A Framework for Proofs and Refutations in School Mathematics: Increasing Content by Deductive Guessing

Science.gov (United States)

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…

Roads to infinity the mathematics of truth and proof

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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

The State of Proof in Finnish and Swedish Mathematics Textbooks--Capturing Differences in Approaches to Upper-Secondary Integral Calculus

Science.gov (United States)

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…

Opportunities to Learn Reasoning and Proof in High School Mathematics Textbooks

Science.gov (United States)

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…

Proof patterns

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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.

Proofs and fundamentals a first course in abstract mathematics

CERN Document Server

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 ...

Revisiting the reliability of published mathematical proofs: where do we go next?

Directory of Open Access Journals (Sweden)

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.

Proofs without Words: A Visual Application of Reasoning and Proof

Science.gov (United States)

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…

Skolem and pessimism about proof in mathematics.

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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.

The Effects of GeoGebra Software on Pre-Service Mathematics Teachers' Attitudes and Views toward Proof and Proving

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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…

The effects of GeoGebra software on pre-service mathematics teachers' attitudes and views toward proof and proving

Science.gov (United States)

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.

Prospective Teachers' Conceptions of Proof Comprehension: Revisiting a Proof of the Pythagorean Theorem

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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…

The challenge of computer mathematics.

Science.gov (United States)

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.

Teaching Proofs and Algorithms in Discrete Mathematics with Online Visual Logic Puzzles

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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…

Mathematically Gifted High School Students' Approaches to Developing Visual Proofs (VP) and Preliminary Ideas about VP

Science.gov (United States)

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…

Writing proofs in analysis

CERN Document Server

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...

Students Thinking Process in Compiling Mathematical Proof with Semantics Strategy

Directory of Open Access Journals (Sweden)

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

Proof Problems with Diagrams: An Opportunity for Experiencing Proofs and Refutations

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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…

Towards a comprehensive knowledge package for teaching proof: A focus on the misconception that empirical arguments are proofs

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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.

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 ...

Advances in proof theory

CERN Document Server

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 ...

Foundational aspects of non standard mathematics

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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 Mapping

Science.gov (United States)

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…

Proofs that Develop Insight

Science.gov (United States)

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…

Proof and knowledge in mathematics

CERN Document Server

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,

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.

Teachers’ learning and assessing of mathematical processes with emphasis on representations, reasoning and proof

Directory of Open Access Journals (Sweden)

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.

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

How Mathematicians Determine if an Argument Is a Valid Proof

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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;…

Three Styles Characterising Mathematicians' Pedagogical Perspectives on Proof

Science.gov (United States)

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…

From Inductive Reasoning to Proof

Science.gov (United States)

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…

Values and Norms of Proof for Mathematicians and Students

Science.gov (United States)

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…

Mathematical physics

CERN Document Server

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

The written mathematical communication profile of prospective math teacher in mathematical proving

Science.gov (United States)

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.

Feferman on foundations logic, mathematics, philosophy

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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

Science.gov (United States)

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'…

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.

Implicit proofs

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

Mathematical and empirical proof of principle for an on-body personal lift augmentation device (PLAD).

Science.gov (United States)

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.

Theoretical Mathematics

Science.gov (United States)

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.

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.

Problems and proofs in numbers and algebra

CERN Document Server

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...

Mathematicians' Perspectives on Features of a Good Pedagogical Proof

Science.gov (United States)

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,…

The tools of mathematical reasoning

CERN Document Server

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 writing

CERN Document Server

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...

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

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

Explanatory Unification by Proofs in School Mathematics

Science.gov (United States)

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…

Proof and Pedagogy in Ancient China: Examples from Liu Hui's Commentary on "JIU ZHANG SUAN SHU".

Science.gov (United States)

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.)…

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.

Focus in High School Mathematics: Reasoning and Sense Making in Geometry

Science.gov (United States)

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…

Pluralism in mathematics a new position in philosophy of mathematics

CERN Document Server

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...

Pedagogical Applications from Real Analysis for Secondary Mathematics Teachers

Science.gov (United States)

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…

Helping Children Learn Mathematics through Multiple Intelligences and Standards for School Mathematics.

Science.gov (United States)

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…

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)

A discrete transition to advanced mathematics

CERN Document Server

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

Secondary Teachers' Knowledge of Elementary Number Theory Proofs: The Case of General-Cover Proofs

Science.gov (United States)

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…

Proofs with monotone cuts

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

Illustrating Mathematics using 3D Printers

OpenAIRE

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...

The argument of mathematics

CERN Document Server

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.

New zero-input overflow stability proofs based on Lyapunov theory

NARCIS (Netherlands)

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

Mathematical Observations: The Genesis of Mathematical Discovery in the Classroom

Science.gov (United States)

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…

Informal Content and Student Note-Taking in Advanced Mathematics Classes

Science.gov (United States)

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…

Computerized Proof Techniques for Undergraduates

Science.gov (United States)

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…

Affecting the Flow of a Proof by Creating Presence--A Case Study in Number Theory

Science.gov (United States)

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…

Accounting for Proof Test Data in a Reliability Based Design Optimization Framework

Science.gov (United States)

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.

STEM Gives Meaning to Mathematics

Science.gov (United States)

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…

Mathematics for natural scientists II advanced methods

CERN Document Server

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.

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)

Mathematics a minimal introduction

CERN Document Server

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

Proof and Rhetoric: The Structure and Origin of Proof--From Ancient Greece to Abraham Lincoln's Speech in Defence of the Union and Paul Keating's Mabo Speech

Science.gov (United States)

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…

Lakatos' Proofs and Refutations Comes Alive in an Elementary Classroom.

Science.gov (United States)

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.…

Proof and Proving: Logic, Impasses, and the Relationship to Problem Solving

Science.gov (United States)

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…

Mathematical Modeling in the Undergraduate Curriculum

Science.gov (United States)

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…

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

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

A Coordinate-Based Proof of the Scallop Theorem

OpenAIRE

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.

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

The Transition to Formal Thinking in Mathematics

Science.gov (United States)

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 logic foundations for information science

CERN Document Server

Li, Wei

2014-01-01

Mathematical logic is a branch of mathematics that takes axiom systems and mathematical proofs as its objects of study. This book shows how it can also provide a foundation for the development of information science and technology. The first five chapters systematically present the core topics of classical mathematical logic, including the syntax and models of first-order languages, formal inference systems, computability and representability, and Gödel’s theorems. The last five chapters present extensions and developments of classical mathematical logic, particularly the concepts of version sequences of formal theories and their limits, the system of revision calculus, proschemes (formal descriptions of proof methods and strategies) and their properties, and the theory of inductive inference. All of these themes contribute to a formal theory of axiomatization and its application to the process of developing information technology and scientific theories. The book also describes the paradigm of three kinds...

Mathematical logic foundations for information science

CERN Document Server

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.

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.

Mathematical intuitionism

CERN Document Server

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.

Modifying the ECC-based grouping-proof RFID system to increase inpatient medication safety.

Science.gov (United States)

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.

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.

Mathematical modelling as a proof of concept for MPNs as a human inflammation model for cancer development

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...

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

PROOF on Demand

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 modelling as a proof of concept for MPNs as a human inflammation model for cancer development.

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.

Which kind of mathematics was known and referred to by those who wanted to integrate mathematics in «Wisdom»

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...

Math Attendees Find There's Life After Fermat Proof.

Science.gov (United States)

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.

Developing Teaching Material Based on Realistic Mathematics Andoriented to the Mathematical Reasoning and Mathematical Communication

OpenAIRE

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...

Which kind of mathematics was known by and referred to by those who wanted to integrate mathematics in «Wisdom» - Neopythagoreans and others?

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....

Specification Improvement Through Analysis of Proof Structure (SITAPS): High Assurance Software Development

Science.gov (United States)

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

The Logical Heart of a Classic Proof Revisited: A Guide to Godel's "Incompleteness" Theorems

Science.gov (United States)

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…

Real mathematical analysis

CERN Document Server

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...

Proofs from THE BOOK

CERN Document Server

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...

Theorema 2.0: Computer-Assisted Natural-Style Mathematics

Directory of Open Access Journals (Sweden)

Bruno Buchberger

2016-01-01

Full Text Available The Theorema project aims at the development of a computer assistant for the working mathematician. Support should be given throughout all phases of mathematical activity, from introducing new mathematical concepts by definitions or axioms, through first (computational experiments, the formulation of theorems, their justification by an exact proof, the application of a theorem as an algorithm, until to the dissemination of the results in form of a mathematical publication, the build up of bigger libraries of certified mathematical content and the like. This ambitious project is exactly along the lines of the QED manifesto issued in 1994 (see e.g. http://www.cs.ru.nl/~freek/qed/qed.html and it was initiated in the mid-1990s by Bruno Buchberger. The Theorema system is a computer implementation of the ideas behind the Theorema project. One focus lies on the natural style of system input (in form of definitions, theorems, algorithms, etc., system output (mainly in form of mathematical proofs and user interaction. Another focus is theory exploration, i.e. the development of large consistent mathematical theories in a formal frame, in contrast to just proving single isolated theorems. When using the Theorema system, a user should not have to follow a certain style of mathematics enforced by the system (e.g. basing all of mathematics on set theory or certain variants of type theory, rather should the system support the user in her preferred flavour of doing math. The new implementation of the system, which we refer to as Theorema 2.0, is open-source and available through GitHub.

A bridge to advanced mathematics

CERN Document Server

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

Problem Solving Abilities and Perceptions in Alternative Certification Mathematics Teachers

Science.gov (United States)

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…

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.

Stork Color Proofing Technology

Science.gov (United States)

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.

PROOF as a Service on the Cloud: a Virtual Analysis Facility based on the CernVM ecosystem

CERN Document Server

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...

Three views of logic mathematics, philosophy, and computer science

CERN Document Server

Loveland, Donald W; Sterrett, S G

2014-01-01

Demonstrating the different roles that logic plays in the disciplines of computer science, mathematics, and philosophy, this concise undergraduate textbook covers select topics from three different areas of logic: proof theory, computability theory, and nonclassical logic. The book balances accessibility, breadth, and rigor, and is designed so that its materials will fit into a single semester. Its distinctive presentation of traditional logic material will enhance readers' capabilities and mathematical maturity. The proof theory portion presents classical propositional logic and first-orde

The materiality of mathematics: presenting mathematics at the blackboard.

Science.gov (United States)

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.

An Emergent Framework: Views of Mathematical Processes

Science.gov (United States)

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…

Von Neumann's impossibility proof: Mathematics in the service of rhetorics

Science.gov (United States)

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.

The Role of Proof in Comprehending and Teaching Elementary Linear Algebra.

Science.gov (United States)

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)

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

Feasible mathematics II

CERN Document Server

Remmel, Jeffrey

1995-01-01

Perspicuity is part of proof. If the process by means of which I get a result were not surveyable, I might indeed make a note that this number is what comes out - but what fact is this supposed to confirm for me? I don't know 'what is supposed to come out' . . . . 1 -L. Wittgenstein A feasible computation uses small resources on an abstract computa­ tion device, such as a 'lUring machine or boolean circuit. Feasible math­ ematics concerns the study of feasible computations, using combinatorics and logic, as well as the study of feasibly presented mathematical structures such as groups, algebras, and so on. This volume contains contributions to feasible mathematics in three areas: computational complexity theory, proof theory and algebra, with substantial overlap between different fields. In computational complexity theory, the polynomial time hierarchy is characterized without the introduction of runtime bounds by the closure of certain initial functions under safe composition, predicative recursion on nota...

God created the integers the mathematical breakthroughs that changed history

CERN Document Server

2007-01-01

Bestselling author and physicist Stephen Hawking explores the "masterpieces" of mathematics, 25 landmarks spanning 2,500 years and representing the work of 15 mathematicians, including Augustin Cauchy, Bernard Riemann, and Alan Turing. This extensive anthology allows readers to peer into the mind of genius by providing them with excerpts from the original mathematical proofs and results. It also helps them understand the progression of mathematical thought, and the very foundations of our present-day technologies. Each chapter begins with a biography of the featured mathematician, clearly explaining the significance of the result, followed by the full proof of the work, reproduced from the original publication.

Not just a theory--the utility of mathematical models in evolutionary biology.

Directory of Open Access Journals (Sweden)

Maria R Servedio

2014-12-01

Full Text Available Progress in science often begins with verbal hypotheses meant to explain why certain biological phenomena exist. An important purpose of mathematical models in evolutionary research, as in many other fields, is to act as “proof-of-concept” tests of the logic in verbal explanations, paralleling the way in which empirical data are used to test hypotheses. Because not all subfields of biology use mathematics for this purpose, misunderstandings of the function of proof-of-concept modeling are common. In the hope of facilitating communication, we discuss the role of proof-of-concept modeling in evolutionary biology.

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.

On Federated and Proof Of Validation Based Consensus Algorithms In Blockchain

Science.gov (United States)

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.

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.

University Students' Problem Posing Abilities and Attitudes towards Mathematics.

Science.gov (United States)

Grundmeier, Todd A.

2002-01-01

Explores the problem posing abilities and attitudes towards mathematics of students in a university pre-calculus class and a university mathematical proof class. Reports a significant difference in numeric posing versus non-numeric posing ability in both classes. (Author/MM)

Developing teaching material based on realistic mathematics andoriented to the mathematical reasoning and mathematical communication

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.

A beginner's guide to mathematical logic

CERN Document Server

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.

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.

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.

PROOF on a Batch System

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.

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.

Mathematics and Martial Arts as Connected Art Forms

Science.gov (United States)

Hekimoglu, Serkan

2010-01-01

Parallels between martial arts and mathematics are explored. Misguided public perception of both disciplines, students' misconceptions, and the similarities between proofs and katas are among the striking commonalities between martial arts and mathematics. The author also reflects on what he has learned in his martial arts training, and how this…

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

Mathematical concepts

CERN Document Server

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...

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...

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...

Exercises and problems in mathematical methods of physics

CERN Document Server

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...

A history of folding in mathematics mathematizing the margins

CERN Document Server

Friedman, Michael

2018-01-01

While it is well known that the Delian problems are impossible to solve with a straightedge and compass – for example, it is impossible to construct a segment whose length is ∛2 with these instruments – the Italian mathematician Margherita Beloch Piazzolla's discovery in 1934 that one can in fact construct a segment of length ∛2 with a single paper fold was completely ignored (till the end of the 1980s). This comes as no surprise, since with few exceptions paper folding was seldom considered as a mathematical practice, let alone as a mathematical procedure of inference or proof that could prompt novel mathematical discoveries. A few question immediately arise: Why did paper folding become a non-instrument? What caused the marginalisation of this technique? And how was the mathematical knowledge, which was nevertheless transmitted and prompted by paper folding, later treated and conceptualised? Aiming to answer these questions, this volume provides, for the first time, an extensive historical study...

CDM: Teaching Discrete Mathematics to Computer Science Majors

Science.gov (United States)

Sutner, Klaus

2005-01-01

CDM, for computational discrete mathematics, is a course that attempts to teach a number of topics in discrete mathematics to computer science majors. The course abandons the classical definition-theorem-proof model, and instead relies heavily on computation as a source of motivation and also for experimentation and illustration. The emphasis on…

Why and How Mathematicians Read Proofs: An Exploratory Study

Science.gov (United States)

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,…

Mathematics in Aristotle

CERN Document Server

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.

Substitution Frege and extended Frege proof systems in non-classical logics

Czech Academy of Sciences Publication Activity Database

Jeřábek, Emil

2009-01-01

Roč. 159, č. 2 (2009), s. 1-48 ISSN 0168-0072 R&D Projects: GA AV ČR IAA1019401 Institutional research plan: CEZ:AV0Z10190503 Keywords : propositional proof complexity * Frege system * model logic Subject RIV: BA - General Mathematics Impact factor: 0.667, year: 2009

How we understand mathematics conceptual integration in the language of mathematical description

CERN Document Server

Woźny, Jacek

2018-01-01

This volume examines mathematics as a product of the human mind and analyzes the language of "pure mathematics" from various advanced-level sources. Through analysis of the foundational texts of mathematics, it is demonstrated that math is a complex literary creation, containing objects, actors, actions, projection, prediction, planning, explanation, evaluation, roles, image schemas, metonymy, conceptual blending, and, of course, (natural) language. The book follows the narrative of mathematics in a typical order of presentation for a standard university-level algebra course, beginning with analysis of set theory and mappings and continuing along a path of increasing complexity. At each stage, primary concepts, axioms, definitions, and proofs will be examined in an effort to unfold the tell-tale traces of the basic human cognitive patterns of story and conceptual blending. This book will be of interest to mathematicians, teachers of mathematics, cognitive scientists, cognitive linguists, and anyone interested...

Preservice Mathematics Teachers' Perceptions of Drama Based Instruction

Science.gov (United States)

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…

Courses on the Beauty of Mathematics: Our Version of General Education Mathematics Courses

Science.gov (United States)

Rash, Agnes M.; Fillebrown, Sandra

2016-01-01

This article describes various courses designed to incorporate mathematical proofs into courses for non-math and non-science majors. These courses, nicknamed "math beauty" courses, are designed to discuss one topic in-depth rather than to introduce many topics at a superficial level. A variety of courses, each requiring students to…

Introduction to mathematical logic

CERN Document Server

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

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 ...

A note on the proof of Bertrand's theorem

Directory of Open Access Journals (Sweden)

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.

Special functions of mathematical physics a unified introduction with applications

CERN Document Server

Nikiforov, Arnold F

1988-01-01

With students of Physics chiefly in mind, we have collected the material on special functions that is most important in mathematical physics and quan­ tum mechanics. We have not attempted to provide the most extensive collec­ tion possible of information about special functions, but have set ourselves the task of finding an exposition which, based on a unified approach, ensures the possibility of applying the theory in other natural sciences, since it pro­ vides a simple and effective method for the independent solution of problems that arise in practice in physics, engineering and mathematics. For the American edition we have been able to improve a number of proofs; in particular, we have given a new proof of the basic theorem (§3). This is the fundamental theorem of the book; it has now been extended to cover difference equations of hypergeometric type (§§12, 13). Several sections have been simplified and contain new material. We believe that this is the first time that the theory of classical or­ th...

Logic, mathematics, and computer science modern foundations with practical applications

CERN Document Server

Nievergelt, Yves

2015-01-01

This text for the first or second year undergraduate in mathematics, logic, computer science, or social sciences, introduces the reader to logic, proofs, sets, and number theory. It also serves as an excellent independent study reference and resource for instructors. Adapted from Foundations of Logic and Mathematics: Applications to Science and Cryptography © 2002 Birkhӓuser, this second edition provides a modern introduction to the foundations of logic, mathematics, and computers science, developing the theory that demonstrates construction of all mathematics and theoretical computer science from logic and set theory.  The focus is on foundations, with specific statements of all the associated axioms and rules of logic and set theory, and  provides complete details and derivations of formal proofs. Copious references to literature that document historical development is also provided. Answers are found to many questions that usually remain unanswered: Why is the truth table for logical implication so uni...

