Proofs without Words: A Visual Application of Reasoning and Proof

ERIC Educational Resources Information Center

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…

Velocity feedback control with a flywheel proof mass actuator

NASA Astrophysics Data System (ADS)

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.

Proof test and fatigue crack growth modeling on 2024-T3 aluminum alloy

NASA Technical Reports Server (NTRS)

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

1990-01-01

Pressure proof testing of aircraft fuselage structures has been suggested as a means of screening critical crack sizes and of extending their useful life. The objective of this paper is to study the proof-test concept and to model the crack-growth process on a ductile material. Simulated proof and operational fatigue life tests have been conducted on cracked panels made of 2024-T3 aluminum alloy sheet material. A fatigue crack-closure model was modified to simulate the proof test and operational fatigue cycling. Using crack-growth rate and resistance-curve data, the model was able to predict crack growth during and after the proof load. These tests and analyses indicate that the proof test increases fatigue life; but the beneficial life, after a 1.33 or 1.5 proof, was less than a few hundred cycles.

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

ERIC Educational Resources Information Center

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…

Integrating Algebra and Proof in High School Mathematics: An Exploratory Study

ERIC Educational Resources Information Center

Martinez, Mara V.; Brizuela, Barbara M.; Superfine, Alison Castro

2011-01-01

Frequently, in the US students' work with proofs is largely concentrated to the domain of high school geometry, thus providing students with a distorted image of what proof entails, which is at odds with the central role that proof plays in mathematics. Despite the centrality of proof in mathematics, there is a lack of studies addressing how to…

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

ERIC Educational Resources Information Center

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…

Rethinking the Discovery Function of Proof within the Context of Proofs and Refutations

ERIC Educational Resources Information Center

Komatsu, Kotaro; Tsujiyama, Yosuke; Sakamaki, Aruta

2014-01-01

Proof and proving are important components of school mathematics and have multiple functions in mathematical practice. Among these functions of proof, this paper focuses on the discovery function that refers to invention of a new statement or conjecture by reflecting on or utilizing a constructed proof. Based on two cases in which eighth and ninth…

Proof test methodology for composites

NASA Technical Reports Server (NTRS)

Wu, Edward M.; Bell, David K.

1992-01-01

The special requirements for proof test of composites are identified based on the underlying failure process of composites. Two proof test methods are developed to eliminate the inevitable weak fiber sites without also causing flaw clustering which weakens the post-proof-test composite. Significant reliability enhancement by these proof test methods has been experimentally demonstrated for composite strength and composite life in tension. This basic proof test methodology is relevant to the certification and acceptance of critical composite structures. It can also be applied to the manufacturing process development to achieve zero-reject for very large composite structures.

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

NASA Technical Reports Server (NTRS)

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.

An evaluation of the pressure proof test concept for thin sheet 2024-T3

NASA Technical Reports Server (NTRS)

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

1990-01-01

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 fuselage. The results revealed that the remaining fatigue life after a proof test was longer than that without the proof test 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 test 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.

An evaluation of the pressure proof test concept for thin sheet 2024-T3

NASA Technical Reports Server (NTRS)

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

1990-01-01

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 test was longer than that without the proof test 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 test 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.

[Understanding mistake-proofing].

PubMed

de Saint Maurice, G; Giraud, N; Ausset, S; Auroy, Y; Lenoir, B; Amalberti, R

2011-01-01

The mistake-proofing concept often refers to physical devices that prevent actors from making a wrong action. In anaesthesiology, one immediately thinks to specific design of outlets for medical gases. More generally, the principle of mistake-proofing is to avoid an error, by placing knowledge in the world rather than knowledge in the head. As it often happens in risk management, healthcare has received information transfers from the industry. Computer is changing the concept of mistake-proofing, initially based on physical design, such as aerospace and automotive industry. The mistake-proofing concept may be applied to prevention, detection, and mitigation of errors. The forcing functions are a specific part of mistake-proofing: they prevent a wrong action or they force a virtuous one. Grout proposes a little shortcut to identify mistake-proofing devices: "If it is not possible to picture it in action, it is probably not a mistake-proofing device". Copyright © 2010 Elsevier Masson SAS. All rights reserved.

28 CFR 79.25 - Proof of onset of leukemia at least two years after first exposure, and proof of onset of a...

Code of Federal Regulations, 2010 CFR

2010-07-01

... years after first exposure, and proof of onset of a specified compensable disease more than five years... Specified Diseases Contracted After Exposure in an Affected Area (âDownwindersâ) § 79.25 Proof of onset of leukemia at least two years after first exposure, and proof of onset of a specified compensable disease...

28 CFR 79.25 - Proof of onset of leukemia at least two years after first exposure, and proof of onset of a...

Code of Federal Regulations, 2011 CFR

2011-07-01

... years after first exposure, and proof of onset of a specified compensable disease more than five years... Specified Diseases Contracted After Exposure in an Affected Area (âDownwindersâ) § 79.25 Proof of onset of leukemia at least two years after first exposure, and proof of onset of a specified compensable disease...

28 CFR 79.25 - Proof of onset of leukemia at least two years after first exposure, and proof of onset of a...

Code of Federal Regulations, 2012 CFR

2012-07-01

... years after first exposure, and proof of onset of a specified compensable disease more than five years... Specified Diseases Contracted After Exposure in an Affected Area (âDownwindersâ) § 79.25 Proof of onset of leukemia at least two years after first exposure, and proof of onset of a specified compensable disease...

28 CFR 79.25 - Proof of onset of leukemia at least two years after first exposure, and proof of onset of a...

Code of Federal Regulations, 2014 CFR

2014-07-01

... years after first exposure, and proof of onset of a specified compensable disease more than five years... Specified Diseases Contracted After Exposure in an Affected Area (âDownwindersâ) § 79.25 Proof of onset of leukemia at least two years after first exposure, and proof of onset of a specified compensable disease...

28 CFR 79.25 - Proof of onset of leukemia at least two years after first exposure, and proof of onset of a...

Code of Federal Regulations, 2013 CFR

2013-07-01

... years after first exposure, and proof of onset of a specified compensable disease more than five years... Specified Diseases Contracted After Exposure in an Affected Area (âDownwindersâ) § 79.25 Proof of onset of leukemia at least two years after first exposure, and proof of onset of a specified compensable disease...

Comparative Analysis on the Nature of Proof to Be Taught in Geometry: The Cases of French and Japanese Lower Secondary Schools

ERIC Educational Resources Information Center

Miyakawa, Takeshi

2017-01-01

This paper reports the results of an international comparative study on the nature of proof to be taught in geometry. Proofs in French and Japanese lower secondary schools were explored by analyzing curricular documents: mathematics textbooks and national curricula. Analyses on the three aspects of proof--statement, proof, and theory--suggested by…

An integrated experimental and computational approach to material selection for sound proof thermally insulted enclosure of a power generation system

NASA Astrophysics Data System (ADS)

Waheed, R.; Tarar, W.; Saeed, H. A.

2016-08-01

Sound proof canopies for diesel power generators are fabricated with a layer of sound absorbing material applied to all the inner walls. The physical properties of the majority of commercially available sound proofing materials reveal that a material with high sound absorption coefficient has very low thermal conductivity. Consequently a good sound absorbing material is also a good heat insulator. In this research it has been found through various experiments that ordinary sound proofing materials tend to rise the inside temperature of sound proof enclosure in certain turbo engines by capturing the heat produced by engine and not allowing it to be transferred to atmosphere. The same phenomenon is studied by creating a finite element model of the sound proof enclosure and performing a steady state and transient thermal analysis. The prospects of using aluminium foam as sound proofing material has been studied and it is found that inside temperature of sound proof enclosure can be cut down to safe working temperature of power generator engine without compromise on sound proofing.

The Wording of a Proof: Hardy's Second "Elegant" Proof--The Pythagorean School's Irrationality of Square Root of 2

ERIC Educational Resources Information Center

Padula, Janice

2006-01-01

One of the most interesting and important proofs in the history of mathematics is the Pythagorean school's proof of the "irrationality" of the square root of 2. After a brief look at G. H. Hardy (1941) thoughts regarding it, two versions of the classic Pythagorean proof are examined and discussed in this article, one written by an American…

Optimal periodic proof test based on cost-effective and reliability criteria

NASA Technical Reports Server (NTRS)

Yang, J.-N.

1976-01-01

An exploratory study for the optimization of periodic proof tests for fatigue-critical structures is presented. The optimal proof load level and the optimal number of periodic proof tests are determined by minimizing the total expected (statistical average) cost, while the constraint on the allowable level of structural reliability is satisfied. The total expected cost consists of the expected cost of proof tests, the expected cost of structures destroyed by proof tests, and the expected cost of structural failure in service. It is demonstrated by numerical examples that significant cost saving and reliability improvement for fatigue-critical structures can be achieved by the application of the optimal periodic proof test. The present study is relevant to the establishment of optimal maintenance procedures for fatigue-critical structures.

A Semantic Basis for Proof Queries and Transformations

NASA Technical Reports Server (NTRS)

Aspinall, David; Denney, Ewen W.; Luth, Christoph

2013-01-01

We extend the query language PrQL, designed for inspecting machine representations of proofs, to also allow transformation of proofs. PrQL natively supports hiproofs which express proof structure using hierarchically nested labelled trees, which we claim is a natural way of taming the complexity of huge proofs. Query-driven transformations enable manipulation of this structure, in particular, to transform proofs produced by interactive theorem provers into forms that assist their understanding, or that could be consumed by other tools. In this paper we motivate and define basic transformation operations, using an abstract denotational semantics of hiproofs and queries. This extends our previous semantics for queries based on syntactic tree representations.We define update operations that add and remove sub-proofs, and manipulate the hierarchy to group and ungroup nodes. We show that

On Mathematical Proving

NASA Astrophysics Data System (ADS)

Stefaneas, Petros; Vandoulakis, Ioannis M.

2015-12-01

This paper outlines a logical representation of certain aspects of the process of mathematical proving that are important from the point of view of Artificial Intelligence. Our starting-point is the concept of proof-event or proving, introduced by Goguen, instead of the traditional concept of mathematical proof. The reason behind this choice is that in contrast to the traditional static concept of mathematical proof, proof-events are understood as processes, which enables their use in Artificial Intelligence in such contexts, in which problem-solving procedures and strategies are studied. We represent proof-events as problem-centered spatio-temporal processes by means of the language of the calculus of events, which captures adequately certain temporal aspects of proof-events (i.e. that they have history and form sequences of proof-events evolving in time). Further, we suggest a "loose" semantics for the proof-events, by means of Kolmogorov's calculus of problems. Finally, we expose the intented interpretations for our logical model from the fields of automated theorem-proving and Web-based collective proving.

