' mathematical representation ability. It adopted a quasi-experimental method with the non-randomized control group pretest-posttest design and the 2x3 factorial model. Based on analysis of the data, it is found that the increase in the mathematical representation ability of students who were treated with mathematics instruction applying the brain-based learning principles aided by GeoGebra was greater than the increase of the students given conventional instruction, both as a whole and based on the categories of students' initial mathematical ability.
Directory of Open Access Journals (Sweden)
Karlimah
2018-01-01
Full Text Available Many studies suggest that classical music can inccrease the listeners’ intelligence, including mathematical intelligence [3, 12, 2, 11]. In this research, we used the classical music of Baroque era as the backsound during math learning. The research method used was quasi experiment with nonequivalent pretest-posttest control group design to grade V SD students in Tasikmalaya city. The results show that the use of classical music of Baroque era during the learning of mathematics gave a high contribution to the mathematical intelligence of fifth grade elementary school students. The student's mathematical intelligence can be seen in the cognitive abilities which were at the high level in the knowledge up to analysis, and at the low level in the synthesis and evaluation. Low mathematical intelligence was shown by students in calculating amount and difference of time, and projecting word problem into the form of mathematical problems. High mathematical intelligence arose in reading and writing integers in words and numbers. Thus, the mathematical intelligence of fifth grade Elementary School students will be better if classical music of Baroque era is used as the backsound in mathematics learning about solving math problems.
Student’s mathematical understanding ability based on self-efficacy
Ramdhani, M. R.; Usodo, B.; Subanti, S.
2017-11-01
Materials in mathematics are provided not only as an ability to memorize, but also to train the ability of mathematical understanding. Students’ mathematical understanding ability is influenced by the students’ belief in solving the given problems. This research aim to determine the mathematical understanding ability of junior high school students. This research is descriptive qualitative research. Data collection was done through a test, questionnaire, and interview. The result showed that students with high self-efficacy category could master the three indicators of students’ mathematical understanding ability well, namely translation, interpretation, and exploration. Students with moderate self-efficacy category can master translation indicator and able to achieve interpretation indicator but they unable to reach exploration indicator. Students with low self-efficacy category only master the translation, but they cannot achieve the interpretation and exploration indicators. So, the students who have high, moderate or low self-efficacy master the indicator of mathematical understanding based on the level of understanding capabilities on each student.
Mekarina, M.; Ningsih, Y. P.
2017-09-01
This classroom action research is based by the facts that the students motivation and achievement mathematics learning is less. One of the factors causing is learning that does not provide flexibility to students to empower the potential of the brain optimally. The aim of this research was to improve the student motivation and achievement in mathematics learning by implementing brain based learning approach. The subject of this research was student of grade XI in senior high school. The research consisted of two cycles. Data of student achievement from test, and the student motivation through questionnaire. Furthermore, the finding of this research showed the result of the analysis was the implementation of brain based learning approach can improve student’s achievement and motivation in mathematics learning.
Pedagogical Applications from Real Analysis for Secondary Mathematics Teachers
Wasserman, Nicholas; Weber, Keith
2017-01-01
In this article, we consider the potential influences of the study of proofs in advanced mathematics on secondary mathematics teaching. Thus far, the literature has highlighted the benefits of applying the conclusions of particular proofs to secondary content and of developing a more general sense of disciplinary practices in mathematics in…
Scaffolding norms of argumentation-based inquiry in a primary mathematics classroom
Makar, Katie; Bakker, Arthur; Ben-Zvi, Dani
2015-01-01
Developing argumentation-based inquiry practices requires teachers and students to be explicit about classroom norms that support these practices. In this study, we asked: How can a teacher scaffold the development of argumentation-based inquiry norms and practices in a mathematics classroom? A
Students' Mathematics Word Problem-Solving Achievement in a Computer-Based Story
Gunbas, N.
2015-01-01
The purpose of this study was to investigate the effect of a computer-based story, which was designed in anchored instruction framework, on sixth-grade students' mathematics word problem-solving achievement. Problems were embedded in a story presented on a computer as computer story, and then compared with the paper-based version of the same story…
Directory of Open Access Journals (Sweden)
Alexander B. Bakulev
2012-11-01
Full Text Available This article deals with mathematical models and algorithms, providing mobility of sequential programs parallel representation on the high-level language, presents formal model of operation environment processes management, based on the proposed model of programs parallel representation, presenting computation process on the base of multi-core processors.
Problem-Based Learning in K-8 Mathematics and Science Education: A Literature Review
Merritt, Joi; Lee, Mi Yeon; Rillero, Peter; Kinach, Barbara M.
2017-01-01
This systematic literature review was conducted to explore the effectiveness of problem-based and project-based learning (PBL) implemented with students in early elementary to grade 8 (ages 3-14) in mathematics and science classrooms. Nine studies met the following inclusion criteria: (a) focus on PBL, (b) experimental study, (c) kindergarten to…
Furness, Trentham; Joseph, Corey; Welsh, Liam; Naughton, Geraldine; Lorenzen, Christian
2013-11-11
The potential of whole-body vibration (WBV) as a mode of dyspnoea free physical activity for people with chronic obstructive pulmonary disease (COPD) is unknown among community-based settings. Furthermore, the acute effects of WBV on people with COPD have not been profiled in community-based settings. The aim of this community-based proof-of-concept trial was to describe acute effects of WBV by profiling subjective and objective responses to physical activity. Seventeen community-dwelling older adults with COPD were recruited to participate in two sessions; WBV and sham WBV (SWBV). Each session consisted of five one-minute bouts interspersed with five one-minute passive rest periods. The gravitational force was ~2.5 g for WBV and ~0.0 g for SWBV. Reliability of baseline dyspnoea, heart rate, and oxygen saturation was first established and then profiled for both sessions. Acute responses to both WBV and SWBV were compared with repeated measures analysis of variance and repeated contrasts. Small changes in dyspnoea and oxygen saturation lacked subjective and clinical meaningfulness. One session of WBV and SWBV significantly increased heart rate (p ≤ 0.02), although there was no difference among WBV and SWBV (p = 0.67). This community-based proof-of-concept trial showed that a session of WBV can be completed with the absence of dyspnoea for people with COPD. Furthermore, there were no meaningful differences among WBV and SWBV for heart rate and oxygen saturation. There is scope for long-term community-based intervention research using WBV given the known effects of WBV on peripheral muscle function and functional independence.
Directory of Open Access Journals (Sweden)
M. Sievers
2018-06-01
Full Text Available In this short communication, we investigated the synthesis and mixing of porphyrin and pyridine functionalized copolymers as a proof of concept for a velcro-like interaction. A functionalized porphyrin monomer with one polymerizable side chain was synthesized following a rational synthetic pathway. Subsequent copolymerization and careful removal of residual free porphyrin led to poly(n-butyl acrylate-co-5,10,15-triphenyl-20-(3-vinylphenylporphyrin. The immobilized porphyrin was transformed into the corresponding zinc(II complex, which is capable of the coordinative binding of one pyridine moiety. Complete metallation was proven by absorption spectroscopy. 4-Vinylpyridine was immobilized by copolymerization with n-butyl acrylate, too. Via controlled radical polymerization conditions, the molecular weight of poly(n-butyl acrylate-co-4-vinylpyridine was limited to one tenth of the molecular weight of the porphyrin containing copolymer. This large difference in the molecular weight easily allowed identifying the polymers in the mixture of both. With the help of diffusion ordered nuclear magnetic resonance spectroscopy, the complete and temperature-stable precipitation of the porphyrin containing copolymer was observed, proving the expected attractive interaction and supramolecular network formation.
Proof Nets for Lambek Calculus
Roorda, Dirk
1992-01-01
The proof nets of linear logic are adapted to the non-commutative Lambek calculus. A different criterion for soundness of proof nets is given, which gives rise to new algorithms for proof search. The order sensitiveness of the Lambek calculus is reflected by the planarity condition on proof nets;
Tikhomirov, V. G.; Gudkov, A. G.; Agasieva, S. V.; Gorlacheva, E. N.; Shashurin, V. D.; Zybin, A. A.; Evseenkov, A. S.; Parnes, Y. M.
2017-11-01
The numerical impact modeling of some external effects on the CVC of biosensors based on AlGaN/GaN heterostructures (HEMT) was carried out. The mathematical model was created that allowed to predict the behavior of the drain current depending on condition changes on the heterostructure surface in the gate region and to start the process of directed construction optimization of the biosensors based on AlGaN/GaN HEMT with the aim of improving their performance. The calculation of the drain current of the biosensor construction was carried out to confirm the reliability of the developed mathematical model and obtained results.
DEFF Research Database (Denmark)
Høyrup, Jens
2016-01-01
Plato, so the story goes, held mathematics in high esteem, and those philosopher-kings that ought to rule his republic should have a thorough foundation in mathematics. This may well be true – but an observation made by Aristotle suggests that the mathematics which Plato intends is not the one...... based on theorems and proofs which we normally identify with “Greek mathematics”. Most other ancient writers who speak of mathematics as a road toward Wisdom also appear to be blissfully ignorant of the mathematics of Euclid, Archimedes, Apollonios, etc. – though not necessarily of their names. The aim...... of the paper is to identify the kinds of mathematics which were available as external sources for this current (on the whole leaving out of consideration Liberal-Arts mathematics as not properly external). A number of borrowings can be traced to various practitioners' traditions – but always as bits borrowed...
Directory of Open Access Journals (Sweden)
Reviandari Widyatiningtyas
2015-07-01
Full Text Available The study was report the findings of an only post-test control group research design and aims to analyze the influence of problem-based learning approach, school level, and students’ prior mathematical ability to student’s mathematics critical thinking ability. The research subjects were 140 grade ten senior high school students coming from excellent and moderate school level. The research instruments a set of mathematical critical thinking ability test, and the data were analyzed by using two ways ANOVA and t-test. The research found that the problem based learning approach has significant impact to the ability of students’ mathematics critical thinking in terms of school level and students’ prior mathematical abilities. Furthermore. This research also found that there is no interaction between learning approach and school level, and learning approach and students’ prior mathematics ability to students’ mathematics critical thinking ability.
Jarnawi Afgani Dahlan; Yaya Sukjaya Kusumah; Mr Heri Sutarno
2011-01-01
The focus of this research is on the development of mathematics teaching and learning activity which is based on the application of computer software. The aim of research is as follows : 1) to identify some mathematics topics which feasible to be presented by computer-based e-learning, 2) design, develop, and implement computer-based e-learning on mathematics, and 3) analyze the impact of computer-based e-learning in the enhancement of SMA students’ high order mathematical thinking. All activ...
Applying Mathematical Optimization Methods to an ACT-R Instance-Based Learning Model.
Said, Nadia; Engelhart, Michael; Kirches, Christian; Körkel, Stefan; Holt, Daniel V
2016-01-01
Computational models of cognition provide an interface to connect advanced mathematical tools and methods to empirically supported theories of behavior in psychology, cognitive science, and neuroscience. In this article, we consider a computational model of instance-based learning, implemented in the ACT-R cognitive architecture. We propose an approach for obtaining mathematical reformulations of such cognitive models that improve their computational tractability. For the well-established Sugar Factory dynamic decision making task, we conduct a simulation study to analyze central model parameters. We show how mathematical optimization techniques can be applied to efficiently identify optimal parameter values with respect to different optimization goals. Beyond these methodological contributions, our analysis reveals the sensitivity of this particular task with respect to initial settings and yields new insights into how average human performance deviates from potential optimal performance. We conclude by discussing possible extensions of our approach as well as future steps towards applying more powerful derivative-based optimization methods.
Mathematical Modelling of a Hybrid Micro-Cogeneration Group Based on a Four Stroke Diesel Engine
Directory of Open Access Journals (Sweden)
Apostol Valentin
2014-06-01
Full Text Available The paper presents a part of the work conducted in the first stage of a Research Grant called ”Hybrid micro-cogeneration group of high efficiency equipped with an electronically assisted ORC” acronym GRUCOHYB. The hybrid micro-cogeneration group is equipped with a four stroke Diesel engine having a maximum power of 40 kW. A mathematical model of the internal combustion engine is presented. The mathematical model is developed based on the Laws of Thermodynamics and takes into account the real, irreversible processes. Based on the mathematical model a computation program was developed. The results obtained were compared with those provided by the Diesel engine manufacturer. Results show a very high correlation between the manufacturer’s data and the simulation results for an engine running at 100% load. Future developments could involve using an exergetic analysis to show the ability of the ORC to generate electricity from recovered heat
MATHEMATICAL APPARATUS FOR KNOWLEDGE BASE PROJECT MANAGEMENT OF OCCUPATIONAL SAFETY
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Валентина Николаевна ПУРИЧ
2015-05-01
Full Text Available The occupational safety project (OSP management is aimed onto a rational choice implementation. With respect to the subjectivity of management goals the project selection is considered as a minimum formalization level information process, The proposed project selection model relies upon the enterprise’s occupational and industrial safety assessment using fuzzy logic and linguistic variables based on occupational safety knowledge base.
A mathematical framework for agent based models of complex biological networks.
Hinkelmann, Franziska; Murrugarra, David; Jarrah, Abdul Salam; Laubenbacher, Reinhard
2011-07-01
Agent-based modeling and simulation is a useful method to study biological phenomena in a wide range of fields, from molecular biology to ecology. Since there is currently no agreed-upon standard way to specify such models, it is not always easy to use published models. Also, since model descriptions are not usually given in mathematical terms, it is difficult to bring mathematical analysis tools to bear, so that models are typically studied through simulation. In order to address this issue, Grimm et al. proposed a protocol for model specification, the so-called ODD protocol, which provides a standard way to describe models. This paper proposes an addition to the ODD protocol which allows the description of an agent-based model as a dynamical system, which provides access to computational and theoretical tools for its analysis. The mathematical framework is that of algebraic models, that is, time-discrete dynamical systems with algebraic structure. It is shown by way of several examples how this mathematical specification can help with model analysis. This mathematical framework can also accommodate other model types such as Boolean networks and the more general logical models, as well as Petri nets.
Energy Technology Data Exchange (ETDEWEB)
Schmitt, Marcus [AREVA NP GmbH, Erlangen (Germany)
2013-07-01
Even before the Fukushima event occurred some German nuclear power plants (NPP) have considered flooding scenarios. As a result of one of these studies, AREVA performed an upgrade project in NPP Isar 1 with flood-proof motors as a replacement of existing air-cooled low-voltage and high-voltage motors of the emergency cooling chain. After the Fukushima event, in which the cooling chains failed, the topic flood-proof equipment gets more and more into focus. This compact will introduce different kinds of flood-proof electrical motors which are currently installed or planned for installation into NPPs over the world. Moreover the process of qualification, as it was performed during the project in NPP Isar 1, will be shown. (orig.)
International Nuclear Information System (INIS)
Schmitt, Marcus
2013-01-01
Even before the Fukushima event occurred some German nuclear power plants (NPP) have considered flooding scenarios. As a result of one of these studies, AREVA performed an upgrade project in NPP Isar 1 with flood-proof motors as a replacement of existing air-cooled low-voltage and high-voltage motors of the emergency cooling chain. After the Fukushima event, in which the cooling chains failed, the topic flood-proof equipment gets more and more into focus. This compact will introduce different kinds of flood-proof electrical motors which are currently installed or planned for installation into NPPs over the world. Moreover the process of qualification, as it was performed during the project in NPP Isar 1, will be shown. (orig.)
On the proof of the first Carnot theorem in thermodynamics
International Nuclear Information System (INIS)
Morad, M R; Momeni, F
2013-01-01
The proof of the first Carnot theorem in classical thermodynamics is revisited in this study. The underlying conditions of a general proof of this principle presented by Senft (1978 Phys. Educ. 13 35–37) are explored and discussed. These conditions are analysed in more detail using a physical description of heat and work to present a simpler proof of the first principle prior to using the violation of the second law of thermodynamics. Finally, a new simple proof is also presented based on Gibbs relation. This discussion will benefit the teaching of classical thermodynamics and promote better understanding of the proof of the first Carnot theorem in general form. (paper)
Students’ Mathematical Literacy in Solving PISA Problems Based on Keirsey Personality Theory
Masriyah; Firmansyah, M. H.
2018-01-01
This research is descriptive-qualitative research. The purpose is to describe students’ mathematical literacy in solving PISA on space and shape content based on Keirsey personality theory. The subjects are four junior high school students grade eight with guardian, artisan, rational or idealist personality. Data collecting methods used test and interview. Data of Keirsey Personality test, PISA test, and interview were analysed. Profile of mathematical literacy of each subject are described as follows. In formulating, guardian subject identified mathematical aspects are formula of rectangle area and sides length; significant variables are terms/conditions in problem and formula of ever encountered question; translated into mathematical language those are measurement and arithmetic operations. In employing, he devised and implemented strategies using ease of calculation on area-subtraction principle; declared truth of result but the reason was less correct; didn’t use and switch between different representations. In interpreting, he declared result as area of house floor; declared reasonableness according measurement estimation. In formulating, artisan subject identified mathematical aspects are plane and sides length; significant variables are solution procedure on both of daily problem and ever encountered question; translated into mathematical language those are measurement, variables, and arithmetic operations as well as symbol representation. In employing, he devised and implemented strategies using two design comparison; declared truth of result without reason; used symbol representation only. In interpreting, he expressed result as floor area of house; declared reasonableness according measurement estimation. In formulating, rational subject identified mathematical aspects are scale and sides length; significant variables are solution strategy on ever encountered question; translated into mathematical language those are measurement, variable, arithmetic
Development of syntax of intuition-based learning model in solving mathematics problems
Yeni Heryaningsih, Nok; Khusna, Hikmatul
2018-01-01
The aim of the research was to produce syntax of Intuition Based Learning (IBL) model in solving mathematics problem for improving mathematics students’ achievement that valid, practical and effective. The subject of the research were 2 classes in grade XI students of SMAN 2 Sragen, Central Java. The type of the research was a Research and Development (R&D). Development process adopted Plomp and Borg & Gall development model, they were preliminary investigation step, design step, realization step, evaluation and revision step. Development steps were as follow: (1) Collected the information and studied of theories in Preliminary Investigation step, studied about intuition, learning model development, students condition, and topic analysis, (2) Designed syntax that could bring up intuition in solving mathematics problem and then designed research instruments. They were several phases that could bring up intuition, Preparation phase, Incubation phase, Illumination phase and Verification phase, (3) Realized syntax of Intuition Based Learning model that has been designed to be the first draft, (4) Did validation of the first draft to the validator, (5) Tested the syntax of Intuition Based Learning model in the classrooms to know the effectiveness of the syntax, (6) Conducted Focus Group Discussion (FGD) to evaluate the result of syntax model testing in the classrooms, and then did the revision on syntax IBL model. The results of the research were produced syntax of IBL model in solving mathematics problems that valid, practical and effective. The syntax of IBL model in the classroom were, (1) Opening with apperception, motivations and build students’ positive perceptions, (2) Teacher explains the material generally, (3) Group discussion about the material, (4) Teacher gives students mathematics problems, (5) Doing exercises individually to solve mathematics problems with steps that could bring up students’ intuition: Preparations, Incubation, Illumination, and
Kuneni, Erna; Mardiyana, Pramudya, Ikrar
2017-08-01
Geometry is the most important branch in mathematics. The purpose of teaching this material is to develop students' level of thinking for a better understanding. Otherwise, geometry in particular, has contributed students' failure in mathematics examinations. This problem occurs due to special feature in geometry which has complexity of correlation among its concept. This relates to mathematical connection. It is still difficult for students to improve this ability. This is because teachers' lack in facilitating students towards it. Eventhough, facilitating students can be in the form of teaching material. A learning module can be a solution because it consists of series activities that should be taken by students to achieve a certain goal. A series activities in this case is adopted by the phases of discovery-based learning model. Through this module, students are facilitated to discover concept by deep instruction and guidance. It can build the mathematical habits of mind and also strengthen the mathematical connection. Method used in this research was ten stages of research and development proposed by Bord and Gall. The research purpose is to create a valid learning module to improve students' mathematical connection in teaching quadrilateral. The retrieved valid module based on media expert judgment is 2,43 for eligibility chart aspect, 2,60 for eligibility presentation aspect, and 3,00 for eligibility contents aspect. Then the retrieved valid module based on material expert judgment is 3,10 for eligibility content aspect, 2,87 for eligibility presentation aspect, and 2,80 for eligibility language and legibility aspect.
Mathematical Observations: The Genesis of Mathematical Discovery in the Classroom
Beaugris, Louis M.