Mathematical Biology Modules Based on Modern Molecular Biology and Modern Discrete Mathematics

Science.gov (United States)

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

Mathematical biology modules based on modern molecular biology and modern discrete mathematics.

Science.gov (United States)

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 Justification as Non-Conceptualized Practice: the Babylonian Example

DEFF Research Database (Denmark)

Høyrup, Jens

2012-01-01

cultures do not speak about mathematics involving demonstration. However, Old Babylonian mathematical texts (c. 1800–1600 BCE) reveal both aspects of mathematical demonstration as we know it for instance from the ancient Greeks: arguments showing why the steps undertaken do lead to the required result......; and “critique” (in Kantian sense) investigating the presuppositions behind and limits of these arguments. This is argued on a sample of characteristic but relatively simple texts in translation. Critique plays a minor role only in Old Babylonian mathematics; still, the Babylonian example shows that mathematical...... proof may be present in a mathematical culture even if unsupported by extra-mathematical philosophy or ideology....

On the mathematical treatment of the Born-Oppenheimer approximation

International Nuclear Information System (INIS)

Jecko, Thierry

2014-01-01

Motivated by the paper by Sutcliffe and Woolley [“On the quantum theory of molecules,” J. Chem. Phys. 137, 22A544 (2012)], we present the main ideas used by mathematicians to show the accuracy of the Born-Oppenheimer approximation for molecules. Based on mathematical works on this approximation for molecular bound states, in scattering theory, in resonance theory, and for short time evolution, we give an overview of some rigorous results obtained up to now. We also point out the main difficulties mathematicians are trying to overcome and speculate on further developments. The mathematical approach does not fit exactly to the common use of the approximation in Physics and Chemistry. We criticize the latter and comment on the differences, contributing in this way to the discussion on the Born-Oppenheimer approximation initiated by Sutcliffe and Woolley. The paper neither contains mathematical statements nor proofs. Instead, we try to make accessible mathematically rigourous results on the subject to researchers in Quantum Chemistry or Physics

On the mathematical treatment of the Born-Oppenheimer approximation

Energy Technology Data Exchange (ETDEWEB)

Jecko, Thierry, E-mail: thierry.jecko@u-cergy.fr [AGM, UMR 8088 du CNRS, Université de Cergy-Pontoise, Département de mathématiques, site de Saint Martin, 2 avenue Adolphe Chauvin, F-95000 Pontoise (France)

2014-05-15

Motivated by the paper by Sutcliffe and Woolley [“On the quantum theory of molecules,” J. Chem. Phys. 137, 22A544 (2012)], we present the main ideas used by mathematicians to show the accuracy of the Born-Oppenheimer approximation for molecules. Based on mathematical works on this approximation for molecular bound states, in scattering theory, in resonance theory, and for short time evolution, we give an overview of some rigorous results obtained up to now. We also point out the main difficulties mathematicians are trying to overcome and speculate on further developments. The mathematical approach does not fit exactly to the common use of the approximation in Physics and Chemistry. We criticize the latter and comment on the differences, contributing in this way to the discussion on the Born-Oppenheimer approximation initiated by Sutcliffe and Woolley. The paper neither contains mathematical statements nor proofs. Instead, we try to make accessible mathematically rigourous results on the subject to researchers in Quantum Chemistry or Physics.

On the Relationships between (Relatively) Advanced Mathematical Knowledge and (Relatively) Advanced Problem-Solving Behaviours

Science.gov (United States)

Koichu, Boris

2010-01-01

This article discusses an issue of inserting mathematical knowledge within the problem-solving processes. Relatively advanced mathematical knowledge is defined in terms of "three mathematical worlds"; relatively advanced problem-solving behaviours are defined in terms of taxonomies of "proof schemes" and "heuristic behaviours". The relationships…

Developing Instructional Mathematical Physics Book Based on Inquiry Approach to Improve Students’ Mathematical Problem Solving Ability

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.

Popular lectures on mathematical logic

CERN Document Server

Wang, Hao

2014-01-01

A noted logician and philosopher addresses various forms of mathematical logic, discussing both theoretical underpinnings and practical applications. Author Hao Wang surveys the central concepts and theories of the discipline in a historical and developmental context, and then focuses on the four principal domains of contemporary mathematical logic: set theory, model theory, recursion theory and constructivism, and proof theory.Topics include the place of problems in the development of theories of logic and logic's relation to computer science. Specific attention is given to Gödel's incomplete

Mathematical methods for physicists a comprehensive guide

CERN Document Server

Arfken, George B; Harris, Frank E

2012-01-01

Now in its 7th edition, Mathematical Methods for Physicists continues to provide all the mathematical methods that aspiring scientists and engineers are likely to encounter as students and beginning researchers. This bestselling text provides mathematical relations and their proofs essential to the study of physics and related fields. While retaining the key features of the 6th edition, the new edition provides a more careful balance of explanation, theory, and examples. Taking a problem-solving-skills approach to incorporating theorems with applications, the book's improved focus w

The proof and the pudding what mathematicians, cooks, and you have in common

CERN Document Server

Henle, Jim

2015-01-01

Tie on your apron and step into Jim Henle's kitchen as he demonstrates how two equally savory pursuits-cooking and mathematics-have more in common than you realize. A tasty dish for gourmets of popular math, The Proof and the Pudding offers a witty and flavorful blend of mathematical treats and gastronomic delights that reveal how life in the mathematical world is tantalizingly similar to life in the kitchen. Take a tricky Sudoku puzzle and a cake that fell. Henle shows you that the best way to deal with cooking disasters is also the best way to solve math problems. Or take an L-shaped billi

Student Teachers’ Proof Schemes on Proof Tasks Involving Inequality: Deductive or Inductive?

Science.gov (United States)

Rosyidi, A. H.; Kohar, A. W.

2018-01-01

Exploring student teachers’ proof ability is crucial as it is important for improving the quality of their learning process and help their future students learn how to construct a proof. Hence, this study aims at exploring at the proof schemes of student teachers in the beginning of their studies. Data were collected from 130 proofs resulted by 65 Indonesian student teachers on two proof tasks involving algebraic inequality. To analyse, the proofs were classified into the refined proof schemes level proposed by Lee (2016) ranging from inductive, which only provides irrelevant inferences, to deductive proofs, which consider addressing formal representation. Findings present several examples of each of Lee’s level on the student teachers’ proofs spanning from irrelevant inferences, novice use of examples or logical reasoning, strategic use examples for reasoning, deductive inferences with major and minor logical coherence, and deductive proof with informal and formal representation. Besides, it was also found that more than half of the students’ proofs coded as inductive schemes, which does not meet the requirement for doing the proof for the proof tasks examined in this study. This study suggests teacher educators in teacher colleges to reform the curriculum regarding proof learning which can accommodate the improvement of student teachers’ proving ability from inductive to deductive proof as well from informal to formal proof.

Developing Conceptual Understanding and Definitional Clarity in Linear Algebra through the Three Worlds of Mathematical Thinking

Science.gov (United States)

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…

Why is there Philosophy of Mathematics AT ALL? | Hacking | South ...

African Journals Online (AJOL)

Mathematics plays an inordinate role in the work of many of famous Western philosophers, from the time of Plato, through Husserl and Wittgenstein, and even to the present. Why? This paper points to the experience of learning or making mathematics, with an emphasis on proof. It distinguishes two sources of the perennial ...

Implementation of Bourbaki's Elements of Mathematics in Coq: Part One, Theory of Sets

Directory of Open Access Journals (Sweden)

José Grimm

2010-01-01

Full Text Available This paper presents a formalization of the first book of the series ``Elements of Mathematics'' by Nicolas Bourbaki, using the Coq proof assistant.It discusses formalization of mathematics, and explains in which sense a computer proof of a statement corresponds to a proof in the Bourbaki sense, given that the Coq quantifiers are not defined in terms of Hilbert's epsilon function. The list of axioms and axiom schemes of Bourbaki is compared to the more usual Zermelo-Fraenkel theory, and to those proposed by Carlos Simpson, which form the basis of the Gaia software. Some basic constructions (union, intersection, product, function, equivalence and order relation are described, as well as some properties; this corresponds to Sections 1 to 6 of Chapter II, and the first two sections of Chapter III. A commented proof of Zermelo's theorem is also given. The code (including almost all exercises is available on the Web, underhttp://www-sop.inria.fr/apics/gaia.

Partial differential equations of mathematical physics

CERN Document Server

Sobolev, S L

1964-01-01

Partial Differential Equations of Mathematical Physics emphasizes the study of second-order partial differential equations of mathematical physics, which is deemed as the foundation of investigations into waves, heat conduction, hydrodynamics, and other physical problems. The book discusses in detail a wide spectrum of topics related to partial differential equations, such as the theories of sets and of Lebesgue integration, integral equations, Green's function, and the proof of the Fourier method. Theoretical physicists, experimental physicists, mathematicians engaged in pure and applied math

A readable introduction to real mathematics

CERN Document Server

Rosenthal, Daniel; Rosenthal, Peter

2014-01-01

Designed for an undergraduate course or for independent study, this text presents sophisticated mathematical ideas in an elementary and friendly fashion. The fundamental purpose of this book is to engage the reader and to teach a real understanding of mathematical thinking while conveying the beauty and elegance of mathematics. The text focuses on teaching the understanding of mathematical proofs. The material covered has applications both to mathematics and to other subjects. The book contains a large number of exercises of varying difficulty, designed to help reinforce basic concepts and to motivate and challenge the reader. The sole prerequisite for understanding the text is basic high school algebra; some trigonometry is needed for Chapters 9 and 12. Topics covered include: * mathematical induction * modular arithmetic * the fundamental theorem of arithmetic * Fermat's little theorem * RSA encryption * the Euclidean algorithm * rational and irrational numbers * complex numbers * cardinality * Euclidean pl...

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...

Computer-Game-Based Tutoring of Mathematics

Science.gov (United States)

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,…

Mathematics and God’s Point of View1

Directory of Open Access Journals (Sweden)

Król Zbigniew

2016-03-01

Full Text Available In this paper the final stages of the historical process of the emergence of actual infinity in mathematics are considered. The application of God’s point of view – i.e. the possibility to create mathematics from a divine perspective, i.e. from the point of view of an eternal, timeless, omniscience and unlimited subject of cognition – is one of the main factors in this process. Nicole Oresme is the first man who systematically used actual infinity in mathematical reasoning, constructions and proofs in geometry.

Journey through genius the great theorems of mathematics

CERN Document Server

Dunham, William

1990-01-01

In Journey through Genius, author William Dunham strikes an extraordinary balance between the historical and technical. He devotes each chapter to a principal result of mathematics, such as the solution of the cubic series and the divergence of the harmonic series. Not only does this book tell the stories of the people behind the math, but it also includes discussions and rigorous proofs of the relevant mathematical results.

The mathematics of games of strategy

CERN Document Server

Dresher, Melvin

1981-01-01

A noted research mathematician explores decision making in the absence of perfect information. His clear presentation of the mathematical theory of games of strategy encompasses applications to many fields, including economics, military, business, and operations research. No advanced algebra or non-elementary calculus occurs in most of the proofs.

Type classes for mathematics in type theory

OpenAIRE

Spitters, Bas; Van der Weegen, Eelis

2011-01-01

The introduction of first-class type classes in the Coq system calls for re-examination of the basic interfaces used for mathematical formalization in type theory. We present a new set of type classes for mathematics and take full advantage of their unique features to make practical a particularly flexible approach formerly thought infeasible. Thus, we address both traditional proof engineering challenges as well as new ones resulting from our ambition to build upon this development a library...

Another proof of Gell-Mann and Low's theorem

OpenAIRE

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.

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.

Proof in geometry with "mistakes in geometric proofs"

CERN Document Server

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.

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

DEVELOPMENT OF THE MATHEMATICAL INTUITION OF STUDENTS IN TRAINING THE INVERSE PROBLEMS FOR DIFFERENTIAL EQUATIONS

Directory of Open Access Journals (Sweden)

Виктор Семенович Корнилов

2017-12-01

Full Text Available In article attention to that fact that at students of higher educational institutions of the physical and mathematical and natural-science directions of preparation when training in the reverse tasks for differential equations the mathematical intuition which is an important component of their creative potential develops is paid. The mathematical intuition helps students to comprehend a physical sense of the researched application-oriented task, to select effective methods of mathematical physics for the decision of the reverse task for differential equations.The mathematical intuition of students develops in many respects in case of the decision of different educational jobs. Among such educational jobs: creation of system of integrable equations of the reverse task for differential equations, the proof of the conditional correctness of the decision of the reverse task for differential equations, creation of the difference analog of the reverse task for a differential equation; finding of the numerical decision of the reverse task, the proof of convergence of approximate solution of the reverse task to the exact decision, reasons for the idea of the proof of a correctness (the conditional correctness of the decision of the reverse task for differential equations, a statement of logical outputs of application-oriented or humanitarian character on the basis of the conducted research of the reverse task and other educational jobs.In the course of such training students create system of fundamental knowledge in the field of the reverse and incorrect tasks, acquire new scientific knowledge in the field of applied and calculus mathematics, but, obviously, and develop a mathematical intuition.

AfterMath: the work of proof in the age of human-machine collaboration.

Science.gov (United States)

Dick, Stephanie

2011-09-01

During the 1970s and 1980s, a team of Automated Theorem Proving researchers at the Argonne National Laboratory near Chicago developed the Automated Reasoning Assistant, or AURA, to assist human users in the search for mathematical proofs. The resulting hybrid humans+AURA system developed the capacity to make novel contributions to pure mathematics by very untraditional means. This essay traces how these unconventional contributions were made and made possible through negotiations between the humans and the AURA at Argonne and the transformation in mathematical intuition they produced. At play in these negotiations were experimental practices, nonhumans, and nonmathematical modes of knowing. This story invites an earnest engagement between historians of mathematics and scholars in the history of science and science studies interested in experimental practice, material culture, and the roles of nonhumans in knowledge making.

On the Nature and Role of Peer Review in Mathematics.

Science.gov (United States)

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.

A student's guide to the study, practice, and tools of modern mathematics

CERN Document Server

Bindner, Donald

2010-01-01

A Student's Guide to the Study, Practice, and Tools of Modern Mathematics provides an accessible introduction to the world of mathematics. It offers tips on how to study and write mathematics as well as how to use various mathematical tools, from LaTeX and Beamer to Mathematica® and Maple™ to MATLAB® and R. Along with a color insert, the text includes exercises and challenges to stimulate creativity and improve problem solving abilities.The first section of the book covers issues pertaining to studying mathematics. The authors explain how to write mathematical proofs and papers, how to perform

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.)

How to think like a mathematician a companion to undergraduate mathematics

CERN Document Server

Houston, Kevin

2009-01-01

Looking for a head start in your undergraduate degree in mathematics? Maybe you've already started your degree and feel bewildered by the subject you previously loved? Don't panic! This friendly companion will ease your transition to real mathematical thinking. Working through the book you will develop an arsenal of techniques to help you unlock the meaning of definitions, theorems and proofs, solve problems, and write mathematics effectively. All the major methods of proof - direct method, cases, induction, contradiction and contrapositive - are featured. Concrete examples are used throughout, and you'll get plenty of practice on topics common to many courses such as divisors, Euclidean algorithms, modular arithmetic, equivalence relations, and injectivity and surjectivity of functions. The material has been tested by real students over many years so all the essentials are covered. With over 300 exercises to help you test your progress, you'll soon learn how to think like a mathematician.

Principle-Based Mathematics: An Exploratory Study

OpenAIRE

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...

Proceedings – Mathematical Sciences | Indian Academy of Sciences

Indian Academy of Sciences (India)

Home; Journals; Proceedings – Mathematical Sciences; Volume 114; Issue 2. A Variational Proof for the Existence of a Conformal Metric with Preassigned Negative Gaussian Curvature for Compact Riemann Surfaces of Genus >1. Rukmini Dey. Erratum Volume 114 Issue 2 May 2004 pp 215-215 ...

Mathematics for natural scientists fundamentals and basics

CERN Document Server

Kantorovich, Lev

2016-01-01

This book, the first in a two part series, covers a course of mathematics tailored specifically for physics, engineering and chemistry students at the undergraduate level. It is unique in that it begins with logical concepts of mathematics first encountered at A-level and covers them in thorough detail, filling in the gaps in students' knowledge and reasoning. Then the book aids the leap between A-level and university-level mathematics, with complete proofs provided throughout and all complex mathematical concepts and techniques presented in a clear and transparent manner. Numerous examples and problems (with answers) are given for each section and, where appropriate, mathematical concepts are illustrated in a physics context. This text gives an invaluable foundation to students and a comprehensive aid to lecturers. Mathematics for Natural Scientists: Fundamentals and Basics is the first of two volumes. Advanced topics and their applications in physics are covered in the second volume.

Semantics and correctness proofs for programs with partial functions

International Nuclear Information System (INIS)

Yakhnis, A.; Yakhnis, V.

1996-01-01

This paper presents a portion of the work on specification, design, and implementation of safety-critical systems such as reactor control systems. A natural approach to this problem, once all the requirements are captured, would be to state the requirements formally and then either to prove (preferably via automated tools) that the system conforms to spec (program verification), or to try to simultaneously generate the system and a mathematical proof that the requirements are being met (program derivation). An obstacle to this is frequent presence of partially defined operations within the software and its specifications. Indeed, the usual proofs via first order logic presuppose everywhere defined operations. Recognizing this problem, David Gries, in ''The Science of Programming,'' 1981, introduced the concept of partial functions into the mainstream of program correctness and gave hints how his treatment of partial functions could be formalized. Still, however, existing theorem provers and software verifiers have difficulties in checking software with partial functions, because of absence of uniform first order treatment of partial functions within classical 2-valued logic. Several rigorous mechanisms that took partiality into account were introduced [Wirsing 1990, Breu 1991, VDM 1986, 1990, etc.]. However, they either did not discuss correctness proofs or departed from first order logic. To fill this gap, the authors provide a semantics for software correctness proofs with partial functions within classical 2-valued 1st order logic. They formalize the Gries treatment of partial functions and also cover computations of functions whose argument lists may be only partially available. An example is nuclear reactor control relying on sensors which may fail to deliver sense data. This approach is sufficiently general to cover correctness proofs in various implementation languages

Factors Influencing Elementary Mathematics Teachers' Beliefs in Reform-Based Teaching

Science.gov (United States)

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…

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

Mathematical Concepts and Proofs from Nicole Oresme: Using the History of Calculus to Teach Mathematics

Science.gov (United States)

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…

Characteristics of mathematics teaching in Shanghai, China: Through the lens of a Malaysian

Science.gov (United States)

Lim, Chap Sam

2007-06-01

The mathematical performance of Chinese students, from mainland China, Hong Kong and Taiwan, is widely acclaimed in international comparisons of mathematics achievement. However, in the eyes of the Western educators, the environments established in Chinese schools are deemed relatively unfavourable for mathematics learning. This paper reports on a study that investigates the characteristics of effective mathematics teaching in five Shanghai schools. Findings reveal that those characteristics include (a) teaching with variation; (b) emphasis of precise and elegant mathematical language; (c) emphasis of logical reasoning, mathematical thinking and proofing during teaching; (d) order and serious classroom discipline; (e) strong and coherence teacher-student rapport, and (f) strong collaborative culture amongst mathematics teachers.