Deriving Safety Cases from Automatically Constructed Proofs

NASA Technical Reports Server (NTRS)

Basir, Nurlida; Denney, Ewen; Fischer, Bernd

2009-01-01

Formal proofs provide detailed justification for the validity of claims and are widely used in formal software development methods. However, they are often complex and difficult to understand, because the formalism in which they are constructed and encoded is usually machine-oriented, and they may also be based on assumptions that are not justified. This causes concerns about the trustworthiness of using formal proofs as arguments in safety-critical applications. Here, we present an approach to develop safety cases that correspond to formal proofs found by automated theorem provers and reveal the underlying argumentation structure and top-level assumptions. We concentrate on natural deduction style proofs, which are closer to human reasoning than resolution proofs, and show how to construct the safety cases by covering the natural deduction proof tree with corresponding safety case fragments. We also abstract away logical book-keeping steps, which reduces the size of the constructed safety cases. We show how the approach can be applied to the proofs found by the Muscadet prover.

Assurance Cases for Proofs as Evidence

NASA Technical Reports Server (NTRS)

Chaki, Sagar; Gurfinkel, Arie; Wallnau, Kurt; Weinstock, Charles

2009-01-01

Proof-carrying code (PCC) provides a 'gold standard' for establishing formal and objective confidence in program behavior. However, in order to extend the benefits of PCC - and other formal certification techniques - to realistic systems, we must establish the correspondence of a mathematical proof of a program's semantics and its actual behavior. In this paper, we argue that assurance cases are an effective means of establishing such a correspondence. To this end, we present an assurance case pattern for arguing that a proof is free from various proof hazards. We also instantiate this pattern for a proof-based mechanism to provide evidence about a generic medical device software.

16 CFR 23.10 - Misuse of “corrosion proof,” “noncorrosive,” “corrosion resistant,” “rust proof,” “rust resistant...

Code of Federal Regulations, 2010 CFR

2010-01-01

... INDUSTRIES § 23.10 Misuse of “corrosion proof,” “noncorrosive,” “corrosion resistant,” “rust proof,” “rust...,” “rust proof,” or any other term of similar meaning to describe an industry product unless all parts of the product will be immune from rust and other forms of corrosion during the life expectancy of the...

16 CFR 23.10 - Misuse of “corrosion proof,” “noncorrosive,” “corrosion resistant,” “rust proof,” “rust resistant...

Code of Federal Regulations, 2011 CFR

2011-01-01

... INDUSTRIES § 23.10 Misuse of “corrosion proof,” “noncorrosive,” “corrosion resistant,” “rust proof,” “rust...,” “rust proof,” or any other term of similar meaning to describe an industry product unless all parts of the product will be immune from rust and other forms of corrosion during the life expectancy of the...

16 CFR 23.10 - Misuse of “corrosion proof,” “noncorrosive,” “corrosion resistant,” “rust proof,” “rust resistant...

Code of Federal Regulations, 2013 CFR

2013-01-01

... INDUSTRIES § 23.10 Misuse of “corrosion proof,” “noncorrosive,” “corrosion resistant,” “rust proof,” “rust...,” “rust proof,” or any other term of similar meaning to describe an industry product unless all parts of the product will be immune from rust and other forms of corrosion during the life expectancy of the...

16 CFR 23.10 - Misuse of “corrosion proof,” “noncorrosive,” “corrosion resistant,” “rust proof,” “rust resistant...

Code of Federal Regulations, 2014 CFR

2014-01-01

... INDUSTRIES § 23.10 Misuse of “corrosion proof,” “noncorrosive,” “corrosion resistant,” “rust proof,” “rust...,” “rust proof,” or any other term of similar meaning to describe an industry product unless all parts of the product will be immune from rust and other forms of corrosion during the life expectancy of the...

16 CFR 23.10 - Misuse of “corrosion proof,” “noncorrosive,” “corrosion resistant,” “rust proof,” “rust resistant...

Code of Federal Regulations, 2012 CFR

2012-01-01

... INDUSTRIES § 23.10 Misuse of “corrosion proof,” “noncorrosive,” “corrosion resistant,” “rust proof,” “rust...,” “rust proof,” or any other term of similar meaning to describe an industry product unless all parts of the product will be immune from rust and other forms of corrosion during the life expectancy of the...

Mathematical Proof. Description of Teacher Inservice Education Materials.

ERIC Educational Resources Information Center

National Education Association, Washington, DC. Project on Utilization of Inservice Education R & D Outcomes.

The learning module described here is designed to help teachers plan and present a lesson on mathematical proof to pupils. The main topics covered are structure, hypothesis and conclusion, analysis, contrapositive, proof by contradiction, part proof worksheet, and conclusion and posttest. This descriptive report provides information on the…

Optimum structural design based on reliability and proof-load testing

NASA Technical Reports Server (NTRS)

Shinozuka, M.; Yang, J. N.

1969-01-01

Proof-load test eliminates structures with strength less than the proof load and improves the reliability value in analysis. It truncates the distribution function of strength at the proof load, thereby alleviating verification of a fitted distribution function at the lower tail portion where data are usually nonexistent.

Preparing for Formal Proofs in Geometry

ERIC Educational Resources Information Center

Johnson, Art

2009-01-01

One way in which geometry teachers can help students develop their reasoning is by providing proof-readiness experiences. Blum and Kirsch (1991) suggest that "preformal proofs" can help students develop deductive reasoning. Preformal proofs, which follow the basic principles of deductive reasoning, can help prepare students for formal deduction in…

38 CFR 10.28 - Proof of death evidence.

Code of Federal Regulations, 2010 CFR

2010-07-01

... 38 Pensions, Bonuses, and Veterans' Relief 1 2010-07-01 2010-07-01 false Proof of death evidence... COMPENSATION Adjusted Compensation; General § 10.28 Proof of death evidence. Evidence required in establishing proof of death under the act, as amended, shall conform with the requirements set forth in the...

16 CFR 614.1 - Appropriate proof of identity.

Code of Federal Regulations, 2010 CFR

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...

16 CFR 614.1 - Appropriate proof of identity.

Code of Federal Regulations, 2011 CFR

2011-01-01

... 16 Commercial Practices 1 2011-01-01 2011-01-01 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...

16 CFR 614.1 - Appropriate proof of identity.

Code of Federal Regulations, 2012 CFR

2012-01-01

... 16 Commercial Practices 1 2012-01-01 2012-01-01 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...

38 CFR 10.28 - Proof of death evidence.

Code of Federal Regulations, 2014 CFR

2014-07-01

... 38 Pensions, Bonuses, and Veterans' Relief 1 2014-07-01 2014-07-01 false Proof of death evidence... COMPENSATION Adjusted Compensation; General § 10.28 Proof of death evidence. Evidence required in establishing proof of death under the act, as amended, shall conform with the requirements set forth in the...

38 CFR 10.28 - Proof of death evidence.

Code of Federal Regulations, 2013 CFR

2013-07-01

... 38 Pensions, Bonuses, and Veterans' Relief 1 2013-07-01 2013-07-01 false Proof of death evidence... COMPENSATION Adjusted Compensation; General § 10.28 Proof of death evidence. Evidence required in establishing proof of death under the act, as amended, shall conform with the requirements set forth in the...

38 CFR 10.28 - Proof of death evidence.

Code of Federal Regulations, 2011 CFR

2011-07-01

... 38 Pensions, Bonuses, and Veterans' Relief 1 2011-07-01 2011-07-01 false Proof of death evidence... COMPENSATION Adjusted Compensation; General § 10.28 Proof of death evidence. Evidence required in establishing proof of death under the act, as amended, shall conform with the requirements set forth in the...

38 CFR 10.28 - Proof of death evidence.

Code of Federal Regulations, 2012 CFR

2012-07-01

... 38 Pensions, Bonuses, and Veterans' Relief 1 2012-07-01 2012-07-01 false Proof of death evidence... COMPENSATION Adjusted Compensation; General § 10.28 Proof of death evidence. Evidence required in establishing proof of death under the act, as amended, shall conform with the requirements set forth in the...

Proof Construction and Evaluation Practices of Prospective Mathematics Educators

ERIC Educational Resources Information Center

Imamoglu, Yesim; Togrol, Aysenur Yontar

2015-01-01

This study was conducted with 93 freshmen and 82 senior prospective mathematicians and mathematics teachers in order to investigate how they construct and evaluate proofs and whether there are any significant differences in their proof construction (with respect to department and grade) and proof evaluation (with respect to department)…

Micromachined force-balance feedback accelerometer with optical displacement detection

DOEpatents

Nielson, Gregory N.; Langlois, Eric; Baker, Michael; Okandan, Murat; Anderson, Robert

2014-07-22

An accelerometer includes a proof mass and a frame that are formed in a handle layer of a silicon-on-an-insulator (SOI). The proof mass is separated from the frame by a back-side trench that defines a boundary of the proof mass. The accelerometer also includes a reflector coupled to a top surface of the proof mass. An optical detector is located above the reflector at the device side. The accelerometer further includes at least one suspension spring. The suspension spring has a handle anchor that extends downwards from the device side to the handle layer to mechanically support upward and downward movement of the proof mass relative to a top surface of the proof mass.

Deriving Safety Cases from Machine-Generated Proofs

NASA Technical Reports Server (NTRS)

Basir, Nurlida; Fischer, Bernd; Denney, Ewen

2009-01-01

Proofs provide detailed justification for the validity of claims and are widely used in formal software development methods. However, they are often complex and difficult to understand, because they use machine-oriented formalisms; they may also be based on assumptions that are not justified. This causes concerns about the trustworthiness of using formal proofs as arguments in safety-critical applications. Here, we present an approach to develop safety cases that correspond to formal proofs found by automated theorem provers and reveal the underlying argumentation structure and top-level assumptions. We concentrate on natural deduction proofs and show how to construct the safety cases by covering the proof tree with corresponding safety case fragments.

Granularity analysis for mathematical proofs.