2013-01-01
In his "Proofs and Refutations," Lakatos identifies the "Primitive Conjecture" as the first stage in the pattern of mathematical discovery. In this article, I am interested in ways of reaching the "Primitive Conjecture" stage in an undergraduate classroom. I adapted Realistic Mathematics Education methods in an…
Zhang, Jianshu; Du, Jun; Dai, Lirong
2017-01-01
In this study, we present a novel end-to-end approach based on the encoder-decoder framework with the attention mechanism for online handwritten mathematical expression recognition (OHMER). First, the input two-dimensional ink trajectory information of handwritten expression is encoded via the gated recurrent unit based recurrent neural network (GRU-RNN). Then the decoder is also implemented by the GRU-RNN with a coverage-based attention model. The proposed approach can simultaneously accompl...
Lee, Young-Jin
2017-01-01
Purpose: The purpose of this paper is to develop a quantitative model of problem solving performance of students in the computer-based mathematics learning environment. Design/methodology/approach: Regularized logistic regression was used to create a quantitative model of problem solving performance of students that predicts whether students can…
Saragih, Sahat; Napitupulu, E. Elvis; Fauzi, Amin
2017-01-01
This research aims to develop a student-centered learning model based on local culture and instrument of mathematical higher order thinking of junior high school students in the frame of the 2013-Curriculum in North Sumatra, Indonesia. The subjects of the research are seventh graders which are taken proportionally random consisted of three public…
The Effect of Cluster-Based Instruction on Mathematic Achievement in Inclusive Schools
Gunarhadi, Sunardi; Anwar, Mohammad; Andayani, Tri Rejeki; Shaari, Abdull Sukor
2016-01-01
The research aimed to investigate the effect of Cluster-Based Instruction (CBI) on the academic achievement of Mathematics in inclusive schools. The sample was 68 students in two intact classes, including those with learning disabilities, selected using a cluster random technique among 17 inclusive schools in the regency of Surakarta. The two…
Project-Based Social Justice Mathematics: A Case Study of Five 6th Grade Students
McHugh, Maighread L.
2015-01-01
The purpose of this qualitative multiple case study was to explore how five sixth grade female students navigated the process of project-based learning as they designed and implemented their own project centered on mathematics while using a social justice lens. The theoretical frameworks of Authentic Intellectual Work and Social Justice…
Structural analysis of online handwritten mathematical symbols based on support vector machines
Simistira, Foteini; Papavassiliou, Vassilis; Katsouros, Vassilis; Carayannis, George
2013-01-01
Mathematical expression recognition is still a very challenging task for the research community mainly because of the two-dimensional (2d) structure of mathematical expressions (MEs). In this paper, we present a novel approach for the structural analysis between two on-line handwritten mathematical symbols of a ME, based on spatial features of the symbols. We introduce six features to represent the spatial affinity of the symbols and compare two multi-class classification methods that employ support vector machines (SVMs): one based on the "one-against-one" technique and one based on the "one-against-all", in identifying the relation between a pair of symbols (i.e. subscript, numerator, etc). A dataset containing 1906 spatial relations derived from the Competition on Recognition of Online Handwritten Mathematical Expressions (CROHME) 2012 training dataset is constructed to evaluate the classifiers and compare them with the rule-based classifier of the ILSP-1 system participated in the contest. The experimental results give an overall mean error rate of 2.61% for the "one-against-one" SVM approach, 6.57% for the "one-against-all" SVM technique and 12.31% error rate for the ILSP-1 classifier.
Petersen, Richard H.
1997-01-01
The objectives of the Institute were: (a) increase participants' content knowledge about aeronautics, science, mathematics, and technology, (b) model and promote the use of scientific inquiry through problem-based learning, (c) investigate the use of instructional technologies and their applications to curricula, and (d) encourage the dissemination of TEI experiences to colleagues, students, and parents.
Affording and Constraining Local Moral Orders in Teacher-Led Ability-Based Mathematics Groups
Tait-McCutcheon, Sandi; Shuker, Mary Jane; Higgins, Joanna; Loveridge, Judith
2015-01-01
How teachers position themselves and their students can influence the development of afforded or constrained local moral orders in ability-based teacher-led mathematics lessons. Local moral orders are the negotiated discursive practices and interactions of participants in the group. In this article, the developing local moral orders of 12 teachers…
A Computer-Based Game That Promotes Mathematics Learning More than a Conventional Approach
McLaren, Bruce M.; Adams, Deanne M.; Mayer, Richard E.; Forlizzi, Jodi
2017-01-01
Excitement about learning from computer-based games has been papable in recent years and has led to the development of many educational games. However, there are relatively few sound empirical studies in the scientific literature that have shown the benefits of learning mathematics from games as opposed to more traditional approaches. The…
Digital Game-Based Learning for K-12 Mathematics Education: A Meta-Analysis
Byun, JaeHwan; Joung, Eunmi
2018-01-01
Digital games (e.g., video games or computer games) have been reported as an effective educational method that can improve students' motivation and performance in mathematics education. This meta-analysis study (a) investigates the current trend of digital game-based learning (DGBL) by reviewing the research studies on the use of DGBL for…
Mathematics Achievement with Digital Game-Based Learning in High School Algebra 1 Classes
Ferguson, Terri Lynn Kurley
2014-01-01
This study examined the impact of digital game-based learning (DGBL) on mathematics achievement in a rural high school setting in North Carolina. A causal comparative research design was used in this study to collect data to determine the effectiveness of DGBL in high school Algebra 1 classes. Data were collected from the North Carolina…
Effects of Computer-Based Visual Representation on Mathematics Learning and Cognitive Load
Yung, Hsin I.; Paas, Fred
2015-01-01
Visual representation has been recognized as a powerful learning tool in many learning domains. Based on the assumption that visual representations can support deeper understanding, we examined the effects of visual representations on learning performance and cognitive load in the domain of mathematics. An experimental condition with visual…
Cook, Samuel A.; Borkovitz, Debra K.
2017-01-01
In this paper we present data from one-on-one interviews conducted with students who have taken intermediate and advanced inquiry-based mathematics courses in a program that prepares future preK-8 teachers. Many of these students entered college with a fear of math, but then gained confidence from a required introductory math course and chose to…
DEFF Research Database (Denmark)
Palla, Mirko; Bosco, Filippo Giacomo; Yang, Jaeyoung
2015-01-01
This paper presents the development of a novel statistical method for quantifying trace amounts of biomolecules by surface-enhanced Raman spectroscopy (SERS) using a rigorous, single molecule (SM) theory based mathematical derivation. Our quantification framework could be generalized for planar...
ter Vrugte, Judith; de Jong, Anthonius J.M.; Vandercruysse, Sylke; Wouters, Pieter; van Oostendorp, Herre; Elen, Jan
2015-01-01
The present study addresses the effectiveness of an educational mathematics game for improving proportional reasoning in students from prevocational education. Though in theory game-based learning is promising, research shows that results are ambiguous and that we should look into ways to support
Magee, Paula A.; Flessner, Ryan
2012-01-01
This study examines the effect of promoting inquiry-based teaching (IBT) through collaboration between a science methods course and mathematics methods course in an elementary teacher education program. During the collaboration, preservice elementary teacher (PST) candidates experienced 3 different types of inquiry as a way to foster increased…
Nezhnov, Peter; Kardanova, Elena; Vasilyeva, Marina; Ludlow, Larry
2015-01-01
The present study tested the possibility of operationalizing levels of knowledge acquisition based on Vygotsky's theory of cognitive growth. An assessment tool (SAM-Math) was developed to capture a hypothesized hierarchical structure of mathematical knowledge consisting of procedural, conceptual, and functional levels. In Study 1, SAM-Math was…
Math Path: Encouraging Female Students in Mathematics through Project-Based Learning
Evans, Riley; Friedman, Jane; McGrath, Lynn; Myers, Perla; Ruiz, Amanda
2018-01-01
Although the number of bachelor's degrees in the U.S. awarded to women has gone up, engagement of women in science, technology, engineering, and mathematics (STEM) continues to be low. This paper presents a project-based learning program, informed by education research best practices, designed to provide research experiences to female students…
Exploring the Effects of Project-Based Learning in Secondary Mathematics Education
Holmes, Vicki-Lynn; Hwang, Yooyeun
2016-01-01
This mixed-method, longitudinal study investigated the benefits of project-based learning (PBL) on secondary-mathematics students' academic skill development and motivated strategies for learning (i.e., cognitive, social, and motivational). The focus of this study was academic skill development (algebra- and geometry-assessment scores) and other…
Developing Teaching Materials PISA-Based for Mathematics and Science of Junior High School
Somakim; Suharman, Andi; Madang, Kodri; Taufiq
2016-01-01
This research aims to develop valid and practical teaching materials for mathematics and science lesson PISA-based for junior high school students and to determine potential effects on students in scientific activity. Subjects of this study were students of Junior High School 9 Palembang (SMP Negeri 9 Palembang). The method used in this study is…
Badru, Ademola K.
2016-01-01
The study investigated Problem-based Instructional Strategy and Numerical ability as determinants of Senior Secondary Achievement in Mathematics. This study used 4 x 2 x 2 non-randomised control group Pretest-Posttest Quasi-experimental Factorial design. It consisted of two independent variables (treatment and Numerical ability) and one moderating…
Verschaffel, Lieven; Van Dooren, W.; Star, J.
2017-01-01
This special issue comprises contributions that address the breadth of current lines of recent research from cognitive psychology that appear promising for positively impacting students' learning of mathematics. More specifically, we included contributions (a) that refer to cognitive psychology based principles and techniques, such as explanatory…
Design-Based Research for Professional Learning for "Cultural Mathematics"
Kravia, Geori; Owens, Kay
2014-01-01
Design-based research is being used to develop and refine the principles used in professional learning workshops with teachers from three different Papua New Guinean ecologies: highlands, coastal, and inland in a coastal province. The appropriateness of the design of principles for Papua New Guinean Elementary Schools is tried over several phases…
Parallel interactive data analysis with PROOF
International Nuclear Information System (INIS)
Ballintijn, Maarten; Biskup, Marek; Brun, Rene; Canal, Philippe; Feichtinger, Derek; Ganis, Gerardo; Kickinger, Guenter; Peters, Andreas; Rademakers, Fons
2006-01-01
The Parallel ROOT Facility, PROOF, enables the analysis of much larger data sets on a shorter time scale. It exploits the inherent parallelism in data of uncorrelated events via a multi-tier architecture that optimizes I/O and CPU utilization in heterogeneous clusters with distributed storage. The system provides transparent and interactive access to gigabytes today. Being part of the ROOT framework PROOF inherits the benefits of a performant object storage system and a wealth of statistical and visualization tools. This paper describes the data analysis model of ROOT and the latest developments on closer integration of PROOF into that model and the ROOT user environment, e.g. support for PROOF-based browsing of trees stored remotely, and the popular TTree::Draw() interface. We also outline the ongoing developments aimed to improve the flexibility and user-friendliness of the system
Recent Advances of Malaria Parasites Detection Systems Based on Mathematical Morphology
Directory of Open Access Journals (Sweden)
Andrea Loddo
2018-02-01
Full Text Available Malaria is an epidemic health disease and a rapid, accurate diagnosis is necessary for proper intervention. Generally, pathologists visually examine blood stained slides for malaria diagnosis. Nevertheless, this kind of visual inspection is subjective, error-prone and time-consuming. In order to overcome the issues, numerous methods of automatic malaria diagnosis have been proposed so far. In particular, many researchers have used mathematical morphology as a powerful tool for computer aided malaria detection and classification. Mathematical morphology is not only a theory for the analysis of spatial structures, but also a very powerful technique widely used for image processing purposes and employed successfully in biomedical image analysis, especially in preprocessing and segmentation tasks. Microscopic image analysis and particularly malaria detection and classification can greatly benefit from the use of morphological operators. The aim of this paper is to present a review of recent mathematical morphology based methods for malaria parasite detection and identification in stained blood smears images.
Recent Advances of Malaria Parasites Detection Systems Based on Mathematical Morphology.
Loddo, Andrea; Di Ruberto, Cecilia; Kocher, Michel
2018-02-08
Malaria is an epidemic health disease and a rapid, accurate diagnosis is necessary for proper intervention. Generally, pathologists visually examine blood stained slides for malaria diagnosis. Nevertheless, this kind of visual inspection is subjective, error-prone and time-consuming. In order to overcome the issues, numerous methods of automatic malaria diagnosis have been proposed so far. In particular, many researchers have used mathematical morphology as a powerful tool for computer aided malaria detection and classification. Mathematical morphology is not only a theory for the analysis of spatial structures, but also a very powerful technique widely used for image processing purposes and employed successfully in biomedical image analysis, especially in preprocessing and segmentation tasks. Microscopic image analysis and particularly malaria detection and classification can greatly benefit from the use of morphological operators. The aim of this paper is to present a review of recent mathematical morphology based methods for malaria parasite detection and identification in stained blood smears images.
Munahefi, D. N.; Waluya, S. B.; Rochmad
2018-03-01
The purpose of this research identified the effectiveness of Problem Based Learning (PBL) models based on Self Regulation Leaning (SRL) on the ability of mathematical creative thinking and analyzed the ability of mathematical creative thinking of high school students in solving mathematical problems. The population of this study was students of grade X SMA N 3 Klaten. The research method used in this research was sequential explanatory. Quantitative stages with simple random sampling technique, where two classes were selected randomly as experimental class was taught with the PBL model based on SRL and control class was taught with expository model. The selection of samples at the qualitative stage was non-probability sampling technique in which each selected 3 students were high, medium, and low academic levels. PBL model with SRL approach effectived to students’ mathematical creative thinking ability. The ability of mathematical creative thinking of low academic level students with PBL model approach of SRL were achieving the aspect of fluency and flexibility. Students of academic level were achieving fluency and flexibility aspects well. But the originality of students at the academic level was not yet well structured. Students of high academic level could reach the aspect of originality.
Karlimah
2018-01-01
Many studies suggest that classical music can inccrease the listeners’ intelligence, including mathematical intelligence [3, 12, 2, 11]. In this research, we used the classical music of Baroque era as the backsound during math learning. The research method used was quasi experiment with nonequivalent pretest-posttest control group design to grade V SD students in Tasikmalaya city. The results show that the use of classical music of Baroque era during the learning of mathematics gave a high co...
Indian Academy of Sciences (India)
Home; Journals; Resonance – Journal of Science Education; Volume 12; Issue 5. Gödel's Proof - Incompleteness Theorems. S M Srivastava. General Article Volume 12 Issue 5 May 2007 pp 71-84. Fulltext. Click here to view fulltext PDF. Permanent link: https://www.ias.ac.in/article/fulltext/reso/012/05/0071-0084. Keywords.
Visualizing Probabilistic Proof
Guerra-Pujol, Enrique
2015-01-01
The author revisits the Blue Bus Problem, a famous thought-experiment in law involving probabilistic proof, and presents simple Bayesian solutions to different versions of the blue bus hypothetical. In addition, the author expresses his solutions in standard and visual formats, i.e. in terms of probabilities and natural frequencies.
On the mathematical foundations of mutually unbiased bases
Thas, Koen
2018-02-01
In order to describe a setting to handle Zauner's conjecture on mutually unbiased bases (MUBs) (stating that in C^d, a set of MUBs of the theoretical maximal size d + 1 exists only if d is a prime power), we pose some fundamental questions which naturally arise. Some of these questions have important consequences for the construction theory of (new) sets of maximal MUBs. Partial answers will be provided in particular cases; more specifically, we will analyze MUBs with associated operator groups that have nilpotence class 2, and consider MUBs of height 1. We will also confirm Zauner's conjecture for MUBs with associated finite nilpotent operator groups.
Proof in geometry with "mistakes in geometric proofs"
Fetisov, A I
2006-01-01
This single-volume compilation of 2 books explores the construction of geometric proofs. It offers useful criteria for determining correctness and presents examples of faulty proofs that illustrate common errors. 1963 editions.
Hannah, John; Stewart, Sepideh; Thomas, Michael
2016-01-01
Linear algebra is one of the first abstract mathematics courses that students encounter at university. Research shows that many students find the dense presentation of definitions, theorems and proofs difficult to comprehend. Using a case study approach, we report on a teaching intervention based on Tall's three worlds (embodied, symbolic and…
On Mathematicians' Proof Skimming: A Reply to Inglis and Alcock
Weber, Keith; Mejia-Ramos, Juan Pablo
2013-01-01
n a recent article, Inglis and Alcock (2012) contended that their data challenge the claim that when mathematicians validate proofs, they initially skim a proof to grasp its main idea before reading individual parts of the proof more carefully. This result is based on the fact that when mathematicians read proofs in their study, on average their…
Padula, Janice
2016-01-01
According to the latest news about declining standards in mathematics learning in Australia, boys, and girls, in particular, need to be more engaged in mathematics learning. Only 30% of mathematics students at university level in Australia are female. Proofs are made up of words and mathematical symbols. One can assume the words would assist…
Parametric synthesis of a robust controller on a base of mathematical programming method
Khozhaev, I. V.; Gayvoronskiy, S. A.; Ezangina, T. A.
2018-05-01
Considered paper is dedicated to deriving sufficient conditions, linking root indices of robust control quality with coefficients of interval characteristic polynomial, on the base of mathematical programming method. On the base of these conditions, a method of PI- and PID-controllers, providing aperiodic transient process with acceptable stability degree and, subsequently, acceptable setting time, synthesis was developed. The method was applied to a problem of synthesizing a controller for a depth control system of an unmanned underwater vehicle.
Digital game based learning: A new method in teaching and learning mathematics
Hussain, Sayed Yusoff bin Syed; Hoe, Tan Wee; Idris, Muhammad Zaffwan bin
2017-05-01
Digital game-based learning (DGBL) had been regarded as a sound learning strategy in raising pupils' willingness and interest in many disciplines. Normally, video and digital games are used in the teaching and learning mathematics. based on literature, digital games have proven its capability in making pupils motivated and are more likely to contribute to effective learning mathematics. Hence this research aims to construct a DGBL in the teaching of Mathematics for Year 1 pupils. Then, a quasi-experimental study was carried out in a school located in Gua Musang, Kelantan, involving 39 pupils. Specifically, this article tests the effectiveness of the use of DGBL in the teaching of the topic Addition of Less than 100 on pupil's achievement. This research employed a quasi-experiment, Pre and Post Test of Non-equivalent Control Group design. The data were analysed using the Nonparametric test namely the Mann-Whitney U. The research finding shows the use of the DGBL could increase the pupils' achievement in the topic of Addition of Less than 100. In practice, this research indicates that the DBGL can utilized as an alternative reference strategy for Mathematics teacher.
Directory of Open Access Journals (Sweden)
A.O. Fatade
2014-02-01
Full Text Available The study investigated the effect of problem-based learning (PBL on senior secondary school students' beliefs about Further Mathematics in Nigeria within the blueprint of pre-test-post-test non-equivalent control group quasi-experimental design. Intact classes were used and in all, 96 students participated in the study (42 in the experimental group taught with the PBL and 54 in the control group taught using the Traditional Method (TM. One research instrument tagged Beliefs about Further Mathematics Questionnaire (BFMQ, Cronbach alpha (α=.86 was developed and used for the study and data collected were analysed using the descriptive statistics of mean and standard deviation which served as precursor to testing the null hypothesis for the study using an independent samples t-test and analysis of variance. Results showed that participants held strong beliefs about further mathematics and there was a statistically significant difference in the mean post-treatment scores on BFMQ (t=-6.22, p=.000 for t-test and (F(1,95=38.49; p<.001 for ANOVA between students exposed to the PBL and those exposed to the TM, in favour of the PBL group. Based on the results, the study recommended that PBL should be adopted as an instructional strategy for promoting meaningful learning in and enhancing beliefs about further mathematics and efforts should be made to integrate the philosophy of PBL into the preservice teachers' curriculum at the teacher-preparation institutions in Nigeria.
A proof of Bertrand's postulate
Directory of Open Access Journals (Sweden)
Andrea Asperti
2012-01-01
Full Text Available We discuss the formalization, in the Matita Interactive Theorem Prover, of some results by Chebyshev concerning the distribution of prime numbers, subsuming, as a corollary, Bertrand's postulate.Even if Chebyshev's result has been later superseded by the stronger prime number theorem, his machinery, and in particular the two functions psi and theta still play a central role in the modern development of number theory. The proof makes use of most part of the machinery of elementary arithmetics, and in particular of properties of prime numbers, gcd, products and summations, providing a natural benchmark for assessing the actual development of the arithmetical knowledge base.