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.

A mathematical tapestry demonstrating the beautiful unity of mathematics

CERN Document Server

Hilton, Peter; Donmoyer, Sylvie

2010-01-01

This easy-to-read 2010 book demonstrates how a simple geometric idea reveals fascinating connections and results in number theory, the mathematics of polyhedra, combinatorial geometry, and group theory. Using a systematic paper-folding procedure it is possible to construct a regular polygon with any number of sides. This remarkable algorithm has led to interesting proofs of certain results in number theory, has been used to answer combinatorial questions involving partitions of space, and has enabled the authors to obtain the formula for the volume of a regular tetrahedron in around three steps, using nothing more complicated than basic arithmetic and the most elementary plane geometry. All of these ideas, and more, reveal the beauty of mathematics and the interconnectedness of its various branches. Detailed instructions, including clear illustrations, enable the reader to gain hands-on experience constructing these models and to discover for themselves the patterns and relationships they unearth.

Proof of cipher text ownership based on convergence encryption

Science.gov (United States)

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.

Using Mental Imagery Processes for Teaching and Research in Mathematics and Computer Science

Science.gov (United States)

Arnoux, Pierre; Finkel, Alain

2010-01-01

The role of mental representations in mathematics and computer science (for teaching or research) is often downplayed or even completely ignored. Using an ongoing work on the subject, we argue for a more systematic study and use of mental representations, to get an intuition of mathematical concepts, and also to understand and build proofs. We…

The Proof by Cases Property and its Variants in Structural Consequence Relations

Czech Academy of Sciences Publication Activity Database

Cintula, Petr; Noguera, Carles

2013-01-01

Roč. 101, č. 4 (2013), s. 713-747 ISSN 0039-3215 R&D Project s: GA MŠk(CZ) 1M0545 EU Project s: European Commission(XE) 247584 - MATOMUVI Institutional research plan: CEZ:AV0Z1030915 Institutional support: RVO:67985556 Keywords : Abstract Algebraic Logic * Generalized disjunction * Proof by cases properties * Consequence relations * Filter-distributive logics * Protoalgebraic logics Subject RIV: BA - General Mathematics Impact factor: 0.330, year: 2013

The Proof by Cases Property and its Variants in Structural Consequence Relations

Czech Academy of Sciences Publication Activity Database

Cintula, Petr; Noguera, Carles

2013-01-01

Roč. 101, č. 4 (2013), s. 713-747 ISSN 0039-3215 R&D Projects: GA MŠk(CZ) 1M0545 EU Projects: European Commission(XE) 247584 - MATOMUVI Institutional research plan: CEZ:AV0Z1030915 Institutional support: RVO:67985556 Keywords : Abstract Algebraic Logic * Generalized disjunction * Proof by cases properties * Consequence relations * Filter-distributive logics * Protoalgebraic logics Subject RIV: BA - General Mathematics Impact factor: 0.330, year: 2013

Wronski's Foundations of Mathematics.

Science.gov (United States)

Wagner, Roi

2016-09-01

Argument This paper reconstructs Wronski's philosophical foundations of mathematics. It uses his critique of Lagrange's algebraic analysis as a vignette to introduce the problems that he raised, and argues that these problems have not been properly appreciated by his contemporaries and subsequent commentators. The paper goes on to reconstruct Wronski's mathematical law of creation and his notions of theory and techne, in order to put his objections to Lagrange in their philosophical context. Finally, Wronski's proof of his universal law (the expansion of a given function by any series of functions) is reviewed in terms of the above reconstruction. I argue that Wronski's philosophical approach poses an alternative to the views of his contemporary mainstream mathematicians, which brings up the contingency of their choices, and bridges the foundational concerns of early modernity with those of the twentieth-century foundations crisis. I also argue that Wronski's views may be useful to contemporary philosophy of mathematical practice, if they are read against their metaphysical grain.

Analogy, explanation, and proof

Science.gov (United States)

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

Analogy, Explanation, and Proof

Directory of Open Access Journals (Sweden)

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.

On Mathematicians' Proof Skimming: A Reply to Inglis and Alcock

Science.gov (United States)

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…

Mathematical modeling based on ordinary differential equations: A promising approach to vaccinology.

Science.gov (United States)

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.

Mathematical mechanic using physical reasoning to solve problems

CERN Document Server

Levi, Mark

2009-01-01

Everybody knows that mathematics is indispensable to physics--imagine where we'd be today if Einstein and Newton didn't have the math to back up their ideas. But how many people realize that physics can be used to produce many astonishing and strikingly elegant solutions in mathematics? Mark Levi shows how in this delightful book, treating readers to a host of entertaining problems and mind-bending puzzlers that will amuse and inspire their inner physicist. Levi turns math and physics upside down, revealing how physics can simplify proofs and lead to quicker solutions and new theorems, and how physical solutions can illustrate why results are true in ways lengthy mathematical calculations never can

Riot at the calc exam and other mathematically bent stories

CERN Document Server

Adams, Colin

2009-01-01

What's so funny about math? Lots! Especially if you're mathematically bent. In the world of Colin Adams, differential equations bring on tears of laughter. Hollywood producers hire algebraic geometers to punch up a script. In this world, math and humor are synonymous. Riot at the Calc Exam is a proof of this fact. A collection of humorous math stories, this book gives a window into mathematics and the culture of mathematicians. Appropriate for mathematicians, math students, math teachers, lay people with an interest in mathematics, and indeed everyone else. This book is a romp through the wild

A PROOF Analysis Framework

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.

Mathematical Representation Ability by Using Project Based Learning on the Topic of Statistics

Science.gov (United States)

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.

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)

Conversations about Curriculum Change: Mathematical Thinking and Team-Based Learning in a Discrete Mathematics Course

Science.gov (United States)

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…

Mathematics and Science Teachers' Use of and Confidence in Empirical Reasoning: Implications for STEM Teacher Preparation

Science.gov (United States)

Wasserman, Nicholas H.; Rossi, Dara

2015-01-01

The recent trend to unite mathematically related disciplines (science, technology, engineering, and mathematics) under the broader umbrella of STEM education has advantages. In this new educational context of integration, however, STEM teachers need to be able to distinguish between sufficient proof and reasoning across different disciplines,…

Effects of reading-oriented tasks on students' reading comprehension of geometry proof

Science.gov (United States)

Yang, Kai-Lin; Lin, Fou-Lai

2012-06-01

This study compared the effects of reading-oriented tasks and writing-oriented tasks on students' reading comprehension of geometry proof (RCGP). The reading-oriented tasks were designed with reading strategies and the idea of problem posing. The writing-oriented tasks were consistent with usual proof instruction for writing a proof and applying it. Twenty-two classes of ninth-grade students ( N = 683), aged 14 to 15 years, and 12 mathematics teachers participated in this quasi-experimental classroom study. While the experimental group was instructed to read and discuss the reading tasks in two 45-minute lessons, the control group was instructed to prove and apply the same propositions. Generalised estimating equation (GEE) method was used to compare the scores of the post-test and the delayed post-test with the pre-test scores as covariates. Results showed that the total scores of the delayed post-test of the experimental group were significantly higher than those of the control group. Furthermore, the scores of the experimental group on all facets of reading comprehension except the application facet were significantly higher than those of the control group for both the post-test and delayed post-test.

Mathematical Knowledge for Teaching, Standards-Based Mathematics Teaching Practices, and Student Achievement in the Context of the "Responsive Classroom Approach"

Science.gov (United States)

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…

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

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.

Lectures on the mathematics of quantum mechanics I

CERN Document Server

Dell'Antonio, Gianfausto

2015-01-01

The first volume (General Theory) differs from most textbooks as it emphasizes the mathematical structure and mathematical rigor, while being adapted to the teaching the first semester of an advanced course in Quantum Mechanics (the content of the book are the lectures of courses actually delivered.). It differs also from the very few texts in Quantum Mechanics that give emphasis to the mathematical aspects because this book, being written as Lecture Notes, has the structure of lectures delivered in a course, namely introduction of the problem, outline of the relevant points, mathematical tools needed, theorems, proofs. This makes this book particularly useful for self-study and for instructors in the preparation of a second course in Quantum Mechanics (after a first basic course). With some minor additions it can be used also as a basis of a first course in Quantum Mechanics for students in mathematics curricula. The second part (Selected Topics) are lecture notes of a more advanced course aimed at giving th...

Inevitable randomness in discrete mathematics

CERN Document Server

Beck, Jozsef

2009-01-01

Mathematics has been called the science of order. The subject is remarkably good for generalizing specific cases to create abstract theories. However, mathematics has little to say when faced with highly complex systems, where disorder reigns. This disorder can be found in pure mathematical arenas, such as the distribution of primes, the 3n+1 conjecture, and class field theory. The purpose of this book is to provide examples--and rigorous proofs--of the complexity law: (1) discrete systems are either simple or they exhibit advanced pseudorandomness; (2) a priori probabilities often exist even when there is no intrinsic symmetry. Part of the difficulty in achieving this purpose is in trying to clarify these vague statements. The examples turn out to be fascinating instances of deep or mysterious results in number theory and combinatorics. This book considers randomness and complexity. The traditional approach to complexity--computational complexity theory--is to study very general complexity classes, such as P...

A MATLAB-Aided Method for Teaching Calculus-Based Business Mathematics

Science.gov (United States)

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…

towards a theory-based multi-dimensional framework for assessment in mathematics: The "SEA" framework

Science.gov (United States)

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 Nets for Lambek Calculus

NARCIS (Netherlands)

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;

Tools of the trade introduction to advanced mathematics

CERN Document Server

Sally, Jr, Paul J

2008-01-01

This book provides a transition from the formula-full aspects of the beginning study of college level mathematics to the rich and creative world of more advanced topics. It is designed to assist the student in mastering the techniques of analysis and proof that are required to do mathematics. Along with the standard material such as linear algebra, construction of the real numbers via Cauchy sequences, metric spaces and complete metric spaces, there are three projects at the end of each chapter that form an integral part of the text. These projects include a detailed discussion of topics such

Students’ Critical Mathematical Thinking Skills and Character:Experiments for Junior High School Students through Realistic Mathematics Education Culture-Based

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

On the Mechanization of the Proof of Hessenberg's Theorem in Coherent Logic

NARCIS (Netherlands)

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

A mathematical primer on quantum mechanics

CERN Document Server

Teta, Alessandro

2018-01-01

This book offers a rigorous yet elementary approach to quantum mechanics that will meet the needs of Master’s-level Mathematics students and is equally suitable for Physics students who are interested in gaining a deeper understanding of the mathematical structure of the theory. Throughout the coverage, which is limited to single-particle quantum mechanics, the focus is on formulating theory and developing applications in a mathematically precise manner. Following a review of selected key concepts in classical physics and the historical background, the basic elements of the theory of operators in Hilbert spaces are presented and used to formulate the rules of quantum mechanics. The discussion then turns to free particles, harmonic oscillators, delta potential, and hydrogen atoms, providing rigorous proofs of the corresponding dynamical properties. Starting from an analysis of these applications, readers are subsequently introduced to more advanced topics such as the classical limit, scattering theory, and s...

Proofs, Upside Down

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...

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)

PENGEMBANGAN MODEL COMPREHENSIVE MATHEMATICS INSTRUCTION (CMI DALAM MEMBANGUN KEMAMPUAN MATHEMATICAL THINKING SISWA

Directory of Open Access Journals (Sweden)

Nita Delima

2017-03-01

Full Text Available Kesetaraan dalam pendidikan merupakan elemen penting dari beberapa standar visi NCTM dalam pendidikan matematika. Kesetaraan yang dimaksud, tidak berarti bahwa setiap siswa harus menerima pembelajaran yang identik dari guru; sebaliknya, menuntut sebuah pembelajaran yang mengakomodasi sebuah akses dalam mencapai kemampuan setiap siswa. Selain itu, NCTM juga mengemukakan bahwa dalam pembelajaran matematika terdapat lima standar proses yang harus terpenuhi, yakni problem solving, reasoning and proof, connections, communication, dan representation. Sementara itu, kemampuan problem solving yang dimiliki oleh seseorang akan mempengaruhi pada fleksibilitas proses berpikir mereka. Proses berpikir yang dimaksud dapat berupa proses dinamik yang memuat kompleksitas ide–ide matematik yang dimiliki serta dapat mengekspansi pemahaman tentang matematika yang disebut sebagai mathematical thinking. Dengan demikian, diperlukan sebuah model pembelajaran yang dapat berfungsi sebagai alat pedagogis guru, baik sebelum, selama dan setelah pembelajaran, terutama dalam membangun mathematical thinking siswa. Kerangka Comprehensive Mathematics Instruction (CMI merupakan sebuah kerangka prinsip – prinsip praktek pembelajaran yang bertujuan untuk menciptakan pengalaman matematika yang seimbang, sehingga siswa dapat memiliki pemikiran dan pemahaman matematika secara mendalam, kerangka CMI memiliki semua kriteria sebuah model pembelajaran. Adapun syntax untuk model CMI terdiri dari develop, solidify dan practice. Dalam penerapannya, setiap syntax tersebut meliputi tiga tahapan, yakni tujuan (purpose, peran guru (teacher role dan peran siswa (student role. Berdasarkan hasil analisis eksploratif yang telah dilakukan, dapat disimpulkan bahwa model pembelajaran CMI ini dapat menjadi sebuah alat pedagogis yang baru bagi guru yang dapat digunakan, baik sebelum, selama dan setelah pembelajaran dalam membangun kemampuan mathematical thinking siswa.    Kata Kunci: Comprehensive

Mathematical analysis I

CERN Document Server

Canuto, Claudio

2015-01-01

The purpose of the volume is to provide a support for a first course in Mathematics. The contents are organised to appeal especially to Engineering, Physics and Computer Science students, all areas in which mathematical tools play a crucial role. Basic notions and methods of differential and integral calculus for functions of one real variable are presented in a manner that elicits critical reading and prompts a hands-on approach to concrete applications. The layout has a specifically-designed modular nature, allowing the instructor to make flexible didactical choices when planning an introductory lecture course. The book may in fact be employed at three levels of depth. At the elementary level the student is supposed to grasp the very essential ideas and familiarise with the corresponding key techniques. Proofs to the main results befit the intermediate level, together with several remarks and complementary notes enhancing the treatise. The last, and farthest-reaching, level requires the additional study of ...

Mathematical methods of many-body quantum field theory

CERN Document Server

Lehmann, Detlef

2004-01-01

Mathematical Methods of Many-Body Quantum Field Theory offers a comprehensive, mathematically rigorous treatment of many-body physics. It develops the mathematical tools for describing quantum many-body systems and applies them to the many-electron system. These tools include the formalism of second quantization, field theoretical perturbation theory, functional integral methods, bosonic and fermionic, and estimation and summation techniques for Feynman diagrams. Among the physical effects discussed in this context are BCS superconductivity, s-wave and higher l-wave, and the fractional quantum Hall effect. While the presentation is mathematically rigorous, the author does not focus solely on precise definitions and proofs, but also shows how to actually perform the computations.Presenting many recent advances and clarifying difficult concepts, this book provides the background, results, and detail needed to further explore the issue of when the standard approximation schemes in this field actually work and wh...

Tattoo-based noninvasive glucose monitoring: a proof-of-concept study.

Science.gov (United States)

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.

Using the Van Hiele theory to analyze primary school teachers' written work on geometrical proof problems

Science.gov (United States)

Jupri, A.

2018-05-01

The lack of ability of primary school teachers in deductive thinking, such as doing geometrical proof, is an indispensable issue to be dealt with. In this paper, we report on results of a three-step of the field document study. The study was part of a pilot study for improving deductive thinking ability of primary school teachers. First, we designed geometrical proof problems adapted from literature. Second, we administered an individual written test involving nine master students of primary education program, in which they are having experiences as primary school mathematics teachers. Finally, we analyzed the written work from the view of the Van Hiele theory. The results revealed that even if about the half of the teachers show ability in doing formal proof, still the rest provides inappropriate proving. For further investigation, we wonder whether primary school teachers would show better deductive thinking if the teaching of geometry is designed in a systematic and appropriate manner according to the Van Hiele theory.

Development of Mathematics Learning Strategy Module, Based on Higher Order Thinking Skill (Hots) To Improve Mathematic Communication And Self Efficacy On Students Mathematics Department

Science.gov (United States)

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.

Final report SmartProofS. Results of projects of the SmartProofS program; Eindrapport SmartProofS. Projectresultaten van het SmartProofS programma

Energy Technology Data Exchange (ETDEWEB)

Van Hoorik, P.; Westerga, R. [Energy Valley, Groningen (Netherlands)

2011-05-15

The SmartProofs program aims to develop tools which must show that the principle of a Smart Power System (SPS) works and how. An SPS can ensure that the supply and demand of electricity in the grid is balanced, even in case more decentralized energy techniques will be put into use. This final report summarizes the main results and conclusions of the SmartProofs program. As part of the SPS program attention is paid to the impacts on the girds, the effects of centralized and decentralized management, disaster resilience, pricing models, potential benefits of control and new business models [Dutch] Het SmartProofs programma heeft tot doel om een concept van een Smart Power System (SPS) te ontwikkelen waarmee kan worden aangetoond dat het principe van een SPS werkt en op welke manier. Een SPS kan zorgen dat het aanbod van elektriciteit op het net op elk moment van de dag overeenkomt met de vraag, ook als er straks veel meer decentrale energietechnieken gebruikt worden waarmee zowel de vraag als het aanbod van elektriciteit onvoorspelbaar wordt. Dit eindrapport geeft een overzicht van de belangrijkste resultaten en conclusies van het SmartProofs programma. Het programma heeft in de werkpakketten deelvraagstukken rondom SmartProofS onderzocht rondom de effecten op onze energienetten, de effecten van zowel centrale- als decentrale aansturing, disaster resilience, prijsmodellen, mogelijke baten van aansturing en nieuwe business modellen.

Proof Pad: A New Development Environment for ACL2

Directory of Open Access Journals (Sweden)

Caleb Eggensperger

2013-04-01

Full Text Available Most software development projects rely on Integrated Development Environments (IDEs based on the desktop paradigm, with an interactive, mouse-driven user interface. The standard installation of ACL2, on the other hand, is designed to work closely with Emacs. ACL2 experts, on the whole, like this mode of operation, but students and other new programmers who have learned to program with desktop IDEs often react negatively to the process of adapting to an unfamiliar form of interaction. This paper discusses Proof Pad, a new IDE for ACL2. Proof Pad is not the only attempt to provide ACL2 IDEs catering to students and beginning programmers. The ACL2 Sedan and DrACuLa systems arose from similar motivations. Proof Pad builds on the work of those systems, while also taking into account the unique workflow of the ACL2 theorem proving system. The design of Proof Pad incorporated user feedback from the outset, and that process continued through all stages of development. Feedback took the form of direct observation of users interacting with the IDE as well as questionnaires completed by users of Proof Pad and other ACL2 IDEs. The result is a streamlined interface and fast, responsive system that supports using ACL2 as a programming language and a theorem proving system. Proof Pad also provides a property-based testing environment with random data generation and automated interpretation of properties as ACL2 theorem definitions.