PubMed

Schiller, Marvin R G

2013-04-01

Mathematical proofs generally allow for various levels of detail and conciseness, such that they can be adapted for a particular audience or purpose. Using automated reasoning approaches for teaching proof construction in mathematics presupposes that the step size of proofs in such a system is appropriate within the teaching context. This work proposes a framework that supports the granularity analysis of mathematical proofs, to be used in the automated assessment of students' proof attempts and for the presentation of hints and solutions at a suitable pace. Models for granularity are represented by classifiers, which can be generated by hand or inferred from a corpus of sample judgments via machine-learning techniques. This latter procedure is studied by modeling granularity judgments from four experts. The results provide support for the granularity of assertion-level proofs but also illustrate a degree of subjectivity in assessing step size. Copyright © 2013 Cognitive Science Society, Inc.

45 CFR 81.85 - Offer of proof.

Code of Federal Regulations, 2011 CFR

2011-10-01

... 45 Public Welfare 1 2011-10-01 2011-10-01 false Offer of proof. 81.85 Section 81.85 Public Welfare DEPARTMENT OF HEALTH AND HUMAN SERVICES GENERAL ADMINISTRATION PRACTICE AND PROCEDURE FOR HEARINGS UNDER PART 80 OF THIS TITLE Hearing Procedures § 81.85 Offer of proof. An offer of proof made in connection with...

45 CFR 81.85 - Offer of proof.

Code of Federal Regulations, 2010 CFR

2010-10-01

... 45 Public Welfare 1 2010-10-01 2010-10-01 false Offer of proof. 81.85 Section 81.85 Public Welfare DEPARTMENT OF HEALTH AND HUMAN SERVICES GENERAL ADMINISTRATION PRACTICE AND PROCEDURE FOR HEARINGS UNDER PART 80 OF THIS TITLE Hearing Procedures § 81.85 Offer of proof. An offer of proof made in connection with...

Using Sudoku to Introduce Proof Techniques

ERIC Educational Resources Information Center

Snyder, Brian A.

2010-01-01

In this article we show how the Sudoku puzzle and the three simple rules determining its solution can be used as an introduction to proof-based mathematics. In the completion of the puzzle, students can construct multi-step solutions that involve sequencing of steps, use methods such as backtracking and proof by cases, and proof by contradiction…

Key Ideas: What Are They and How Can They Help Us Understand How People View Proof?

ERIC Educational Resources Information Center

Raman, Manya

2003-01-01

Examines the views of proof held by university-level mathematics students and teachers. Develops a framework for characterizing people's views of proof based on a distinction between public and private aspects of proof and the key ideas that link these two domains. (Author/KHR)

Proof-Related Reasoning in High School Textbooks

ERIC Educational Resources Information Center

Johnson, Gwendolyn J.; Thompson, Denisse R.; Senk, Sharon L.

2010-01-01

Recognizing that textbooks play a prominent role in fostering students' understanding of reasoning and proof, the authors conducted a study to examine the extent to which textbooks used in U.S. high schools provide opportunities for students to encounter proof-related reasoning and how the nature of proof-related reasoning in textbooks varies by…

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

Code of Federal Regulations, 2010 CFR

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...

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

Code of Federal Regulations, 2012 CFR

2012-07-01

... 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... participated onsite in the atmospheric detonation of a nuclear device. ...

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

Code of Federal Regulations, 2014 CFR

2014-07-01

... 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... participated onsite in the atmospheric detonation of a nuclear device. ...

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

Code of Federal Regulations, 2013 CFR

2013-07-01

... 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... participated onsite in the atmospheric detonation of a nuclear device. ...

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

Code of Federal Regulations, 2011 CFR

2011-07-01

... 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... participated onsite in the atmospheric detonation of a nuclear device. ...

47 CFR 76.1704 - Proof-of-performance test data.

Code of Federal Regulations, 2012 CFR

2012-10-01

... 47 Telecommunication 4 2012-10-01 2012-10-01 false Proof-of-performance test data. 76.1704 Section 76.1704 Telecommunication FEDERAL COMMUNICATIONS COMMISSION (CONTINUED) BROADCAST RADIO SERVICES MULTICHANNEL VIDEO AND CABLE TELEVISION SERVICE Documents to be Maintained for Inspection § 76.1704 Proof-of-performance test data. (a) The proof of...

47 CFR 76.1704 - Proof-of-performance test data.

Code of Federal Regulations, 2014 CFR

2014-10-01

... 47 Telecommunication 4 2014-10-01 2014-10-01 false Proof-of-performance test data. 76.1704 Section 76.1704 Telecommunication FEDERAL COMMUNICATIONS COMMISSION (CONTINUED) BROADCAST RADIO SERVICES MULTICHANNEL VIDEO AND CABLE TELEVISION SERVICE Documents to be Maintained for Inspection § 76.1704 Proof-of-performance test data. (a) The proof of...

28 CFR 79.34 - Proof of medical condition.

Code of Federal Regulations, 2012 CFR

2012-07-01

... 28 Judicial Administration 2 2012-07-01 2012-07-01 false Proof of medical condition. 79.34 Section... COMPENSATION ACT Eligibility Criteria for Claims by Onsite Participants § 79.34 Proof of medical condition. Proof of medical condition under this subpart will be made in the same manner and according to the same...

28 CFR 79.34 - Proof of medical condition.

Code of Federal Regulations, 2013 CFR

2013-07-01

... 28 Judicial Administration 2 2013-07-01 2013-07-01 false Proof of medical condition. 79.34 Section... COMPENSATION ACT Eligibility Criteria for Claims by Onsite Participants § 79.34 Proof of medical condition. Proof of medical condition under this subpart will be made in the same manner and according to the same...

39 CFR 501.5 - Burden of proof standard.

Code of Federal Regulations, 2010 CFR

2010-07-01

... 39 Postal Service 1 2010-07-01 2010-07-01 false Burden of proof standard. 501.5 Section 501.5 Postal Service UNITED STATES POSTAL SERVICE POSTAGE PROGRAMS AUTHORIZATION TO MANUFACTURE AND DISTRIBUTE POSTAGE EVIDENCING SYSTEMS § 501.5 Burden of proof standard. The burden of proof is on the Postal Service...

28 CFR 79.34 - Proof of medical condition.

Code of Federal Regulations, 2010 CFR

2010-07-01

... 28 Judicial Administration 2 2010-07-01 2010-07-01 false Proof of medical condition. 79.34 Section... COMPENSATION ACT Eligibility Criteria for Claims by Onsite Participants § 79.34 Proof of medical condition. Proof of medical condition under this subpart will be made in the same manner and according to the same...

12 CFR 1022.123 - Appropriate proof of identity.

Code of Federal Regulations, 2013 CFR

2013-01-01

... 12 Banks and Banking 8 2013-01-01 2013-01-01 false Appropriate proof of identity. 1022.123 Section...) Duties of Consumer Reporting Agencies Regarding Identity Theft § 1022.123 Appropriate proof of identity... information consumers shall provide to constitute proof of identity for purposes of sections 605A, 605B, and...

12 CFR 1022.123 - Appropriate proof of identity.

Code of Federal Regulations, 2014 CFR

2014-01-01

... 12 Banks and Banking 8 2014-01-01 2014-01-01 false Appropriate proof of identity. 1022.123 Section...) Duties of Consumer Reporting Agencies Regarding Identity Theft § 1022.123 Appropriate proof of identity... information consumers shall provide to constitute proof of identity for purposes of sections 605A, 605B, and...

12 CFR 1022.123 - Appropriate proof of identity.

Code of Federal Regulations, 2012 CFR

2012-01-01

... 12 Banks and Banking 8 2012-01-01 2012-01-01 false Appropriate proof of identity. 1022.123 Section...) Duties of Consumer Reporting Agencies Regarding Identity Theft § 1022.123 Appropriate proof of identity... information consumers shall provide to constitute proof of identity for purposes of sections 605A, 605B, and...

7 CFR 319.56-42 - Peppers from the Republic of Korea.

Code of Federal Regulations, 2011 CFR

2011-01-01

... Republic of Korea in insect-proof greenhouses approved by and registered with the National Plant Quarantine... approved production sites. The peppers must be safeguarded by an insect-proof mesh screen or plastic... peppers must be packed in insect-proof cartons or containers, or covered with insect-proof mesh or plastic...

Mathematicians' Perspectives on Features of a Good Pedagogical Proof

ERIC Educational Resources Information Center

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,…

30 CFR 778.21 - Proof of publication.

Code of Federal Regulations, 2013 CFR

2013-07-01

... 30 Mineral Resources 3 2013-07-01 2013-07-01 false Proof of publication. 778.21 Section 778.21....21 Proof of publication. A copy of the newspaper advertisements of the application for a permit, significant revision of a permit, or renewal of a permit, or proof of publication of the advertisements which...

38 CFR 8.20 - Proof of death, age, relationship and marriage.

Code of Federal Regulations, 2014 CFR

2014-07-01

... 38 Pensions, Bonuses, and Veterans' Relief 1 2014-07-01 2014-07-01 false Proof of death, age... AFFAIRS NATIONAL SERVICE LIFE INSURANCE Proof of Death, Age, Or Relationship § 8.20 Proof of death, age, relationship and marriage. Whenever it is necessary for a claimant to prove death, age, relationship or...

38 CFR 8.20 - Proof of death, age, relationship and marriage.

Code of Federal Regulations, 2012 CFR

2012-07-01

... 38 Pensions, Bonuses, and Veterans' Relief 1 2012-07-01 2012-07-01 false Proof of death, age... AFFAIRS NATIONAL SERVICE LIFE INSURANCE Proof of Death, Age, Or Relationship § 8.20 Proof of death, age, relationship and marriage. Whenever it is necessary for a claimant to prove death, age, relationship or...

38 CFR 8.20 - Proof of death, age, relationship and marriage.

Code of Federal Regulations, 2013 CFR

2013-07-01

... 38 Pensions, Bonuses, and Veterans' Relief 1 2013-07-01 2013-07-01 false Proof of death, age... AFFAIRS NATIONAL SERVICE LIFE INSURANCE Proof of Death, Age, Or Relationship § 8.20 Proof of death, age, relationship and marriage. Whenever it is necessary for a claimant to prove death, age, relationship or...

29 CFR 1919.28 - Unit proof tests-cranes and gear accessory thereto.

Code of Federal Regulations, 2010 CFR

2010-07-01

... 29 Labor 7 2010-07-01 2010-07-01 false Unit proof tests-cranes and gear accessory thereto. 1919.28... ADMINISTRATION, DEPARTMENT OF LABOR (CONTINUED) GEAR CERTIFICATION Certification of Vessels: Tests and Proof Loads; Heat Treatment; Competent Persons § 1919.28 Unit proof tests—cranes and gear accessory thereto...