Syukriani, Andi; Juniati, Dwi; Siswono, Tatag Yuli Eko
2017-08-01
The purpose of this study was to explore the strategic competence of senior secondary school students in solving mathematics problems. Terdapat dua subjek, satu bergaya kognitif field-independent dan satu bergaya kognitif field-dependent tetapi keduanya memiliki tingkat prestasi belajar matematika yang setara. There were two subjects, one field-independent cognitive style and one field-dependent cognitive style. They had an equivalent high level of mathematics achievement. Keduanya dipilih berdasarkan hasil tes kompetensi matematika dan GEFT (Group Embedded Figures Test). Subjects were selected based on the test results of mathematics competence and GEFT (Group Embedded Figures Test). Kompetensi strategis dapat merangsang perkembangan otonomi dan fleksibilitas dalam diri siswa karena merupakan keterampilan yang sangat dibutuhkan di sepanjang abad 21. Gaya kognitif merupakan kecenderungan siswa dalam mengolah informasi sangat mempengaruhi performance dalam menyelesaikan masalah matematika. Strategic competence can stimulate the development of autonomy and flexibility of students and they are skills which are needed in the 21st century. Cognitive style is the tendency of students in processing informations and it greatly affects the performance in solving mathematics problems. Hasil penelitian menunjukkan bahwa subjek FI cenderung analitis baik pada pembentukan bayangannya maupun pada gambar yang dibuatnya untuk memproses informasi berdasarkan dengan struktur pengetahuannya sendiri (Internally directed). The research result showed that subject FI tended to be analytical both in forming the mental imagination and the picture to process information in accordance with his own knowledge structure (internally directed). Subjek FD kurang analitis dan tidak dapat mengenal bentuk sederhana (konsep matematika) dari bentuk yang kompleks (Exeternally directed) sehingga menerima ide sebagaimana yang disajikan. Subject FD was less analytical and unable to recognize simple form
Performance-based classrooms: A case study of two elementary teachers of mathematics and science
Jones, Kenneth W.
This case study depicts how two elementary teachers develop classrooms devoted to performance-based instruction in mathematics and science. The purpose is to develop empirical evidence of classroom practices that leads to a conceptual framework about the nature of performance-based instruction. Performance-based assessment and instruction are defined from the literature to entail involving students in tasks that are complex and engaging, requiring them to apply knowledge and skills in authentic contexts. In elementary mathematics and science, such an approach emphasizes problem solving, exploration, inquiry, and reasoning. The body of the work examines teacher beliefs, curricular orientations, instructional strategies, assessment approaches, management and organizational skills, and interpersonal relationships. The focus throughout is on those aspects that foster student performance in elementary mathematics and science. The resulting framework describes five characteristics that contribute to performance-based classrooms: a caring classroom community, a connectionist learning theory, a thinking and doing curriculum, diverse opportunities for learning, and ongoing assessment, feedback, and adjustment. The conclusion analyzes factors external to the classroom that support or constrain the development of performance-based classrooms and discusses the implications for educational policy and further research.
International Nuclear Information System (INIS)
Peregrin, Jaroslav
2007-01-01
The usual way of interpreting Goedel's (1931) incompleteness result is as showing that there is a gap between truth and provability, i.e. that we can never prove everything that is true. Moreover, this result is supposed to show that there are unprovable truths which we can know to be true. This, so the story goes, shows that we are more than machines that are restricted to acting as proof systems. Hence our minds are 'not mechanical'
Wijayanti, R.; Waluya, S. B.; Masrukan
2018-03-01
The purpose of this research are (1) to analyze the learning quality of MEAs with MURDER strategy, (2) to analyze students’ mathematical literacy ability based on goal orientation in MEAs learning with MURDER strategy. This research is a mixed method research of concurrent embedded type where qualitative method as the primary method. The data were obtained using the methods of scale, observation, test and interviews. The results showed that (1) MEAs Learning with MURDER strategy on students' mathematical literacy ability is qualified, (2) Students who have mastery goal characteristics are able to master the seven components of mathematical literacy process although there are still two components that the solution is less than the maximum. Students who have performance goal characteristics have not mastered the components of mathematical literacy process with the maximum, they are only able to master the ability of using mathematics tool and the other components of mathematical literacy process is quite good.
A short impossibility proof of quantum bit commitment
Energy Technology Data Exchange (ETDEWEB)
Chiribella, Giulio, E-mail: gchiribella@mail.tsinghua.edu.cn [Center for Quantum Information, Institute for Interdisciplinary Information Sciences, Tsinghua University (China); D' Ariano, Giacomo Mauro, E-mail: dariano@unipv.it [QUIT group, Dipartimento di Fisica, via Bassi 6, 27100 Pavia (Italy); INFN Gruppo IV, Sezione di Pavia, via Bassi, 6, 27100 Pavia (Italy); Perinotti, Paolo, E-mail: paolo.perinotti@unipv.it [QUIT group, Dipartimento di Fisica, via Bassi 6, 27100 Pavia (Italy); INFN Gruppo IV, Sezione di Pavia, via Bassi, 6, 27100 Pavia (Italy); Schlingemann, Dirk, E-mail: d.schlingemann@tu-bs.de [ISI Foundation, Quantum Information Theory Unit, Viale S. Severo 65, 10133 Torino (Italy); Werner, Reinhard, E-mail: Reinhard.Werner@itp.uni-hannover.de [Institut für Theoretische Physik, Leibniz Universität Hannover, Appelstrasse 2, 30167 Hannover (Germany)
2013-06-17
Bit commitment protocols, whose security is based on the laws of quantum mechanics alone, are generally held to be impossible on the basis of a concealment–bindingness tradeoff (Lo and Chau, 1997 [1], Mayers, 1997 [2]). A strengthened and explicit impossibility proof has been given in D'Ariano et al. (2007) [3] in the Heisenberg picture and in a C{sup ⁎}-algebraic framework, considering all conceivable protocols in which both classical and quantum information is exchanged. In the present Letter we provide a new impossibility proof in the Schrödinger picture, greatly simplifying the classification of protocols and strategies using the mathematical formulation in terms of quantum combs (Chiribella et al., 2008 [4]), with each single-party strategy represented by a conditioned comb. We prove that assuming a stronger notion of concealment—for each classical communication history, not in average—allows Alice's cheat to pass also the worst-case Bob's test. The present approach allows us to restate the concealment–bindingness tradeoff in terms of the continuity of dilations of probabilistic quantum combs with the metric given by the comb discriminability-distance.
A short impossibility proof of quantum bit commitment
International Nuclear Information System (INIS)
Chiribella, Giulio; D'Ariano, Giacomo Mauro; Perinotti, Paolo; Schlingemann, Dirk; Werner, Reinhard
2013-01-01
Bit commitment protocols, whose security is based on the laws of quantum mechanics alone, are generally held to be impossible on the basis of a concealment–bindingness tradeoff (Lo and Chau, 1997 [1], Mayers, 1997 [2]). A strengthened and explicit impossibility proof has been given in D'Ariano et al. (2007) [3] in the Heisenberg picture and in a C ⁎ -algebraic framework, considering all conceivable protocols in which both classical and quantum information is exchanged. In the present Letter we provide a new impossibility proof in the Schrödinger picture, greatly simplifying the classification of protocols and strategies using the mathematical formulation in terms of quantum combs (Chiribella et al., 2008 [4]), with each single-party strategy represented by a conditioned comb. We prove that assuming a stronger notion of concealment—for each classical communication history, not in average—allows Alice's cheat to pass also the worst-case Bob's test. The present approach allows us to restate the concealment–bindingness tradeoff in terms of the continuity of dilations of probabilistic quantum combs with the metric given by the comb discriminability-distance.
A simple proof of renormalization group equation in the minimal subtraction scheme
International Nuclear Information System (INIS)
Chetyrkin, K.G.
1989-04-01
We give a simple combinatorial proof of the renormalization group equation in the minimal subtraction scheme. Being mathematically rigorous, the proof avoids both the notorious complexity of techniques using parametric representations of Feynman diagrams and heuristic arguments of usual ''proofs'' calling up bare fields living in the space-time of complex dimension. It also copes easily with the general case of Green functions of arbitrary number of composite fields. (author). 24 refs
McLoughlin, M. Padraig M. M.
2008-01-01
The author of this paper submits the thesis that learning requires doing; only through inquiry is learning achieved, and hence this paper proposes a programme of use of a modified Moore method in a Probability and Mathematical Statistics (PAMS) course sequence to teach students PAMS. Furthermore, the author of this paper opines that set theory…
Energy Technology Data Exchange (ETDEWEB)
Yamamoto, T; Boone, J [University of California Davis School of Medicine, Sacramento, CA (United States); Kent, M; Wisner, E [University of California Davis School of Veterinary Medicine, Davis, CA (United States); Fujita, Y [Tokai University, Isehara (Japan)
2015-06-15
Purpose: Pulmonary perfusion imaging has provided significant insights into pulmonary diseases, and can be useful in radiotherapy. The purpose of this study was to prospectively establish proof-of-principle in a canine model for single-energy CT-based perfusion imaging, which has the potential for widespread clinical implementation. Methods: Single-energy CT perfusion imaging is based on: (1) acquisition of inspiratory breath-hold CT scans before and after intravenous injection of iodinated contrast medium, (2) deformable image registration (DIR) of the two CT image data sets, and (3) subtraction of the pre-contrast image from post-contrast image, yielding a map of Hounsfield unit (HU) enhancement. These subtraction image data sets hypothetically represent perfused blood volume, a surrogate for perfusion. In an IACUC-approved clinical trial, we acquired pre- and post-contrast CT scans in the prone posture for six anesthetized, mechanically-ventilated dogs. The elastix algorithm was used for DIR. The registration accuracy was quantified using the target registration errors (TREs) for 50 pulmonary landmarks in each dog. The gradient of HU enhancement between gravity-dependent (ventral) and non-dependent (dorsal) regions was evaluated to quantify the known effect of gravity, i.e., greater perfusion in ventral regions. Results: The lung volume difference between the two scans was 4.3±3.5% on average (range 0.3%–10.1%). DIR demonstrated an average TRE of 0.7±1.0 mm. HU enhancement in lung parenchyma was 34±10 HU on average and varied considerably between individual dogs, indicating the need for improvement of the contrast injection protocol. HU enhancement in ventral (gravity-dependent) regions was found to be greater than in dorsal regions. A population average ventral-to-dorsal gradient of HU enhancement was strong (R{sup 2}=0.94) and statistically significant (p<0.01). Conclusion: This canine study demonstrated relatively accurate DIR and a strong ventral
International Nuclear Information System (INIS)
Yamamoto, T; Boone, J; Kent, M; Wisner, E; Fujita, Y
2015-01-01
Purpose: Pulmonary perfusion imaging has provided significant insights into pulmonary diseases, and can be useful in radiotherapy. The purpose of this study was to prospectively establish proof-of-principle in a canine model for single-energy CT-based perfusion imaging, which has the potential for widespread clinical implementation. Methods: Single-energy CT perfusion imaging is based on: (1) acquisition of inspiratory breath-hold CT scans before and after intravenous injection of iodinated contrast medium, (2) deformable image registration (DIR) of the two CT image data sets, and (3) subtraction of the pre-contrast image from post-contrast image, yielding a map of Hounsfield unit (HU) enhancement. These subtraction image data sets hypothetically represent perfused blood volume, a surrogate for perfusion. In an IACUC-approved clinical trial, we acquired pre- and post-contrast CT scans in the prone posture for six anesthetized, mechanically-ventilated dogs. The elastix algorithm was used for DIR. The registration accuracy was quantified using the target registration errors (TREs) for 50 pulmonary landmarks in each dog. The gradient of HU enhancement between gravity-dependent (ventral) and non-dependent (dorsal) regions was evaluated to quantify the known effect of gravity, i.e., greater perfusion in ventral regions. Results: The lung volume difference between the two scans was 4.3±3.5% on average (range 0.3%–10.1%). DIR demonstrated an average TRE of 0.7±1.0 mm. HU enhancement in lung parenchyma was 34±10 HU on average and varied considerably between individual dogs, indicating the need for improvement of the contrast injection protocol. HU enhancement in ventral (gravity-dependent) regions was found to be greater than in dorsal regions. A population average ventral-to-dorsal gradient of HU enhancement was strong (R"2=0.94) and statistically significant (p<0.01). Conclusion: This canine study demonstrated relatively accurate DIR and a strong ventral
Winkelman, James W; Tanasijevic, Milenko J; Zahniser, David J
2017-08-01
- A novel automated slide-based approach to the complete blood count and white blood cell differential count is introduced. - To present proof of concept for an image-based approach to complete blood count, based on a new slide preparation technique. A preliminary data comparison with the current flow-based technology is shown. - A prototype instrument uses a proprietary method and technology to deposit a precise volume of undiluted peripheral whole blood in a monolayer onto a glass microscope slide so that every cell can be distinguished, counted, and imaged. The slide is stained, and then multispectral image analysis is used to measure the complete blood count parameters. Images from a 600-cell white blood cell differential count, as well as 5000 red blood cells and a variable number of platelets, that are present in 600 high-power fields are made available for a technologist to view on a computer screen. An initial comparison of the basic complete blood count parameters was performed, comparing 1857 specimens on both the new instrument and a flow-based hematology analyzer. - Excellent correlations were obtained between the prototype instrument and a flow-based system. The primary parameters of white blood cell, red blood cell, and platelet counts resulted in correlation coefficients (r) of 0.99, 0.99, and 0.98, respectively. Other indices included hemoglobin (r = 0.99), hematocrit (r = 0.99), mean cellular volume (r = 0.90), mean corpuscular hemoglobin (r = 0.97), and mean platelet volume (r = 0.87). For the automated white blood cell differential counts, r values were calculated for neutrophils (r = 0.98), lymphocytes (r = 0.97), monocytes (r = 0.76), eosinophils (r = 0.96), and basophils (r = 0.63). - Quantitative results for components of the complete blood count and automated white blood cell differential count can be developed by image analysis of a monolayer preparation of a known volume of peripheral blood.
Zhao, Hui; Wei, Jingxuan
2014-09-01
The key to the concept of tunable wavefront coding lies in detachable phase masks. Ojeda-Castaneda et al. (Progress in Electronics Research Symposium Proceedings, Cambridge, USA, July 5-8, 2010) described a typical design in which two components with cosinusoidal phase variation operate together to make defocus sensitivity tunable. The present study proposes an improved design and makes three contributions: (1) A mathematical derivation based on the stationary phase method explains why the detachable phase mask of Ojeda-Castaneda et al. tunes the defocus sensitivity. (2) The mathematical derivations show that the effective bandwidth wavefront coded imaging system is also tunable by making each component of the detachable phase mask move asymmetrically. An improved Fisher information-based optimization procedure was also designed to ascertain the optimal mask parameters corresponding to specific bandwidth. (3) Possible applications of the tunable bandwidth are demonstrated by simulated imaging.
Practical mathematical optimization basic optimization theory and gradient-based algorithms
Snyman, Jan A
2018-01-01
This textbook presents a wide range of tools for a course in mathematical optimization for upper undergraduate and graduate students in mathematics, engineering, computer science, and other applied sciences. Basic optimization principles are presented with emphasis on gradient-based numerical optimization strategies and algorithms for solving both smooth and noisy discontinuous optimization problems. Attention is also paid to the difficulties of expense of function evaluations and the existence of multiple minima that often unnecessarily inhibit the use of gradient-based methods. This second edition addresses further advancements of gradient-only optimization strategies to handle discontinuities in objective functions. New chapters discuss the construction of surrogate models as well as new gradient-only solution strategies and numerical optimization using Python. A special Python module is electronically available (via springerlink) that makes the new algorithms featured in the text easily accessible and dir...
Guerrero, Shannon; Dugdale, Sharon
2009-01-01
The past few decades have seen middle school teachers in the United States hit especially hard by contradictory messages about the use and importance of technology in support of their standards-based mathematics teaching. This paper considers this dichotomy with respect to the California Mathematics Education Technology Site (CMETS), a…
Mudrich, Rachel Marie
2017-01-01
The purpose of this research study was to determine if project-based learning activities (PBLA) incorporated into an eighth-grade mathematics classroom have an effect on students' academic achievement and motivation toward learning. The control group used the traditional instruction method to cover mathematic objective skills that are Common Core…
2015-08-03
AND SUBTITLE Mobile STEMship Discovery Center: K-12 Aerospace-Based Science, Technology, Engineering, and Mathematics (STEM) Mobile Teaching Vehicle...Center program to be able to expose Science Technology, Engineering and Mathematics (STEM) space-inspired science centers for DC Metro beltway schools
Directory of Open Access Journals (Sweden)
Volodymyr Valentynovych Tkach
2012-07-01
Full Text Available The electroanalytic process of the detection of biosubstances, realized by the biosensor, based in conducting polyheterocyclic compounds, the function of which contained autocatalytic stage, was mathematically described. The correspondent mathematical model was analyzed by linear stability theory and bifurcational analysis. The electrochemical instabilities, capable to succeed in this process, were explained in the terms of this model.
Widyatiningtyas, Reviandari; Kusumah, Yaya S.; Sumarmo, Utari; Sabandar, Jozua
2015-01-01
The study reported the findings of an only post-test control group research design and aims to analyze the influence of problem-based learning approach, school level, and students' prior mathematical ability to student's mathematics critical thinking ability. The research subjects were 140 grade ten senior high school students coming from…
Zetriuslita; Wahyudin; Jarnawi
2017-01-01
This research aims to describe and analyze result of applying Problem-Based Learning and Cognitive Conflict Strategy (PBLCCS) in increasing students' Mathematical Critical Thinking (MCT) ability and Mathematical Curiosity Attitude (MCA). Adopting a quasi-experimental method with pretest-posttest control group design and using mixed method with…
Darma, I. K.
2018-01-01
This research is aimed at determining: 1) the differences of mathematical problem solving ability between the students facilitated with problem-based learning model and conventional learning model, 2) the differences of mathematical problem solving ability between the students facilitated with authentic and conventional assessment model, and 3) interaction effect between learning and assessment model on mathematical problem solving. The research was conducted in Bali State Polytechnic, using the 2x2 experiment factorial design. The samples of this research were 110 students. The data were collected using a theoretically and empirically-validated test. Instruments were validated by using Aiken’s approach of technique content validity and item analysis, and then analyzed using anova stylistic. The result of the analysis shows that the students facilitated with problem-based learning and authentic assessment models get the highest score average compared to the other students, both in the concept understanding and mathematical problem solving. The result of hypothesis test shows that, significantly: 1) there is difference of mathematical problem solving ability between the students facilitated with problem-based learning model and conventional learning model, 2) there is difference of mathematical problem solving ability between the students facilitated with authentic assessment model and conventional assessment model, and 3) there is interaction effect between learning model and assessment model on mathematical problem solving. In order to improve the effectiveness of mathematics learning, collaboration between problem-based learning model and authentic assessment model can be considered as one of learning models in class.
Normal Forms for Fuzzy Logics: A Proof-Theoretic Approach
Czech Academy of Sciences Publication Activity Database
Cintula, Petr; Metcalfe, G.
2007-01-01
Roč. 46, č. 5-6 (2007), s. 347-363 ISSN 1432-0665 R&D Projects: GA MŠk(CZ) 1M0545 Institutional research plan: CEZ:AV0Z10300504 Keywords : fuzzy logic * normal form * proof theory * hypersequents Subject RIV: BA - General Mathematics Impact factor: 0.620, year: 2007
Ontological Proofs of Existence and Non-Existence
Czech Academy of Sciences Publication Activity Database
Hájek, Petr
2008-01-01
Roč. 90, č. 2 (2008), s. 257-262 ISSN 0039-3215 R&D Projects: GA AV ČR IAA100300503 Institutional research plan: CEZ:AV0Z10300504 Keywords : ontological proofs * existence * non-existence * Gödel * Caramuel Subject RIV: BA - General Mathematics
Why and How Mathematicians Read Proofs: An Exploratory Study
Weber, Keith; Mejia-Ramos, Juan Pablo
2011-01-01
In this paper, we report a study in which nine research mathematicians were interviewed with regard to the goals guiding their reading of published proofs and the type of reasoning they use to reach these goals. Using the data from this study as well as data from a separate study (Weber, "Journal for Research in Mathematics Education" 39:431-459,…
The Role of Proof in Comprehending and Teaching Elementary Linear Algebra.
Uhlig, Frank
2002-01-01
Describes how elementary linear algebra can be taught successfully while introducing students to the concept and practice of mathematical proof. Suggests exploring the concept of solvability of linear systems first via the row echelon form (REF). (Author/KHR)
García, S.J.; Fischer, H.R.; White, P.A.; Mardel, J.; González-García, Y.; Mol, J.M.C.; Hughes, A.E.
2011-01-01
In this paper a self-healing anticorrosive organic coating based on an encapsulated water reactive organic agent is presented. A reactive silyl ester is proposed as a new organic reactive healing agent and its synthesis, performance, incorporation into an organic coating and evaluation of
Mathematical Modelling of Optimization of Structures of Monolithic Coverings Based on Liquid Rubbers
Turgumbayeva, R. Kh; Abdikarimov, M. N.; Mussabekov, R.; Sartayev, D. T.