Student’s mathematical understanding ability based on self-efficacy

Science.gov (United States)

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.

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)

Inquiry based learning: a student centered learning to develop mathematical habits of mind

Science.gov (United States)

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.

The students’ mathematical argumentation in geometry

Science.gov (United States)

Sukirwan; Darhim; Herman, T.; Prahmana, R. C. I.

2017-12-01

The main objective of this research is to analyze the student's mathematical argumentation when dealing with geometry. The method is used qualitative method with grounded theory to know how the students provide an explanation or an answer against claims so that the quality of the vernacular students will be drawn up with clear from how students compose a series of arguments. The results showed that there were still many students basically experiencing constraints in argumentation, but the quality of the reasoning appears to be a variation of the argument appeared, include: inductive, algebra, visual and perceptual. In addition, the starting point of the students composes a series of arguments generally starts from claims that arise in a matter. Proof of claim further builds upon the relationship between the characteristics of data with mathematical objects that appear in the acquired mathematical knowledge from previous students. Relationship spelled out in a series of statements and reasons which support the claims through the fourth argument.

Didactic trajectory of research in mathematics education using research-based learning

Science.gov (United States)

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.

A Forward-secure Grouping-proof Protocol for Multiple RFID Tags

Directory of Open Access Journals (Sweden)

Liu Ya-li

2012-09-01

Full Text Available Designing secure and robust grouping-proof protocols based on RFID characteristics becomes a hotspot in the research of security in Internet of Things (IOT. The proposed grouping-proof protocols recently have security and/or privacy omission and these schemes afford order-dependence by relaying message among tags through an RFID reader. In consequence, aiming at enhancing the robustness, improving scalability, reducing the computation costs on resource-constrained devices, and meanwhile combing Computational Intelligence (CI with Secure Multi-party Communication (SMC, a Forward-Secure Grouping-Proof Protocol (FSGP for multiple RFID tags based on Shamir's (, secret sharing is proposed. In comparison with the previous grouping-proof protocols, FSGP has the characteristics of forward-security and order-independence addressing the scalability issue by avoiding relaying message. Our protocol provides security enhancement, performance improvement, and meanwhile controls the computation cost, which equilibrates both security and low cost requirements for RFID tags.

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)

Two Project-Based Strategies in an Interdisciplinary Mathematical Modeling in Biology Course

Science.gov (United States)

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…

The Failure to Construct Proof Based on Assimilation and Accommodation Framework from Piaget

Science.gov (United States)

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…

An improved smartcard for the South African Social Security Agency (SASSA): A proof of life based solution

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...

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.

First course in mathematical logic

CERN Document Server

Suppes, Patrick

2010-01-01

In modern mathematics, both the theory of proof and the derivation of theorems from axioms bear an unquestioned importance. The necessary skills behind these methods, however, are frequently underdeveloped. This book counters that neglect with a rigorous introduction that is simple enough in presentation and context to permit relatively easy comprehension. It comprises the sentential theory of inference, inference with universal quantifiers, and applications of the theory of inference developed to the elementary theory of commutative groups. Throughout the book, the authors emphasize the perva

Mathematics Literacy on Problem Based Learning with Indonesian Realistic Mathematics Education Approach Assisted E-Learning Edmodo

Science.gov (United States)

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.

The Constructed Objectivity of Mathematics and the Cognitive Subject

Science.gov (United States)

Longo, Giuseppe

Mathematics is engendered in conjunction with other forms of knowledge, physics in particular. It is a "genealogy of concepts" (Riemann), that stems from our active reconstruction of the world. Mathematics organizes space and time. It stabilizes notions and concepts as no other language, while isolating by them a few intelligible fragments of "reality" at the phenomenal level. Thus an epistemological analysis of mathematics is proposed, as a foundation that departs from and complements the logico-formal approaches: Mathematics is grounded in a formation of sense, of a congnitive and historical nature, which preceeds the explicit formulation of axioms and rules. The genesis of some conceptual invariants will be sketched (numbers, continua, infinity, proofs, etc.). From these, categories as structural invariants (objects) and "invariant preserving maps" (morphisms, functors) are derived, in a reflective equilibrium of theories that parallels our endeavour to gain knowledge of the physical world.

A correctness proof of the bakery protocol in $ mu $CRL

NARCIS (Netherlands)

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

Un estudio exploratorio de los esquemas que emplean los alumnos de bachillerato para validar resultados matemáticos/ An exploratory study of schemes used by senior high school students to validate mathematic results

Directory of Open Access Journals (Sweden)

Víctor Larios Osorio

2018-04-01

Full Text Available Mathematics, as a body of scientific knowledge, includes not only a set of concepts and theories described in books and scientific journals but a procedural knowledge used for solving problems and proving the resulting solution. There is a tool for proving solutions, the so-called mathematical proof, which is worth to be included in the educational process. To complete the study herein described a random stratified sample was selected and given a test demanding to explain the answers given. However, high school students (15-18 years old do not rely on the use of the known proof scheme. For that reason, a diagnostic study was carried out at the Autonomous University of Querétaro (UAQ in order to identify the strategies the students are currently following and finding ways to teach such mathematical proof scheme. The findings are a description of individual students’ argumentative practices and the identification and grouping of the most frequently used proof scheme.

Mathematics Instructional Model Based on Realistic Mathematics Education to Promote Problem Solving Ability at Junior High School Padang

OpenAIRE

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...

A Correctness Proof of the Bakery Protocol in μCRL

NARCIS (Netherlands)

Groote, J.F.; Korver, H.

1992-01-01

A specification of the bakery protocol is given in μCRL. We provide a simple correctness criterion for the protocol. Then the protocol is proven correct using a proof system that has been developed for μCRL. The proof primarily consists of algebraic manipulations based on specifications of

Lectures on the mathematics of quantum mechanics II selected topics

CERN Document Server

Dell'Antonio, Gianfausto

2016-01-01

The first volume (General Theory) differs from most textbooks as it emphasizes the mathematical structure and mathematical rigor, while being adapted to the teaching the first semester of an advanced course in Quantum Mechanics (the content of the book are the lectures of courses actually delivered.). It differs also from the very few texts in Quantum Mechanics that give emphasis to the mathematical aspects because this book, being written as Lecture Notes, has the structure of lectures delivered in a course, namely introduction of the problem, outline of the relevant points, mathematical tools needed, theorems, proofs. This makes this book particularly useful for self-study and for instructors in the preparation of a second course in Quantum Mechanics (after a first basic course). With some minor additions it can be used also as a basis of a first course in Quantum Mechanics for students in mathematics curricula. The second part (Selected Topics) are lecture notes of a more advanced course aimed at giving th...

Flood-proof motors

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.)

Flood-proof motors

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.)

Proof Rules for Recursive Procedures

NARCIS (Netherlands)

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

Theological Metaphors in Mathematics

Directory of Open Access Journals (Sweden)

Krajewski Stanisław

2016-03-01

Full Text Available Examples of possible theological influences upon the development of mathematics are indicated. The best known connection can be found in the realm of infinite sets treated by us as known or graspable, which constitutes a divine-like approach. Also the move to treat infinite processes as if they were one finished object that can be identified with its limits is routine in mathematicians, but refers to seemingly super-human power. For centuries this was seen as wrong and even today some philosophers, for example Brian Rotman, talk critically about “theological mathematics”. Theological metaphors, like “God’s view”, are used even by contemporary mathematicians. While rarely appearing in official texts they are rather easily invoked in “the kitchen of mathematics”. There exist theories developing without the assumption of actual infinity the tools of classical mathematics needed for applications (For instance, Mycielski’s approach. Conclusion: mathematics could have developed in another way. Finally, several specific examples of historical situations are mentioned where, according to some authors, direct theological input into mathematics appeared: the possibility of the ritual genesis of arithmetic and geometry, the importance of the Indian religious background for the emergence of zero, the genesis of the theories of Cantor and Brouwer, the role of Name-worshipping for the research of the Moscow school of topology. Neither these examples nor the previous illustrations of theological metaphors provide a certain proof that religion or theology was directly influencing the development of mathematical ideas. They do suggest, however, common points and connections that merit further exploration.

The bounded proof property via step algebras and step frames

NARCIS (Netherlands)

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

An Excel-Aided Method for Teaching Calculus-Based Business Mathematics

Science.gov (United States)

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…

Piloting a Web-Based Homework System in Developmental Mathematics Classrooms

Science.gov (United States)

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,…

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.

Mathematical Understanding and Proving Abilities: Experiment With Undergraduate Student By Using Modified Moore Learning Approach

Directory of Open Access Journals (Sweden)

Rippi Maya

2011-07-01

Full Text Available This paper reports findings of  a  post test experimental control group design conducted to investigate the role of modified Moore learning approach  on improving students’ mathematical understanding and proving abilities. Subject of study were 56 undergradute students of one state university in Bandung, who took advanced abstract algebra course. Instrument of study were a set test of mathematical understanding ability, a set test of mathematical proving ability, and a set of students’ opinion scale on modified Moore learning approach. Data were analyzed by using two path ANOVA. The study found that proof construction process was more difficult than mathematical understanding  task  for all students, and students still posed some difficulties on constructing mathematical proof task.  The study also found there were not differences  between students’  abilities on mathematical understanding and on proving abilities of  the both classes, and both abilities were classified as mediocre. However, in modified Moore learning approach class there were more students who got above average grades on mathematical understanding than those of conventional class. Moreover, students performed positive  opinion toward  modified Moore learning approach. They  were  active in questioning and solving problems, and in explaining their works in front of class as well, while students of conventional teaching prefered to listen to lecturer’s explanation. The study also found that there was no interaction between learning approach and students’ prior mathematics ability on mathematical understanding and proving abilities,  but  there were  quite strong  association between students’ mathematical understanding and proving abilities.Keywords:  modified Moore learning approach, mathematical understanding ability, mathematical proving ability. DOI: http://dx.doi.org/10.22342/jme.2.2.751.231-250

Mathematics creative thinking levels based on interpersonal intelligence

Science.gov (United States)

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.

A course in mathematical analysis

CERN Document Server

Garling, D J H

The three volumes of A Course in Mathematical Analysis provide a full and detailed account of all those elements of real and complex analysis that an undergraduate mathematics student can expect to encounter in the first two or three years of study. Containing hundreds of exercises, examples and applications, these books will become an invaluable resource for both students and instructors. Volume 1 focuses on the analysis of real-valued functions of a real variable. Volume 2 goes on to consider metric and topological spaces. This third volume develops the classical theory of functions of a complex variable. It carefully establishes the properties of the complex plane, including a proof of the Jordan curve theorem. Lebesgue measure is introduced, and is used as a model for other measure spaces, where the theory of integration is developed. The RadonÐNikodym theorem is proved, and the differentiation of measures discussed.

Formalism and beyond on the nature of mathematical discourse

CERN Document Server

Link, Godehard

2014-01-01

The essays collected in this volume focus on the role of formalist aspects in mathematical theorizing and practice, examining issues such as infinity, finiteness, and proof procedures, as well as central historical figures in the field, including Frege, Russell, Hilbert and Wittgenstein. Using modern logico-philosophical tools and systematic conceptual and logical analyses, the volume provides a thorough, up-to-date account of the subject.

Project-Based Learning and Design-Focused Projects to Motivate Secondary Mathematics Students

Science.gov (United States)

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…

Analysis of creative mathematic thinking ability in problem based learning model based on self-regulation learning

Science.gov (United States)

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.

What Is the Problem in Problem-Based Learning in Higher Education Mathematics

Science.gov (United States)

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…

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

PENGEMBANGAN MODEL COMPUTER-BASED E-LEARNING UNTUK MENINGKATKAN KEMAMPUAN HIGH ORDER MATHEMATICAL THINKING SISWA SMA

OpenAIRE

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...

What is the problem in problem-based learning in higher education mathematics

Science.gov (United States)

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.

Context-based mathematics tasks in Indonesia : Toward better practice and achievement

OpenAIRE

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...

46 CFR 201.144 - Offer of proof.

Science.gov (United States)

2010-10-01

... 46 Shipping 8 2010-10-01 2010-10-01 false Offer of proof. 201.144 Section 201.144 Shipping... PROCEDURE Evidence (Rule 14) § 201.144 Offer of proof. An offer of proof made in connection with an... accompany the record as the offer of proof. ...

Non-linear wave equations:Mathematical techniques

International Nuclear Information System (INIS)

1978-01-01

An account of certain well-established mathematical methods, which prove useful to deal with non-linear partial differential equations is presented. Within the strict framework of Functional Analysis, it describes Semigroup Techniques in Banach Spaces as well as variational approaches towards critical points. Detailed proofs are given of the existence of local and global solutions of the Cauchy problem and of the stability of stationary solutions. The formal approach based upon invariance under Lie transformations deserves attention due to its wide range of applicability, even if the explicit solutions thus obtained do not allow for a deep analysis of the equations. A compre ensive introduction to the inverse scattering approach and to the solution concept for certain non-linear equations of physical interest are also presented. A detailed discussion is made about certain convergence and stability problems which arise in importance need not be emphasized. (author) [es

The Development of Mathematical Knowledge for Teaching for Quantitative Reasoning Using Video-Based Instruction

Science.gov (United States)

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

45 CFR 81.85 - Offer of proof.

Science.gov (United States)

2010-10-01

... 45 Public Welfare 1 2010-10-01 2010-10-01 false Offer of proof. 81.85 Section 81.85 Public Welfare... 80 OF THIS TITLE Hearing Procedures § 81.85 Offer of proof. An offer of proof made in connection with... identification and shall accompany the record as the offer of proof. ...

Differential geometry and mathematical physics

CERN Document Server

Rudolph, Gerd

Starting from an undergraduate level, this book systematically develops the basics of • Calculus on manifolds, vector bundles, vector fields and differential forms, • Lie groups and Lie group actions, • Linear symplectic algebra and symplectic geometry, • Hamiltonian systems, symmetries and reduction, integrable systems and Hamilton-Jacobi theory. The topics listed under the first item are relevant for virtually all areas of mathematical physics. The second and third items constitute the link between abstract calculus and the theory of Hamiltonian systems. The last item provides an introduction to various aspects of this theory, including Morse families, the Maslov class and caustics. The book guides the reader from elementary differential geometry to advanced topics in the theory of Hamiltonian systems with the aim of making current research literature accessible. The style is that of a mathematical textbook,with full proofs given in the text or as exercises. The material is illustrated by numerous d...

PROOF on the Cloud for ALICE using PoD and OpenNebula

International Nuclear Information System (INIS)

Berzano, D; Bagnasco, S; Brunetti, R; Lusso, S

2012-01-01

In order to optimize the use and management of computing centres, their conversion to cloud facilities is becoming increasingly popular. In a medium to large cloud facility, many different virtual clusters may concur for the same resources: unused resources can be freed either by turning off idle virtual machines, or by lowering resources assigned to a virtual machine at runtime. PROOF, a ROOT-based parallel and interactive analysis framework, is officially endorsed in the computing model of the ALICE experiment as complementary to the Grid, and it has become very popular over the last three years. The locality of PROOF-based analysis facilities forces system administrators to scavenge resources, yet the chaotic nature of user analysis tasks deems them unstable and inconstantly used, making PROOF a typical use-case for HPC cloud computing. Currently, PoD dynamically and easily provides a PROOF-enabled cluster by submitting agents to a job scheduler. Unfortunately, a Tier-2 does not comfortably share the same queue between interactive and batch jobs, due to the very large average time to completion of the latter: an elastic cloud approach would enable interactive virtual machines to temporarily subtract resources to the batch ones, without a noticeable impact on them. In this work we describe our setup of a dynamic PROOF-based cloud analysis facility based on PoD and OpenNebula, orchestrated by a simple and lightweight control daemon that makes virtualization transparent for the user.

Impact- and earthquake- proof roof structure

International Nuclear Information System (INIS)

Shohara, Ryoichi.

1990-01-01

Building roofs are constituted with roof slabs, an earthquake proof layer at the upper surface thereof and an impact proof layer made of iron-reinforced concrete disposed further thereover. Since the roofs constitute an earthquake proof structure loading building dampers on the upper surface of the slabs by the concrete layer, seismic inputs of earthquakes to the buildings can be moderated and the impact-proof layer is formed, to ensure the safety to external conditions such as earthquakes or falling accidents of airplane in important facilities such as reactor buildings. (T.M.)

Lowering Preservice Teachers' Mathematics Anxiety through an Experience-Based Mathematics Methods Course.

Science.gov (United States)

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…

On the burden of proof in civil procedure

Directory of Open Access Journals (Sweden)

Keča Ranko

2013-01-01

Full Text Available The appliance of burden of proof rules is conceived of assumption that evidences are taken and that court didn't reach the required degree of conviction of a particular fact, what implies limitation of application of these rules on proceedings in which the judgment is rendered after the plenary proceedings. The Code of Civil Procedure (CCP has no suitable answers for the problems arising from new conception of the principle of party control of facts and means of proof in Serbian litigation legislature, by which the court has no more power to take the evidence ex offo. There is no answer to the question how should court conduct when evidence is not taken because of a lack of parties' indication of the means of proof. In this case courts practice somehow wider conception of burden of proof rules, which however has no explicit legal ground. They are applying them even though evidences are not taken. In any case it would be useful to reformulate basic rule of burden of proof in manner which would correspondent to the new conception of the principle of party presentation. The rule of burden of proof applies when the high degree of conviction of facts is demanded from the court, in order to render the judgment. Consequently this rule loses its' sense when mere probability of factual findings is demanded. The broader conception of parties' representation principle however does not liberate court from his responsibility to clarify facts that should be base for adjudication. Circumstance that CCP does mention the principle of material truth anymore should not be seen as argument for liberation of mentioned responsibility. It is still expected from the court to be active. Only when joint effort of the court and parties is left without of goal, in sense that court doesn't reach the high degree conviction, there would be ground for burden of proof rule's application. In this situation court also must justify why he couldn't reach required degree of

A mathematical framework for agent based models of complex biological networks.

Science.gov (United States)

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.

Analytical derivation: An epistemic game for solving mathematically based physics problems

Science.gov (United States)

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.

The Computer Student Worksheet Based Mathematical Literacy for Statistics

Science.gov (United States)

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%.