43 CFR 3863.1-2 - Proof of improvements for patent.

Code of Federal Regulations, 2013 CFR

2013-10-01

... 43 Public Lands: Interior 2 2013-10-01 2013-10-01 false Proof of improvements for patent. 3863.1-2... MANAGEMENT, DEPARTMENT OF THE INTERIOR MINERALS MANAGEMENT (3000) MINERAL PATENT APPLICATIONS Placer Mining Claim Patent Applications § 3863.1-2 Proof of improvements for patent. The proof of improvements must...

43 CFR 3863.1-2 - Proof of improvements for patent.

Code of Federal Regulations, 2012 CFR

2012-10-01

... 43 Public Lands: Interior 2 2012-10-01 2012-10-01 false Proof of improvements for patent. 3863.1-2... MANAGEMENT, DEPARTMENT OF THE INTERIOR MINERALS MANAGEMENT (3000) MINERAL PATENT APPLICATIONS Placer Mining Claim Patent Applications § 3863.1-2 Proof of improvements for patent. The proof of improvements must...

43 CFR 3863.1-2 - Proof of improvements for patent.

Code of Federal Regulations, 2014 CFR

2014-10-01

... 43 Public Lands: Interior 2 2014-10-01 2014-10-01 false Proof of improvements for patent. 3863.1-2... MANAGEMENT, DEPARTMENT OF THE INTERIOR MINERALS MANAGEMENT (3000) MINERAL PATENT APPLICATIONS Placer Mining Claim Patent Applications § 3863.1-2 Proof of improvements for patent. The proof of improvements must...

43 CFR 3863.1-2 - Proof of improvements for patent.

Code of Federal Regulations, 2011 CFR

2011-10-01

... 43 Public Lands: Interior 2 2011-10-01 2011-10-01 false Proof of improvements for patent. 3863.1-2... MANAGEMENT, DEPARTMENT OF THE INTERIOR MINERALS MANAGEMENT (3000) MINERAL PATENT APPLICATIONS Placer Mining Claim Patent Applications § 3863.1-2 Proof of improvements for patent. The proof of improvements must...

Guidelines for Proof Test Analysis

NASA Technical Reports Server (NTRS)

Chell, G. G.; McClung, R. C.; Kuhlman, C. J.; Russell, D. A.; Garr, K.; Donnelly, B.

1999-01-01

These guidelines integrate state-of-the-art elastic-plastic fracture mechanics (EPFM) and proof test implementation issues into a comprehensive proof test analysis procedure in the form of a road map which identifies the types of data, fracture mechanics based parameters, and calculations needed to perform flaw screening and minimum proof load analyses of fracture critical components. Worked examples are presented to illustrate the application of the road map to proof test analysis. The state-of-the art fracture technology employed in these guidelines is based on the EPFM parameter, J, and a pictorial representation of a J fracture analysis, called the failure assessment diagram (FAD) approach. The recommended fracture technology is validated using finite element J results, and laboratory and hardware fracture test results on the nickel-based superalloy Inconel 718, the aluminum alloy 2024-T3511, and ferritic pressure vessel steels. In all cases the laboratory specimens and hardware failed by ductile mechanisms. Advanced proof test analyses involving probability analysis and multiple-cycle proof testing (MCPT) are addressed. Finally, recommendations are provided on how to account for the effects of the proof test overload on subsequent service fatigue and fracture behaviors.

Elucidation of covariant proofs in general relativity: example of the use of algebraic software in the shear-free conjecture in MAPLE

NASA Astrophysics Data System (ADS)

Huf, P. A.; Carminati, J.

2018-01-01

In this paper we explore the use of a new algebraic software package in providing independent covariant proof of a conjecture in general relativity. We examine the proof of two sub-cases of the shear-free conjecture σ =0 => ω Θ =0 by Senovilla et al. (Gen. Relativ. Gravit 30:389-411, 1998): case 1: for dust; case 2: for acceleration parallel to vorticity. We use TensorPack, a software package recently released for the Maple environment. In this paper, we briefly summarise the key features of the software and then demonstrate its use by providing and discussing examples of independent proofs of the paper in question. A full set of our completed proofs is available online at http://www.bach2roq.com/science/maths/GR/ShearFreeProofs.html. We are in agreeance with the equations provided in the original paper, noting that the proofs often require many steps. Furthermore, in our proofs we provide fully worked algebraic steps in such a way that the proofs can be examined systematically, and avoiding hand calculation. It is hoped that the elucidated proofs may be of use to other researchers in verifying the algebraic consistency of the expressions in the paper in question, as well as related literature. Furthermore we suggest that the appropriate use of algebraic software in covariant formalism could be useful for developing research and teaching in GR theory.

31 CFR 341.4 - Proof of purchase.

Code of Federal Regulations, 2010 CFR

2010-07-01

... 31 Money and Finance: Treasury 2 2010-07-01 2010-07-01 false Proof of purchase. 341.4 Section 341... BONDS § 341.4 Proof of purchase. At the time a Retirement Plan Bond is issued, the issuing agent will... name the bond is inscribed, to the registered owner as well, proof of the purchase on Form PD 3550. The...

Research-Based Interventions in the Area of Proof: The Past, the Present, and the Future

ERIC Educational Resources Information Center

Stylianides, Gabriel J.; Stylianides, Andreas J.

2017-01-01

The concept of "proof" has attracted considerable research attention over the past decades in part due to its indisputable importance to the discipline of mathematics and to students' learning of mathematics. Yet, the teaching and learning of proof is an instructionally arduous territory, with proof being recognized as a hard-to-teach…

Using Toulmin Analysis to Analyse an Instructor's Proof Presentation in Abstract Algebra

ERIC Educational Resources Information Center

Fukawa-Connelly, Timothy

2014-01-01

This paper provides a method for analysing undergraduate teaching of proof-based courses using Toulmin's model (1969) of argumentation. It presents a case study of one instructor's presentation of proofs. The analysis shows that the instructor presents different levels of detail in different proofs; thus, the students have an inconsistent set of…

Bridging the Gap between Graphical Arguments and Verbal-Symbolic Proofs in a Real Analysis Context

ERIC Educational Resources Information Center

Zazkis, Dov; Weber, Keith; Mejía-Ramos, Juan Pablo

2016-01-01

We examine a commonly suggested proof construction strategy from the mathematics education literature--that students first produce a graphical argument and then work to construct a verbal-symbolic proof based on that graphical argument. The work of students who produce such graphical arguments when solving proof construction tasks was analyzed to…

Preservice and Novice Teachers' Knowledge on Preformal Proofs: Triangle Postulate as an Example

ERIC Educational Resources Information Center

Leung, Kui Chiu Issic; Lee, Chun Yeung

2017-01-01

By considering the example of proving the triangle postulate, this study aimed to explore Hong Kong preservice and novice teachers' knowledge competencies and their beliefs about preformal and formal proofs. The findings revealed that such teachers are not proficient in using preformal proofs and do not realize that preformal proofs are a useful…

Should Proof Be Minimal? Ms T's Evaluation of Secondary School Students' Proofs

ERIC Educational Resources Information Center

Tsamir, Pessia; Tirosh, Dina; Dreyfus, Tommy; Barkai, Ruthi; Tabach, Michal

2009-01-01

Calls for reform in mathematics education around the world state that proofs should be part of school mathematics at all levels. Turning these calls into a reality falls on teachers' shoulders. This paper focuses on one secondary school teacher's reactions to students' suggested proofs and justifications in elementary number theory. To determine…

7 CFR 1.657 - What is the standard of proof?

Code of Federal Regulations, 2010 CFR

2010-01-01

... 7 Agriculture 1 2010-01-01 2010-01-01 false What is the standard of proof? 1.657 Section 1.657 Agriculture Office of the Secretary of Agriculture ADMINISTRATIVE REGULATIONS Conditions in FERC Hydropower Licenses Hearing, Briefing, and Decision § 1.657 What is the standard of proof? The standard of proof is a...

38 CFR 10.38 - Proof of age of veteran's child.

Code of Federal Regulations, 2014 CFR

2014-07-01

... 38 Pensions, Bonuses, and Veterans' Relief 1 2014-07-01 2014-07-01 false Proof of age of veteran's... ADJUSTED COMPENSATION Adjusted Compensation; General § 10.38 Proof of age of veteran's child. A child of a veteran shall be required to submit proof of age in accordance with the requirements set forth in the...

38 CFR 10.38 - Proof of age of veteran's child.

Code of Federal Regulations, 2012 CFR

2012-07-01

... 38 Pensions, Bonuses, and Veterans' Relief 1 2012-07-01 2012-07-01 false Proof of age of veteran's... ADJUSTED COMPENSATION Adjusted Compensation; General § 10.38 Proof of age of veteran's child. A child of a veteran shall be required to submit proof of age in accordance with the requirements set forth in the...

38 CFR 10.38 - Proof of age of veteran's child.

Code of Federal Regulations, 2013 CFR

2013-07-01

... 38 Pensions, Bonuses, and Veterans' Relief 1 2013-07-01 2013-07-01 false Proof of age of veteran's... ADJUSTED COMPENSATION Adjusted Compensation; General § 10.38 Proof of age of veteran's child. A child of a veteran shall be required to submit proof of age in accordance with the requirements set forth in the...

77 FR 61661 - Price for the American Eagle Silver Proof and Uncirculated Coins and the America the Beautiful...

Federal Register 2010, 2011, 2012, 2013, 2014

2012-10-10

... DEPARTMENT OF THE TREASURY United States Mint Price for the American Eagle Silver Proof and... price of silver, the United States Mint is raising the price of its American Eagle Silver Proof and... price 2012 American Eagle Silver Proof $59.95 2012 American Eagle Silver Uncirculated 50.95 2011...

Ten Things to Consider when Teaching Proof

ERIC Educational Resources Information Center

Cirillo, Michelle

2009-01-01

As she sat in a high school geometry class and observed a beginning teacher, Matt (a pseudonym), teaching proof for the first time, the author was reminded of her own experiences in teaching formal proof to secondary school students. Matt seemed to struggle with some of the same challenges she encountered when she began teaching proof. For…

How Mathematicians Determine if an Argument Is a Valid Proof

ERIC Educational Resources Information Center

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;…

Shorter unentangled proofs for ground state connectivity

NASA Astrophysics Data System (ADS)

Caha, Libor; Nagaj, Daniel; Schwarz, Martin

2018-07-01

Can one considerably shorten a proof for a quantum problem by using a protocol with a constant number of unentangled provers? We consider a frustration-free variant of the sf {QCMA}-complete ground state connectivity (GSCON) problem for a system of size n with a proof of superlinear size. We show that we can shorten this proof in sf {QMA}(2): There exists a two-copy, unentangled proof with length of order n, up to logarithmic factors, while the completeness-soundness gap of the new protocol becomes a small inverse polynomial in n.