2018-05-01
The paper considers optimization of monolithic coatings compositions using a computer and MPE methods. The goal of the paper was to construct a mathematical model of the complete factorial experiment taking into account its plan and conditions. Several regression equations were received. Dependence between content components and parameters of rubber, as well as the quantity of a rubber crumb, was considered. An optimal composition for manufacturing the material of monolithic coatings compositions was recommended based on experimental data.
The human body metabolism process mathematical simulation based on Lotka-Volterra model
Oliynyk, Andriy; Oliynyk, Eugene; Pyptiuk, Olexandr; DzierŻak, RóŻa; Szatkowska, Małgorzata; Uvaysova, Svetlana; Kozbekova, Ainur
2017-08-01
The mathematical model of metabolism process in human organism based on Lotka-Volterra model has beeng proposed, considering healing regime, nutrition system, features of insulin and sugar fragmentation process in the organism. The numerical algorithm of the model using IV-order Runge-Kutta method has been realized. After the result of calculations the conclusions have been made, recommendations about using the modeling results have been showed, the vectors of the following researches are defined.
Bridging the Gap: A Design-based Case Study of a Mathematics Skills Intervention Program
Safaralian, Leila
2017-01-01
Abstract of the DissertationBridge the Gap: A Design-based Case Study of a Mathematics Skills Intervention ProgrambyLeila SafaralianDoctor of Education in Educational LeadershipUniversity of California, San Diego, 2017California State University, San Marcos, 2017Kenneth P. Gonzalez, ChairMany students aspire to continue their educational journey, but far too many enter college without the basic content knowledge, skills, or habits of mind needed to succeed. Research on college readiness indic...
The Logical Heart of a Classic Proof Revisited: A Guide to Godel's "Incompleteness" Theorems
Padula, Janice
2011-01-01
The study of Kurt Godel's proof of the "incompleteness" of a formal system such as "Principia Mathematica" is a great way to stimulate students' thinking and creative processes and interest in mathematics and its important developments. This article describes salient features of the proof together with ways to deal with potential difficulties for…
Proof and Proving: Logic, Impasses, and the Relationship to Problem Solving
Savic, Milos
2012-01-01
Becoming a skillful prover is critical for success in advanced undergraduate and graduate mathematics courses. In this dissertation, I report my investigations of proof and the proving process in three separate studies. In the first study, I examined the amount of logic used in student-constructed proofs to help in the design of…
Murray, James D
1993-01-01
The book is a textbook (with many exercises) giving an in-depth account of the practical use of mathematical modelling in the biomedical sciences. The mathematical level required is generally not high and the emphasis is on what is required to solve the real biological problem. The subject matter is drawn, e.g. from population biology, reaction kinetics, biological oscillators and switches, Belousov-Zhabotinskii reaction, reaction-diffusion theory, biological wave phenomena, central pattern generators, neural models, spread of epidemics, mechanochemical theory of biological pattern formation and importance in evolution. Most of the models are based on real biological problems and the predictions and explanations offered as a direct result of mathematical analysis of the models are important aspects of the book. The aim is to provide a thorough training in practical mathematical biology and to show how exciting and novel mathematical challenges arise from a genuine interdisciplinary involvement with the biosci...
Ma'rufi, Budayasa, I. Ketut; Juniati, Dwi
2017-08-01
The aim of this study was to describe the analysis of mathematics teachers' learning on algebra function limit material based on teaching experience difference. The purpose of this study is to describe the analysis of mathematics teacher's learning on limit algebraic functions in terms of the differences of teaching experience. Learning analysis focused on Pedagogical Content Knowledge (PCK) of teachers in mathematics on limit algebraic functions related to the knowledge of pedagogy. PCK of teachers on limit algebraic function is a type of specialized knowledge for teachers on how to teach limit algebraic function that can be understood by students. Subjects are two high school mathematics teacher who has difference of teaching experience they are one Novice Teacher (NP) and one Experienced Teacher (ET). Data are collected through observation of learning in the class, videos of learning, and then analyzed using qualitative analysis. Teacher's knowledge of Pedagogic defined as a knowledge and understanding of teacher about planning and organizing of learning, and application of learning strategy. The research results showed that the Knowledge of Pedagogy on subject NT in mathematics learning on the material of limit function algebra showed that the subject NT tended to describe procedurally, without explaining the reasons why such steps were used, asking questions which tended to be monotonous not be guiding and digging deeper, and less varied in the use of learning strategies while subject ET gave limited guidance and opportunities to the students to find their own answers, exploit the potential of students to answer questions, provide an opportunity for students to interact and work in groups, and subject ET tended to combine conceptual and procedural explanation.
Directory of Open Access Journals (Sweden)
Annabelle Ballesta
2011-09-01
Full Text Available Circadian timing largely modifies efficacy and toxicity of many anticancer drugs. Recent findings suggest that optimal circadian delivery patterns depend on the patient genetic background. We present here a combined experimental and mathematical approach for the design of chronomodulated administration schedules tailored to the patient molecular profile. As a proof of concept we optimized exposure of Caco-2 colon cancer cells to irinotecan (CPT11, a cytotoxic drug approved for the treatment of colorectal cancer. CPT11 was bioactivated into SN38 and its efflux was mediated by ATP-Binding-Cassette (ABC transporters in Caco-2 cells. After cell synchronization with a serum shock defining Circadian Time (CT 0, circadian rhythms with a period of 26 h 50 (SD 63 min were observed in the mRNA expression of clock genes REV-ERBα, PER2, BMAL1, the drug target topoisomerase 1 (TOP1, the activation enzyme carboxylesterase 2 (CES2, the deactivation enzyme UDP-glucuronosyltransferase 1, polypeptide A1 (UGT1A1, and efflux transporters ABCB1, ABCC1, ABCC2 and ABCG2. DNA-bound TOP1 protein amount in presence of CPT11, a marker of the drug PD, also displayed circadian variations. A mathematical model of CPT11 molecular pharmacokinetics-pharmacodynamics (PK-PD was designed and fitted to experimental data. It predicted that CPT11 bioactivation was the main determinant of CPT11 PD circadian rhythm. We then adopted the therapeutics strategy of maximizing efficacy in non-synchronized cells, considered as cancer cells, under a constraint of maximum toxicity in synchronized cells, representing healthy ones. We considered exposure schemes in the form of an initial concentration of CPT11 given at a particular CT, over a duration ranging from 1 to 27 h. For any dose of CPT11, optimal exposure durations varied from 3h40 to 7h10. Optimal schemes started between CT2h10 and CT2h30, a time interval corresponding to 1h30 to 1h50 before the nadir of CPT11 bioactivation rhythm in
Laursen, Sandra L.; Hassi, Marja-Liisa; Hough, Sarah
2016-02-01
This mixed-methods study describes classroom characteristics and student outcomes from university mathematics courses that are based in mathematics departments, targeted to future pre-tertiary teachers, and taught with inquiry-based learning (IBL) approaches. The study focused on three two-term sequences taught at two research universities, separately targeting elementary and secondary pre-service teachers. Classroom observation established that the courses were taught with student-centred methods that were comparable to those used in IBL courses for students in mathematics-intensive fields at the same institutions. To measure pre-service teachers' gains in mathematical knowledge for teaching, we administered the Learning Mathematics for Teaching (LMT) instrument developed by Hill, Ball and Schilling for in-service teacher professional development. Results from the LMT show that pre-service teachers made significant score gains from beginning to end of their course, while data from interviews and from surveys of learning gains show that pre-service teachers viewed their gains as relevant to their future teaching work. Measured changes on pre-/post-surveys of attitudes and beliefs were generally supportive of learning mathematics but modest in magnitude. The study is distinctive in applying the LMT to document pre-service teachers' growth in mathematical knowledge for teaching. The study also suggests IBL is an approach well suited to mathematics departments seeking to strengthen their pre-service teacher preparation offerings in ways consistent with research-based recommendations.
Evans, M. E.; Merow, C.; Record, S.; Menlove, J.; Gray, A.; Cundiff, J.; McMahon, S.; Enquist, B. J.
2013-12-01
Current attempts to forecast how species' distributions will change in response to climate change suffer under a fundamental trade-off: between modeling many species superficially vs. few species in detail (between correlative vs. mechanistic models). The goals of this talk are two-fold: first, we present a Bayesian multilevel modeling framework, dynamic range modeling (DRM), for building process-based forecasts of many species' distributions at a time, designed to address the trade-off between detail and number of distribution forecasts. In contrast to 'species distribution modeling' or 'niche modeling', which uses only species' occurrence data and environmental data, DRMs draw upon demographic data, abundance data, trait data, occurrence data, and GIS layers of climate in a single framework to account for two processes known to influence range dynamics - demography and dispersal. The vision is to use extensive databases on plant demography, distributions, and traits - in the Botanical Information and Ecology Network, the Forest Inventory and Analysis database (FIA), and the International Tree Ring Data Bank - to develop DRMs for North American trees. Second, we present preliminary results from building the core submodel of a DRM - an integral projection model (IPM) - for a sample of dominant tree species in western North America. IPMs are used to infer demographic niches - i.e., the set of environmental conditions under which population growth rate is positive - and project population dynamics through time. Based on >550,000 data points derived from FIA for nine tree species in western North America, we show IPM-based models of their current and future distributions, and discuss how IPMs can be used to forecast future forest productivity, mortality patterns, and inform efforts at assisted migration.
Pluralism in mathematics a new position in philosophy of mathematics
Friend, Michèle
2014-01-01
This book is about philosophy, mathematics and logic, giving a philosophical account of Pluralism which is a family of positions in the philosophy of mathematics. There are four parts to this book, beginning with a look at motivations for Pluralism by way of Realism, Maddy's Naturalism, Shapiro's Structuralism and Formalism. In the second part of this book the author covers: the philosophical presentation of Pluralism; using a formal theory of logic metaphorically; rigour and proof for the Pluralist; and mathematical fixtures. In the third part the author goes on to focus on the transcendental presentation of Pluralism, and in part four looks at applications of Pluralism, such as a Pluralist approach to proof in mathematics and how Pluralism works in regard to together-inconsistent philosophies of mathematics. The book finishes with suggestions for further Pluralist enquiry. In this work the author takes a deeply radical approach in developing a new position that will either convert readers, or act as a stron...
International Nuclear Information System (INIS)
Qiu, R.; Li, J.; Zhang, Z.; Liu, L.; Bi, L.; Ren, L.
2009-01-01
A set of conversion coefficients from kerma free-in-air to the organ-absorbed dose are presented for external monoenergetic photon beams from 10 keV to 10 MeV based on the Chinese mathematical phantom, a whole-body mathematical phantom model. The model was developed based on the methods of the Oak Ridge National Laboratory mathematical phantom series and data from the Chinese Reference Man and the Reference Asian Man. This work is carried out to obtain the conversion coefficients based on this model, which represents the characteristics of the Chinese population, as the anatomical parameters of the Chinese are different from those of Caucasians. Monte Carlo simulation with MCNP code is carried out to calculate the organ dose conversion coefficients. Before the calculation, the effects from the physics model and tally type are investigated, considering both the calculation efficiency and precision. In the calculation irradiation conditions include anterior-posterior, posterior-anterior, right lateral, left lateral, rotational and isotropic geometries. Conversion coefficients from this study are compared with those recommended in the Publication 74 of International Commission on Radiological Protection (ICRP74) since both the sets of data are calculated with mathematical phantoms. Overall, consistency between the two sets of data is observed and the difference for more than 60% of the data is below 10%. However, significant deviations are also found, mainly for the superficial organs (up to 65.9%) and bone surface (up to 66%). The big difference of the dose conversion coefficients for the superficial organs at high photon energy could be ascribed to kerma approximation for the data in ICRP74. Both anatomical variations between races and the calculation method contribute to the difference of the data for bone surface. (authors)
Qiu, Rui; Li, Junli; Zhang, Zhan; Liu, Liye; Bi, Lei; Ren, Li
2009-02-01
A set of conversion coefficients from kerma free-in-air to the organ-absorbed dose are presented for external monoenergetic photon beams from 10 keV to 10 MeV based on the Chinese mathematical phantom, a whole-body mathematical phantom model. The model was developed based on the methods of the Oak Ridge National Laboratory mathematical phantom series and data from the Chinese Reference Man and the Reference Asian Man. This work is carried out to obtain the conversion coefficients based on this model, which represents the characteristics of the Chinese population, as the anatomical parameters of the Chinese are different from those of Caucasians. Monte Carlo simulation with MCNP code is carried out to calculate the organ dose conversion coefficients. Before the calculation, the effects from the physics model and tally type are investigated, considering both the calculation efficiency and precision. In the calculation irradiation conditions include anterior-posterior, posterior-anterior, right lateral, left lateral, rotational and isotropic geometries. Conversion coefficients from this study are compared with those recommended in the Publication 74 of International Commission on Radiological Protection (ICRP74) since both the sets of data are calculated with mathematical phantoms. Overall, consistency between the two sets of data is observed and the difference for more than 60% of the data is below 10%. However, significant deviations are also found, mainly for the superficial organs (up to 65.9%) and bone surface (up to 66%). The big difference of the dose conversion coefficients for the superficial organs at high photon energy could be ascribed to kerma approximation for the data in ICRP74. Both anatomical variations between races and the calculation method contribute to the difference of the data for bone surface.
Leduc, Nicolas; Atallah, Vincent; Escarmant, Patrick; Vinh-Hung, Vincent
2016-09-08
Monitoring and controlling respiratory motion is a challenge for the accuracy and safety of therapeutic irradiation of thoracic tumors. Various commercial systems based on the monitoring of internal or external surrogates have been developed but remain costly. In this article we describe and validate Madibreast, an in-house-made respiratory monitoring and processing device based on optical tracking of external markers. We designed an optical apparatus to ensure real-time submillimetric image resolution at 4 m. Using OpenCv libraries, we optically tracked high-contrast markers set on patients' breasts. Validation of spatial and time accuracy was performed on a mechanical phantom and on human breast. Madibreast was able to track motion of markers up to a 5 cm/s speed, at a frame rate of 30 fps, with submillimetric accuracy on mechanical phantom and human breasts. Latency was below 100 ms. Concomitant monitoring of three different locations on the breast showed discrepancies in axial motion up to 4 mm for deep-breathing patterns. This low-cost, computer-vision system for real-time motion monitoring of the irradiation of breast cancer patients showed submillimetric accuracy and acceptable latency. It allowed the authors to highlight differences in surface motion that may be correlated to tumor motion.v. © 2016 The Authors.
Wehage, Kristopher; Chenhansa, Panan; Schoenung, Julie M
2017-01-01
GreenScreen® for Safer Chemicals is a framework for comparative chemical hazard assessment. It is the first transparent, open and publicly accessible framework of its kind, allowing manufacturers and governmental agencies to make informed decisions about the chemicals and substances used in consumer products and buildings. In the GreenScreen® benchmarking process, chemical hazards are assessed and classified based on 18 hazard endpoints from up to 30 different sources. The result is a simple numerical benchmark score and accompanying assessment report that allows users to flag chemicals of concern and identify safer alternatives. Although the screening process is straightforward, aggregating and sorting hazard data is tedious, time-consuming, and prone to human error. In light of these challenges, the present work demonstrates the usage of automation to cull chemical hazard data from publicly available internet resources, assign metadata, and perform a GreenScreen® hazard assessment using the GreenScreen® "List Translator." The automated technique, written as a module in the Python programming language, generates GreenScreen® List Translation data for over 3000 chemicals in approximately 30 s. Discussion of the potential benefits and limitations of automated techniques is provided. By embedding the library into a web-based graphical user interface, the extensibility of the library is demonstrated. The accompanying source code is made available to the hazard assessment community. Integr Environ Assess Manag 2017;13:167-176. © 2016 SETAC. © 2016 SETAC.
Stell, F M; Roe, R M; Arellano, C; Kennedy, L; Thornton, H; Saavedra-Rodriguez, K; Wesson, D M; Black, W C; Apperson, C S
2013-09-01
Aedes aegypti L. (Stegomyia aegypti) (Diptera: Culicidae) is the principal vector of dengue and yellow fever viruses in tropical and subtropical regions of the world. Disease management is largely based on mosquito control achieved by insecticides applied to interior resting surfaces and through space sprays. Population monitoring to detect insecticide resistance is a significant component of integrated disease management programmes. We developed a bioassay method for assessing insecticide susceptibility based on the feeding activity of mosquitoes on plant sugars. Our prototype sugar-insecticide feeding bioassay system was composed of inexpensive, disposable components, contained minimal volumes of insecticide, and was compact and highly transportable. Individual mosquitoes were assayed in a plastic cup that contained a sucrose-permethrin solution. Trypan blue dye was added to create a visual marker in the mosquito's abdomen for ingested sucrose-permethrin solution. Blue faecal spots provided further evidence of solution ingestion. With the sugar-insecticide feeding bioassay, the permethrin susceptibility of Ae. aegypti females from two field-collected strains was characterized by probit analysis of dosage-response data. The field strains were also tested by forced contact of females with permethrin residues on filter paper. Dosage-response patterns were similar, indicating that the sugar-insecticide feeding bioassay had appropriately characterized the permethrin susceptibility of the two strains. © 2012 The Royal Entomological Society.
Orubu, Samuel E F; Hobson, Nicholas J; Basit, Abdul W; Tuleu, Catherine
2017-04-01
Dispersible tablets are proposed by the World Health Organization as the preferred paediatric formulation. It was hypothesised that tablets made from a powdered milk-base that disperse in water to form suspensions resembling milk might be a useful platform to improve acceptability in children. Milk-based dispersible tablets containing various types of powdered milk and infant formulae were formulated. The influence of milk type and content on placebo tablet properties was investigated using a design-of-experiments approach. Responses measured included friability, crushing strength and disintegration time. Additionally, the influence of compression force on the tablet properties of a model formulation was studied by compaction simulation. Disintegration times increased as milk content increased. Compaction simulation studies showed that compression force influenced disintegration time. These results suggest that the milk content, rather than type, and compression force were the most important determinants of disintegration. Up to 30% milk could be incorporated to produce 200 mg 10-mm flat-faced placebo tablets by direct compression disintegrating within 3 min in 5-10 ml of water, which is a realistic administration volume in children. The platform could accommodate 30% of a model active pharmaceutical ingredient (caffeine citrate). © 2016 Royal Pharmaceutical Society.
Another proof of Gell-Mann and Low's theorem
Molinari, Luca Guido
2006-01-01
The theorem by Gell-Mann and Low is a cornerstone in QFT and zero-temperature many-body theory. The standard proof is based on Dyson's time-ordered expansion of the propagator; a proof based on exact identities for the time-propagator is here given.
Another proof of Gell-Mann and Low's theorem
International Nuclear Information System (INIS)
Molinari, Luca Guido
2007-01-01
The theorem by Gell-Mann and Low is a cornerstone in quantum field theory and zero-temperature many-body theory. The standard proof is based on Dyson's time-ordered expansion of the propagator; a proof based on exact identities for the time propagator is here given
de Gunzburg, Jean; Ducher, Annie; Modess, Christiane; Wegner, Danilo; Oswald, Stefan; Dressman, Jennifer; Augustin, Violaine; Feger, Céline; Andremont, Antoine; Weitschies, Werner; Siegmund, Werner
2015-01-01
During antibiotic treatments, active residuals reaching the colon profoundly affect the bacterial flora resulting in the emergence of resistance. To prevent these effects, we developed an enteric-coated formulated activated-charcoal based product, DAV132, meant to deliver its adsorbent to the ileum and neutralize antibiotic residues in the proximal colon. In a randomized, control, crossover study, the plasma pharmacokinetics of the probe drugs amoxicillin (500 mg) absorbed in the proximal intestine, and sulfapyridine (25 mg) metabolized from sulfasalazine in the cecum and rapidly absorbed, were compared after a single administration in 18 healthy subjects who had received DAV132, uncoated formulated activated charcoal (FAC) or water 16 and 8 hours before, concomitantly with the probe drugs, and 8 hours thereafter. The AUC0-96 h of amoxicillin was reduced by more than 70% when it was taken with FAC, but bioequivalent when it was taken with water or DAV132. By contrast, the AUC0-96 h of sulfapyridine was reduced by more than 90% when administered with either FAC or DAV132 in comparison with water. The results show that DAV132 can selectively adsorb drug compounds in the proximal colon, without interfering with drug absorption in the proximal small intestine, thereby constituting a proof of concept that DAV132 actually functions in humans. © 2014, The American College of Clinical Pharmacology.