Students' Critical Mathematical Thinking Skills and Character: Experiments for Junior High School Students through Realistic Mathematics Education Culture-Based

Science.gov (United States)

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…

Mathematical model for hysteresis phenomenon in moisture transport of concrete carbonation process

International Nuclear Information System (INIS)

Aiki, Toyohiko; Kumazaki, Kota

2012-01-01

From civil engineering point of view it is very important to construct and analyze a mathematical model for a mechanism of concrete carbonation process. On this subject there are several mathematical results concerned with a one-dimensional model, in which hysteresis effects are neglected. Our aim is to give a model with hysteresis effects appearing in carbonation process. In this paper, as the first step of this research we focus only on moisture transport in the process and propose an initial boundary value problem for a system of partial differential equations as a mathematical model. Also, we give results on the existence of a solution to the problem, globally in time and the uniqueness in only one-dimensional case without proofs.

Nonconvex Model of Material Growth: Mathematical Theory

Science.gov (United States)

Ganghoffer, J. F.; Plotnikov, P. I.; Sokolowski, J.

2018-06-01

The model of volumetric material growth is introduced in the framework of finite elasticity. The new results obtained for the model are presented with complete proofs. The state variables include the deformations, temperature and the growth factor matrix function. The existence of global in time solutions for the quasistatic deformations boundary value problem coupled with the energy balance and the evolution of the growth factor is shown. The mathematical results can be applied to a wide class of growth models in mechanics and biology.

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.

The application of brain-based learning principles aided by GeoGebra to improve mathematical representation ability

Science.gov (United States)

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.

Vibration-proof FBR type reactor

International Nuclear Information System (INIS)

Kawamura, Yutaka.

1992-01-01

In a reactor container in an FBR type reactor, an outer building and upper and lower portions of a reactor container are connected by a load transmission device made of a laminated material of rubber and steel plates. Each of the reactor container and the outer building is disposed on a lower raft disposed on a rock by way of a vibration-proof device made of a laminated material of rubber and steel plates. Vibration-proof elements for providing vertical eigen frequency of the vibration-proof system comprising the reactor building and the vibration-proof device within a range of 3Hz to 5Hz are used. That is, the peak of designed acceleration for response spectrum in the horizontal direction of the reactor structural portions is shifted to side of shorter period from the main frequency region of the reactor structure. Alternatively, rigidity of the vibration-proof elements is decreased to shift the peak to the side of long period from the main frequency region. Designed seismic force can be greatly reduced both horizontally and vertically, to reduce the wall thickness of the structural members, improve the plant economy and to ensure the safety against earthquakes. (N.H.)

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.

Development and validity of mathematical learning assessment instruments based on multiple intelligence

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.

Dynamic PROOF clusters with PoD: architecture and user experience

Science.gov (United States)

Manafov, Anar

2011-12-01

PROOF on Demand (PoD) is a tool-set, which sets up a PROOF cluster on any resource management system. PoD is a user oriented product with an easy to use GUI and a command-line interface. It is fully automated. No administrative privileges or special knowledge is required to use it. PoD utilizes a plug-in system, to use different job submission front-ends. The current PoD distribution is shipped with LSF, Torque (PBS), Grid Engine, Condor, gLite, and SSH plug-ins. The product is to be extended. We therefore plan to implement a plug-in for AliEn Grid as well. Recently developed algorithms made it possible to efficiently maintain two types of connections: packet-forwarding and native PROOF connections. This helps to properly handle most kinds of workers, with and without firewalls. PoD maintains the PROOF environment automatically and, for example, prevents resource misusage in case when workers idle for too long. As PoD matures as a product and provides more plug-ins, it's used as a standard for setting up dynamic PROOF clusters in many different institutions. The GSI Analysis Facility (GSIAF) is in production since 2007. The static PROOF cluster has been phased out end of 2009. GSIAF is now completely based on PoD. Users create private dynamic PROOF clusters on the general purpose batch farm. This provides an easier resource sharing between interactive local batch and Grid usage. The main user communities are FAIR and ALICE.

Structural analysis of online handwritten mathematical symbols based on support vector machines

Science.gov (United States)

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.

38 CFR 18b.64 - Offer of proof.

Science.gov (United States)

2010-07-01

... 38 Pensions, Bonuses, and Veterans' Relief 2 2010-07-01 2010-07-01 false Offer of proof. 18b.64... Procedures § 18b.64 Offer of proof. An offer of proof made in connection with an objection taken to any... record as the offer of proof. ...

A course in mathematical statistics and large sample theory

CERN Document Server

Bhattacharya, Rabi; Patrangenaru, Victor

2016-01-01

This graduate-level textbook is primarily aimed at graduate students of statistics, mathematics, science, and engineering who have had an undergraduate course in statistics, an upper division course in analysis, and some acquaintance with measure theoretic probability. It provides a rigorous presentation of the core of mathematical statistics. Part I of this book constitutes a one-semester course on basic parametric mathematical statistics. Part II deals with the large sample theory of statistics — parametric and nonparametric, and its contents may be covered in one semester as well. Part III provides brief accounts of a number of topics of current interest for practitioners and other disciplines whose work involves statistical methods. Large Sample theory with many worked examples, numerical calculations, and simulations to illustrate theory Appendices provide ready access to a number of standard results, with many proofs Solutions given to a number of selected exercises from Part I Part II exercises with ...

The mathematical career of Pierre de Fermat 1601-1665

CERN Document Server

Mahoney, Michael Sean

1994-01-01

Hailed as one of the greatest mathematical results of the twentieth century, the recent proof of Fermat's Last Theorem by Andrew Wiles brought to public attention the enigmatic problem-solver Pierre de Fermat, who centuries ago stated his famous conjecture in a margin of a book, writing that he did not have enough room to show his "truly marvelous demonstration" Along with formulating this proposition-xn+yn=zn has no rational solution for n > 2-Fermat, an inventor of analytic geometry, also laid the foundations of differential and integral calculus, established, together with Pascal, the conceptual guidelines of the theory of probability, and created modern number theory. In one of the first full-length investigations of Fermat's life and work, Michael Sean Mahoney provides rare insight into the mathematical genius of a hobbyist who never sought to publish his work, yet who ranked with his contemporaries Pascal and Descartes in shaping the course of modern mathematics.

Focused labeled proof systems for modal logic

OpenAIRE

Miller , Dale; Volpe , Marco

2015-01-01

International audience; Focused proofs are sequent calculus proofs that group inference rules into alternating positive and negative phases. These phases can then be used to define macro-level inference rules from Gentzen's original and tiny introduction and structural rules. We show here that the inference rules of labeled proof systems for modal logics can similarly be described as pairs of such phases within the LKF focused proof system for first-order classical logic. We consider the syst...

Proust: A Nano Proof Assistant

Directory of Open Access Journals (Sweden)

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 evaluation of the pressure proof test concept for 2024-T3 aluminium alloy sheet

Science.gov (United States)

Dawicke, D. S.; Poe, C. C., Jr.; Newman, J. C.; Harris, C. E.

1991-01-01

The concept of pressure proof testing of fuselage structures with fatigue cracks to insure structural integrity was evaluated from a fracture mechanics viewpoint. A generic analytical and experimental investigation was conducted on uniaxially loaded flat panels with crack configurations and stress levels typical of longitudinal lap splice joints in commercial transport aircraft fuselages. The results revealed that the remaining fatigue life after a proof cycle was longer than that without the proof cycle because of crack growth retardation due to increased crack closure. However, based on a crack length that is slightly less than the critical value at the maximum proof stress, the minimum assured life or proof test interval must be no more than 550 pressure cycles for a 1.33 proof factor and 1530 pressure cycles for a 1.5 proof factor to prevent in-flight failures.

Experiences of Student Mathematics-Teachers in Computer-Based Mathematics Learning Environment

Science.gov (United States)

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…

Distributed analysis with PROOF in ATLAS collaboration

International Nuclear Information System (INIS)

Panitkin, S Y; Ernst, M; Ito, H; Maeno, T; Majewski, S; Rind, O; Tarrade, F; Wenaus, T; Ye, S; Benjamin, D; Montoya, G Carillo; Guan, W; Mellado, B; Xu, N; Cranmer, K; Shibata, A

2010-01-01

The Parallel ROOT Facility - PROOF is a distributed analysis system which allows to exploit inherent event level parallelism of high energy physics data. PROOF can be configured to work with centralized storage systems, but it is especially effective together with distributed local storage systems - like Xrootd, when data are distributed over computing nodes. It works efficiently on different types of hardware and scales well from a multi-core laptop to large computing farms. From that point of view it is well suited for both large central analysis facilities and Tier 3 type analysis farms. PROOF can be used in interactive or batch like regimes. The interactive regime allows the user to work with typically distributed data from the ROOT command prompt and get a real time feedback on analysis progress and intermediate results. We will discuss our experience with PROOF in the context of ATLAS Collaboration distributed analysis. In particular we will discuss PROOF performance in various analysis scenarios and in multi-user, multi-session environments. We will also describe PROOF integration with the ATLAS distributed data management system and prospects of running PROOF on geographically distributed analysis farms.

Distributed analysis with PROOF in ATLAS collaboration

Energy Technology Data Exchange (ETDEWEB)

Panitkin, S Y; Ernst, M; Ito, H; Maeno, T; Majewski, S; Rind, O; Tarrade, F; Wenaus, T; Ye, S [Brookhaven National Laboratory, Upton, NY 11973 (United States); Benjamin, D [Duke University, Durham, NC 27708 (United States); Montoya, G Carillo; Guan, W; Mellado, B; Xu, N [University of Wisconsin-Madison, Madison, WI 53706 (United States); Cranmer, K; Shibata, A [New York University, New York, NY 10003 (United States)

2010-04-01

The Parallel ROOT Facility - PROOF is a distributed analysis system which allows to exploit inherent event level parallelism of high energy physics data. PROOF can be configured to work with centralized storage systems, but it is especially effective together with distributed local storage systems - like Xrootd, when data are distributed over computing nodes. It works efficiently on different types of hardware and scales well from a multi-core laptop to large computing farms. From that point of view it is well suited for both large central analysis facilities and Tier 3 type analysis farms. PROOF can be used in interactive or batch like regimes. The interactive regime allows the user to work with typically distributed data from the ROOT command prompt and get a real time feedback on analysis progress and intermediate results. We will discuss our experience with PROOF in the context of ATLAS Collaboration distributed analysis. In particular we will discuss PROOF performance in various analysis scenarios and in multi-user, multi-session environments. We will also describe PROOF integration with the ATLAS distributed data management system and prospects of running PROOF on geographically distributed analysis farms.

Complex proofs of real theorems

CERN Document Server

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 ...

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.

7 CFR 1430.605 - Proof of production.

Science.gov (United States)

2010-01-01

... establish the commercial marketing and production history of the dairy operation so that dairy production...) Adequate proof of production history of the dairy operation under paragraph (b) of this section must be based on milk marketing statements obtained from the dairy operation's milk handler or marketing...

Image analysis and mathematical modelling for the supervision of the dough fermentation process

Science.gov (United States)

Zettel, Viktoria; Paquet-Durand, Olivier; Hecker, Florian; Hitzmann, Bernd

2016-10-01

The fermentation (proof) process of dough is one of the quality-determining steps in the production of baking goods. Beside the fluffiness, whose fundaments are built during fermentation, the flavour of the final product is influenced very much during this production stage. However, until now no on-line measurement system is available, which can supervise this important process step. In this investigation the potential of an image analysis system is evaluated, that enables the determination of the volume of fermented dough pieces. The camera is moving around the fermenting pieces and collects images from the objects by means of different angles (360° range). Using image analysis algorithms the volume increase of individual dough pieces is determined. Based on a detailed mathematical description of the volume increase, which based on the Bernoulli equation, carbon dioxide production rate of yeast cells and the diffusion processes of carbon dioxide, the fermentation process is supervised. Important process parameters, like the carbon dioxide production rate of the yeast cells and the dough viscosity can be estimated just after 300 s of proofing. The mean percentage error for forecasting the further evolution of the relative volume of the dough pieces is just 2.3 %. Therefore, a forecast of the further evolution can be performed and used for fault detection.

Pythagoras on the rocks. A proof with bricks

Directory of Open Access Journals (Sweden)

Michele Cagol

2016-04-01

Full Text Available In this short paper a practical and simple proof of the Pythagorean theorem is proposed. It uses colourful interlocking plastic bricks with two shapes: a cube that measures two centimeters on each side and a right prism where the base is a right-angled isosceles triangle and the two equal rectangular faces are the same as those of the cubic brick. The proof is designed for primary school children (but also for preschool children and begins by telling the legend of Pythagoras, who discovered his theorem by looking at the floor tile pattern of Polycrates’ palace. This proof takes into account only right-angled isosceles triangle but it is possible to show the validity of Pythagorean theorem for all right-angled triangles by building a simple proof by rearrangement. Pitagora on the rocks. Una dimostrazione con i mattonciniIn questo breve contributo viene proposta una semplice dimostrazione pratica del teorema di Pitagora, utilizzando mattoncini a incastro di plastica colorata di due forme: un cubo di due centimetri per lato e un prisma retto la cui base è un triangolo isoscele rettangolo e nel quale le due facce equivalenti sono uguali a quelle del mattoncino cubico. La dimostrazione è rivolta a bambini della scuola primaria (ma, eventualmente, anche in età prescolare e prende le mosse dalla leggenda secondo la quale Pitagora avrebbe scoperto il suo teorema mentre stava osservando il pavimento piastrellato del palazzo di Policrate, tiranno di Samo. Da questa dimostrazione – che prende in considerazione solo triangoli rettangoli isosceli – è poi possibile passare a una dimostrazione del teorema di Pitagora per tutti i triangoli rettangoli.

Peac – A set of tools to quickly enable Proof on a cluster

International Nuclear Information System (INIS)

Ganis, G; Vala, M

2012-01-01

With advent of the analysis phase of Lhcdata-processing, interest in Proof technology has considerably increased. While setting up a simple Proof cluster for basic usage is reasonably straightforward, exploiting the several new functionalities added in recent times may be complicated. Peac, standing for Proof Enabled Analysis Cluster, is a set of tools aiming to facilitate the setup and management of a Proof cluster. Peac is based on the experience made by setting up Proof for the Alice analysis facilities. It allows to easily build and configure Root and the additional software needed on the cluster, and may serve as distributor of binaries via Xrootd. Peac uses Proof-On-Demand (PoD) for resource management (start, stop or daemons). Finally, Peac sets-up and configures dataset management (using the Afdsmgrd daemon), as well as cluster monitoring (machine status and Proof query summaries) using MonAlisa. In this respect, a MonAlisa page has been dedicated to Peac users, so that a cluster managed by Peac can be automatically monitored. In this paper we present and describe the status and main components of Peac and show details about its usage.

A proof of the Kochen–Specker theorem can always be converted to a state-independent noncontextuality inequality

International Nuclear Information System (INIS)

Yu, Xiao-Dong; Tong, D M; Guo, Yan-Qing

2015-01-01

Quantum contextuality is one of the fundamental notions in quantum mechanics. Proofs of the Kochen–Specker theorem and noncontextuality inequalities are two means for revealing the contextuality phenomenon in quantum mechanics. It has been found that some proofs of the Kochen-Specker theorem, such as those based on rays, can be converted to a state-independent noncontextuality inequality, but it remains open whether this is true in general, i.e., whether any proof of the Kochen-Specker theorem can always be converted to a noncontextuality inequality. In this paper, we address this issue. We prove that all kinds of proofs of the Kochen-Specker theorem, based on rays or any other observables, can always be converted to state-independent noncontextuality inequalities. Besides, our constructive proof also provides a general approach for deriving a state-independent noncontextuality inequality from a proof of the KS theorem. (paper)

2nd International Conference on Proof-Theoretic Semantics

CERN Document Server

Schroeder-Heister, Peter

2016-01-01

This volume is the first ever collection devoted to the field of proof-theoretic semantics. Contributions address topics including the systematics of introduction and elimination rules and proofs of normalization, the categorial characterization of deductions, the relation between Heyting's and Gentzen's approaches to meaning, knowability paradoxes, proof-theoretic foundations of set theory, Dummett's justification of logical laws, Kreisel's theory of constructions, paradoxical reasoning, and the defence of model theory. The field of proof-theoretic semantics has existed for almost 50 years, but the term itself was proposed by Schroeder-Heister in the 1980s. Proof-theoretic semantics explains the meaning of linguistic expressions in general and of logical constants in particular in terms of the notion of proof. This volume emerges from presentations at the Second International Conference on Proof-Theoretic Semantics in Tübingen in 2013, where contributing authors were asked to provide a self-contained descri...

Proviola: a tool for proof re-animation

NARCIS (Netherlands)

Tankink, C.; Geuvers, J.H.; McKinna, J.; Wiedijk, F.; Autexier, S.; Calmet, J.; Delahaye, D.; Ion, P.D.F.; Rideau, L.; Rioboo, R.; Sexton, A.P.

2010-01-01

To improve on existing models of interaction with a proof assistant (PA), in particular for storage and replay of proofs, we introduce three related concepts, those of: a proof movie, consisting of frames which record both user input and the corresponding PA response; a camera, which films a user’s

Short proofs of strong normalization

OpenAIRE

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.

Unraveling the Culture of the Mathematics Classroom: A Video-Based Study in Sixth Grade

Science.gov (United States)

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…

7 CFR 1430.305 - Proof of production.

Science.gov (United States)

2010-01-01

... commercial marketing and production history of the dairy operation so that production and spoilage losses can... dairy herd increases or decreases to the satisfaction of FSA. (c) Adequate proof of production history of the dairy operation under paragraph (b) of this section must be based on milk marketing statements...

Mathematical verification of a nuclear power plant protection system function with combined CPN and PVS

Energy Technology Data Exchange (ETDEWEB)

Koo, Seo Ryong; Son, Han Seong; Seong, Poong Hyun [Korea Advanced Institute of Science and Technology, Taejon (Korea, Republic of)

1999-12-31

In this work, an automatic software verification method for Nuclear Power Plant (NPP) protection system is developed. This method utilizes Colored Petri Net (CPN) for modeling and Prototype Verification System (PVS) for mathematical verification. In order to help flow-through from modeling by CPN to mathematical proof by PVS, a translator has been developed in this work. The combined method has been applied to a protection system function of Wolsong NPP SDS2(Steam Generator Low Level Trip) and found to be promising for further research and applications. 7 refs., 10 figs. (Author)

Mathematical verification of a nuclear power plant protection system function with combined CPN and PVS

Energy Technology Data Exchange (ETDEWEB)

Koo, Seo Ryong; Son, Han Seong; Seong, Poong Hyun [Korea Advanced Institute of Science and Technology, Taejon (Korea, Republic of)

1998-12-31

In this work, an automatic software verification method for Nuclear Power Plant (NPP) protection system is developed. This method utilizes Colored Petri Net (CPN) for modeling and Prototype Verification System (PVS) for mathematical verification. In order to help flow-through from modeling by CPN to mathematical proof by PVS, a translator has been developed in this work. The combined method has been applied to a protection system function of Wolsong NPP SDS2(Steam Generator Low Level Trip) and found to be promising for further research and applications. 7 refs., 10 figs. (Author)

49 CFR 604.43 - Offer of proof.

Science.gov (United States)

2010-10-01

... 49 Transportation 7 2010-10-01 2010-10-01 false Offer of proof. 604.43 Section 604.43..., DEPARTMENT OF TRANSPORTATION CHARTER SERVICE Hearings. § 604.43 Offer of proof. A party whose evidence has... respond to the offer of proof, may offer the evidence on the record when filing an appeal. ...