Proponents of Creationism but not Proponents of Evolution Frame the Origins Debate in Terms of Proof

NASA Astrophysics Data System (ADS)

Barnes, Ralph M.; Church, Rebecca A.

2013-03-01

In Study 1, 72 internet documents containing creationism, ID (intelligent design), or evolution content were selected for analysis. All instances of proof cognates (the word "proof" and related terms such as "proven", "disproof", etc.) contained within these documents were identified and labeled in terms of the manner in which the terms were used. In Study 2, frequency counts for six terms (proof, evidence, establish, experiment, test, trial) were conducted on a sample of peer-reviewed research articles in the journal Science and the 72 internet documents included in Study 1. Quantitative and qualitative analyses revealed that proponents of creationism were much more likely than proponents of evolution to frame the creationism/evolution issue in terms of proof (ID proponents fell partway between the other two). Proponents of creationism frequently described empirical data favoring their position as proof of their position. Even more frequently, proponents of creationism described evolutionary scientists as being engaged in failed attempts to prove the truth of the evolutionary position. Evolution documents included fewer proof cognates than creationism or ID documents and the few proof cognates found in evolution documents were rarely used to describe the status of the theory of evolution. Qualitative data analysis indicated that proof cognates were often used to indicate certainty. The asymmetry between evolution and creationism documents was limited primarily to proof cognates; there were no major asymmetries for the terms evidence, establish, experiment, test, and trial. The results may reveal differences in the epistemological commitments of the involved parties.

A Historical Note on the Proof of the Area of a Circle

ERIC Educational Resources Information Center

Wilamowsky, Yonah; Epstein, Sheldon; Dickman, Bernard

2011-01-01

Proofs that the area of a circle is nr[superscript 2] can be found in mathematical literature dating as far back as the time of the Greeks. The early proofs, e.g. Archimedes, involved dividing the circle into wedges and then fitting the wedges together in a way to approximate a rectangle. Later more sophisticated proofs relied on arguments…

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

Code of Federal Regulations, 2010 CFR

2010-07-01

... years after first exposure, and proof of onset of a specified compensable disease more than five years... a specified compensable disease more than five years after first exposure. Absent any indication to... the specified compensable disease. Proof of the onset of leukemia shall be established in accordance...

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

Code of Federal Regulations, 2011 CFR

2011-07-01

... years after first exposure, and proof of onset of a specified compensable disease more than five years... a specified compensable disease more than five years after first exposure. Absent any indication to... the specified compensable disease. Proof of the onset of leukemia shall be established in accordance...

One Problem, Nine Student-Produced Proofs

ERIC Educational Resources Information Center

Birky, Geoffrey; Campbell, Connie M.; Raman, Manya; Sandefur, James; Somers, Kay

2011-01-01

This paper tells the story of what happened when students in the authors' sophomore-level introduction-to-proof classes were given a theorem to prove with no expectation about what proof method to use. The paper discusses the nine different student-produced proofs of the statement: If "n" is an integer such that "n" is greater than or equal to 3,…

29 CFR 1919.71 - Unit proof test and examination of cranes.

Code of Federal Regulations, 2011 CFR

2011-07-01

... 29 Labor 7 2011-07-01 2011-07-01 false Unit proof test and examination of cranes. 1919.71 Section... § 1919.71 Unit proof test and examination of cranes. (a) Unit proof tests of cranes shall be carried out at the following times: (1) In the cases of new cranes, before initial use and every 4 years...

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

Code of Federal Regulations, 2013 CFR

2013-07-01

... years after first exposure, and proof of onset of a specified compensable disease more than five years... a specified compensable disease more than five years after first exposure. Absent any indication to... the specified compensable disease. Proof of the onset of leukemia shall be established in accordance...

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

Code of Federal Regulations, 2014 CFR

2014-07-01

... years after first exposure, and proof of onset of a specified compensable disease more than five years... a specified compensable disease more than five years after first exposure. Absent any indication to... the specified compensable disease. Proof of the onset of leukemia shall be established in accordance...

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

Code of Federal Regulations, 2012 CFR

2012-07-01

... years after first exposure, and proof of onset of a specified compensable disease more than five years... a specified compensable disease more than five years after first exposure. Absent any indication to... the specified compensable disease. Proof of the onset of leukemia shall be established in accordance...

29 CFR 1919.71 - Unit proof test and examination of cranes.

Code of Federal Regulations, 2010 CFR

2010-07-01

... 29 Labor 7 2010-07-01 2010-07-01 false Unit proof test and examination of cranes. 1919.71 Section... § 1919.71 Unit proof test and examination of cranes. (a) Unit proof tests of cranes shall be carried out at the following times: (1) In the cases of new cranes, before initial use and every 4 years...

27 CFR 30.71 - Optional method for determination of proof for spirits containing solids of 400 milligrams or...

Code of Federal Regulations, 2011 CFR

2011-04-01

... determination of proof for spirits containing solids of 400 milligrams or less per 100 milliliters. 30.71... determination of proof for spirits containing solids of 400 milligrams or less per 100 milliliters. The proof of... containing solids of 400 milligrams or less per 100 milliliters shall be determined by the use of a...

27 CFR 30.71 - Optional method for determination of proof for spirits containing solids of 400 milligrams or...

Code of Federal Regulations, 2010 CFR

2010-04-01

... determination of proof for spirits containing solids of 400 milligrams or less per 100 milliliters. 30.71... determination of proof for spirits containing solids of 400 milligrams or less per 100 milliliters. The proof of... containing solids of 400 milligrams or less per 100 milliliters shall be determined by the use of a...

NASA Contractor Report: Guidelines for Proof Test Analysis

NASA Technical Reports Server (NTRS)

Chell, G. G.; McClung, R. C.; Kuhlman, C. J.; Russell, D. A.; Garr, K.; Donnelly, B.

1997-01-01

These Guidelines integrate state-of-the-art Elastic-Plastic Fracture Mechanics (EPFM) and proof test implementation issues into a comprehensive proof test analysis procedure in the form of a Road Map which identifies the types of data, fracture mechanics based parameters, and calculations needed to perform flaw screening and minimum proof load analyses of fracture critical components. Worked examples are presented to illustrate the application of the Road Map to proof test analysis. The state-of-the-art fracture technology employed in these Guidelines is based on the EPFM parameter, J, and a pictorial representation of a J fracture analysis, called the Failure Assessment Diagram (FAD) approach. The recommended fracture technology is validated using finite element J results, and laboratory and hardware fracture test results on the nickel-based superalloy IN-718, the aluminum alloy 2024-T351 1, and ferritic pressure vessel steels. In all cases the laboratory specimens and hardware failed by ductile mechanisms. Advanced proof test analyses involving probability analysis and Multiple Cycle Proof Testing (MCPT) are addressed. Finally, recommendations are provided on to how to account for the effects of the proof test overload on subsequent service fatigue and fracture behaviors.

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

NASA Astrophysics Data System (ADS)

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).

An Empirical Evaluation of Automated Theorem Provers in Software Certification

NASA Technical Reports Server (NTRS)

Denney, Ewen; Fischer, Bernd; Schumann, Johann

2004-01-01

We describe a system for the automated certification of safety properties of NASA software. The system uses Hoare-style program verification technology to generate proof obligations which are then processed by an automated first-order theorem prover (ATP). We discuss the unique requirements this application places on the ATPs, focusing on automation, proof checking, and usability. For full automation, however, the obligations must be aggressively preprocessed and simplified, and we demonstrate how the individual simplification stages, which are implemented by rewriting, influence the ability of the ATPs to solve the proof tasks. Our results are based on 13 certification experiments that lead to more than 25,000 proof tasks which have each been attempted by Vampire, Spass, e-setheo, and Otter. The proofs found by Otter have been proof-checked by IVY.

Microelectromechanical inertial sensor

DOEpatents

Okandan, Murat [Edgewood, NM; Nielson, Gregory N [Albuquerque, NM

2012-06-26

A microelectromechanical (MEM) inertial sensor is disclosed which can be used to sense a linear acceleration, or a Coriolis acceleration due to an angular rotation rate, or both. The MEM inertial sensor has a proof mass which is supported on a bridge extending across an opening through a substrate, with the proof mass being balanced on the bridge by a pivot, or suspended from the bridge by the pivot. The proof mass can be oscillated in a tangential direction in the plane of the substrate, with any out-of-plane movement of the proof mass in response to a sensed acceleration being optically detected using transmission gratings located about an outer edge of the proof mass to generate a diffracted light pattern which changes with the out-of-plane movement of the proof mass.

ECC-based grouping-proof RFID for inpatient medication safety.

PubMed

Lin, Qiping; Zhang, Fangguo

2012-12-01

Several papers were proposed in which symmetric cryptography was used to design RFID grouping-proof for medication safety in the Journal of Medical Systems. However, if we want to ensure privacy, authentication and protection against the tracking of RFID-tags without losing system scalability, we must design an asymmetric cryptography-based RFID. This paper will propose a new ECC-based grouping-proof for RFID. Our ECC-based grouping-proof reduces the computation of tags and prevents timeout problems from occurring in n-party grouping-proof protocol. Based on asymmetric cryptography, the proposed scheme is practical, secure and efficient for medication applications.

31 CFR 306.75 - Individual fiduciaries.

Code of Federal Regulations, 2012 CFR

2012-07-01

... fiduciaries must be supported by appropriate proof. This requires: (1) Proof of the death, resignation... apply. (Form PD 2446 may be used to furnish proof of incumbency of fiduciaries.) Assignments by...

31 CFR 306.75 - Individual fiduciaries.

Code of Federal Regulations, 2011 CFR

2011-07-01

... fiduciaries must be supported by appropriate proof. This requires: (1) Proof of the death, resignation... apply. (Form PD 2446 may be used to furnish proof of incumbency of fiduciaries.) Assignments by...

31 CFR 306.75 - Individual fiduciaries.

Code of Federal Regulations, 2013 CFR

2013-07-01

... fiduciaries must be supported by appropriate proof. This requires: (1) Proof of the death, resignation... apply. (Form PD 2446 may be used to furnish proof of incumbency of fiduciaries.) Assignments by...