Zetriuslita Zetriuslita; Wahyudin Wahyudin; Jarnawi Afgani Dahlan
2018-01-01
This research aims to find out the association amongMathematical Critical Thinking (MCT) ability, Mathematical Communication, and Mathematical Curiosity Attitude (MCA) as the impact of applying Problem-Based Learning Cognitive Conflict Strategy(PBLCCS) in Number Theory course. The research method is correlative study. The instruments include a test for mathematical critical thinking skill and communication, and questionnaire to obtain the scores of mathematical curiosity attitude. The finding...
Madsen, Jens Koed; Pilditch, Toby D
2018-01-01
In political campaigns, perceived candidate credibility influences the persuasiveness of messages. In campaigns aiming to influence people's beliefs, micro-targeted campaigns (MTCs) that target specific voters using their psychological profile have become increasingly prevalent. It remains open how effective MTCs are, notably in comparison to population-targeted campaign strategies. Using an agent-based model, the paper applies recent insights from cognitive models of persuasion, extending them to the societal level in a novel framework for exploring political campaigning. The paper provides an initial treatment of the complex dynamics of population level political campaigning in a psychologically informed manner. Model simulations show that MTCs can take advantage of the psychology of the electorate by targeting voters favourable disposed towards the candidate. Relative to broad campaigning, MTCs allow for efficient and adaptive management of complex campaigns. Findings show that disliked MTC candidates can beat liked population-targeting candidates, pointing to societal questions concerning campaign regulations.
Naraghi, Safa; Mutsvangwa, Tinashe; Goliath, René; Rangaka, Molebogeng X; Douglas, Tania S
2018-05-08
The tuberculin skin test is the most widely used method for detecting latent tuberculosis infection in adults and active tuberculosis in children. We present the development of a mobile-phone based screening tool for measuring the tuberculin skin test induration. The tool makes use of a mobile application developed on the Android platform to capture images of an induration, and photogrammetric reconstruction using Agisoft PhotoScan to reconstruct the induration in 3D, followed by 3D measurement of the induration with the aid of functions from the Python programming language. The system enables capture of images by the person being screened for latent tuberculosis infection. Measurement precision was tested using a 3D printed induration. Real-world use of the tool was simulated by application to a set of mock skin indurations, created by a make-up artist, and the performance of the tool was evaluated. The usability of the application was assessed with the aid of a questionnaire completed by participants. The tool was found to measure the 3D printed induration with greater precision than the current ruler and pen method, as indicated by the lower standard deviation produced (0.3 mm versus 1.1 mm in the literature). There was high correlation between manual and algorithm measurement of mock skin indurations. The height of the skin induration and the definition of its margins were found to influence the accuracy of 3D reconstruction and therefore the measurement error, under simulated real-world conditions. Based on assessment of the user experience in capturing images, a simplified user interface would benefit wide-spread implementation. The mobile application shows good agreement with direct measurement. It provides an alternative method for measuring tuberculin skin test indurations and may remove the need for an in-person follow-up visit after test administration, thus improving latent tuberculosis infection screening throughput. Copyright © 2018 Elsevier Ltd
Designing of Holistic Mathematic Education Model Based-"System Among" at Low Grade Elementary School
Hayati, R.; Fauzan, A.; Iswari, M.; Khaidir, A.
2018-04-01
The purpose of this study was to develop a model of Holistic Mathematics Education (HME) among systems based on low-grade primary school students so that students have a solid foundation when entering a higher behavior. This type of research is desaign research developed by Plomp to have three stages, namely the preliminary research, development or prototyping phase, and assessement Phase. This research resulted in a model Holistic Mathematics Education (HME) -based system is among the primary school students low grade consists of 10 stages, namely 1) Recap through the neighborhood, 2) Discussion groups by exploiting the environment, 3) Demonstration Group, 4) Exercise individuals, 5) mathematical modeling, 6) Demonstration of individuals, 7) Reflections, 8) impressions and messages, and giving meaning, 9) Celebrations and 10) A thorough assessment. Furthermore, this model also produces 7 important components that should be developed teacher, namely 1) constructivism, 2) the nature of nature, 3) independence, 4) parable, 5) inquiry, 6) cooperation, and 7) strengthening. This model will produce a model in the form of books, student books and teacher's guide book as a support system that can help users in its application.
Applying Mathematical Optimization Methods to an ACT-R Instance-Based Learning Model.
Directory of Open Access Journals (Sweden)
Nadia Said
Full Text Available Computational models of cognition provide an interface to connect advanced mathematical tools and methods to empirically supported theories of behavior in psychology, cognitive science, and neuroscience. In this article, we consider a computational model of instance-based learning, implemented in the ACT-R cognitive architecture. We propose an approach for obtaining mathematical reformulations of such cognitive models that improve their computational tractability. For the well-established Sugar Factory dynamic decision making task, we conduct a simulation study to analyze central model parameters. We show how mathematical optimization techniques can be applied to efficiently identify optimal parameter values with respect to different optimization goals. Beyond these methodological contributions, our analysis reveals the sensitivity of this particular task with respect to initial settings and yields new insights into how average human performance deviates from potential optimal performance. We conclude by discussing possible extensions of our approach as well as future steps towards applying more powerful derivative-based optimization methods.
A 4D global respiratory motion model of the thorax based on CT images: A proof of concept.
Fayad, Hadi; Gilles, Marlene; Pan, Tinsu; Visvikis, Dimitris
2018-05-17
Respiratory motion reduces the sensitivity and specificity of medical images especially in the thoracic and abdominal areas. It may affect applications such as cancer diagnostic imaging and/or radiation therapy (RT). Solutions to this issue include modeling of the respiratory motion in order to optimize both diagnostic and therapeutic protocols. Personalized motion modeling required patient-specific four-dimensional (4D) imaging which in the case of 4D computed tomography (4D CT) acquisition is associated with an increased dose. The goal of this work was to develop a global respiratory motion model capable of relating external patient surface motion to internal structure motion without the need for a patient-specific 4D CT acquisition. The proposed global model is based on principal component analysis and can be adjusted to a given patient anatomy using only one or two static CT images in conjunction with a respiratory synchronized patient external surface motion. It is based on the relation between the internal motion described using deformation fields obtained by registering 4D CT images and patient surface maps obtained either from optical imaging devices or extracted from CT image-based patient skin segmentation. 4D CT images of six patients were used to generate the global motion model which was validated by adapting it on four different patients having skin segmented surfaces and two other patients having time of flight camera acquired surfaces. The reproducibility of the proposed model was also assessed on two patients with two 4D CT series acquired within 2 weeks of each other. Profile comparison shows the efficacy of the global respiratory motion model and an improvement while using two CT images in order to adapt the model. This was confirmed by the correlation coefficient with a mean correlation of 0.9 and 0.95 while using one or two CT images respectively and when comparing acquired to model generated 4D CT images. For the four patients with segmented
DEFF Research Database (Denmark)
Carugati, Andrea
2002-01-01
has been initiated with the scope of investigating the questions that mathematical modelling technology poses to traditional information systems development projects. Based on the past body of research, this study proposes a framework to guide decision making for managing projects of information......The advancements in complexity and sophistication of mathematical models for manufacturing scheduling and control and the increase of the ratio power/cost of computers are beginning to provide the manufacturing industry with new software tools to improve production. A Danish action research project...... systems development. In a presented case the indications of the model are compared with the decisions taken during the development. The results highlight discrepancies between the structure and predictions of the model and the case observations, especially with regard to the importance given to the users...
Misnasanti; Dien, C. A.; Azizah, F.
2018-03-01
This study is aimed to describe Lesson Study (LS) activity and its roles in the development of mathematics learning instruments based on Learning Trajectory (LT). This study is a narrative study of teacher’s experiences in joining LS activity. Data collecting in this study will use three methods such as observation, documentations, and deep interview. The collected data will be analyzed with Milles and Huberman’s model that consists of reduction, display, and verification. The study result shows that through LS activity, teachers know more about how students think. Teachers also can revise their mathematics learning instrument in the form of lesson plan. It means that LS activity is important to make a better learning instruments and focus on how student learn not on how teacher teach.
Energy Technology Data Exchange (ETDEWEB)
De la Camp, H.J.; Feser, G.; Hofmann, A.; Wolf, B.; Schmidt, H. [TUeV Sueddeutschland Bau und Betrieb GmbH, Muenchen (Germany); Herforth, H.E.; Juengling, K.H.; Schmidt, W. [TUeV Anlagentechnik GmbH, Berlin-Schoeneberg (Germany). Unternehmensgruppe TUeV Rheinland/Berlin-Brandenburg
2002-01-01
The report is aimed at collecting and documenting the state of the art and the extensive know how of experts and pipeline operators with regard to judging the structural integrity of pipelines. In order to assess the actual mechanical strength of pipelines based on measurement results obtained by inspection pigs, guidance is given for future processing, which eventually can be used as a basis for an industry standard. A literature study of the commercially available types of inspection pigs describes and synoptically lists the respective pros and cons. In essence the report comprises besides check lists of operating data for the pipeline and the pig runs mainly the evaluation of defects and respective calculating procedures. Included are recommendations regarding maintenance planning, verification of defects as well as repetition of pig runs. (orig.) [German] Ziel des Berichtes ist die Erfassung und Dokumentation zum derzeitigen Stand der Technik und des vorhandenen umfangreichen Know-how von Sachverstaendigen und Pipelinebetreibern auf dem Gebiet der sicherheitstechnischen Beurteilung von Pipelines. Fuer den Festigkeitsnachweis von Pipelines aufgrund der Messergebnisse von Pruefmolchen wurde ein Leitfaden als Basis fuer die zukuenftige Vorgehensweise erstellt, der eventuell die Grundlage eines normativen Regelwerkes bilden kann. In einer Literaturstudie wurden die auf dem Markt befindlichen Pruefmolchtypen zusammenfassend beschrieben und ihre Vor- und Nachteile tabellarisch gegenuebergestellt und bewertet. Neben der Erstellung von Checklisten fuer notwendige Daten zum Betrieb der Pipeline und der Molchlaeufe bildet die Fehlerbewertung mit entsprechenden Berechnungsverfahren den Hauptteil dieses Berichtes. Hinweise zur Instandhaltungsplanung (Fehlerverifikation und Molchlaufwiederholung) werden gegeben. (orig.)
The Proof of the Pudding?: A Case Study of an "At-Risk" Design-Based Inquiry Science Curriculum
Chue, Shien; Lee, Yew-Jin
2013-12-01
When students collaboratively design and build artifacts that require relevant understanding and application of science, many aspects of scientific literacy are developed. Design-based inquiry (DBI) is one such pedagogy that can serve these desired goals of science education well. Focusing on a Projectile Science curriculum previously found to be implemented with satisfactory fidelity, we investigate the many hidden challenges when using DBI with Grade 8 students from one school in Singapore. A case study method was used to analyze video recordings of DBI lessons conducted over 10 weeks, project presentations, and interviews to ascertain the opportunities for developing scientific literacy among participants. One critical factor that hindered learning was task selection by teachers, which emphasized generic scientific process skills over more important cognitive and epistemic learning goals. Teachers and students were also jointly engaged in forms of inquiry that underscored artifact completion over deeper conceptual and epistemic understanding of science. Our research surfaced two other confounding factors that undermined the curriculum; unanticipated teacher effects and the underestimation of the complexity of DBI and of inquiry science in general. Thus, even though motivated or experienced teachers can implement an inquiry science curriculum with good fidelity and enjoy school-wide support, these by themselves will not guarantee deep learning of scientific literacy in DBI. Recommendations are made for navigating the hands- and minds-on aspects of learning science that is an asset as well as inherent danger during DBI teaching.
Math Attendees Find There's Life After Fermat Proof.
Cipra, B
1994-02-04
The uncertain status of the recent proof of Fermat's Last Theorem (Science, 24 December 1993, p. 1967) was the hot topic in the hallways at the joint meetings of the American Mathematical Society and the Mathematical Association of America, held 12-15 January in Cincinnati. But a few other topics did manage to get discussed. Among them: How gambling pays off in computing the volume of high-dimensional shapes; how a mathematical description of water dripping down a window pane might lead to the design of digital pulses that could race through the optical fibers of the future; and how one can be fooled infinitely often by another theorem of Fermat's.
Directory of Open Access Journals (Sweden)
Samuel Adejare Awolola
2011-06-01
Full Text Available One dominant factor on how well students learn mathematics is the quality of teaching. Studies have shown that typical mathematics classroom is frosted with teaching technique that centered on explain – practice – memorize. There is a paucity particularly in Nigeria. This study therefore, investigated the effect of brain-based learning strategy on the achievement regarding the learning of Mathematics of 522 Senior Secondary School Students in Oyo State, Nigeria. The moderator effect of cognitive style was also examined on independent variable (instructional strategy and dependent variable (mathematics achievement. The study adopted a pretest-posttest non-equivalent control group design in a quasi – experimental setting. The ANCOVA statistic was used to analyzed the data collected fro the study. The result revealed significant main effect of treatment, (F(1,510 = 75.0; P < 0.05, cognitive style (F(1,510 = 23.78; P < 0.05 and significant interaction effect of treatment and cognitive style (F(1,510 = 5.027; P < 0.05 on achievement in mathematics. The result showed that brain-based instructional strategy enhanced students’ achievement in mathematics more than the conventional lecture method. It is therefore recommended that Teachers of mathematics should adopt the strategy in teaching mathematics in senior secondary school.
de Vries, Peter W; van den Berg, Stéphanie M; Midden, Cees
2015-12-01
The present research addresses the question of how trust in systems is formed when unequivocal information about system accuracy and reliability is absent, and focuses on the interaction of indirect information (others' evaluations) and direct (experiential) information stemming from the interaction process. Trust in decision-supporting technology, such as route planners, is important for satisfactory user interactions. Little is known, however, about trust formation in the absence of outcome feedback, that is, when users have not yet had opportunity to verify actual outcomes. Three experiments manipulated others' evaluations ("endorsement cues") and various forms of experience-based information ("process feedback") in interactions with a route planner and measured resulting trust using rating scales and credits staked on the outcome. Subsequently, an overall analysis was conducted. Study 1 showed that effectiveness of endorsement cues on trust is moderated by mere process feedback. In Study 2, consistent (i.e., nonrandom) process feedback overruled the effect of endorsement cues on trust, whereas inconsistent process feedback did not. Study 3 showed that although the effects of consistent and inconsistent process feedback largely remained regardless of face validity, high face validity in process feedback caused higher trust than those with low face validity. An overall analysis confirmed these findings. Experiential information impacts trust even if outcome feedback is not available, and, moreover, overrules indirect trust cues-depending on the nature of the former. Designing systems so that they allow novice users to make inferences about their inner workings may foster initial trust. © 2015, Human Factors and Ergonomics Society.
Bird, John
2014-01-01
A practical introduction to the core mathematics required for engineering study and practiceNow in its seventh edition, Engineering Mathematics is an established textbook that has helped thousands of students to succeed in their exams.John Bird's approach is based on worked examples and interactive problems. This makes it ideal for students from a wide range of academic backgrounds as the student can work through the material at their own pace. Mathematical theories are explained in a straightforward manner, being supported by practical engineering examples and applications in order to ensure
Magrans de Abril, Ildefons; Yoshimoto, Junichiro; Doya, Kenji
2018-06-01
This article presents a review of computational methods for connectivity inference from neural activity data derived from multi-electrode recordings or fluorescence imaging. We first identify biophysical and technical challenges in connectivity inference along the data processing pipeline. We then review connectivity inference methods based on two major mathematical foundations, namely, descriptive model-free approaches and generative model-based approaches. We investigate representative studies in both categories and clarify which challenges have been addressed by which method. We further identify critical open issues and possible research directions. Copyright © 2018 The Author(s). Published by Elsevier Ltd.. All rights reserved.
Image de-noising based on mathematical morphology and multi-objective particle swarm optimization
Dou, Liyun; Xu, Dan; Chen, Hao; Liu, Yicheng
2017-07-01
To overcome the problem of image de-noising, an efficient image de-noising approach based on mathematical morphology and multi-objective particle swarm optimization (MOPSO) is proposed in this paper. Firstly, constructing a series and parallel compound morphology filter based on open-close (OC) operation and selecting a structural element with different sizes try best to eliminate all noise in a series link. Then, combining multi-objective particle swarm optimization (MOPSO) to solve the parameters setting of multiple structural element. Simulation result shows that our algorithm can achieve a superior performance compared with some traditional de-noising algorithm.
Post secondary project-based learning in science, technology, engineering and mathematics
Ralph, Rachel A.
2016-01-01
Project-based learning (PjBL - to distinguish from problem-based learning - PBL) has become a recurrent practice in K-12 classroom environments. As PjBL has become prominent in K-12 classrooms, it has also surfaced in post-secondary institutions. The purpose of this paper is to examine the research that has studied a variety of science, technology, engineering and mathematic subjects using PjBL in post-secondary classrooms. Eleven articles (including qualitative, quantitative and mixed metho...
Virdi, Surinder; Virdi, Narinder Kaur
2014-01-01
Construction Mathematics is an introductory level mathematics text, written specifically for students of construction and related disciplines. Learn by tackling exercises based on real-life construction maths. Examples include: costing calculations, labour costs, cost of materials and setting out of building components. Suitable for beginners and easy to follow throughout. Learn the essential basic theory along with the practical necessities. The second edition of this popular textbook is fully updated to match new curricula, and expanded to include even more learning exercises. End of chapter exercises cover a range of theoretical as well as practical problems commonly found in construction practice, and three detailed assignments based on practical tasks give students the opportunity to apply all the knowledge they have gained. Construction Mathematics addresses all the mathematical requirements of Level 2 construction NVQs from City & Guilds/CITB and Edexcel courses, including the BTEC First Diploma in...
Bistatic SAR: Proof of Concept.
Energy Technology Data Exchange (ETDEWEB)
Yocky, David A.; Doren, Neall E.; Bacon, Terry A.; Wahl, Daniel E.; Eichel, Paul H.; Jakowatz, Charles V,; Delaplain, Gilbert G.; Dubbert, Dale F.; Tise, Bertice L.; White, Kyle R.
2014-10-01
Typical synthetic aperture RADAR (SAR) imaging employs a co-located RADAR transmitter and receiver. Bistatic SAR imaging separates the transmitter and receiver locations. A bistatic SAR configuration allows for the transmitter and receiver(s) to be in a variety of geometric alignments. Sandia National Laboratories (SNL) / New Mexico proposed the deployment of a ground-based RADAR receiver. This RADAR receiver was coupled with the capability of digitizing and recording the signal collected. SNL proposed the possibility of creating an image of targets the illuminating SAR observes. This document describes the developed hardware, software, bistatic SAR configuration, and its deployment to test the concept of a ground-based bistatic SAR. In the proof-of-concept experiments herein, the RADAR transmitter will be a commercial SAR satellite and the RADAR receiver will be deployed at ground level, observing and capturing RADAR ground/targets illuminated by the satellite system.
Adams, Thomasenia Lott
2001-01-01
Focuses on the National Council of Teachers of Mathematics 2000 process-oriented standards of problem solving, reasoning and proof, communication, connections, and representation as providing a framework for using the multiple intelligences that children bring to mathematics learning. Presents ideas for mathematics lessons and activities to…
Proof testing of CANDU concrete containment structures
International Nuclear Information System (INIS)
Pandey, M.D.
1996-05-01
Prior to commissioning of a CANDU reactor, a proof pressure test is required to demonstrate the structural integrity of the containment envelope. The test pressure specified by AECB Regulatory Document R-7 (1991) was selected without a rigorous consideration of uncertainties associated with estimates of accident pressure and conatinment resistance. This study was undertaken to develop a reliability-based philosophy for defining proof testing requirements that are consistent with the current limit states design code for concrete containments (CSA N287.3).It was shown that the upodated probability of failure after a successful test is always less than the original estimate
Indian Academy of Sciences (India)
An Introduction to Math- ematical Logic ... mathematical logic and topology. ... G Äodelto exam ine questions about a theory such as N um ... In the last tw o parts of this article, w e presented an overview ... at the level of II Year BSc/BTech/. BE.
Tamper proofing of safeguards monitors
International Nuclear Information System (INIS)
Riley, R.J.
1982-11-01
The tamper proofing of safeguards monitors is essential if the data they produce is, and can be seen to be, reliable. This report discusses the problem of tamper proofing and gives guidance on when and how to apply tamper proofing techniques. The report is split into two parts. The first concerns the fundamental problem of how much tamper proofing to apply and the second describes methods of tamper proofing and discusses their usefulness. Both sections are applicable to all safeguards monitors although particular reference will be made to doorway monitors in some cases. The phrase 'tamper proofing' is somewhat misleading as it is impossible to completely tamper proof any device. Given enough time and resources, even the most elaborate tamper proofing can be overcome. In safeguards applications we are more interested in making the device tamper resistant and tamper indicating. That is, it should be able to resist a certain amount of tampering, and if tampering proves successful, that fact should be immediately obvious. Techniques of making a device tamper indicating and tamper resistant will be described below. The phrase tamper proofing will be used throughout this report as a generic term, including both tamper resistance and tamper indicating. (author)
Teaching Syllogistics Through Gamification and Interactive Proofs
DEFF Research Database (Denmark)
Øhrstrøm, Peter; Sandborg-Petersen, Ulrik; Thorvaldsen, Steinar
2015-01-01
teaching through the use of interactive systems and also to do learning analytics based on the log-data from the use of the systems. The aim of the present paper is to investigate whether the use of gamification and an interactive proof system formulated in terms of controlled natural language can...