36 CFR 1150.79 - Offer of proof.

Science.gov (United States)

2010-07-01

... 36 Parks, Forests, and Public Property 3 2010-07-01 2010-07-01 false Offer of proof. 1150.79... BOARD PRACTICE AND PROCEDURES FOR COMPLIANCE HEARINGS Hearing Procedures § 1150.79 Offer of proof. An offer of proof made in connection with an objection taken to a ruling of the judge rejecting or...

Effect of Digital Game Based Learning on Ninth Grade Students' Mathematics Achievement

Science.gov (United States)

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…

Examining Teaching Based on Errors in Mathematics Amongst Pupils with Learning Disabilities

Science.gov (United States)

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…

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

Towards the proof of the cosmic censorship hypothesis

Energy Technology Data Exchange (ETDEWEB)

Krolak, Andrzej

1986-05-01

An attempt is made to formulate the cosmic censorship hypothesis put forward by Penrose (1969, Riv. Nuovo Cimento Ser. 1 Num. Spec. 1 252) as a theorem which could be subject to mathematical proof. It is proved that a weakly asymptotically simple and empty spacetime must be future asymptotically predictable if the energy and the strong causality conditions hold and either all singularities are of Tipler's strong curvature type and once singularity occurs there exists a marginally outgoing null geodesic or each singularity is preceded by the occurrence of a closed trapped surface. The marginally outgoing null geodesics may not be admitted by general naked singularities. However, it is shown that they occur if on the Cauchy horizon the global hyperbolicity in violated is such a way that causal simplicity does not hold. This means that a wide class of nakedly singular spacetimes is considered. This result gives some support to the validity of Penrose's hypothesis.

Towards the proof of the cosmic censorship hypothesis

International Nuclear Information System (INIS)

Krolak, Andrzej

1986-01-01

An attempt is made to formulate the cosmic censorship hypothesis put forward by Penrose [1969, Riv. Nuovo Cimento Ser. 1 Num. Spec. 1 252] as a theorem which could be subject to mathematical proof. It is proved that a weakly asymptotically simple and empty spacetime must be future asymptotically predictable if the energy and the strong causality conditions hold and either all singularities are of Tipler's strong curvature type and once singularity occurs there exists a marginally outgoing null geodesic or each singularity is preceded by the occurrence of a closed trapped surface. The marginally outgoing null geodesics may not be admitted by general naked singularities. However, it is shown that they occur if on the Cauchy horizon the global hyperbolicity in violated is such a way that causal simplicity does not hold. This means that a wide class of nakedly singular spacetimes is considered. This result gives some support to the validity of Penrose's hypothesis. (author)

Integrating PROOF Analysis in Cloud and Batch Clusters

International Nuclear Information System (INIS)

Rodríguez-Marrero, Ana Y; Fernández-del-Castillo, Enol; López García, Álvaro; Marco de Lucas, Jesús; Matorras Weinig, Francisco; González Caballero, Isidro; Cuesta Noriega, Alberto

2012-01-01

High Energy Physics (HEP) analysis are becoming more complex and demanding due to the large amount of data collected by the current experiments. The Parallel ROOT Facility (PROOF) provides researchers with an interactive tool to speed up the analysis of huge volumes of data by exploiting parallel processing on both multicore machines and computing clusters. The typical PROOF deployment scenario is a permanent set of cores configured to run the PROOF daemons. However, this approach is incapable of adapting to the dynamic nature of interactive usage. Several initiatives seek to improve the use of computing resources by integrating PROOF with a batch system, such as Proof on Demand (PoD) or PROOF Cluster. These solutions are currently in production at Universidad de Oviedo and IFCA and are positively evaluated by users. Although they are able to adapt to the computing needs of users, they must comply with the specific configuration, OS and software installed at the batch nodes. Furthermore, they share the machines with other workloads, which may cause disruptions in the interactive service for users. These limitations make PROOF a typical use-case for cloud computing. In this work we take profit from Cloud Infrastructure at IFCA in order to provide a dynamic PROOF environment where users can control the software configuration of the machines. The Proof Analysis Framework (PAF) facilitates the development of new analysis and offers a transparent access to PROOF resources. Several performance measurements are presented for the different scenarios (PoD, SGE and Cloud), showing a speed improvement closely correlated with the number of cores used.

34 CFR 101.85 - Offer of proof.

Science.gov (United States)

2010-07-01

... 34 Education 1 2010-07-01 2010-07-01 false Offer of proof. 101.85 Section 101.85 Education... PRACTICE AND PROCEDURE FOR HEARINGS UNDER PART 100 OF THIS TITLE Hearing Procedures § 101.85 Offer of proof. An offer of proof made in connection with an objection taken to any ruling of the presiding officer...

7 CFR 15.122 - Offer of proof.

Science.gov (United States)

2010-01-01

... 7 Agriculture 1 2010-01-01 2010-01-01 false Offer of proof. 15.122 Section 15.122 Agriculture..., Decisions and Administrative Review Under the Civil Rights Act of 1964 Hearing Procedures § 15.122 Offer of proof. An offer of proof made in connection with an objection taken to any ruling of the hearing officer...

43 CFR 4.840 - Offer of proof.

Science.gov (United States)

2010-10-01

... the Interior-Effectuation of Title VI of the Civil Rights Act of 1964 Hearing § 4.840 Offer of proof. An offer of proof made in connection with an objection taken to any ruling of the administrative law... 43 Public Lands: Interior 1 2010-10-01 2010-10-01 false Offer of proof. 4.840 Section 4.840 Public...

Proof of Nishida's Conjecture on Anharmonic Lattices

Science.gov (United States)

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.

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...

An Architecture for Proof Planning Systems

OpenAIRE

Dennis, Louise Abigail

2005-01-01

This paper presents a generic architecture for proof planning systems in terms of an interaction between a customisable proof module and search module. These refer to both global and local information contained in reasoning states.

Implementation and outcomes of inquiry-based learning in mathematics content courses for pre-service teachers

Science.gov (United States)

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.

Image-based Proof of Work Algorithm for the Incentivization of Blockchain Archival of Interesting Images

OpenAIRE

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...

Development of syntax of intuition-based learning model in solving mathematics problems

Science.gov (United States)

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

Teaching logic using a state-of-art proof assistant

Directory of Open Access Journals (Sweden)

Maxim Hendriks

2010-06-01

Full Text Available This article describes the system ProofWeb developed for teaching logic to undergraduate computer science students. The system is based on the higher order proof assistant Coq, and is made available to the students through an interactive web interface. Part of this system is a large database of logic problems. This database will also hold the solutions of the students. The students do not need to install anything to be able to use the system (not even a browser plug-in, and the teachers are able to centrally track progress of the students. The system makes the full power of Coq available to the students, but simultaneously presents the logic problems in a way that is customary in undergraduate logic courses. Both styles of presenting natural deduction proofs (Gentzen-style `tree view' and Fitch-style `box view' are supported. Part of the system is a parser that indicates whether the students used the automation of Coq to solve their problems or that they solved it themselves using only the inference rules of the logic. For these inference rules dedicated tactics for Coq have been developed. The system has already been used in type theory courses and logic undergraduate courses. The ProofWeb system can be tried at http://proofweb.cs.ru.nl/.

Computer-Based Mathematics Instructions for Engineering Students

Science.gov (United States)

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.

Ergodicity, Maximum Entropy Production, and Steepest Entropy Ascent in the Proofs of Onsager's Reciprocal Relations

Science.gov (United States)

Benfenati, Francesco; Beretta, Gian Paolo

2018-04-01

We show that to prove the Onsager relations using the microscopic time reversibility one necessarily has to make an ergodic hypothesis, or a hypothesis closely linked to that. This is true in all the proofs of the Onsager relations in the literature: from the original proof by Onsager, to more advanced proofs in the context of linear response theory and the theory of Markov processes, to the proof in the context of the kinetic theory of gases. The only three proofs that do not require any kind of ergodic hypothesis are based on additional hypotheses on the macroscopic evolution: Ziegler's maximum entropy production principle (MEPP), the principle of time reversal invariance of the entropy production, or the steepest entropy ascent principle (SEAP).

Two proofs of Fine's theorem

International Nuclear Information System (INIS)

Halliwell, J.J.

2014-01-01

Fine's theorem concerns the question of determining the conditions under which a certain set of probabilities for pairs of four bivalent quantities may be taken to be the marginals of an underlying probability distribution. The eight CHSH inequalities are well-known to be necessary conditions, but Fine's theorem is the striking result that they are also sufficient conditions. Here two transparent and self-contained proofs of Fine's theorem are presented. The first is a physically motivated proof using an explicit local hidden variables model. The second is an algebraic proof which uses a representation of the probabilities in terms of correlation functions. - Highlights: • A discussion of the various approaches to proving Fine's theorem. • A new physically-motivated proof using a local hidden variables model. • A new algebraic proof. • A new form of the CHSH inequalities

New SUSYQM coherent states for Pöschl-Teller potentials: a detailed mathematical analysis

Science.gov (United States)

Bergeron, H.; Siegl, P.; Youssef, A.

2012-06-01

In a recent short note (Bergeron et al 2010 Europhys. Lett. 92 60003), we have presented the good properties of a new family of semi-classical states for Pöschl-Teller potentials. These states are built from a supersymmetric quantum mechanics (SUSYQM) approach and the parameters of these ‘coherent’ states are points in the classical phase space. In this paper, we develop all the mathematical aspects that have been left out of the previous paper (proof of the resolution of unity, detailed calculations of the quantized version of classical observables and mathematical study of the resulting operators: problems of domains, self-adjointness or self-adjoint extensions). Some additional questions such as asymptotic behavior are also studied. Moreover, the framework is extended to a larger class of Pöschl-Teller potentials. This article is part of a special issue of Journal of Physics A: Mathematical and Theoretical devoted to ‘Coherent states: mathematical and physical aspects’.

New SUSYQM coherent states for Pöschl–Teller potentials: a detailed mathematical analysis

International Nuclear Information System (INIS)

Bergeron, H; Siegl, P; Youssef, A

2012-01-01

In a recent short note (Bergeron et al 2010 Europhys. Lett. 92 60003), we have presented the good properties of a new family of semi-classical states for Pöschl–Teller potentials. These states are built from a supersymmetric quantum mechanics (SUSYQM) approach and the parameters of these ‘coherent’ states are points in the classical phase space. In this paper, we develop all the mathematical aspects that have been left out of the previous paper (proof of the resolution of unity, detailed calculations of the quantized version of classical observables and mathematical study of the resulting operators: problems of domains, self-adjointness or self-adjoint extensions). Some additional questions such as asymptotic behavior are also studied. Moreover, the framework is extended to a larger class of Pöschl–Teller potentials. This article is part of a special issue of Journal of Physics A: Mathematical and Theoretical devoted to ‘Coherent states: mathematical and physical aspects’. (paper)

An analysis of primary school students’ representational ability in mathematics based on gender perspective

Science.gov (United States)

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).

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.

The Vice: Some Historically Inspired and Proof-Generated Steps to Limits of Sequences

Science.gov (United States)

Burn, Bob

2005-01-01

This paper proposes a genetic development of the concept of limit of a sequence leading to a definition, through a succession of proofs rather than through a succession of sequences or a succession of epsilons. The major ideas on which it is based are historical and depend on Euclid, Archimedes, Fermat, Wallis and Newton. Proofs of equality by…

The Impact of Problem-Based Learning Approach to Senior High School Students’ Mathematics Critical Thinking Ability

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.

The statistical strength of nonlocality proofs

NARCIS (Netherlands)

Dam, van W.; Gill, R.D.; Grünwald, P.D.

2005-01-01

There exist numerous proofs of Bell's theorem, stating that quantum mechanics is incompatible with local realistic theories of nature. Here the strength of such nonlocality proofs is defined in terms of the amount of evidence against local realism provided by the corresponding experiments.

Web-Based Implementation of Discrete Mathematics

Science.gov (United States)

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…

Multiparty session types as coherence proofs

DEFF Research Database (Denmark)

Carbone, Marco; Montesi, Fabrizio; Schürmann, Carsten

2017-01-01

We propose a Curry–Howard correspondence between a language for programming multiparty sessions and a generalisation of Classical Linear Logic (CLL). In this framework, propositions correspond to the local behaviour of a participant in a multiparty session type, proofs to processes, and proof nor...

Velocity feedback control with a flywheel proof mass actuator

Science.gov (United States)

Kras, Aleksander; Gardonio, Paolo

2017-08-01

This paper presents four new proof mass actuators to be used in velocity feedback control systems for the control of vibrations of machines and flexible structures. A classical proof mass actuator is formed by a coil-magnet linear motor, with either the magnet or the armature-coil proof mass suspended on soft springs. This arrangement produces a net force effect at frequencies above the fundamental resonance frequency of the springs-proof mass system. Thus, it can be used to implement point velocity feedback loops, although the dynamic response and static deflection of the springs-proof mass system poses some stability and control performance limitations. The four proof mass actuators presented in this study include a flywheel element, which is used to augment the inertia effect of the suspended proof mass. The paper shows that the flywheel element modifies both the dynamic response and static deflection of the springs-proof mass system in such a way as the stability and control performance of velocity feedback loops using these actuators are significantly improved.

Hybrid Logic and its Proof-Theory

CERN Document Server

Brauner, Torben

2011-01-01

This is the first book-length treatment of hybrid logic and its proof-theory. Hybrid logic is an extension of ordinary modal logic which allows explicit reference to individual points in a model (where the points represent times, possible worlds, states in a computer, or something else). This is useful for many applications, for example when reasoning about time one often wants to formulate a series of statements about what happens at specific times. There is little consensus about proof-theory for ordinary modal logic. Many modal-logical proof systems lack important properties and the relatio

Mathematical modeling of acid-base physiology.

Science.gov (United States)

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.

Design based Investigation on Construction of Mathematical Modelling Problems: Example of Financial Content

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

A geometric proof of confluence by decreasing diagrams

NARCIS (Netherlands)

Klop, J.W.; Oostrom, V. van; Vrijer, R. de

The criterion for confluence using decreasing diagrams is a generalization of several well-known confluence criteria in abstract rewriting, such as the strong confluence lemma. We give a new proof of the decreasing diagram theorem based on a geometric study of in finite reduction diagrams, arising

Student Perspectives of Web-Based Mathematics

Science.gov (United States)

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…

16 CFR 614.1 - Appropriate proof of identity.

Science.gov (United States)

2010-01-01

... 16 Commercial Practices 1 2010-01-01 2010-01-01 false Appropriate proof of identity. 614.1 Section... IDENTITY § 614.1 Appropriate proof of identity. (a) Consumer reporting agencies shall develop and implement reasonable requirements for what information consumers shall provide to constitute proof of identity for...

The implementation of multiple intelligences based teaching model to improve mathematical problem solving ability for student of junior high school

Science.gov (United States)

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.

Evaluating Google compute engine with PROOF

International Nuclear Information System (INIS)

Ganis, Gerardo; Panitkin, Sergey

2014-01-01

The advent of private and commercial cloud platforms has opened the question of evaluating the cost-effectiveness of such solution for computing in High Energy Physics . Google Compute Engine (GCE) is a IaaS product launched by Google as an experimental platform during 2012 and now open to the public market. In this contribution we present the results of a set of CPU-intensive and I/O-intensive tests we have run with PROOF on a GCE resources made available by Google for test purposes. We have run tests on large scale PROOF clusters (up to 1000 workers) to study the overall scalability of coordinated multi-process jobs. We have studied and compared the performance of ephemeral and persistent storage with PROOF-Lite on the single machines and of standard PROOF on the whole cluster. We will discuss our results in perspective, in particular with respect to the typical analysis needs of an LHC experiment.

Learning Mathematics by Designing, Programming, and Investigating with Interactive, Dynamic Computer-Based Objects

Science.gov (United States)

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…

29 CFR 1919.31 - Proof tests-loose gear.

Science.gov (United States)

2010-07-01

... 29 Labor 7 2010-07-01 2010-07-01 false Proof tests-loose gear. 1919.31 Section 1919.31 Labor... (CONTINUED) GEAR CERTIFICATION Certification of Vessels: Tests and Proof Loads; Heat Treatment; Competent Persons § 1919.31 Proof tests—loose gear. (a) Chains, rings, shackles and other loose gear (whether...

Mathematics and Astronomy: Inquire Based Scientific Education at School

Science.gov (United States)

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.

An Investigation of Mathematical Modeling with Pre-Service Secondary Mathematics Teachers

Science.gov (United States)

Thrasher, Emily Plunkett

2016-01-01

The goal of this thesis was to investigate and enhance our understanding of what occurs while pre-service mathematics teachers engage in a mathematical modeling unit that is broadly based upon mathematical modeling as defined by the Common Core State Standards for Mathematics (National Governors Association Center for Best Practices & Council…

An existence proof of a symmetric periodic orbit in the octahedral six-body problem

OpenAIRE

Cavalcanti, Anete Soares

2016-01-01

We present a proof of the existence of a periodic orbit for the Newtonian six-body problem with equal masses. This orbit has three double collisions each period and no multiple collisions. Our proof is based on the minimization of the Lagrangian action functional on a well chosen class of symmetric loops.

Digital game based learning: A new method in teaching and learning mathematics

Science.gov (United States)

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.

RGLite, an interface between ROOT and gLite—proof on the grid

Science.gov (United States)

Malzacher, P.; Manafov, A.; Schwarz, K.

2008-07-01

Using the gLitePROOF package it is possible to perform PROOF-based distributed data analysis on the gLite Grid. The LHC experiments managed to run globally distributed Monte Carlo productions on the Grid, now the development of tools for data analysis is in the foreground. To grant access interfaces must be provided. The ROOT/PROOF framework is used as a starting point. Using abstract ROOT classes (TGrid, ...) interfaces can be implemented, via which Grid access from ROOT can be accomplished. A concrete implementation exists for the ALICE Grid environment AliEn. Within the D-Grid project an interface to the common Grid middleware of all LHC experiments, gLite, has been created. Therefore it is possible to query Grid File Catalogues from ROOT for the location of the data to be analysed. Grid jobs can be submitted into a gLite based Grid. The status of the jobs can be asked for, and their results can be obtained.