31 CFR 306.75 - Individual fiduciaries.

Code of Federal Regulations, 2014 CFR

2014-07-01

... fiduciaries must be supported by appropriate proof. This requires: (1) Proof of the death, resignation... apply. (Form PD 2446 may be used to furnish proof of incumbency of fiduciaries.) Assignments by...

31 CFR 306.75 - Individual fiduciaries.

Code of Federal Regulations, 2010 CFR

2010-07-01

... fiduciaries must be supported by appropriate proof. This requires: (1) Proof of the death, resignation... apply. (Form PD 2446 may be used to furnish proof of incumbency of fiduciaries.) Assignments by...

Analysis of the Cognitive Unity or Rupture between Conjecture and Proof When Learning to Prove on a Grade 10 Trigonometry Course

ERIC Educational Resources Information Center

Fiallo, Jorge; Gutiérrez, Angel

2017-01-01

We present results from a classroom-based intervention designed to help a class of grade 10 students (14-15 years old) learn proof while studying trigonometry in a dynamic geometry software environment. We analysed some students' solutions to conjecture-and-proof problems that let them gain experience in stating conjectures and developing proofs.…

Querying Proofs

NASA Technical Reports Server (NTRS)

Aspinall, David; Denney, Ewen; Lueth, Christoph

2012-01-01

We motivate and introduce a query language PrQL designed for inspecting machine representations of proofs. PrQL natively supports hiproofs which express proof structure using hierarchical nested labelled trees. The core language presented in this paper is locally structured (first-order), with queries built using recursion and patterns over proof structure and rule names. We define the syntax and semantics of locally structured queries, demonstrate their power, and sketch some implementation experiments.

Putting time into proof outlines

NASA Technical Reports Server (NTRS)

Schneider, Fred B.; Bloom, Bard; Marzullo, Keith

1993-01-01

A logic for reasoning about timing properties of concurrent programs is presented. The logic is based on Hoare-style proof outlines and can handle maximal parallelism as well as certain resource-constrained execution environments. The correctness proof for a mutual exclusion protocol that uses execution timings in a subtle way illustrates the logic in action. A soundness proof using structural operational semantics is outlined in the appendix.

Pre-service middle school mathematics teachers' evaluations of discussions: the case of proof by contradiction

NASA Astrophysics Data System (ADS)

Demiray, Esra; Işıksal Bostan, Mine

2017-03-01

The purposes of this study are to investigate whether pre-service middle school mathematics teachers evaluate discussions in the cases regarding proof by contradiction correctly, to what extent they explain their correct evaluations by referring to proof by contradiction, and the reasons of their misinterpretations of discussions in the cases regarding proof by contradiction. Data were collected from pre-service middle school mathematics teachers enrolled in a state university in Ankara, Turkey, by asking them to evaluate discussions in two cases related to proof by contradiction. In data analysis, descriptive statistics and item-based analysis were employed. The results of the study indicated that pre-service middle school mathematics teachers are successful in evaluating discussions in the cases regarding proof by contradiction. In terms of year level, it was found that the percentage of the second year students' correct answers was the lowest in both cases. Moreover, the first year students were the most successful group in the first case, and the third year students were the most successful group in the second case. Nearly half of the students explained their correct answers by referring to proof by contradiction in the first case while the percentage of students who explained their correct answers by mentioning proof by contradiction in the second case was considerably low. When incorrect answers of pre-service middle school mathematics teachers were analyzed, two reasons of their misinterpretations of discussions were emerged as "misunderstanding of the assumption" and "perceiving proof as unnecessary".

Decidability of formal theories and hyperincursivity theory

NASA Astrophysics Data System (ADS)

Grappone, Arturo G.

2000-05-01

This paper shows the limits of the Proof Standard Theory (briefly, PST) and gives some ideas of how to build a proof anticipatory theory (briefly, PAT) that has no such limits. Also, this paper considers that Gödel's proof of the undecidability of Principia Mathematica formal theory is not valid for axiomatic theories that use a PAT to build their proofs because the (hyper)incursive functions are self-representable.

An Investigation of Pre-Service Middle School Mathematics Teachers' Ability to Conduct Valid Proofs, Methods Used, and Reasons for Invalid Arguments

ERIC Educational Resources Information Center

Demiray, Esra; Isiksal Bostan, Mine

2017-01-01

The purposes of this study are to investigate Turkish pre-service middle school mathematics teachers' ability in conducting valid proofs for statements regarding numbers and algebra in terms of their year of enrollment in a teacher education program, to determine the proof methods used in their valid proofs, and to examine the reasons for their…

Proof of factorization using background field method of QCD

NASA Astrophysics Data System (ADS)

Nayak, Gouranga C.

2010-02-01

Factorization theorem plays the central role at high energy colliders to study standard model and beyond standard model physics. The proof of factorization theorem is given by Collins, Soper and Sterman to all orders in perturbation theory by using diagrammatic approach. One might wonder if one can obtain the proof of factorization theorem through symmetry considerations at the lagrangian level. In this paper we provide such a proof.

Proof of factorization using background field method of QCD

DOE Office of Scientific and Technical Information (OSTI.GOV)

Nayak, Gouranga C.

Factorization theorem plays the central role at high energy colliders to study standard model and beyond standard model physics. The proof of factorization theorem is given by Collins, Soper and Sterman to all orders in perturbation theory by using diagrammatic approach. One might wonder if one can obtain the proof of factorization theorem through symmetry considerations at the lagrangian level. In this paper we provide such a proof.

The Origin of Alcohol Proof

ERIC Educational Resources Information Center

Jensen, William B.

2004-01-01

The origin of the "proof" system for measuring the ethanol content of alcoholic beverages is presented. The proof system was originally established for purposes of taxing liquors according to their alcohol content and is different in different countries.

Proof test diagrams for Zerodur glass-ceramic

NASA Technical Reports Server (NTRS)

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.

18 CFR 4.6 - Burden of proof.

Code of Federal Regulations, 2011 CFR

2011-04-01

... PROJECT COSTS Determination of Cost of Projects Constructed Under License § 4.6 Burden of proof. The burden of proof to sustain each item of claimed cost shall be upon the licensee and only such items as...

18 CFR 4.6 - Burden of proof.

Code of Federal Regulations, 2010 CFR

2010-04-01

... PROJECT COSTS Determination of Cost of Projects Constructed Under License § 4.6 Burden of proof. The burden of proof to sustain each item of claimed cost shall be upon the licensee and only such items as...

18 CFR 4.6 - Burden of proof.

Code of Federal Regulations, 2014 CFR

2014-04-01

... PROJECT COSTS Determination of Cost of Projects Constructed Under License § 4.6 Burden of proof. The burden of proof to sustain each item of claimed cost shall be upon the licensee and only such items as...

18 CFR 4.6 - Burden of proof.

Code of Federal Regulations, 2012 CFR

2012-04-01

... PROJECT COSTS Determination of Cost of Projects Constructed Under License § 4.6 Burden of proof. The burden of proof to sustain each item of claimed cost shall be upon the licensee and only such items as...

18 CFR 4.6 - Burden of proof.

Code of Federal Regulations, 2013 CFR

2013-04-01

... PROJECT COSTS Determination of Cost of Projects Constructed Under License § 4.6 Burden of proof. The burden of proof to sustain each item of claimed cost shall be upon the licensee and only such items as...

14 CFR 13.224 - Burden of proof.

Code of Federal Regulations, 2010 CFR

2010-01-01

... INVESTIGATIVE AND ENFORCEMENT PROCEDURES Rules of Practice in FAA Civil Penalty Actions § 13.224 Burden of proof... otherwise provided by statute or rule, the proponent of a motion, request, or order has the burden of proof...

On New Proofs of Fundamental Inequalities with Applications

ERIC Educational Resources Information Center

Ray, Partha

2010-01-01

By using the Cauchy-Schwarz inequality a new proof of several standard inequalities is given. A new proof of Young's inequality is given by using Holder's inequality. A new application of the above inequalities is included.

Formal proof of the AVM-1 microprocessor using the concept of generic interpreters

NASA Technical Reports Server (NTRS)

Windley, P.; Levitt, K.; Cohen, G. C.

1991-01-01

A microprocessor designated AVM-1 was designed to demonstrate the use of generic interpreters in verifying hierarchically decomposed microprocessor specifications. This report is intended to document the high-order language (HOL) code verifying AVM-1. The organization of the proof is discussed and some technical details concerning the execution of the proof scripts in HOL are presented. The proof scripts used to verify AVM-1 are also presented.

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

PubMed

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.

A Machine-Checked Proof of A State-Space Construction Algorithm

NASA Technical Reports Server (NTRS)

Catano, Nestor; Siminiceanu, Radu I.

2010-01-01

This paper presents the correctness proof of Saturation, an algorithm for generating state spaces of concurrent systems, implemented in the SMART tool. Unlike the Breadth First Search exploration algorithm, which is easy to understand and formalise, Saturation is a complex algorithm, employing a mutually-recursive pair of procedures that compute a series of non-trivial, nested local fixed points, corresponding to a chaotic fixed point strategy. A pencil-and-paper proof of Saturation exists, but a machine checked proof had never been attempted. The key element of the proof is the characterisation theorem of saturated nodes in decision diagrams, stating that a saturated node represents a set of states encoding a local fixed-point with respect to firing all events affecting only the node s level and levels below. For our purpose, we have employed the Prototype Verification System (PVS) for formalising the Saturation algorithm, its data structures, and for conducting the proofs.

Reliability analysis of structures under periodic proof tests in service

NASA Technical Reports Server (NTRS)

Yang, J.-N.

1976-01-01

A reliability analysis of structures subjected to random service loads and periodic proof tests treats gust loads and maneuver loads as random processes. Crack initiation, crack propagation, and strength degradation are treated as the fatigue process. The time to fatigue crack initiation and ultimate strength are random variables. Residual strength decreases during crack propagation, so that failure rate increases with time. When a structure fails under periodic proof testing, a new structure is built and proof-tested. The probability of structural failure in service is derived from treatment of all the random variables, strength degradations, service loads, proof tests, and the renewal of failed structures. Some numerical examples are worked out.

Using Toulmin analysis to analyse an instructor's proof presentation in abstract algebra

NASA Astrophysics Data System (ADS)

Fukawa-connelly, Timothy

2014-01-01

This paper provides a method for analysing undergraduate teaching of proof-based courses using Toulmin's model (1969) of argumentation. It presents a case study of one instructor's presentation of proofs. The analysis shows that the instructor presents different levels of detail in different proofs; thus, the students have an inconsistent set of written models for their work. Similarly, the analysis shows that the details the instructor says aloud differ from what she writes down. Although her verbal commentary provides additional detail and appears to have pedagogical value, for instance, by modelling thinking that supports proof writing, this value might be better realized if she were to change her teaching practices.