Proofs of Contracted Length Non-covariance
International Nuclear Information System (INIS)
Strel'tsov, V.N.
1994-01-01
Different proofs of contracted length non covariance are discussed. The way based on the establishment of interval inconstancy (dependence on velocity) seems to be the most convincing one. It is stressed that the known non covariance of the electromagnetic field energy and momentum of a moving charge ('the problem 4/3') is a direct consequence of contracted length non covariance. 8 refs
Proof of Nishida's Conjecture on Anharmonic Lattices
Rink, Bob
2006-02-01
We prove Nishida's 1971 conjecture stating that almost all low-energetic motions of the anharmonic Fermi-Pasta-Ulam lattice with fixed endpoints are quasi-periodic. The proof is based on the formal computations of Nishida, the KAM theorem, discrete symmetry considerations and an algebraic trick that considerably simplifies earlier results.
A correctness proof of the bakery protocol in $ mu $CRL
J.F. Groote (Jan Friso); H.P. Korver
1994-01-01
textabstractA specification of a bakery protocol is given in $mu$CRL. We provide a simple correctness criterion for the protocol. Then the protocol is proven correct using a proof system that has been developed for $mu$CRL. The proof primarily consists of algebraic manipulations based on
The bounded proof property via step algebras and step frames
Bezhanishvili, N.; Ghilardi, Silvio
2013-01-01
We develop a semantic criterion for a specific rule-based calculus Ax axiomatizing a given logic L to have the so-called bounded proof property. This property is a kind of an analytic subformula property limiting the proof search space. Our main tools are one-step frames and one-step algebras. These
Sukmawati, Zuhairoh, Faihatuz
2017-05-01
The purpose of this research was to develop authentic assessment model based on showcase portfolio on learning of mathematical problem solving. This research used research and development Method (R & D) which consists of four stages of development that: Phase I, conducting a preliminary study. Phase II, determining the purpose of developing and preparing the initial model. Phase III, trial test of instrument for the initial draft model and the initial product. The respondents of this research are the students of SMAN 8 and SMAN 20 Makassar. The collection of data was through observation, interviews, documentation, student questionnaire, and instrument tests mathematical solving abilities. The data were analyzed with descriptive and inferential statistics. The results of this research are authentic assessment model design based on showcase portfolio which involves: 1) Steps in implementing the authentic assessment based Showcase, assessment rubric of cognitive aspects, assessment rubric of affective aspects, and assessment rubric of skill aspect. 2) The average ability of the students' problem solving which is scored by using authentic assessment based on showcase portfolio was in high category and the students' response in good category.
A bridge to advanced mathematics
Sentilles, Dennis
2011-01-01
This helpful workbook-style ""bridge"" book introduces students to the foundations of advanced mathematics, spanning the gap between a practically oriented calculus sequence and subsequent courses in algebra and analysis with a more theoretical slant. Part 1 focuses on logic and number systems, providing the most basic tools, examples, and motivation for the manner, method, and concerns of higher mathematics. Part 2 covers sets, relations, functions, infinite sets, and mathematical proofs and reasoning. Author Dennis Sentilles also discusses the history and development of mathematics as well a
International Nuclear Information System (INIS)
Pan Yi; Mao Wanchong
2010-01-01
The parameter measurement of nuclear track occupies an important position in the field of nuclear technology. However, traditional artificial counting method has many limitations. In recent years, DSP and digital image processing technology have been applied in nuclear field more and more. For the sake of reducing errors of visual measurement in artificial counting method, an automatic counting system for nuclear track based on DM642 real-time image processing platform is introduced in this article, which is able to effectively remove interferences from the background and noise points, as well as automatically extract nuclear track-points by using mathematical morphology algorithm. (authors)
Mathematical Analysis for Non-reciprocal-interaction-based Model of Collective Behavior
Kano, Takeshi; Osuka, Koichi; Kawakatsu, Toshihiro; Ishiguro, Akio
2017-12-01
In many natural and social systems, collective behaviors emerge as a consequence of non-reciprocal interaction between their constituents. As a first step towards understanding the core principle that underlies these phenomena, we previously proposed a minimal model of collective behavior based on non-reciprocal interactions by drawing inspiration from friendship formation in human society, and demonstrated via simulations that various non-trivial patterns emerge by changing parameters. In this study, a mathematical analysis of the proposed model wherein the system size is small is performed. Through the analysis, the mechanism of the transition between several patterns is elucidated.
Saturation flow mathematical model based on multiple combinations of lane groups
Energy Technology Data Exchange (ETDEWEB)
Racila, L.
2016-07-01
The ideal value of the traffic stream that can pass through an intersection is known as the saturation flow rate per hour on vehicle green time. The saturation flow is important in the understanding of the traffic light cycle and from there the understanding the Level of Service. The paper wishes to evaluate through a series of applied mathematical methods the effect of different lane grouping and critical lane group concept on the saturation flow rate. The importance of this method is that it creates a base for a signalized intersections timing plan. (Author)
Tipping, Jonathan; Boogaard, Floris; Jaeger, R.; Duffy, A.; Klomp, T.; Manenschijn, M.
2015-01-01
Over recent years, there has been an explosion in the number and diversity of projects undertaken to address urban resilience and climate proofing. Sharing the knowledge gained from these projects demands increasingly innovative and accessible methods. This paper details the outcomes of one such
Wang, Ching-Fu; Yang, Shih-Hung; Lin, Sheng-Huang; Chen, Po-Chuan; Lo, Yu-Chun; Pan, Han-Chi; Lai, Hsin-Yi; Liao, Lun-De; Lin, Hui-Ching; Chen, Hsu-Yan; Huang, Wei-Chen; Huang, Wun-Jhu; Chen, You-Yin
Deep brain stimulation (DBS) has been applied as an effective therapy for treating Parkinson's disease or essential tremor. Several open-loop DBS control strategies have been developed for clinical experiments, but they are limited by short battery life and inefficient therapy. Therefore, many closed-loop DBS control systems have been designed to tackle these problems by automatically adjusting the stimulation parameters via feedback from neural signals, which has been reported to reduce the power consumption. However, when the association between the biomarkers of the model and stimulation is unclear, it is difficult to develop an optimal control scheme for other DBS applications, i.e., DBS-enhanced instrumental learning. Furthermore, few studies have investigated the effect of closed-loop DBS control for cognition function, such as instrumental skill learning, and have been implemented in simulation environments. In this paper, we proposed a proof-of-principle design for a closed-loop DBS system, cognitive-enhancing DBS (ceDBS), which enhanced skill learning based on in vivo experimental data. The ceDBS acquired local field potential (LFP) signal from the thalamic central lateral (CL) nuclei of animals through a neural signal processing system. A strong coupling of the theta oscillation (4-7 Hz) and the learning period was found in the water reward-related lever-pressing learning task. Therefore, the theta-band power ratio, which was the averaged theta band to averaged total band (1-55 Hz) power ratio, could be used as a physiological marker for enhancement of instrumental skill learning. The on-line extraction of the theta-band power ratio was implemented on a field-programmable gate array (FPGA). An autoregressive with exogenous inputs (ARX)-based predictor was designed to construct a CL-thalamic DBS model and forecast the future physiological marker according to the past physiological marker and applied DBS. The prediction could further assist the design of
Kartika, H.
2018-03-01
The issue related to making mistake while learning such as negative emotion is found while students learn mathematics with the aid of a computer. When the computer output showed a mistake message, the students considered it as a computer software malfunction. Based on this issue, the writer designs an instructional model based on learning by mistake approach and which is Scilab assisted. The method used in this research is research design involving undergraduate students in matrix algebra courses. The data collected throught survey with questionnaire to gain feedback about the approach implemented. The data analyzed using quantitative descriptive. The instructional design proposed is the student act as a mistake corrector while the teacher acts as a mistake maker. Teacher deliberately makes mistakes with the help of Scilab software. On the other hand, students correct, analyze and explain errors resulting from Scilab software. The result of this research is an ICT based instructional design which is expected to be applicable as an alternative learning in directing students to think positively about mistakes in learning. Furthermore, students are also expected to improve their ability in understanding and thinking critically while solving problems and improving themselves in learning mathematics.
Data-based mathematical modeling of vectorial transport across double-transfected polarized cells.
Bartholomé, Kilian; Rius, Maria; Letschert, Katrin; Keller, Daniela; Timmer, Jens; Keppler, Dietrich
2007-09-01
Vectorial transport of endogenous small molecules, toxins, and drugs across polarized epithelial cells contributes to their half-life in the organism and to detoxification. To study vectorial transport in a quantitative manner, an in vitro model was used that includes polarized MDCKII cells stably expressing the recombinant human uptake transporter OATP1B3 in their basolateral membrane and the recombinant ATP-driven efflux pump ABCC2 in their apical membrane. These double-transfected cells enabled mathematical modeling of the vectorial transport of the anionic prototype substance bromosulfophthalein (BSP) that has frequently been used to examine hepatobiliary transport. Time-dependent analyses of (3)H-labeled BSP in the basolateral, intracellular, and apical compartments of cells cultured on filter membranes and efflux experiments in cells preloaded with BSP were performed. A mathematical model was fitted to the experimental data. Data-based modeling was optimized by including endogenous transport processes in addition to the recombinant transport proteins. The predominant contributions to the overall vectorial transport of BSP were mediated by OATP1B3 (44%) and ABCC2 (28%). Model comparison predicted a previously unrecognized endogenous basolateral efflux process as a negative contribution to total vectorial transport, amounting to 19%, which is in line with the detection of the basolateral efflux pump Abcc4 in MDCKII cells. Rate-determining steps in the vectorial transport were identified by calculating control coefficients. Data-based mathematical modeling of vectorial transport of BSP as a model substance resulted in a quantitative description of this process and its components. The same systems biology approach may be applied to other cellular systems and to different substances.
Short proofs of strong normalization
Wojdyga, Aleksander
2008-01-01
This paper presents simple, syntactic strong normalization proofs for the simply-typed lambda-calculus and the polymorphic lambda-calculus (system F) with the full set of logical connectives, and all the permutative reductions. The normalization proofs use translations of terms and types to systems, for which strong normalization property is known.
Introduction to mathematical logic
Mendelson, Elliott
2015-01-01
The new edition of this classic textbook, Introduction to Mathematical Logic, Sixth Edition explores the principal topics of mathematical logic. It covers propositional logic, first-order logic, first-order number theory, axiomatic set theory, and the theory of computability. The text also discusses the major results of Gödel, Church, Kleene, Rosser, and Turing.The sixth edition incorporates recent work on Gödel's second incompleteness theorem as well as restoring an appendix on consistency proofs for first-order arithmetic. This appendix last appeared in the first edition. It is offered in th
Mathematical model of rolling an elastic wheel over deformable support base
Volskaia, V. N.; Zhileykin, M. M.; Zakharov, A. Y.
2018-02-01
One of the main direction of economic growth in Russia remains to be a speedy development of north and northeast regions that are the constituents of the 60 percent of the country territory. The further development of these territories requires new methods and technologies for solving transport and technological problems when off-road transportation of cargoes and people is conducting. One of the fundamental methods of patency prediction is imitation modeling of wheeled vehicles movement in different operating conditions. Both deformable properties of tires and physical and mechanical properties of the ground: normal tire deflection and gauge depth; variation of contact patch area depending on the load and pressure of air in the tire; existence of hysteresis losses in the tire material which are influencing on the rolling resistance due to friction processes between tire and ground in the contact patch; existence of the tangential reaction from the ground by entire contact area influence on the tractive patency. Nowadays there are two main trends in theoretical research of interaction wheeled propulsion device with ground: analytical method involving mathematical description of explored process and finite element method based on computational modeling. Mathematical models of interaction tire with the ground are used both in processes of interaction individual wheeled propulsion device with ground and researches of mobile vehicle dynamical models operated in specific road and climate conditions. One of the most significant imperfection of these models is the description of interaction wheel with flat deformable support base whereas profile of real support base surface has essential height of unevenness which is commensurate with radius of the wheel. The description of processes taking place in the ground under influence of the wheeled propulsion device using the finite element method is relatively new but most applicable lately. The application of this method allows
Sowanto; Kusumah, Y. S.
2018-05-01
This research was conducted based on the problem of a lack of students’ mathematical representation ability as well as self-efficacy in accomplishing mathematical tasks. To overcome this problem, this research used situation-based learning (SBL) assisted by geometer’s sketchpad program (GSP). This research investigated students’ improvement of mathematical representation ability who were taught under situation-based learning (SBL) assisted by geometer’s sketchpad program (GSP) and regular method that viewed from the whole students’ prior knowledge (high, average, and low level). In addition, this research investigated the difference of students’ self-efficacy after learning was given. This research belongs to quasi experiment research using non-equivalent control group design with purposive sampling. The result of this research showed that students’ enhancement in their mathematical representation ability taught under SBL assisted by GSP was better than the regular method. Also, there was no interaction between learning methods and students prior knowledge in student’ enhancement of mathematical representation ability. There was significant difference of students’ enhancement of mathematical representation ability taught under SBL assisted by GSP viewed from students’ prior knowledge. Furthermore, there was no significant difference in terms of self-efficacy between those who were taught by SBL assisted by GSP with the regular method.
Lamothe, Martin; McDuff, Pierre; Pastore, Yves D; Duval, Michel; Sultan, Serge
2018-01-05
To assess the feasibility and acceptability of a mindfulness-based stress reduction (MBSR)-based intervention and determine if the intervention is associated with a significant signal on empathy and emotional competencies. Two pre-post proof-of-concept studies. Participants were recruited at the University of Montreal's Psychology Department (Study 1) and the CHU Sainte-Justine Department of Hematology-Oncology (Study 2). Study 1: 12 students completed the 8-week programme (mean age 24, range 18-34). Study 2: 25 professionals completed the 8-week programme (mean age 48, range 27-63). Standard MBSR programme including 8-week mindfulness programme consisting of 8 consecutive weekly 2-hour sessions and a full-day silent retreat. Mindfulness as measured by the Mindful Attention Awareness Scale; empathy as measured by the Interpersonal Reactivity Index (IRI)'s Perspective Taking and Empathic Concern subscales; identification of one's own emotions and those of others as measured by the Profile of Emotional Competence (PEC)'s Identify my Emotions and Identify Others' Emotions subscales; emotional acceptance as measured by the Acceptance and Action Questionnaire-II (AAQ-II) and the Emotion Regulation Scale (ERQ)'s Expressive Suppression subscale; and recognition of emotions in others as measured by the Geneva Emotion Recognition Test (GERT). In both studies, retention rates (80%-81%) were acceptable. Participants who completed the programme improved on all measures except the PEC's Identify Others' Emotions and the IRI's Empathic Concern (Cohen's d median=0.92, range 45-1.72). In Study 2, favourable effects associated with the programme were maintained over 3 months on the PEC's Identify my Emotions, the AAQ-II, the ERQ's Expressive Suppression and the GERT. The programme was feasible and acceptable. It was associated with a significant signal on the following outcomes: perspective taking, the identification of one's own emotions and emotional acceptance, thus, justifying
Lamothe, Martin; McDuff, Pierre; Pastore, Yves D; Duval, Michel; Sultan, Serge
2018-01-01
Objectives To assess the feasibility and acceptability of a mindfulness-based stress reduction (MBSR)-based intervention and determine if the intervention is associated with a significant signal on empathy and emotional competencies. Design Two pre–post proof-of-concept studies. Setting Participants were recruited at the University of Montreal’s Psychology Department (Study 1) and the CHU Sainte-Justine Department of Hematology-Oncology (Study 2). Participants Study 1: 12 students completed the 8-week programme (mean age 24, range 18–34). Study 2: 25 professionals completed the 8-week programme (mean age 48, range 27–63). Intervention Standard MBSR programme including 8-week mindfulness programme consisting of 8 consecutive weekly 2-hour sessions and a full-day silent retreat. Outcomes measures Mindfulness as measured by the Mindful Attention Awareness Scale; empathy as measured by the Interpersonal Reactivity Index (IRI)’s Perspective Taking and Empathic Concern subscales; identification of one’s own emotions and those of others as measured by the Profile of Emotional Competence (PEC)’s Identify my Emotions and Identify Others’ Emotions subscales; emotional acceptance as measured by the Acceptance and Action Questionnaire-II (AAQ-II) and the Emotion Regulation Scale (ERQ)’s Expressive Suppression subscale; and recognition of emotions in others as measured by the Geneva Emotion Recognition Test (GERT). Results In both studies, retention rates (80%–81%) were acceptable. Participants who completed the programme improved on all measures except the PEC’s Identify Others’ Emotions and the IRI’s Empathic Concern (Cohen’s d median=0.92, range 45–1.72). In Study 2, favourable effects associated with the programme were maintained over 3 months on the PEC’s Identify my Emotions, the AAQ-II, the ERQ’s Expressive Suppression and the GERT. Conclusions The programme was feasible and acceptable. It was associated with a significant signal on the
International Nuclear Information System (INIS)
Geoffrey Chase, J; Starfinger, Christina; Hann, Christopher E; Lambermont, Bernard; Ghuysen, Alexandre; Kolh, Philippe; Dauby, Pierre C; Desaive, Thomas; Shaw, Geoffrey M
2011-01-01
identification process for validation. Importantly, all identified parameter trends match physiologically and clinically and experimentally expected changes, indicating that no diagnostic power is lost. This work represents a further with human subjects validation for this model-based approach to cardiovascular diagnosis and therapy guidance in monitoring endotoxic disease states. The results and methods obtained can be readily extended from this case study to the other animal model results presented previously. Overall, these results provide further support for prospective, proof of concept clinical testing with humans
The Big Fish-Little Pond Effect on Affective Factors Based on PISA 2012 Mathematics Achievement
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Dilara BAKAN KALAYCIOĞLU
2017-03-01
Full Text Available In this study, the 2012 PISA Turkey student questionnaire data is considered to determine the big fish-little pond effect. The mathematics self-efficacy, self-concept and anxiety affective factors are examined to explain the relation of each of them with the school type, gender, socioeconomic status, student’s mathematics achievement and school’s mathematics achievement covariates. A total number of 771 students from 88 high schools are in the sample. Factor analyses’ results support the construct validity of the Student Questionnaire’s mathematics self-efficacy, anxiety and self-concept items. Data set is analyzed with Multiple Indicator Multiple Cause Model and the patterns of association with covariates and affective factors were tested simultaneously. According to the results, Anatolian high school students have a higher mathematics self-efficacy and lower mathematics anxiety than do the general high school students. However, when the student mathematics achievement and school mathematics achievement variables were inserted to the model, school type was not associated with mathematics self-efficacy. Moreover, Anatolian high school student’s mathematics anxiety was higher than that of the general high school students. Student’s mathematics achievement was the most significant predictor of the mathematics self-efficacy, anxiety and self-concept factors. Finally, school’s mathematics achievement was a significant predictor of only mathematics self-concept. The identification of increase in school’s mathematics achievement yields a decrease in the student’s mathematics self-concept may be considered as the most important result of this study. These results provide evidence about the Anatolian high schools’ students experience big fish-little pond effect.
Agyei, D.D.; Voogt, Joke; Resta, P.
2012-01-01
Mathematics education research has shown that too few students have adequate mathematics comprehension or problem-solving skills. To make up for this lapse in student outcomes, mathematics teachers should be among the most enthusiastic in seeking to maximize technologies’ potential to develop
Observing and analyzing children’s mathematical development, based on action theory
Bunck, M. J. A.; Terlien, E.; van Groenestijn, L.M.; Toll, S. W. M.; Van Luit, J. E. H.