RGLite, an interface between ROOT and gLite-proof on the grid

International Nuclear Information System (INIS)

Malzacher, P; Manafov, A; Schwarz, K

2008-01-01

Using the gLitePROOF package it is possible to perform PROOF-based distributed data analysis on the gLite Grid. The LHC experiments managed to run globally distributed Monte Carlo productions on the Grid, now the development of tools for data analysis is in the foreground. To grant access interfaces must be provided. The ROOT/PROOF framework is used as a starting point. Using abstract ROOT classes (TGrid, ...) interfaces can be implemented, via which Grid access from ROOT can be accomplished. A concrete implementation exists for the ALICE Grid environment AliEn. Within the D-Grid project an interface to the common Grid middleware of all LHC experiments, gLite, has been created. Therefore it is possible to query Grid File Catalogues from ROOT for the location of the data to be analysed. Grid jobs can be submitted into a gLite based Grid. The status of the jobs can be asked for, and their results can be obtained

Other trigonometric proofs of Pythagoras theorem

OpenAIRE

Luzia, Nuno

2015-01-01

Only very recently a trigonometric proof of the Pythagoras theorem was given by Zimba \\cite{1}, many authors thought this was not possible. In this note we give other trigonometric proofs of Pythagoras theorem by establishing, geometrically, the half-angle formula $\\cos\\theta=1-2\\sin^2 \\frac{\\theta}{2}$.

Mathematics Instructional Model Based on Realistic Mathematics Education to Promote Problem Solving Ability at Junior High School Padang

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.

Scaffolding norms of argumentation-based inquiry in a primary mathematics classroom

NARCIS (Netherlands)

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

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.

Generalization of the Greenberger-Horne-Zeilinger algebraic proof of nonlocality

International Nuclear Information System (INIS)

Clifton, R.K.; Redhead, M.L.G.; Butterfield, J.N.

1991-01-01

The authors further develop a recent new proof (by Greenberger, Horne, and Zeilinger - GHZ) that local deterministic hidden-variable theories are inconsistent with certain strict correlations predicted by quantum mechanics. First, they generalize GHZ's proof so that it applied to factorable stochastic theories in which apparatus hidden variables are casually relevant to measurement results, and theories in which the hidden variables evolve indeterministically prior to the particle-apparatus interactions. Then they adopt a more general measure-theoretic approach which requires that GHZ's argument be modified in order to produce a valid proof. Finally, they motivate the more general proof's assumptions in a somewhat different way from previous authors in order to strengthen the implications of the proof as much as possible. After developing GHZ's proof along these lines, they then consider the analogue, for their proof, of Bohr's reply to the EPR argument, and conclude (pace GHZ) that in at least one respect (viz, that of most concern to Bohr) the proof is no more powerful than Bell's. Nevertheless, they point out some new advantages of their proof over Bell's, and over other algebraic proofs of nonlocality. And they conclude by giving a modified version of their proof that, like Bell's does not rely on experimentally unrealizable strict correlations, but still leads to a testable quasi-algebraic locality inequality

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,” ...

International Conference on Differential Equations and Mathematical Physics

CERN Document Server

Saitō, Yoshimi

1987-01-01

The meeting in Birmingham, Alabama, provided a forum for the discussion of recent developments in the theory of ordinary and partial differential equations, both linear and non-linear, with particular reference to work relating to the equations of mathematical physics. The meeting was attended by about 250 mathematicians from 22 countries. The papers in this volume all involve new research material, with at least outline proofs; some papers also contain survey material. Topics covered include: Schrödinger theory, scattering and inverse scattering, fluid mechanics (including conservative systems and inertial manifold theory attractors), elasticity, non-linear waves, and feedback control theory.

Using Mathematical Modeling and Set-Based Design Principles to Recommend an Existing CVL Design

Science.gov (United States)

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

Efforts to Improve Mathematics Teacher Competency Through Training Program on Design Olympiad Mathematics Problems Based on Higher Order Thinking Skills in The Junior High School

Science.gov (United States)

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.

On Kripke-style semantics for the provability logic of Gödel’s proof predicate with quantifiers on proofs

NARCIS (Netherlands)

Yavorskiy, R.

Kripke-style semantics is suggested for the provability logic with quantifiers on proofs corresponding to the standard Gödel proof predicate. It is proved that the set of valid formulas is decidable. The arithmetical completeness is still an open issue.

The possibilities of a modelling perspective for school mathematics

Directory of Open Access Journals (Sweden)

Dirk Wessels

2009-09-01

complex teaching methodology requires in-depth thinking about the role of the teacher, the role of the learner, the nature of the classroom culture, the nature of the negotiation of meaning between the teacher and individuals or groups, the nature of selected problems and material, as well as the kind of integrative assessment used in the mathematics classroom. Modelling is closely related to the problem-centred teaching approach, but it also smoothly relates to bigger and longer mathematical tasks. This article gives a theoretical exposition of the scope and depth of mathematical modelling. It is possible to introduce modelling at every school phase in our educational sytem. Modelling in school mathematics seems to make the learning of mathematics more effective. The mastering of problem solving and modelling strategies has definitely changed the orientation, the competencies and performances of learners at each school level. It would appear from research that learners like the application side of mathematics and that they want to see it in action. Genuine real life problems should be selected, which is why a modelling perspective is so important for the teaching and mastering of mathematics. Modelling should be integrated into the present curriculum because learners will then get full access to involvement in the classroom, to mathematisation, to doing problems, to criticising arguments, to finding proofs, to recognising concepts and to obtaining the ability to abstract these from the realistic situation. Modelling should be given a full opportunity in mathematics teacher education so that our learners can get the full benefit of it. This will put the mathematical performances of learners in our country on a more solid base, which will make our learners more competitive at all levels in the future. 

How to solve it a new aspect of mathematical method

CERN Document Server

Polya, G

2014-01-01

A perennial bestseller by eminent mathematician G. Polya, How to Solve It will show anyone in any field how to think straight. In lucid and appealing prose, Polya reveals how the mathematical method of demonstrating a proof or finding an unknown can be of help in attacking any problem that can be "reasoned" out-from building a bridge to winning a game of anagrams. Generations of readers have relished Polya's deft-indeed, brilliant-instructions on stripping away irrelevancies and going straight to the heart of the problem.

Proof test diagrams for Zerodur glass-ceramic

Science.gov (United States)

Tucker, D. S.

1991-01-01

Proof test diagrams for Zerodur glass-ceramics are calculated from available fracture mechanics data. It is shown that the environment has a large effect on minimum time-to-failure as predicted by proof test diagrams.

Analysis of mathematical problem-solving ability based on metacognition on problem-based learning

Science.gov (United States)

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.

Practical mathematical optimization basic optimization theory and gradient-based algorithms

CERN Document Server

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...

Proof in Algebra: Reasoning beyond Examples

Science.gov (United States)

Otten, Samuel; Herbel-Eisenmann, Beth A.; Males, Lorraine M.

2010-01-01

The purpose of this article is to provide an image of what proof could look like in beginning algebra, a course that nearly every secondary school student encounters. The authors present an actual classroom vignette in which a rich opportunity for student reasoning arose. After analyzing the proof schemes at play, the authors provide a…

The posterior communicating artery: morphometric study in 3D angio-computed tomography reconstruction. The proof of the mathematical definition of the hypoplasia.

Science.gov (United States)

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

The development of a valid discovery-based learning module to improve students' mathematical connection

Science.gov (United States)

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.

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...

Prospective Mathematics Teachers' Understanding of the Base Concept

Science.gov (United States)

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…

Applying Mathematical Optimization Methods to an ACT-R Instance-Based Learning Model.

Science.gov (United States)

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.

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.

Algebraic Reasoning in Solving Mathematical Problem Based on Learning Style

Science.gov (United States)

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.

Mathematics and Humor: John Allen Paulos and the Numeracy Crusade

Directory of Open Access Journals (Sweden)

Paul H. Grawe

2015-07-01

Full Text Available John Allen Paulos at minimum gave the Numeracy movement a name through his book Innumeracy: Mathematical Illiteracy and Its Consequences. What may not be so obvious was Paulos’ strong interest in the relationship between mathematics and mathematicians on the one hand and humor and stand-up-comedian joke structures on the other. Innumeracy itself could be seen as a typically mathematical Gotcha joke on American culture generally. In this perspective, a Minnesotan acculturated to Minnesota-Nice Humor of Self-Immolation Proclivities (SImP looks at the more raw-boned, take-no-prisoners humor style Paulos outlined in Mathematics and Humor and implemented in Innumeracy. Despite the difference in humor styles, there is much to applaud in Paulos’ analysis of the relationship between certain types of humor and professional interests of mathematicians in Mathematics and Humor. Much humor relies on the sense of incongruity which Paulos’ claims to be central to all humor and key to mathematical reductio ad absurdum. Mathematics is rightfully famous for a sense of combinatorial playfulness in its most elegant proofs, as humor often relies on clashing combinations of word play. And a great range of mathematical lore is best understood within a concept of a sudden drop from one sense of certainty to another (essentially a Gotcha on the audience. Innumeracy repeatedly exemplifies Gotchas on the great unwashed and unmathematical majority. Extensive empirical evidence over the last quarter century allows us to synthesize these Paulos observations into the idea that inculcated mathematical humor has strong propensities to complex Intellectual, Advocate, and Crusader humor forms. However, the Paulos humors do not include the Sympathetic Pain humor form, the inclusion of which may increase teaching effectiveness.

Mathematical adventures in performance analysis from storage systems, through airplane boarding, to express line queues

CERN Document Server

Bachmat, Eitan

2014-01-01

This monograph describes problems in the field of performance analysis, primarily the study of storage systems and the diverse mathematical techniques that are required for solving such problems. Topics covered include best practices for scheduling I/O requests to a disk drive, how this problem is related to airplane boarding, and how both problems can be modeled using space-time geometry. The author also explains how Riemann's proof of the analytic continuation and functional equation of the Riemann zeta function can be used to analyze express-line queues in a minimarket. Overall, the book reveals the surprising applicability of abstract mathematical ideas that are not usually associated with applied topics. Advanced undergraduate students or graduate students with an interest in the applications of mathematics will find this book a useful resource. It will also be of interest to professional mathematicians who want exposure to the surprising ways that theoretical mathematics may be applied to engineering pr...

Mathematical verification of a nuclear power plant protection system function with combined CPN and PVS

International Nuclear Information System (INIS)

Koo, Seo Ryong; Son, Han Seong; Seong, Poong Hyun

1999-01-01

In this work, an automatic software verification method for Nuclear Power Plant (NPP) protection system is developed. This method utilizes Colored Petri Net (CPN) for system modeling and Prototype Verification System (PVS) for mathematical verification. In order to help flow-through from modeling by CPN to mathematical proof by PVS, an information extractor from CPN models has been developed in this work. In order to convert the extracted information to the PVS specification language, a translator also has been developed. ML that is a higher-order functional language programs the information extractor and translator. This combined method has been applied to a protection system function of Wolsung NPP SDS2 (Steam Generator Low Level Trip). As a result of this application, we could prove completeness and consistency of the requirement logically. Through this work, in short, an axiom or lemma based-analysis method for CPN models is newly suggested in order to complement CPN analysis methods and a guideline for the use of formal methods is proposed in order to apply them to NPP software verification and validation. (author). 9 refs., 15 figs

Independent Study Workbooks for Proofs in Group Theory

Science.gov (United States)

Alcock, Lara; Brown, Gavin; Dunning, Clare

2015-01-01

This paper describes a small-scale research project based on workbooks designed to support independent study of proofs in a first course on abstract algebra. We discuss the lecturers' aims in designing the workbooks, and set these against a background of research on students' learning of group theory and on epistemological beliefs and study habits…

Effects of Gender, Mathematics Anxiety and Achievement Motivation on College Students’ Achievement in Mathematics

Directory of Open Access Journals (Sweden)

Ajogbeje Oke James

2013-07-01

Full Text Available The urge to excel or perform maximally in mathematics varies from individual to individual because achievement motivation is often developed or learnt during socialization and learning experiences. The study examined the relationship between College of Education students’ achievement motivation and mathematics achievement, correlation coefficient between mathematics anxiety and college students’ achievement motivation as well as mathematics anxiety and mathematics achievement. The sample, 268 College of Education students offering mathematics as one of their subject combination, was selected using purposive sampling techniques. Three research instruments namely: Mathematics Anxiety Scale (MAS, Achievement Motivation Scale (AMS and Mathematics Achievement Test (MAT were used to collect data for the study. Data collected for the study were analyzed using correlational analysis and ANOVA. The results showed that a significantly low negative correlation coefficient existed between mathematics anxiety and mathematics achievement. There is a negative and significant correlation coefficient between mathematics anxiety and achievement motivation. Similarly, a positive and significant correlation coefficient also exists between achievement motivation and mathematics achievement. Based on the findings of the study, it was recommended that mathematics teachers should adopt activity based strategies and conducive learning environment in order to reduce college students’ anxieties in mathematics learning.

Students’ Mathematical Problem-Solving Abilities Through The Application of Learning Models Problem Based Learning

Science.gov (United States)

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.

Whole-body vibration as a mode of dyspnoea free physical activity: a community-based proof-of-concept trial.

Science.gov (United States)

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.

Proof of patient information: Analysis of 201 judicial decisions.

Science.gov (United States)

Dugleux, E; Rached, H; Rougé-Maillart, C

2018-05-01

The ruling by the French Court of Cassation dated February 25, 1997 obliged doctors to provide proof of the information given to patients, reversing more than half a century of case law. In October 1997, it was specified that such evidence could be provided by "all means", including presumption. No hierarchy in respect of means of proof has been defined by case law or legislation. The present study analyzed judicial decisions with a view to determining the means of proof liable to carry the most weight in a suit for failure to provide due patient information. A retrospective qualitative study was conducted for the period from January 2010 to December 2015, by a search on the LexisNexis ® JurisClasseur website. Two hundred and one judicial decisions relating to failure to provide due patient information were selected and analyzed to study the characteristics of the practitioners involved, the content of the information at issue and the means of proof provided. The resulting cohort of practitioners was compared with the medical demographic atlas of the French Order of Medicine, considered as exhaustive. Two hundred and one practitioners were investigated for failure to provide information: 45 medical practitioners (22±3%), and 156 surgeons (78±3%) including 45 orthopedic surgeons (29±3.6% of surgeons). Hundred and ninety-three were private sector (96±1.3%) and 8 public sector (4±1.3%). Hundred and one surgeons (65±3.8% of surgeons), and 26 medical practitioners (58±7.4%) were convicted. Twenty-five of the 45 orthopedic surgeons were convicted (55±7.5%). There was no significant difference in conviction rates between surgeons and medical practitioners: odds ratio, 1.339916; 95% CI [0.6393982; 2.7753764] (Chi 2 test: p=0.49). Ninety-two practitioners based their defense on a single means of proof, and 74 of these were convicted (80±4.2%). Forty practitioners based their defense on several means of proof, and 16 of these were convicted (40±7.8%). There was

Mathematical Practices and Arts Integration in an Activity-Based Projective Geometry Course

Science.gov (United States)

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

Earthquake-proof supporting structure in reactor vessel

International Nuclear Information System (INIS)

Sakurai, Akio; Sekine, Katsuhisa; Madokoro, Manabu; Katoono, Shin-ichi; Konno, Mutsuo; Suzuki, Takuro.

1990-01-01

Conventional earthquake-proof structure comprises a vessel vibration stopper integrated to a reactor vessel, powder for restricting the horizontal displacements, a safety vessel surrounds the outer periphery of the reactor vessel and a safety vessel vibration stopper integrated therewith, which are fixed to buildings. However, there was a problem that a great amount of stresses are generated in the base of the reactor vessel vibration stopper due to reaction of the powders which restrict thermal expansion. In order to remarkably reduce the reaction of the powers, powders are charged into a spaces formed between each of the reactor vessel vibration stopper, the safety vessel vibration stopper and the flexible member disposed between them. According to this constitution, the reactor vessel vibration stopper does not undergo a great reaction of the powers upon thermal expansion of the reactor vessel to moderate the generated stresses, maintain the strength and provide earthquake-proof supporting function. (N.H.)

A Simple Correctness Proof of the Direct-Style Transformation

DEFF Research Database (Denmark)

Nielsen, Lasse Riechstein

2002-01-01

-pass higher-order CPS transformation, and were complicated by having to reason about higher-order functions. In contrast, this work is based on a one-pass CPS transformation that is both compositional and first-order, and therefore the proof simply proceeds by structural induction on syntax....

A survey of noninteractive zero knowledge proof system and its applications.

Science.gov (United States)

Wu, Huixin; Wang, Feng

2014-01-01

Zero knowledge proof system which has received extensive attention since it was proposed is an important branch of cryptography and computational complexity theory. Thereinto, noninteractive zero knowledge proof system contains only one message sent by the prover to the verifier. It is widely used in the construction of various types of cryptographic protocols and cryptographic algorithms because of its good privacy, authentication, and lower interactive complexity. This paper reviews and analyzes the basic principles of noninteractive zero knowledge proof system, and summarizes the research progress achieved by noninteractive zero knowledge proof system on the following aspects: the definition and related models of noninteractive zero knowledge proof system, noninteractive zero knowledge proof system of NP problems, noninteractive statistical and perfect zero knowledge, the connection between noninteractive zero knowledge proof system, interactive zero knowledge proof system, and zap, and the specific applications of noninteractive zero knowledge proof system. This paper also points out the future research directions.

A Survey of Noninteractive Zero Knowledge Proof System and Its Applications

Directory of Open Access Journals (Sweden)

Huixin Wu

2014-01-01

Full Text Available Zero knowledge proof system which has received extensive attention since it was proposed is an important branch of cryptography and computational complexity theory. Thereinto, noninteractive zero knowledge proof system contains only one message sent by the prover to the verifier. It is widely used in the construction of various types of cryptographic protocols and cryptographic algorithms because of its good privacy, authentication, and lower interactive complexity. This paper reviews and analyzes the basic principles of noninteractive zero knowledge proof system, and summarizes the research progress achieved by noninteractive zero knowledge proof system on the following aspects: the definition and related models of noninteractive zero knowledge proof system, noninteractive zero knowledge proof system of NP problems, noninteractive statistical and perfect zero knowledge, the connection between noninteractive zero knowledge proof system, interactive zero knowledge proof system, and zap, and the specific applications of noninteractive zero knowledge proof system. This paper also points out the future research directions.

The Effects of Game-Based Learning on Mathematical Confidence and Performance: High Ability vs. Low Ability

Science.gov (United States)

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,…

Enhancing students’ mathematical representation and selfefficacy through situation-based learning assisted by geometer’s sketchpad program

Science.gov (United States)

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.

The Effects of Brain Based Learning Approach on Motivation and Students Achievement in Mathematics Learning

Science.gov (United States)

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.

An illustration of the explanatory and discovery functions of proof

Directory of Open Access Journals (Sweden)

Michael de Villiers

2012-11-01

Full Text Available This article provides an illustration of the explanatory and discovery functions of proof with an original geometric conjecture made by a Grade 11 student. After logically explaining (proving the result geometrically and algebraically, the result is generalised to other polygons by further reflection on the proof(s. Different proofs are given, each giving different insights that lead to further generalisations. The underlying heuristic reasoning is carefully described in order to provide an exemplar for designing learning trajectories to engage students with these functions of proof.