Computerized proof techniques for undergraduates

NASA Astrophysics Data System (ADS)

Smith, Christopher J.; Tefera, Akalu; Zeleke, Aklilu

2012-12-01

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 mathematics. We demonstrate by examples how one can use these computerized proof techniques to raise students' interests in the discovery and proof of mathematical identities and enhance their problem-solving skills.

Computing Gravitational Fields of Finite-Sized Bodies

NASA Technical Reports Server (NTRS)

Quadrelli, Marco

2005-01-01

A computer program utilizes the classical theory of gravitation, implemented by means of the finite-element method, to calculate the near gravitational fields of bodies of arbitrary size, shape, and mass distribution. The program was developed for application to a spacecraft and to floating proof masses and associated equipment carried by the spacecraft for detecting gravitational waves. The program can calculate steady or time-dependent gravitational forces, moments, and gradients thereof. Bodies external to a proof mass can be moving around the proof mass and/or deformed under thermoelastic loads. An arbitrarily shaped proof mass is represented by a collection of parallelepiped elements. The gravitational force and moment acting on each parallelepiped element of a proof mass, including those attributable to the self-gravitational field of the proof mass, are computed exactly from the closed-form equation for the gravitational potential of a parallelepiped. The gravitational field of an arbitrary distribution of mass external to a proof mass can be calculated either by summing the fields of suitably many point masses or by higher-order Gauss-Legendre integration over all elements surrounding the proof mass that are part of a finite-element mesh. This computer program is compatible with more general finite-element codes, such as NASTRAN, because it is configured to read a generic input data file, containing the detailed description of the finiteelement mesh.

49 CFR 178.520 - Standards for textile bags.

Code of Federal Regulations, 2011 CFR

2011-10-01

... for a sift-proof textile bag; and (3) 5L3 for a water-resistant textile bag. (b) Construction... bag. (2) Bags, sift-proof, 5L2: The bag must be made sift-proof, by appropriate means, such as by the...

27 CFR 19.92 - When gauges are required.

Code of Federal Regulations, 2010 CFR

2010-04-01

... proof. Except for a gauge required by § 19.383 or § 19.517 or in any case where the proof changes as a... accounts, (5) Mixed in the manufacture of a distilled spirits product, (6) Reduced in proof prior to...

Quantum Locality?

NASA Astrophysics Data System (ADS)

Stapp, Henry P.

2012-05-01

Robert Griffiths has recently addressed, within the framework of a `consistent quantum theory' that he has developed, the issue of whether, as is often claimed, quantum mechanics entails a need for faster-than-light transfers of information over long distances. He argues that the putative proofs of this property that involve hidden variables include in their premises some essentially classical-physics-type assumptions that are not entailed by the precepts of quantum mechanics. Thus whatever is proved is not a feature of quantum mechanics, but is a property of a theory that tries to combine quantum theory with quasi-classical features that go beyond what is entailed by quantum theory itself. One cannot logically prove properties of a system by establishing, instead, properties of a system modified by adding properties alien to the original system. Hence Griffiths' rejection of hidden-variable-based proofs is logically warranted. Griffiths mentions the existence of a certain alternative proof that does not involve hidden variables, and that uses only macroscopically described observable properties. He notes that he had examined in his book proofs of this general kind, and concluded that they provide no evidence for nonlocal influences. But he did not examine the particular proof that he cites. An examination of that particular proof by the method specified by his `consistent quantum theory' shows that the cited proof is valid within that restrictive version of quantum theory. An added section responds to Griffiths' reply, which cites general possibilities of ambiguities that might make what is to be proved ill-defined, and hence render the pertinent `consistent framework' ill defined. But the vagaries that he cites do not upset the proof in question, which, both by its physical formulation and by explicit identification, specify the framework to be used. Griffiths confirms the validity of the proof insofar as that pertinent framework is used. The section also shows, in response to Griffiths' challenge, why a putative proof of locality that he has described is flawed.

The Ability of Students’ Mathematical Proof in Determining the Validity of Argument Reviewed from Gender Differences

NASA Astrophysics Data System (ADS)

Feriyanto

2018-01-01

This research aims to describe the ability of students’ mathematical proof in determining the validity of argument reviewed from gender differences. The subjects of this research were one male and one female student of the fifth semester of Mathematic Education study program. The subjects were selected based on the highest mathematics ability which was assesed from their previous assignments and tests. In addition, the communication ability of the subjects was also considered in order to facilitate the researcher in conducting interviews. Based on the result of the test with direct and indirect proof, it could be concluded that the subjects were able to: 1) mention all facts/premises and write about what should be shown (conclusion) in direct proof and write additional premise in indirect proof; 2) connect facts/premises to concepts which must be mastered; 3) use equivalent concept to manipulate and organize the proof; 4) use the concept of syllogism and tollens mode to obtain the desired conclusion; 5) construct mathematical evidence systematically, and logically; 6) complement the reason for each step appropriately. The difference was that the male subject wrote the final conclusion, while the female subject did not write the final conclusion on the proof.

46 CFR 540.3 - Proof of financial responsibility, when required.

Code of Federal Regulations, 2010 CFR

2010-10-01

... 46 Shipping 9 2010-10-01 2010-10-01 false Proof of financial responsibility, when required. 540.3... COMMERCE PASSENGER VESSEL FINANCIAL RESPONSIBILITY Proof of Financial Responsibility, Bonding and Certification of Financial Responsibility for Indemnification of Passengers for Nonperformance of Transportation...

Impossible colorings and Bell's theorem

NASA Astrophysics Data System (ADS)

Aravind, P. K.

1999-11-01

An argument due to Zimba and Penrose is generalized to show how all known non-coloring proofs of the Bell-Kochen-Specker (BKS) theorem can be converted into inequality-free proofs of Bell's nonlocality theorem. A compilation of many such inequality-free proofs is given.

10 CFR 140.15 - Proof of financial protection.

Code of Federal Regulations, 2012 CFR

2012-01-01

... Energy NUCLEAR REGULATORY COMMISSION (CONTINUED) FINANCIAL PROTECTION REQUIREMENTS AND INDEMNITY.... (2) Such proof may alternatively, consist of a copy of the declarations page of a nuclear energy... nuclear energy liability insurance as proof of financial protection if it determines that the provisions...

10 CFR 140.15 - Proof of financial protection.

Code of Federal Regulations, 2014 CFR

2014-01-01

... Energy NUCLEAR REGULATORY COMMISSION (CONTINUED) FINANCIAL PROTECTION REQUIREMENTS AND INDEMNITY.... (2) Such proof may alternatively, consist of a copy of the declarations page of a nuclear energy... nuclear energy liability insurance as proof of financial protection if it determines that the provisions...

10 CFR 140.15 - Proof of financial protection.

Code of Federal Regulations, 2013 CFR

2013-01-01

... Energy NUCLEAR REGULATORY COMMISSION (CONTINUED) FINANCIAL PROTECTION REQUIREMENTS AND INDEMNITY.... (2) Such proof may alternatively, consist of a copy of the declarations page of a nuclear energy... nuclear energy liability insurance as proof of financial protection if it determines that the provisions...

31 CFR 515.543 - Proof of origin.

Code of Federal Regulations, 2010 CFR

2010-07-01

... of goods of Cuban origin are generally not issued unless the applicant submits satisfactory... constitute satisfactory proof varies depending upon the facts of the particular case, it is not possible to... satisfactory proof of origin. Independent corroborating documentary evidence, such as insurance documents...

10 CFR 140.15 - Proof of financial protection.

Code of Federal Regulations, 2010 CFR

2010-01-01

... Energy NUCLEAR REGULATORY COMMISSION (CONTINUED) FINANCIAL PROTECTION REQUIREMENTS AND INDEMNITY.... (2) Such proof may alternatively, consist of a copy of the declarations page of a nuclear energy... nuclear energy liability insurance as proof of financial protection if it determines that the provisions...

10 CFR 140.15 - Proof of financial protection.

Code of Federal Regulations, 2011 CFR

2011-01-01

... Energy NUCLEAR REGULATORY COMMISSION (CONTINUED) FINANCIAL PROTECTION REQUIREMENTS AND INDEMNITY.... (2) Such proof may alternatively, consist of a copy of the declarations page of a nuclear energy... nuclear energy liability insurance as proof of financial protection if it determines that the provisions...

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

PubMed

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.

Stork Color Proofing Technology

NASA Astrophysics Data System (ADS)

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.

Hiproofs

NASA Technical Reports Server (NTRS)

Denney, Ewen; Power, John

2003-01-01

We introduce a hierarchical notion of formal proof, useful in the implementation of theorem provers, which we call highproofs. Two alternative definitions are given, motivated by existing notations used in theorem proving research. We define transformations between these two forms of hiproof, develop notions of underlying proof, and give a suitable definition of refinement in order to model incremental proof development. We show that our transformations preserve both underlying proofs and refinement. The relationship of our theory to existing theorem proving systems is discussed, as is its future extension.

A formal approach to the analysis of clinical computer-interpretable guideline modeling languages.

PubMed

Grando, M Adela; Glasspool, David; Fox, John

2012-01-01

To develop proof strategies to formally study the expressiveness of workflow-based languages, and to investigate their applicability to clinical computer-interpretable guideline (CIG) modeling languages. We propose two strategies for studying the expressiveness of workflow-based languages based on a standard set of workflow patterns expressed as Petri nets (PNs) and notions of congruence and bisimilarity from process calculus. Proof that a PN-based pattern P can be expressed in a language L can be carried out semi-automatically. Proof that a language L cannot provide the behavior specified by a PNP requires proof by exhaustion based on analysis of cases and cannot be performed automatically. The proof strategies are generic but we exemplify their use with a particular CIG modeling language, PROforma. To illustrate the method we evaluate the expressiveness of PROforma against three standard workflow patterns and compare our results with a previous similar but informal comparison. We show that the two proof strategies are effective in evaluating a CIG modeling language against standard workflow patterns. We find that using the proposed formal techniques we obtain different results to a comparable previously published but less formal study. We discuss the utility of these analyses as the basis for principled extensions to CIG modeling languages. Additionally we explain how the same proof strategies can be reused to prove the satisfaction of patterns expressed in the declarative language CIGDec. The proof strategies we propose are useful tools for analysing the expressiveness of CIG modeling languages. This study provides good evidence of the benefits of applying formal methods of proof over semi-formal ones. Copyright © 2011 Elsevier B.V. All rights reserved.