2017-01-01
Children who experience difficulties with learning mathematics should be taught by teachers who focus on the child’s best way of learning. Analyses of the mathematical difficulties are necessary for fine-tuning mathematics education to the needs of these children. For this reason, an instrument for
Teaching Secondary School Mathematics and Statistics: Evidence-Based Practice. Volume 1
Averill, Robin; Harvey, Roger
2009-01-01
"Mathematics is more than skills... it is also the excitement of discovery." This is how Derek Holton, one of the contributing authors to this book, defines mathematics. His enthusiasm and energy are echoed throughout by many of the other writers. This is a book to delight mathematics teachers at all stages: experienced and inexperienced;…
Teaching Secondary School Mathematics and Statistics: Evidence-Based Practice. Volume 2
Averill, Robin; Harvey, Roger
2009-01-01
"We can never be sure that there is not some wild, untamed piece of mathematics ready to spring out on us... This is what keeps mathematics enchanting." This is how Jim Neyland, one of the contributing authors to this book, describes mathematics. His enthusiasm and energy are echoed throughout by many of the other writers. This is a book to…
The Influence of a Reform-Based Mathematics Methods Course on Preservice Teachers' Beliefs
Evans, Brian R.; Leonard, Jacqueline; Krier, Kathleen; Ryan, Steve
2013-01-01
Beliefs about teaching mathematics and urban students' ability to learn mathematics are often overlooked in the discourse on highly qualified teachers. Altering teacher experiences has the potential to change their beliefs. It was found in this qualitative case study that preservice teachers' beliefs about teaching mathematics to urban students…
Observing and Analyzing Children's Mathematical Development, Based on Action Theory
Bunck, M. J. A.; Terlien, E.; van Groenestijn, M.; Toll, S. W. M.; Van Luit, J. E. H.
2017-01-01
Children who experience difficulties with learning mathematics should be taught by teachers who focus on the child's best way of learning. Analyses of the mathematical difficulties are necessary for fine-tuning mathematics education to the needs of these children. For this reason, an instrument for Observing and Analyzing children's Mathematical…
Sheu, Yun Robert; Feder, Elie; Balsim, Igor; Levin, Victor F; Bleicher, Andrew G; Branstetter, Barton F
2010-06-01
Peer review is an essential process for physicians because it facilitates improved quality of patient care and continuing physician learning and improvement. However, peer review often is not well received by radiologists who note that it is time intensive, is subjective, and lacks a demonstrable impact on patient care. Current advances in peer review include the RADPEER() system, with its standardization of discrepancies and incorporation of the peer-review process into the PACS itself. The purpose of this study was to build on RADPEER and similar systems by using a mathematical model to optimally select the types of cases to be reviewed, for each radiologist undergoing review, on the basis of the past frequency of interpretive error, the likelihood of morbidity from an error, the financial cost of an error, and the time required for the reviewing radiologist to interpret the study. The investigators compiled 612,890 preliminary radiology reports authored by residents and attending radiologists at a large tertiary care medical center from 1999 to 2004. Discrepancies between preliminary and final interpretations were classified by severity and validated by repeat review of major discrepancies. A mathematical model was then used to calculate, for each author of a preliminary report, the combined morbidity and financial costs of expected errors across 3 modalities (MRI, CT, and conventional radiography) and 4 departmental divisions (neuroradiology, abdominal imaging, musculoskeletal imaging, and thoracic imaging). A customized report was generated for each on-call radiologist that determined the category (modality and body part) with the highest total cost function. A universal total cost based on probability data from all radiologists was also compiled. The use of mathematical models to guide case selection could optimize the efficiency and effectiveness of physician time spent on peer review and produce more concrete and meaningful feedback to radiologists
Nemchinova, N. V.; Tyutrin, A. A.; Salov, V. M.
2018-03-01
The silicon production process in the electric arc reduction furnaces (EAF) is studied using pelletized charge as an additive to the standard on the basis of the generated mathematical model. The results obtained due to the model will contribute to the analysis of the charge components behavior during melting with the achievement of optimum final parameters of the silicon production process. The authors proposed using technogenic waste as a raw material for the silicon production in a pelletized form using liquid glass and aluminum production dust from the electrostatic precipitators as a binder. The method of mathematical modeling with the help of the ‘Selector’ software package was used as a basis for the theoretical study. A model was simulated with the imitation of four furnace temperature zones and a crystalline silicon phase (25 °C). The main advantage of the created model is the ability to analyze the behavior of all burden materials (including pelletized charge) in the carbothermic process. The behavior analysis is based on the thermodynamic probability data of the burden materials interactions in the carbothermic process. The model accounts for 17 elements entering the furnace with raw materials, electrodes and air. The silicon melt, obtained by the modeling, contained 91.73 % wt. of the target product. The simulation results showed that in the use of the proposed combined charge, the recovery of silicon reached 69.248 %, which is in good agreement with practical data. The results of the crystalline silicon chemical composition modeling are compared with the real silicon samples of chemical analysis data, which showed the results of convergence. The efficiency of the mathematical modeling methods in the studying of the carbothermal silicon obtaining process with complex interphase transformations and the formation of numerous intermediate compounds using a pelletized charge as an additive to the traditional one is shown.
Exercises and problems in mathematical methods of physics
Cicogna, Giampaolo
2018-01-01
This book presents exercises and problems in the mathematical methods of physics with the aim of offering undergraduate students an alternative way to explore and fully understand the mathematical notions on which modern physics is based. The exercises and problems are proposed not in a random order but rather in a sequence that maximizes their educational value. Each section and subsection starts with exercises based on first definitions, followed by groups of problems devoted to intermediate and, subsequently, more elaborate situations. Some of the problems are unavoidably "routine", but others bring to the forenontrivial properties that are often omitted or barely mentioned in textbooks. There are also problems where the reader is guided to obtain important results that are usually stated in textbooks without complete proofs. In all, some 350 solved problems covering all mathematical notions useful to physics are included. While the book is intended primarily for undergraduate students of physics, students...
International Nuclear Information System (INIS)
Mishima, Yoshitsugu
1983-01-01
In order to obtain public understanding on nuclear power plants, tests should be carried out to prove the reliability and safety of present LWR plants. For example, the aseismicity of nuclear power plants must be verified by using a large scale earthquake simulator. Reliability test began in fiscal 1975, and the proof tests on steam generators and on PWR support and flexure pins against stress corrosion cracking have already been completed, and the results have been internationally highly appreciated. The capacity factor of the nuclear power plant operation in Japan rose to 80% in the summer of 1983, and considering the period of regular inspection, it means the operation of almost full capacity. Japanese LWR technology has now risen to the top place in the world after having overcome the defects. The significance of the reliability test is to secure the functioning till the age limit is reached, to confirm the correct forecast of deteriorating process, to confirm the effectiveness of the remedy to defects and to confirm the accuracy of predicting the behavior of facilities. The reliability of nuclear valves, fuel assemblies, the heat affected zones in welding, reactor cooling pumps and electric instruments has been tested or is being tested. (Kako, I.)
Development of problem-based learning material for physics mathematics and its implementation
Directory of Open Access Journals (Sweden)
Pujayanto Pujayanto
2017-02-01
Full Text Available The research aims to develop Problem Based Learning material teaching of Mathematics Physics and to know the effect on the cognitive capability of undergraduate students. The research uses development method of Borg and Gall. There are ten steps such as data collection, planning, product drafting, pretest, pretest revise 1, main test, main test revise 2, posttest, final revision, and dissemination and implementation. The data collection uses questionnaire and cognitive test which will support the qualitative data. The result shows that the criterion of developing problem-based learning teaching materials is 5 level category when 43.33% respondents rate 5 level category and the others give 4 level category. Furthermore, students which use the materials increased and the most of the students have acquired cognitive value exceeds the value of minimum completeness criteria.
International Nuclear Information System (INIS)
Li, X.; He, X.; Lv, J.; Wu, Y.; Luo, Y.; Chen, H.
2013-01-01
High intensive microwave pretreatment is a new method to modify wood for the fabrication of wood-based nano composites. Based on the physical law on heat transfer, a mathematical model to describe the temperature profiles within wood heated by high intensive microwave was established and simulated in this research. The results showed that the temperature profiles within wood were related to microwave heating methods; The temperature inside wood firstly increased and then gradually decreased along the direction of microwave transmission when the unilateral microwave heating was applied, and the temperature difference along the thickness direction of wood was very significant; The temperature with wood firstly increased and then gradually decreased from the wood surface to interior when the bilateral microwave heating was applied. Compared with the unilateral microwave heating, bilateral microwave heating is a better microwave heating method for the more uniform wood microwave pretreatment.
Directory of Open Access Journals (Sweden)
Sayantan Nath
2015-09-01
Full Text Available In this paper, integration between multiple functions of image processing and its statistical parameters for intelligent alarming series based fire detection system is presented. The proper inter-connectivity mapping between processing elements of imagery based on classification factor for temperature monitoring and multilevel intelligent alarm sequence is introduced by abstractive canonical approach. The flow of image processing components between core implementation of intelligent alarming system with temperature wise area segmentation as well as boundary detection technique is not yet fully explored in the present era of thermal imaging. In the light of analytical perspective of convolutive functionalism in thermal imaging, the abstract algebra based inter-mapping model between event-calculus supported DAGSVM classification for step-by-step generation of alarm series with gradual monitoring technique and segmentation of regions with its affected boundaries in thermographic image of coal with respect to temperature distinctions is discussed. The connectedness of the multifunctional operations of image processing based compatible fire protection system with proper monitoring sequence is presently investigated here. The mathematical models representing the relation between the temperature affected areas and its boundary in the obtained thermal image defined in partial derivative fashion is the core contribution of this study. The thermal image of coal sample is obtained in real-life scenario by self-assembled thermographic camera in this study. The amalgamation between area segmentation, boundary detection and alarm series are described in abstract algebra. The principal objective of this paper is to understand the dependency pattern and the principles of working of image processing components and structure an inter-connected modelling technique also for those components with the help of mathematical foundation.
Directory of Open Access Journals (Sweden)
Basuki Widodo
2012-02-01
Full Text Available Corrosion process is a natural case that happened at the various metals, where the corrosion process in electrochemical can be explained by using galvanic cell. The iron corrosion process is based on the acidity degree (pH of a condensation, iron concentration and condensation temperature of electrolyte. Those are applied at electrochemistry cell. The iron corrosion process at this electrochemical cell also able to generate electrical potential and electric current during the process takes place. This paper considers how to build a mathematical model of iron corrosion, electrical potential and electric current. The mathematical model further is solved using the finite element method. This iron corrosion model is built based on the iron concentration, condensation temperature, and iteration time applied. In the electric current density model, the current based on electric current that is happened at cathode and anode pole and the iteration time applied. Whereas on the potential electric model, it is based on the beginning of electric potential and the iteration time applied. The numerical results show that the part of iron metal, that is gristle caused by corrosion, is the part of metal that has function as anode and it has some influences, such as time depth difference, iron concentration and condensation temperature on the iron corrosion process and the sum of reduced mass during corrosion process. Moreover, difference influence of time and beginning electric potential has an effect on the electric potential, which emerges during corrosion process at the electrochemical cell. Whereas, at the electrical current is also influenced by difference of depth time and condensation temperature applied.Keywords: Iron Corrosion, Concentration of iron, Electrochemical Cell and Finite Element Method
Burdens of Proof, Presumptions and Standards of Proof in Criminal ...
African Journals Online (AJOL)
Worku_Y
evidential and persuasive burdens of proof as between the state and the ..... scholars have observed that the evidential burden is a function of the burden of ..... required to convince judges by creating such an intensity of belief in their minds.
Complexity-Based Modeling of Scientific Capital: An Outline of Mathematical Theory
Directory of Open Access Journals (Sweden)
Yurij L. Katchanov
2014-01-01
measuring and assessing the accumulated recognition and the specific scientific power. The concept of scientific capital developed by Bourdieu is used in international social science research to explain a set of scholarly properties and practices. Mathematical modeling is applied as a lens through which the scientific capital is addressed. The principal contribution of this paper is an axiomatic characterization of scientific capital in terms of natural axioms. The application of the axiomatic method to scientific capital reveals novel insights into problem still not covered by mathematical modeling. Proposed model embraces the interrelations between separate sociological variables, providing a unified sociological view of science. Suggested microvariational principle is based upon postulate, which affirms that (under suitable conditions the observed state of the agent in scientific field maximizes scientific capital. Its value can be roughly imagined as a volume of social differences. According to the considered macrovariational principle, the actual state of scientific field makes so-called energy functional (which is associated with the distribution of scientific capital minimal.
Modelers' perception of mathematical modeling in epidemiology: a web-based survey.
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Gilles Hejblum
Full Text Available BACKGROUND: Mathematical modeling in epidemiology (MME is being used increasingly. However, there are many uncertainties in terms of definitions, uses and quality features of MME. METHODOLOGY/PRINCIPAL FINDINGS: To delineate the current status of these models, a 10-item questionnaire on MME was devised. Proposed via an anonymous internet-based survey, the questionnaire was completed by 189 scientists who had published in the domain of MME. A small minority (18% of respondents claimed to have in mind a concise definition of MME. Some techniques were identified by the researchers as characterizing MME (e.g. Markov models, while others-at the same level of sophistication in terms of mathematics-were not (e.g. Cox regression. The researchers' opinions were also contrasted about the potential applications of MME, perceived as highly relevant for providing insight into complex mechanisms and less relevant for identifying causal factors. The quality criteria were those of good science and were not related to the size and the nature of the public health problems addressed. CONCLUSIONS/SIGNIFICANCE: This study shows that perceptions on the nature, uses and quality criteria of MME are contrasted, even among the very community of published authors in this domain. Nevertheless, MME is an emerging discipline in epidemiology and this study underlines that it is associated with specific areas of application and methods. The development of this discipline is likely to deserve a framework providing recommendations and guidance at various steps of the studies, from design to report.
Sari, D. P.; Usodo, B.; Subanti, S.
2018-04-01
This research aims to describe metacognitive experience of mathematics education students with strong, average, and weak intrapersonal intelligence in open start problem solving. Type of this research was qualitative research. The research subject was mathematics education students in Muhammadiyah University of Surakarta in academic year 2017/2018. The selected students consisted of 6 students with details of two students in each intrapersonal intelligence category. The research instruments were questionnaire, open start problem solving task, and interview guidelines. Data validity used time triangulation. Data analyses were done through data collection, data reduction, data presentation, and drawing conclusion. Based on findings, subjects with strong intrapersonal intelligence had high self confidence that they were able to solve problem correctly, able to do planning steps and able to solve the problem appropriately. Subjects with average intrapersonal intelligence had high self-assessment that they were able to solve the problem, able to do planning steps appropriately but they had not maximized in carrying out the plan so that it resulted incorrectness answer. Subjects with weak intrapersonal intelligence had high self confidence in capability of solving math problem, lack of precision in taking plans so their task results incorrectness answer.
Proust: A Nano Proof Assistant
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Prabhakar Ragde
2016-11-01
Full Text Available Proust is a small Racket program offering rudimentary interactive assistance in the development of verified proofs for propositional and predicate logic. It is constructed in stages, some of which are done by students before using it to complete proof exercises, and in parallel with the study of its theoretical underpinnings, including elements of Martin-Lof type theory. The goal is twofold: to demystify some of the machinery behind full-featured proof assistants such as Coq and Agda, and to better integrate the study of formal logic with other core elements of an undergraduate computer science curriculum.
An Emergent Framework: Views of Mathematical Processes
Sanchez, Wendy B.; Lischka, Alyson E.; Edenfield, Kelly W.; Gammill, Rebecca
2015-01-01
The findings reported in this paper were generated from a case study of teacher leaders at a state-level mathematics conference. Investigation focused on how participants viewed the mathematical processes of communication, connections, representations, problem solving, and reasoning and proof. Purposeful sampling was employed to select nine…
A beginner's guide to mathematical logic
Smullyan, Raymond M
2014-01-01
Combining stories of great philosophers, quotations, and riddles with the fundamentals of mathematical logic, this new textbook for first courses in mathematical logic was written by the subject's creative master. Raymond Smullyan offers clear, incremental presentations of difficult logic concepts with creative explanations and unique problems related to proofs, propositional logic and first-order logic, undecidability, recursion theory, and other topics.
On the Nature and Role of Peer Review in Mathematics.
Andersen, Line Edslev
2017-01-01
For the past three decades, peer review practices have received much attention in the literature. But although this literature covers many research fields, only one previous systematic study has been devoted to the practice of peer review in mathematics, namely a study by Geist, Löwe, and Van Kerkhove from 2010. This lack of attention may be due to a view that peer review in mathematics is more reliable, and therefore less interesting as an object of study, than peer review in other fields. In fact, Geist, Löwe, and Van Kerkhove argue that peer review in mathematics is relatively reliable. At the same time, peer review in mathematics differs from peer review in most, if not all, other fields in that papers submitted to mathematical journals are usually only reviewed by a single referee. Furthermore, recent empirical studies indicate that the referees do not check the papers line by line. I argue that, in spite of this, mathematical practice in general and refereeing practices in particular are such that the common practice of mathematical journals of using just one referee is justified from the point of view of proof validity assessment. The argument is based on interviews I conducted with seven mathematicians.
Relativistic particle dynamics: Lagrangian proof of the no-interaction theorem
International Nuclear Information System (INIS)
Marmo, G.; Mukunda, N.; Sudarshan, E.C.G.
1983-11-01
An economical proof is given, in the Lagrangian framework, of the No Interaction Theorem of relativistic particle mechanics. It is based on the assumption that there is a Lagrangian, which if singular is allowed to lead at most to primary first class constraints. The proof works with Lagrange rather than Poisson brackets, leading to considerable simplifications compared to other proofs
On the Mechanization of the Proof of Hessenberg's Theorem in Coherent Logic
Bezem, M.; Hendriks, R.D.A.
2008-01-01
We propose to combine interactive proof construction with proof automation for a fragment of first-order logic called Coherent Logic (CL). CL allows enough existential quantification to make Skolemization unnecessary. Moreover, CL has a constructive proof system based on forward reasoning, which is
Illustrating Mathematics using 3D Printers
Knill, Oliver; Slavkovsky, Elizabeth
2013-01-01
3D printing technology can help to visualize proofs in mathematics. In this document we aim to illustrate how 3D printing can help to visualize concepts and mathematical proofs. As already known to educators in ancient Greece, models allow to bring mathematics closer to the public. The new 3D printing technology makes the realization of such tools more accessible than ever. This is an updated version of a paper included in book Low-Cost 3D Printing for science, education and Sustainable Devel...
Mathematics for natural scientists II advanced methods
Kantorovich, Lev
2016-01-01
This book covers the advanced mathematical techniques useful for physics and engineering students, presented in a form accessible to physics students, avoiding precise mathematical jargon and laborious proofs. Instead, all proofs are given in a simplified form that is clear and convincing for a physicist. Examples, where appropriate, are given from physics contexts. Both solved and unsolved problems are provided in each chapter. Mathematics for Natural Scientists II: Advanced Methods is the second of two volumes. It follows the first volume on Fundamentals and Basics.
A note on the proof of Bertrand's theorem
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Jovanović Vladimir
2015-01-01
Full Text Available In this paper we fill a common gap in the proof of Bertrand' theorem present both the in Bertrand's original paper Théorème relatif au movement d'un point attiré vers un centre fixe and in the Arnold's book Mathematical methods of classical mechanics, by providing missing details which pertain to the problem of how to single out elastic and gravitational potentials among the power law ones.
Complex proofs of real theorems
Lax, Peter D
2011-01-01
Complex Proofs of Real Theorems is an extended meditation on Hadamard's famous dictum, "The shortest and best way between two truths of the real domain often passes through the imaginary one." Directed at an audience acquainted with analysis at the first year graduate level, it aims at illustrating how complex variables can be used to provide quick and efficient proofs of a wide variety of important results in such areas of analysis as approximation theory, operator theory, harmonic analysis, and complex dynamics. Topics discussed include weighted approximation on the line, Müntz's theorem, Toeplitz operators, Beurling's theorem on the invariant spaces of the shift operator, prediction theory, the Riesz convexity theorem, the Paley-Wiener theorem, the Titchmarsh convolution theorem, the Gleason-Kahane-Żelazko theorem, and the Fatou-Julia-Baker theorem. The discussion begins with the world's shortest proof of the fundamental theorem of algebra and concludes with Newman's almost effortless proof of the prime ...