A Concise and Direct Proof of "Fermat's Last Theorem"

OpenAIRE

Ellman, Roger

1998-01-01

The recently developed proof of Fermat's Last Theorem is very lengthy and difficult, so much so as to be beyond all but a small body of specialists. While certainly of value in the developments that resulted, that proof could not be, nor was offered as being, possibly the proof Fermat had in mind. The present proof being brief, direct and concise is a candidate for being what Fermat had in mind. It is also completely accessible to any one trained in common algebra. That critical suggestions o...

28 CFR 79.35 - Proof of onset of leukemia at least two years after first exposure, and proof of onset of a...

Science.gov (United States)

2010-07-01

... 28 Judicial Administration 2 2010-07-01 2010-07-01 false Proof of onset of leukemia at least two... Participants § 79.35 Proof of onset of leukemia at least two years after first exposure, and proof of onset of... be the date of first or initial exposure. The date of onset will be the date of diagnosis as...

[Mathematical exploration of essence of herbal properties based on "Three-Elements" theory].

Science.gov (United States)

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.

Earthquake proof device for nuclear power plant building

International Nuclear Information System (INIS)

Okada, Yasuo.

1991-01-01

The structure of the present invention enables three dimensional vibration proof, i.e., in horizontal and vertical directions of a reactor container building. That is, each of the reactor container building and a reactor auxiliary building is adapted as an independent structure. The periphery of the reactor container building is surrounded by the reactor auxiliary building. The reactor auxiliary building is supported against the ground by way of a horizontal vibration proof device. The reactor container building is supported against the ground by way of a three-dimensional vibration proof device that prevents vibrations in both of the horizontal directions, and the vertical directions. The reactor container building is connected to the auxiliary building by way of a vertical vibration proof device. With such a constitution, although the reactor container building is vibration proof against both of the horizontal and the vertical vibrations, the vertical vibration proofness is an extension of inherent vertical vibration period. Accordingly, the head of the building undergoes rocking vibrations. However, since the reactor container building is connected to the reactor auxiliary building, the rocking vibrations are prevented by the reactor auxiliary building. As a result, safety upon occurrence of an earthquakes can be ensured. (I.S.)

28 CFR 79.13 - Proof of physical presence for the requisite period and proof of participation onsite during a...

Science.gov (United States)

2010-07-01

... participated onsite in the atmospheric detonation of a nuclear device. ... requisite period and proof of participation onsite during a period of atmospheric nuclear testing. 79.13... presence for the requisite period and proof of participation onsite during a period of atmospheric nuclear...

The Use of the History of Mathematics in the Teaching Pre-Service Mathematics Teachers

Science.gov (United States)

Galante, Dianna

2014-01-01

Many scholars have written about using the history of mathematics in the teaching of pre-service mathematics teachers. For this study, pre-service mathematics teachers developed an electronic journal of reflections based on presentations in the history of mathematics in a secondary mathematics education course. The main purpose of the…

Mentoring in mathematics education

CERN Document Server

Hyde, Rosalyn

2013-01-01

Designed to support both teachers and university-based tutors in mentoring pre-service and newly qualified mathematics teachers at both primary and secondary levels, Mentoring Mathematics Teachers offers straightforward practical advice that is based on practice, underpinned by research, and geared specifically towards this challenging subject area.Developed by members of The Association of Mathematics Education Teachers, the authors draw upon the most up-to-date research and theory to provide evidence-based practical guidance. Themes covered include:

Symbolic logic syntax, semantics, and proof

CERN Document Server

Agler, David

2012-01-01

Brimming with visual examples of concepts, derivation rules, and proof strategies, this introductory text is ideal for students with no previous experience in logic. Students will learn translation both from formal language into English and from English into formal language; how to use truth trees and truth tables to test propositions for logical properties; and how to construct and strategically use derivation rules in proofs.

A stream-based mathematical model for distributed information processing systems - SysLab system model

OpenAIRE

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.

Data-oriented scheduling for PROOF

International Nuclear Information System (INIS)

Xu Neng; Guan Wen; Wu Sau Lan; Ganis, Gerardo

2011-01-01

The Parallel ROOT Facility - PROOF - is a distributed analysis system optimized for I/O intensive analysis tasks of HEP data. With LHC entering the analysis phase, PROOF has become a natural ingredient for computing farms at Tier3 level. These analysis facilities will typically be used by a few tenths of users, and can also be federated into a sort of analysis cloud corresponding to the Virtual Organization of the experiment. Proper scheduling is required to guarantee fair resource usage, to enforce priority policies and to optimize the throughput. In this paper we discuss an advanced priority system that we are developing for PROOF. The system has been designed to automatically adapt to unknown length of the tasks, to take into account the data location and availability (including distribution across geographically separated sites), and the {group, user} default priorities. In this system, every element - user, group, dataset, job slot and storage - gets its priority and those priorities are dynamically linked with each other. In order to tune the interplay between the various components, we have designed and started implementing a simulation application that can model various type and size of PROOF clusters. In this application a monitoring package records all the changes of them so that we can easily understand and tune the performance. We will discuss the status of our simulation and show examples of the results we are expecting from it.

Mathematical models with singularities a zoo of singular creatures

CERN Document Server

Torres, Pedro J

2015-01-01

The book aims to provide an unifying view of a variety (a 'zoo') of mathematical models with some kind of singular nonlinearity, in the sense that it becomes infinite when the state variable approaches a certain point. Up to 11 different concrete models are analyzed in separate chapters. Each chapter starts with a discussion of the basic model and its physical significance. Then the main results and typical proofs are outlined, followed by open problems. Each chapter is closed by a suitable list of references. The book may serve as a guide for researchers interested in the modelling of real world processes.

Construction mathematics

CERN Document Server

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...

Verifying Process Algebra Proofs in Type Theory

NARCIS (Netherlands)

Sellink, M.P.A.

In this paper we study automatic verification of proofs in process algebra. Formulas of process algebra are represented by types in typed λ-calculus. Inhabitants (terms) of these types represent proofs. The specific typed λ-calculus we use is the Calculus of Inductive Constructions as implemented

Non-Well-Founded Proofs for the Grzegorczyk Modal Logic

OpenAIRE

Savateev, Yury; Shamkanov, Daniyar

2018-01-01

We present a sequent calculus for the Grzegorczyk modal logic Grz allowing cyclic and other non-well-founded proofs and obtain the cut-elimination theorem for it by constructing a continuous cut-elimination mapping acting on these proofs. As an application, we establish the Lyndon interpolation property for the logic Grz proof-theoretically.

A Calculus of Circular Proofs and its Categorical Semantics

DEFF Research Database (Denmark)

Santocanale, Luigi

2002-01-01

We present a calculus of "circular proofs": the graph underlying a proof is not a finite tree but instead it is allowed to contain a certain amount of cycles.The main challenge in developing a theory for the calculus is to define the semantics of proofs, since the usual method by induction...

Proof of payment for all reimbursement claims

CERN Multimedia

HR Department

2006-01-01

Members of the personnel are kindly requested to note that only documents proving that a payment has been made are accepted as proof of payment for any claims for reimbursement, including specifically the reimbursement of education fees. In particular, the following will be accepted as proof of payment: bank or post office bank statements indicating the name of the institution to which the payment was made; photocopies of cheques made out to the institution to which the payments were made together with bank statements showing the numbers of the relevant cheques; proof of payment in the form of discharged payment slips; invoices with acknowledgement of settlement, receipts, bank statements detailing operations crediting another account or similar documents. As a result, the following documents in particular will no longer be accepted as proof of payment: photocopies of cheques that are not submitted together with bank or post office bank statements showing the numbers of the relevant cheques; details of ...

The Effectiveness of Problem-Based Learning Approach Based on Multiple Intelligences in Terms of Student’s Achievement, Mathematical Connection Ability, and Self-Esteem

Science.gov (United States)

Kartikasari, A.; Widjajanti, D. B.

2017-02-01

The aim of this study is to explore the effectiveness of learning approach using problem-based learning based on multiple intelligences in developing student’s achievement, mathematical connection ability, and self-esteem. This study is experimental research with research sample was 30 of Grade X students of MIA III MAN Yogyakarta III. Learning materials that were implemented consisting of trigonometry and geometry. For the purpose of this study, researchers designed an achievement test made up of 44 multiple choice questions with respectively 24 questions on the concept of trigonometry and 20 questions for geometry. The researcher also designed a connection mathematical test and self-esteem questionnaire that consisted of 7 essay questions on mathematical connection test and 30 items of self-esteem questionnaire. The learning approach said that to be effective if the proportion of students who achieved KKM on achievement test, the proportion of students who achieved a minimum score of high category on the results of both mathematical connection test and self-esteem questionnaire were greater than or equal to 70%. Based on the hypothesis testing at the significance level of 5%, it can be concluded that the learning approach using problem-based learning based on multiple intelligences was effective in terms of student’s achievement, mathematical connection ability, and self-esteem.

Mathematical model of rolling an elastic wheel over deformable support base

Science.gov (United States)

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

A direct proof of Sobolev embeddings for Triebel-Lizorkin spaces, including mixed norms and quasi-homogeneity

DEFF Research Database (Denmark)

Johnsen, Jon

The article deals with a simplified proof of the Sobolev embedding theorem for Triebel-Lizorkin spaces (that contain the $L_p$-Sobolev spaces $H^s_p$ as special cases). The method extends to a proof of the corresponding fact for general Triebel–Lizorkin spaces based on mixed $L_p$-norms...

Mathematical Thinking and Creativity through Mathematical Problem Posing and Solving

Directory of Open Access Journals (Sweden)

María F. Ayllón

2016-04-01

Full Text Available This work shows the relationship between the development of mathematical thinking and creativity with mathematical problem posing and solving. Creativity and mathematics are disciplines that do not usually appear together. Both concepts constitute complex processes sharing elements, such as fluency (number of ideas, flexibility (range of ideas, novelty (unique idea and elaboration (idea development. These factors contribute, among others, to the fact that schoolchildren are competent in mathematics. The problem solving and posing are a very powerful evaluation tool that shows the mathematical reasoning and creative level of a person. Creativity is part of the mathematics education and is a necessary ingredient to perform mathematical assignments. This contribution presents some important research works about problem posing and solving related to the development of mathematical knowledge and creativity. To that end, it is based on various beliefs reflected in the literature with respect to notions of creativity, problem solving and posing.

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

Students' Mathematics Word Problem-Solving Achievement in a Computer-Based Story

Science.gov (United States)

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…

Authentication Based on Non-Interactive Zero-Knowledge Proofs for the Internet of Things.

Science.gov (United States)

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.

Construction of state-independent proofs for quantum contextuality

Science.gov (United States)

Tang, Weidong; Yu, Sixia

2017-12-01

Since the enlightening proofs of quantum contextuality first established by Kochen and Specker, and also by Bell, various simplified proofs have been constructed to exclude the noncontextual hidden variable theory of our nature at the microscopic scale. The conflict between the noncontextual hidden variable theory and quantum mechanics is commonly revealed by Kochen-Specker sets of yes-no tests, represented by projectors (or rays), via either logical contradictions or noncontextuality inequalities in a state-(in)dependent manner. Here we propose a systematic and programmable construction of a state-independent proof from a given set of nonspecific rays in C3 according to their Gram matrix. This approach brings us a greater convenience in the experimental arrangements. Besides, our proofs in C3 can also be generalized to any higher-dimensional systems by a recursive method.

Mathematical physics applied mathematics for scientists and engineers

CERN Document Server

Kusse, Bruce R

2006-01-01

What sets this volume apart from other mathematics texts is its emphasis on mathematical tools commonly used by scientists and engineers to solve real-world problems. Using a unique approach, it covers intermediate and advanced material in a manner appropriate for undergraduate students. Based on author Bruce Kusse's course at the Department of Applied and Engineering Physics at Cornell University, Mathematical Physics begins with essentials such as vector and tensor algebra, curvilinear coordinate systems, complex variables, Fourier series, Fourier and Laplace transforms, differential and integral equations, and solutions to Laplace's equations

Adapting proofs-as-programs the Curry-Howard protocol

CERN Document Server

Poernomo, Iman Hafiz; Crossley, John Newsome

2007-01-01

Details developments in the direction of a practical proofs-as-programs paradigm, which constitutes a set of approaches to developing programs from proofs in constructive logic with applications to industrial-scale, complex software engineering problems.

14 CFR 406.155 - Offer of proof.

Science.gov (United States)

2010-01-01

... 14 Aeronautics and Space 4 2010-01-01 2010-01-01 false Offer of proof. 406.155 Section 406.155... Transportation Adjudications § 406.155 Offer of proof. A party whose evidence has been excluded by a ruling of the administrative law judge may offer the evidence for the record on appeal. ...

Interval logic. Proof theory and theorem proving

DEFF Research Database (Denmark)

Rasmussen, Thomas Marthedal

2002-01-01

of a direction of an interval, and present a sound and complete Hilbert proof system for it. Because of its generality, SIL can conveniently act as a general formalism in which other interval logics can be encoded. We develop proof theory for SIL including both a sequent calculus system and a labelled natural...

14 CFR 25.307 - Proof of structure.

Science.gov (United States)

2010-01-01

... 14 Aeronautics and Space 1 2010-01-01 2010-01-01 false Proof of structure. 25.307 Section 25.307... STANDARDS: TRANSPORT CATEGORY AIRPLANES Structure General § 25.307 Proof of structure. (a) Compliance with... condition. Structural analysis may be used only if the structure conforms to that for which experience has...

14 CFR 23.307 - Proof of structure.

Science.gov (United States)

2010-01-01

... 14 Aeronautics and Space 1 2010-01-01 2010-01-01 false Proof of structure. 23.307 Section 23.307... STANDARDS: NORMAL, UTILITY, ACROBATIC, AND COMMUTER CATEGORY AIRPLANES Structure General § 23.307 Proof of structure. (a) Compliance with the strength and deformation requirements of § 23.305 must be shown for each...

Performance-based classrooms: A case study of two elementary teachers of mathematics and science

Science.gov (United States)

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.

Autonomous intelligent cars: proof that the EPSRC Principles are future-proof

NARCIS (Netherlands)

de Bruin, R.W.; de Cock Buning, M.

2017-01-01

Principle 2 of the EPSRC’s principles of robotics (AISB workshop on PrinciplesofRobotics, 2016) proves to be future proof when applied to the current state of the art of law and technology surrounding autonomous intelligent cars (AICs). Humans, not AICS, are responsible agents. AICs should be

Proof-of-principle experimental realization of a qubit-like qudit-based quantum key distribution scheme

Science.gov (United States)

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.

Filler segmentation of SEM paper images based on mathematical morphology.

Science.gov (United States)

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.

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.

Science.gov (United States)

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.

14 CFR 16.231 - Offer of proof.

Science.gov (United States)

2010-01-01

... 14 Aeronautics and Space 1 2010-01-01 2010-01-01 false Offer of proof. 16.231 Section 16.231... PRACTICE FOR FEDERALLY-ASSISTED AIRPORT ENFORCEMENT PROCEEDINGS Hearings § 16.231 Offer of proof. A party whose evidence has been excluded by a ruling of the hearing officer may offer the evidence on the record...

49 CFR 1503.641 - Offer of proof.

Science.gov (United States)

2010-10-01

... 49 Transportation 9 2010-10-01 2010-10-01 false Offer of proof. 1503.641 Section 1503.641... Rules of Practice in TSA Civil Penalty Actions § 1503.641 Offer of proof. A party whose evidence has been excluded by a ruling of the ALJ may offer the evidence for the record on appeal. ...

[Burden of proof in medical cases--presumption of fact and prima facie evidence. 1. Burden of proof].

Science.gov (United States)

Sliwka, Marcin

2004-01-01

The aim of this paper was to present the main rules concerning the burden of proof in polish civil trials, including medical cases. This paper also describes the subject of evidence were presented and explained. The court influence on evidence procedure was also analysed. The effect of the institution of informed consent on burden of proof in polish civil law is also described. This paper includes numerous High Court sentences on evidential and medical issues.

Web-based international knowledge exchange tool on urban resilience and climate proofing cities : climatescan

NARCIS (Netherlands)

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

Visualizing Probabilistic Proof

OpenAIRE

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.

Proof of Kochen–Specker Theorem: Conversion of Product Rule to Sum Rule

International Nuclear Information System (INIS)

Toh, S.P.; Zainuddin, Hishamuddin

2009-01-01

Valuation functions of observables in quantum mechanics are often expected to obey two constraints called the sum rule and product rule. However, the Kochen–Specker (KS) theorem shows that for a Hilbert space of quantum mechanics of dimension d ≤ 3, these constraints contradict individually with the assumption of value definiteness. The two rules are not irrelated and Peres [Found. Phys. 26 (1996) 807] has conceived a method of converting the product rule into a sum rule for the case of two qubits. Here we apply this method to a proof provided by Mermin based on the product rule for a three-qubit system involving nine operators. We provide the conversion of this proof to one based on sum rule involving ten operators. (general)

14 CFR 13.225 - Offer of proof.

Science.gov (United States)

2010-01-01

... 14 Aeronautics and Space 1 2010-01-01 2010-01-01 false Offer of proof. 13.225 Section 13.225... INVESTIGATIVE AND ENFORCEMENT PROCEDURES Rules of Practice in FAA Civil Penalty Actions § 13.225 Offer of proof. A party whose evidence has been excluded by a ruling of the administrative law judge may offer the...

34 CFR 34.14 - Burden of proof.

Science.gov (United States)

2010-07-01

... 34 Education 1 2010-07-01 2010-07-01 false Burden of proof. 34.14 Section 34.14 Education Office of the Secretary, Department of Education ADMINISTRATIVE WAGE GARNISHMENT § 34.14 Burden of proof. (a... those in § 34.24. (d)(1) If you object on the ground that applicable law bars us from collecting the...

Commognitive analysis of undergraduate mathematics students' first encounter with the subgroup test

Science.gov (United States)

Ioannou, Marios

2018-06-01

This study analyses learning aspects of undergraduate mathematics students' first encounter with the subgroup test, using the commognitive theoretical framework. It focuses on students' difficulties as these are related to the object-level and metalevel mathematical learning in group theory, and, when possible, highlights any commognitive conflicts. In the data analysis, one can identify three types of difficulties, relevant to object-level learning: namely regarding the frequently observed confusion between groups and sets, the object-level rules of visual mediators, and the object-level rules of contextual notions, such as permutations, exponentials, sets and matrices. In addition, data analysis suggests two types of difficulties, relevant to metalevel learning. The first refers to the actual proof that the three conditions of subgroup test hold, and the second is related to syntactic inaccuracies, incomplete argumentation and problematic use of visual mediators. Finally, this study suggests that there are clear links between object-level and metalevel learning, mainly due to the fact that objectification of the various relevant mathematical notions influences the endorsement of the governing metarules.