Wang, Sheng-Yuan; Chang, Shao-Chen; Hwang, Gwo-Jen; Chen, Pei-Ying
2018-01-01
In traditional teacher-centered mathematics instruction, students might show low learning motivation owing to the lack of applied contexts. Game-based learning has been recognized as a potential approach to addressing this issue; however, without proper alignment between the gaming and math-applied contexts, the benefits of game-based learning…
International Nuclear Information System (INIS)
Lim, Young-Chul; Lee, Han-Seung; Noguchi, Takafumi
2009-01-01
This study aims to formulate a resistivity model whereby the concrete resistivity expressing the environment of steel reinforcement can be directly estimated and evaluated based on measurement immediately above reinforcement as a method of evaluating corrosion deterioration in reinforced concrete structures. It also aims to provide a theoretical ground for the feasibility of durability evaluation by electric non-destructive techniques with no need for chipping of cover concrete. This Resistivity Estimation Model (REM), which is a mathematical model using the mirror method, combines conventional four-electrode measurement of resistivity with geometric parameters including cover depth, bar diameter, and electrode intervals. This model was verified by estimation using this model at areas directly above reinforcement and resistivity measurement at areas unaffected by reinforcement in regard to the assessment of the concrete resistivity. Both results strongly correlated, proving the validity of this model. It is expected to be applicable to laboratory study and field diagnosis regarding reinforcement corrosion. (author)
Gustiani, Ineu; Widodo, Ari; Suwarma, Irma Rahma
2017-05-01
This study is intended to examine the development and validation of simple machines instructional material that developed based on Science, Technology, Engineering and Mathematics (STEM) framework that provides guidance to help students learn and practice for real life and enable individuals to use knowledge and skills they need to be an informed citizen. Sample of this study consist of one class of 8th grader at a junior secondary school in Bandung, Indonesia. To measure student learning, a pre-test and post-test were given before and after implementation of the STEM based instructional material. In addition, a questionnaire of readability was given to examine the clarity and difficulty level of each page of instructional material. A questionnaire of students' response towards instructional material given to students and teachers at the end of instructional material reading session to measure layout aspects, content aspects and utility aspects of instructional material for being used in the junior secondary school classroom setting. The results show that readability aspect and students' response towards STEM based instructional material of STEM based instructional material is categorized as very high. Pretest and posttest responses revealed that students retained significant amounts information upon completion of the STEM instructional material. Student overall learning gain is 0.67 which is categorized as moderate. In summary, STEM based instructional material that was developed is valid enough to be used as educational materials necessary for conducting effective STEM education.
Co-constructive Logics for Proofs and Refutations
Directory of Open Access Journals (Sweden)
Trafford James
2015-01-01
Full Text Available This paper considers logics which are formally dual to intuitionistic logic in order to investigate a co-constructive logic for proofs and refutations. This is philosophically motivated by a set of problems regarding the nature of constructive truth, and its relation to falsity. It is well known both that intuitionism can not deal constructively with negative information, and that defining falsity by means of intuitionistic negation leads, under widely-held assumptions, to a justification of bivalence. For example, we do not want to equate falsity with the non-existence of a proof since this would render a statement such as “pi is transcendental” false prior to 1882. In addition, the intuitionist account of negation as shorthand for the derivation of absurdity is inadequate, particularly outside of purely mathematical contexts. To deal with these issues, I investigate the dual of intuitionistic logic, co-intuitionistic logic, as a logic of refutation, alongside intuitionistic logic of proofs. Direct proof and refutation are dual to each other, and are constructive, whilst there also exist syntactic, weak, negations within both logics. In this respect, the logic of refutation is weakly paraconsistent in the sense that it allows for statements for which, neither they, nor their negation, are refuted. I provide a proof theory for the co-constructive logic, a formal dualizing map between the logics, and a Kripke-style semantics. This is given an intuitive philosophical rendering in a re-interpretation of Kolmogorov's logic of problems.
Hiriart-Urruty, Jean-Baptiste
This book contains a collection of exercises (called “tapas”) at undergraduate level, mainly from the fields of real analysis, calculus, matrices, convexity, and optimization. Most of the problems presented here are non-standard and some require broad knowledge of different mathematical subjects in order to be solved. The author provides some hints and (partial) answers and also puts these carefully chosen exercises into context, presents information on their origins, and comments on possible extensions. With stars marking the levels of difficulty, these tapas show or prove something interesting, challenge the reader to solve and learn, and may have surprising results. This first volume of Mathematical Tapas will appeal to mathematicians, motivated undergraduate students from science-based areas, and those generally interested in mathematics.
Mathematics computer-based training tool for pupils with special educational needs
Čeponienė, Lina
2010-01-01
Mathematics has a great influence on the development of world science and education, technology and human culture. Ukeje observes that without mathematics there is no science, without science there is no modern technology and without modern technology there is no modern society. In other words, mathematics is the precursor and the queen of science and technology and the indispensable single element in modern societal development. So, it plays a vital role in developing learners abilities to c...
Makar, Katie; Fielding-Wells, Jill
2018-03-01
The 3-year study described in this paper aims to create new knowledge about inquiry norms in primary mathematics classrooms. Mathematical inquiry addresses complex problems that contain ambiguities, yet classroom environments often do not adopt norms that promote curiosity, risk-taking and negotiation needed to productively engage with complex problems. Little is known about how teachers and students initiate, develop and maintain norms of mathematical inquiry in primary classrooms. The research question guiding this study is, "How do classroom norms develop that facilitate student learning in primary classrooms which practice mathematical inquiry?" The project will (1) analyse a video archive of inquiry lessons to identify signature practices that enhance productive classroom norms of mathematical inquiry and facilitate learning, (2) engage expert inquiry teachers to collaborate to identify and design strategies for assisting teachers to develop and sustain norms over time that are conducive to mathematical inquiry and (3) support and study teachers new to mathematical inquiry adopting these practices in their classrooms. Anticipated outcomes include identification and illustration of classroom norms of mathematical inquiry, signature practices linked to these norms and case studies of primary teachers' progressive development of classroom norms of mathematical inquiry and how they facilitate learning.
Kant's Transcendental Arguments as Conceptual Proofs | Stapleford ...
African Journals Online (AJOL)
The paper is an attempt to explain what a transcendental argument is for Kant. The interpretation is based on a reading of the “Discipline of Pure Reason,” sections 1 and 4, of the first Critique. The author first identifies several statements that Kant makes about the method of proof he followed in the “Analytic of Principles,” ...
Swars, Susan Lee
2015-01-01
This mixed methods study examined the mathematical preparation of elementary teachers in a Teach for America (TFA) program, focal participants for whom there is scant extant research. Data collection occurred before and after a university mathematics methods course, with a particular focus on the participants' (n = 22) mathematical beliefs,…
Newkirk-Turner, Brandi L; Johnson, Valerie E
2018-04-05
The purpose of this tutorial is to discuss the use of curriculum-based language assessment (CBLA) with students who are English language learners and students who speak nonmainstream varieties of English, such as African American English. The article begins with a discussion of the discourse of mathematics and the role of the speech-language pathologist (SLP), followed by a review of studies that includes those that examined the performance of English language learner and nonmainstream dialect-speaking students on word-based math items. The literature review highlights the linguistic and content biases associated with word-based math problems. Useful strategies that SLPs and educators can incorporate in culturally and linguistically appropriate assessments are discussed. The tutorial ends with a discussion of CBLA as a viable assessment approach to use with culturally and linguistically diverse students. Tests used at national, state, and school levels to assess students' math abilities have associated linguistic bias and content bias often leading to an inaccurate depiction of culturally and linguistically diverse students' math skills. CBLA as an assessment method can be used by school-based SLPs to gather valid and useful information about culturally and linguistically diverse students' language for learning math. By using CBLA, SLPs can help modify curricular tasks in broader contexts in an effort to make math, including high-level math, "accessible and achievable for all" students (American Speech-Language-Hearing Association, 2017).
Heath, Thomas
2015-01-01
Originally published in 1949. This meticulously researched book presents a comprehensive outline and discussion of Aristotle's mathematics with the author's translations of the greek. To Aristotle, mathematics was one of the three theoretical sciences, the others being theology and the philosophy of nature (physics). Arranged thematically, this book considers his thinking in relation to the other sciences and looks into such specifics as squaring of the circle, syllogism, parallels, incommensurability of the diagonal, angles, universal proof, gnomons, infinity, agelessness of the universe, surface of water, meteorology, metaphysics and mechanics such as levers, rudders, wedges, wheels and inertia. The last few short chapters address 'problems' that Aristotle posed but couldn't answer, related ethics issues and a summary of some short treatises that only briefly touch on mathematics.
Mathematical calibration procedure of a capacitive sensor-based indexed metrology platform
International Nuclear Information System (INIS)
Brau-Avila, A; Valenzuela-Galvan, M; Herrera-Jimenez, V M; Santolaria, J; Aguilar, J J; Acero, R
2017-01-01
The demand for faster and more reliable measuring tasks for the control and quality assurance of modern production systems has created new challenges for the field of coordinate metrology. Thus, the search for new solutions in coordinate metrology systems and the need for the development of existing ones still persists. One example of such a system is the portable coordinate measuring machine (PCMM), the use of which in industry has considerably increased in recent years, mostly due to its flexibility for accomplishing in-line measuring tasks as well as its reduced cost and operational advantages compared to traditional coordinate measuring machines. Nevertheless, PCMMs have a significant drawback derived from the techniques applied in the verification and optimization procedures of their kinematic parameters. These techniques are based on the capture of data with the measuring instrument from a calibrated gauge object, fixed successively in various positions so that most of the instrument measuring volume is covered, which results in time-consuming, tedious and expensive verification and optimization procedures. In this work the mathematical calibration procedure of a capacitive sensor-based indexed metrology platform (IMP) is presented. This calibration procedure is based on the readings and geometric features of six capacitive sensors and their targets with nanometer resolution. The final goal of the IMP calibration procedure is to optimize the geometric features of the capacitive sensors and their targets in order to use the optimized data in the verification procedures of PCMMs. (paper)
International Nuclear Information System (INIS)
Ataei, Sh; Mahmud, Z; Khalid, M N
2014-01-01
The students learning outcomes clarify what students should know and be able to demonstrate after completing their course. So, one of the issues on the process of teaching and learning is how to assess students' learning. This paper describes an application of the dichotomous Rasch measurement model in measuring the cognitive process of engineering students' learning of mathematics. This study provides insights into the perspective of 54 engineering students' cognitive ability in learning Calculus III based on Bloom's Taxonomy on 31 items. The results denote that some of the examination questions are either too difficult or too easy for the majority of the students. This analysis yields FIT statistics which are able to identify if there is data departure from the Rasch theoretical model. The study has identified some potential misfit items based on the measurement of ZSTD where the removal misfit item was accomplished based on the MNSQ outfit of above 1.3 or less than 0.7 logit. Therefore, it is recommended that these items be reviewed or revised to better match the range of students' ability in the respective course.
Mathematical calibration procedure of a capacitive sensor-based indexed metrology platform
Brau-Avila, A.; Santolaria, J.; Acero, R.; Valenzuela-Galvan, M.; Herrera-Jimenez, V. M.; Aguilar, J. J.
2017-03-01
The demand for faster and more reliable measuring tasks for the control and quality assurance of modern production systems has created new challenges for the field of coordinate metrology. Thus, the search for new solutions in coordinate metrology systems and the need for the development of existing ones still persists. One example of such a system is the portable coordinate measuring machine (PCMM), the use of which in industry has considerably increased in recent years, mostly due to its flexibility for accomplishing in-line measuring tasks as well as its reduced cost and operational advantages compared to traditional coordinate measuring machines. Nevertheless, PCMMs have a significant drawback derived from the techniques applied in the verification and optimization procedures of their kinematic parameters. These techniques are based on the capture of data with the measuring instrument from a calibrated gauge object, fixed successively in various positions so that most of the instrument measuring volume is covered, which results in time-consuming, tedious and expensive verification and optimization procedures. In this work the mathematical calibration procedure of a capacitive sensor-based indexed metrology platform (IMP) is presented. This calibration procedure is based on the readings and geometric features of six capacitive sensors and their targets with nanometer resolution. The final goal of the IMP calibration procedure is to optimize the geometric features of the capacitive sensors and their targets in order to use the optimized data in the verification procedures of PCMMs.
Mathematics related anxiety: Mathematics bogeyman or not?
Directory of Open Access Journals (Sweden)
Videnović Marina
2011-01-01
Full Text Available Data of the PISA 2003 survey indicate high levels of mathematics anxiety of students in Serbia. More than half of our students worry whether they will have difficulties in mathematics class or whether they will earn poor marks. Aims of this study therefore are: examining relationship between math anxiety and achievement at mathematics literacy scale; establishing possible predictors of math anxiety and identification of students' groups in relations to their relationship towards mathematics as a subject. Mathematics anxiety is statistically negatively correlated with school achievement and achievement at mathematics literacy scale. Socio-demographic factors, motivational and cognitive aspects related to learning mathematics, perception of school and classroom climate explain 40% variance of mathematics anxiety. Based on students' relationship towards mathematics they cam be divided into three groups; while dimensions that apart them are uninterested-interested in mathematics and presence-absence of anxiety. The group displaying anxiety scores lowest among the three. Applying qualitative analysis students' and teachers' attitudes on specific issues related to teaching and learning mathematics was examined.
Kelly, Daniel P.; Rutherford, Teomara
2017-01-01
Khan Academy is a large and popular open educational resource (OER) with little empirical study into its impact on student achievement in mathematics when used in schools. In this study, we examined the use of Khan Academy as a mathematics intervention among seventh grade students over a 4-week period versus a control group. We also compared…
Examining Student Opinions on Computer Use Based on the Learning Styles in Mathematics Education
Ozgen, Kemal; Bindak, Recep
2012-01-01
The purpose of this study is to identify the opinions of high school students, who have different learning styles, related to computer use in mathematics education. High school students' opinions on computer use in mathematics education were collected with both qualitative and quantitative approaches in the study conducted with a survey model. For…
Teaching Mathematics Bilingually for Kindergarten Students with Teaching Aids Based on Local Wisdom
Ambarini, Ririn; Setyaji, Arso; Suneki, Sri
2018-01-01
Language and Mathematics are both skills and knowledge that need to master well so that it can be the provision for students' future life when mingling with the community or society. Because of that the integration of teaching both language and Mathematics in bilingual Math learning will give many benefits to the students. They will learn not only…
Demitra; Sarjoko
2018-01-01
Indigenous people of Dayak tribe in Kalimantan, Indonesia have traditionally relied on a system of mutual cooperation called "handep." The cultural context has an influence on students mathematics learning. The "handep" system might be suitable for modern learning situations to develop mathematical problem-solving skill. The…
Ramnarain, Umesh
2014-01-01
A major impediment to problem solving in mathematics in the great majority of South African schools is that disadvantaged students from seriously impoverished learning environments are lacking in the necessary informal mathematical knowledge to develop their own strategies for solving non-routine problems. A randomized pretest-posttest control…
Applying Mathematical Concepts with Hands-On, Food-Based Science Curriculum
Roseno, Ashley T.; Carraway-Stage, Virginia G.; Hoerdeman, Callan; Díaz, Sebastián R.; Geist, Eugene; Duffrin, Melani W.
2015-01-01
This article addresses the current state of the mathematics education system in the United States and provides a possible solution to the contributing issues. As a result of lower performance in primary mathematics, American students are not acquiring the necessary quantitative literacy skills to become successful adults. This study analyzed the…
Comparison of learning models based on mathematics logical intelligence in affective domain
Widayanto, Arif; Pratiwi, Hasih; Mardiyana
2018-04-01
The purpose of this study was to examine the presence or absence of different effects of multiple treatments (used learning models and logical-mathematical intelligence) on the dependent variable (affective domain of mathematics). This research was quasi experimental using 3x3 of factorial design. The population of this research was VIII grade students of junior high school in Karanganyar under the academic year 2017/2018. Data collected in this research was analyzed by two ways analysis of variance with unequal cells using 5% of significance level. The result of the research were as follows: (1) Teaching and learning with model TS lead to better achievement in affective domain than QSH, teaching and learning with model QSH lead to better achievement in affective domain than using DI; (2) Students with high mathematics logical intelligence have better achievement in affective domain than students with low mathematics logical intelligence have; (3) In teaching and learning mathematics using learning model TS, students with moderate mathematics logical intelligence have better achievement in affective domain than using DI; and (4) In teaching and learning mathematics using learning model TS, students with low mathematics logical intelligence have better achievement in affective domain than using QSH and DI.
Classroom-Based Professional Expertise: A Mathematics Teacher's Practice with Technology
Bozkurt, Gulay; Ruthven, Kenneth
2017-01-01
This study examines the classroom practice and craft knowledge underpinning one teacher's integration of the use of GeoGebra software into mathematics teaching. The chosen teacher worked in an English secondary school and was professionally well regarded as an accomplished user of digital technology in mathematics teaching. Designed in accordance…
Mathematics Practicum at St. Olaf College: Project-Based Learning through Academic Civic Engagement
Sanft, Rebecca; Ziegler-Graham, Kathryn
2018-01-01
The Mathematics Practicum has been offered at St. Olaf College for over 30 years. The Practicum is a 4-week, January Interim course where three teams of five students work on consulting problems solicited from area businesses, government agencies, and non-profit organizations. These problems have significant mathematical, statistical, and…
Wekesa, Duncan Wasike
2006-01-01
Mathematical knowledge and understanding is important not only for scientific progress and development but also for its day-to-day application in social sciences and arts, government, business and management studies and household chores. But the general performance in school mathematics in Kenya has been poor over the years. There is evidence that…
Students' Perceptions of the Learning Environment and Attitudes in Game-Based Mathematics Classrooms
Afari, Ernest; Aldridge, Jill M.; Fraser, Barry J.; Khine, Myint Swe
2013-01-01
We investigated whether the introduction of games into college-level mathematics classes in the United Arab Emirates (UAE) was effective in terms of improving students' perceptions of the learning environment and their attitudes towards of mathematics. A pre-post design involved the administration of English and Arabic versions of two surveys (one…
Kaliszyk, C.; Urban, J.; Vyskocil, J.; Geuvers, J.H.; Watt, S.M.; Davenport, J.H.; Sexton, A.P.; Sojka, P.; Urban, J.
2014-01-01
The goal of this project is to (i) accumulate annotated informal/formal mathematical corpora suitable for training semi-automated translation between informal and formal mathematics by statistical machine-translation methods, (ii) to develop such methods oriented at the formalization task, and in
2016-02-01
proof in mathematics. For example, consider the proof of the Pythagorean Theorem illustrated at: http://www.cut-the-knot.org/ pythagoras / where 112...methods and tools have made significant progress in their ability to model software designs and prove correctness theorems about the systems modeled...assumption criticality” or “ theorem root set size” SITAPS detects potentially brittle verification cases. SITAPS provides tools and techniques that
Risnawati; Khairinnisa, S.; Darwis, A. H.
2018-01-01
The purpose of this study was to develop a CORE model-based worksheet with recitation task that were valid and practical and could facilitate students’ communication skills in Linear Algebra course. This study was conducted in mathematics education department of one public university in Riau, Indonesia. Participants of the study were media and subject matter experts as validators as well as students from mathematics education department. The objects of this study are students’ worksheet and students’ mathematical communication skills. The results of study showed that: (1) based on validation of the experts, the developed students’ worksheet was valid and could be applied for students in Linear Algebra courses; (2) based on the group trial, the practicality percentage was 92.14% in small group and 90.19% in large group, so the worksheet was very practical and could attract students to learn; and (3) based on the post test, the average percentage of ideals was 87.83%. In addition, the results showed that the students’ worksheet was able to facilitate students’ mathematical communication skills in linear algebra course.
Mathematical modeling of a radio-frequency path for IEEE 802.11ah based wireless sensor networks
Tyshchenko, Igor; Cherepanov, Alexander; Dmitrii, Vakhnin; Popova, Mariia
2017-09-01
This article discusses the process of creating the mathematical model of a radio-frequency path for an IEEE 802.11ah based wireless sensor networks using M atLab Simulink CAD tools. In addition, it describes occurring perturbing effects and determining the presence of a useful signal in the received mixture.
Gann, Linda
2013-01-01
The research centered on secondary mathematics teachers' beliefs, attitudes, knowledge base, and practices in meeting the academic and language needs of English language learners. Using socio-cultural theory and social practice theory to frame the study, the research design employed a mixed methods approach incorporating self-reported surveys,…
Sikko, S.A.; Lyngved, R.; Pepin, B.
2012-01-01
This paper reports on mathematics and science teachers’ beliefs concerning the use of inquiry-based teaching strategies. Two different surveys were conducted: one with 24 teachers who were to become future instructional leaders; and one with 75 teachers as part of an international baseline study. We
Qudah, Ahmad Hassan
2016-01-01
This study aimed at identify the effect of using a proposed teaching strategy based on the selective thinking in acquire mathematical concepts by Classroom Teacher Students at Al- al- Bayt University, The sample of the study consisted of (74) students, equally distributed into a control group and an experimental group. The selective thinking…
Rockhill, Theron D.
Reported is an attempt to develop and evaluate an individualized instructional program in pre-calculus college mathematics. Four computer based resource units were developed in the areas of set theory, relations and function, algebra, trigonometry, and analytic geometry. Objectives were determined by experienced calculus teachers, and…
Modebelu, M. N.; Ogbonna, C. C.
2014-01-01
This study aimed at determining the effect of reform-based-instructional method learning styles on students' achievement and retention in mathematics. A sample size of 119 students was randomly selected. The quasiexperimental design comprising pre-test, post-test, and randomized control group were employed. The Collin Rose learning styles…