Analytic proof of the existence of the Lorenz attractor in the extended Lorenz model

NASA Astrophysics Data System (ADS)

Ovsyannikov, I. I.; Turaev, D. V.

2017-01-01

We give an analytic (free of computer assistance) proof of the existence of a classical Lorenz attractor for an open set of parameter values of the Lorenz model in the form of Yudovich-Morioka-Shimizu. The proof is based on detection of a homoclinic butterfly with a zero saddle value and rigorous verification of one of the Shilnikov criteria for the birth of the Lorenz attractor; we also supply a proof for this criterion. The results are applied in order to give an analytic proof for the existence of a robust, pseudohyperbolic strange attractor (the so-called discrete Lorenz attractor) for an open set of parameter values in a 4-parameter family of 3D Henon-like diffeomorphisms.

Addendum to the User Manual for NASGRO Elastic-Plastic Fracture Mechanics Software Module

NASA Technical Reports Server (NTRS)

Gregg, M. Wayne (Technical Monitor); Chell, Graham; Gardner, Brian

2003-01-01

The elastic-plastic fracture mechanics modules in NASGRO have been enhanced by the addition of of the following: new J-integral solutions based on the reference stress method and finite element solutions; the extension of the critical crack and critical load modules for cracks with two degrees of freedom that tear and failure by ductile instability; the addition of a proof test analysis module that includes safe life analysis, calculates proof loads, and determines the flaw screening 1 capability for a given proof load; the addition of a tear-fatigue module for ductile materials that simultaneously tear and extend by fatigue; and a multiple cycle proof test module for estimating service reliability following a proof test.

5 CFR 843.406 - Proof of dependency.

Code of Federal Regulations, 2012 CFR

2012-01-01

... 5 Administrative Personnel 2 2012-01-01 2012-01-01 false Proof of dependency. 843.406 Section 843.406 Administrative Personnel OFFICE OF PERSONNEL MANAGEMENT (CONTINUED) CIVIL SERVICE REGULATIONS... Proof of dependency. (a) A child is considered to have been dependent on the deceased employee or...

5 CFR 843.406 - Proof of dependency.

Code of Federal Regulations, 2011 CFR

2011-01-01

... 5 Administrative Personnel 2 2011-01-01 2011-01-01 false Proof of dependency. 843.406 Section 843.406 Administrative Personnel OFFICE OF PERSONNEL MANAGEMENT (CONTINUED) CIVIL SERVICE REGULATIONS... Proof of dependency. (a) A child is considered to have been dependent on the deceased employee or...

5 CFR 843.406 - Proof of dependency.

Code of Federal Regulations, 2014 CFR

2014-01-01

... 5 Administrative Personnel 2 2014-01-01 2014-01-01 false Proof of dependency. 843.406 Section 843.406 Administrative Personnel OFFICE OF PERSONNEL MANAGEMENT (CONTINUED) CIVIL SERVICE REGULATIONS... Proof of dependency. (a) A child is considered to have been dependent on the deceased employee or...

5 CFR 843.406 - Proof of dependency.

Code of Federal Regulations, 2013 CFR

2013-01-01

... 5 Administrative Personnel 2 2013-01-01 2013-01-01 false Proof of dependency. 843.406 Section 843.406 Administrative Personnel OFFICE OF PERSONNEL MANAGEMENT (CONTINUED) CIVIL SERVICE REGULATIONS... Proof of dependency. (a) A child is considered to have been dependent on the deceased employee or...

5 CFR 843.406 - Proof of dependency.

Code of Federal Regulations, 2010 CFR

2010-01-01

... 5 Administrative Personnel 2 2010-01-01 2010-01-01 false Proof of dependency. 843.406 Section 843.406 Administrative Personnel OFFICE OF PERSONNEL MANAGEMENT (CONTINUED) CIVIL SERVICE REGULATIONS... Proof of dependency. (a) A child is considered to have been dependent on the deceased employee or...

49 CFR 178.520 - Standards for textile bags.

Code of Federal Regulations, 2010 CFR

2010-10-01

...) 5L2 for a sift-proof textile bag; and (3) 5L3 for a water-resistant textile bag. (b) Construction... bag. (2) Bags, sift-proof, 5L2: The bag must be made sift-proof, by appropriate means, such as by the...

49 CFR 178.518 - Standards for woven plastic bags.

Code of Federal Regulations, 2011 CFR

2011-10-01

... plastic bag; (2) 5H2 for a sift-proof woven plastic bag; and (3) 5H3 for a water-resistant woven plastic... other equally strong method of closure. (3) Bags, sift-proof, 5H2 must be made sift-proof by appropriate...

Preservice Mathematics Teachers' Metaphorical Perceptions towards Proof and Proving

ERIC Educational Resources Information Center

Ersen, Zeynep Bahar

2016-01-01

Since mathematical proof and proving are in the center of mathematics; preservice mathematics teachers' perceptions against these concepts have a great importance. Therefore, the study aimed to determine preservice mathematics teachers' perceptions towards proof and proving through metaphors. The participants consisted of 192 preservice…

Self-Explanation Training Improves Proof Comprehension

ERIC Educational Resources Information Center

Hodds, Mark; Alcock, Lara; Inglis, Matthew

2014-01-01

In this article we report 3 experiments demonstrating that a simple booklet containing self-explanation training, designed to focus students' attention on logical relationships within a mathematical proof, can significantly improve their proof comprehension. Experiment 1 demonstrated that students who received the training generated higher quality…

ORION - Crew Module Side Hatch: Proof Pressure Test Anomaly Investigation

NASA Technical Reports Server (NTRS)

Evernden, Brent A.; Guzman, Oscar J.

2018-01-01

The Orion Multi-Purpose Crew Vehicle program was performing a proof pressure test on an engineering development unit (EDU) of the Orion Crew Module Side Hatch (CMSH) assembly. The purpose of the proof test was to demonstrate structural capability, with margin, at 1.5 times the maximum design pressure, before integrating the CMSH to the Orion Crew Module structural test article for subsequent pressure testing. The pressure test was performed at lower pressures of 3 psig, 10 psig and 15.75 psig with no apparent abnormal behavior or leaking. During pressurization to proof pressure of 23.32 psig, a loud 'pop' was heard at 21.3 psig. Upon review into the test cell, it was noted that the hatch had prematurely separated from the proof test fixture, thus immediately ending the test. The proof pressure test was expected be a simple verification but has since evolved into a significant joint failure investigation from both Lockheed Martin and NASA.

Dynamic PROOF clusters with PoD: architecture and user experience

NASA Astrophysics Data System (ADS)

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.

Breaking the Equation

ERIC Educational Resources Information Center

Stylianides, Andreas J.

2009-01-01

A proof's potential to promote understanding and conviction is one of the main reasons for which proof is so important for students' learning of mathematics. Unless students realise the limitations of empirical arguments as methods for validating mathematical generalisations, they are unlikely to appreciate the importance of proof in mathematics.…

14 CFR 13.223 - Standard of proof.

Code of Federal Regulations, 2014 CFR

2014-01-01

... 14 Aeronautics and Space 1 2014-01-01 2014-01-01 false Standard of proof. 13.223 Section 13.223 Aeronautics and Space FEDERAL AVIATION ADMINISTRATION, DEPARTMENT OF TRANSPORTATION PROCEDURAL RULES... proof. The administrative law judge shall issue an initial decision or shall rule in a party's favor...

14 CFR 13.223 - Standard of proof.

Code of Federal Regulations, 2012 CFR

2012-01-01

... 14 Aeronautics and Space 1 2012-01-01 2012-01-01 false Standard of proof. 13.223 Section 13.223 Aeronautics and Space FEDERAL AVIATION ADMINISTRATION, DEPARTMENT OF TRANSPORTATION PROCEDURAL RULES... proof. The administrative law judge shall issue an initial decision or shall rule in a party's favor...

40 CFR 164.80 - Order of proceeding and burden of proof.

Code of Federal Regulations, 2011 CFR

2011-07-01

... proof. 164.80 Section 164.80 Protection of Environment ENVIRONMENTAL PROTECTION AGENCY (CONTINUED... RODENTICIDE ACT, ARISING FROM REFUSALS TO REGISTER, CANCELLATIONS OF REGISTRATIONS, CHANGES OF CLASSIFICATIONS... and burden of proof. (a) At the hearing, the proponent of cancellation or change in classification has...

42 CFR 93.516 - Standard and burden of proof.

Code of Federal Regulations, 2010 CFR

2010-10-01

... that are relevant to a decision to impose HHS administrative actions following a research misconduct... RESEARCH MISCONDUCT Opportunity To Contest ORI Findings of Research Misconduct and HHS Administrative Actions Hearing Process § 93.516 Standard and burden of proof. (a) Standard of proof. The standard of...

42 CFR 93.516 - Standard and burden of proof.

Code of Federal Regulations, 2011 CFR

2011-10-01

... that are relevant to a decision to impose HHS administrative actions following a research misconduct... RESEARCH MISCONDUCT Opportunity To Contest ORI Findings of Research Misconduct and HHS Administrative Actions Hearing Process § 93.516 Standard and burden of proof. (a) Standard of proof. The standard of...

An Elementary Proof of the Identity cot [theta] = [image omitted

ERIC Educational Resources Information Center

Ho, Weng Kin; Ho, Foo Him; Lee, Tuo Yeong

2012-01-01

This article gives an elementary proof of the famous identity [image omitted]. Using nothing more than freshman calculus, the present proof is far simpler than many existing ones. This result also leads directly to Euler's and Neville's identities, as well as the identity [image omitted].

Irrational Square Roots

ERIC Educational Resources Information Center

Misiurewicz, Michal

2013-01-01

If students are presented the standard proof of irrationality of [square root]2, can they generalize it to a proof of the irrationality of "[square root]p", "p" a prime if, instead of considering divisibility by "p", they cling to the notions of even and odd used in the standard proof?

7 CFR 1430.605 - Proof of production.

Code of Federal Regulations, 2010 CFR

2010-01-01

... commercial production, including any dumped production and dairy cow purchases, for each month of the... by the dairy operation. (d) Adequate proof of dairy cow additions to the milking herd during the... any other documents available to confirm the cow purchases. (e) If adequate proof of normally marketed...

From Inductive Reasoning to Proof

ERIC Educational Resources Information Center

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…

New Proofs of Some q-Summation and q-Transformation Formulas

PubMed Central

Liu, Xian-Fang; Bi, Ya-Qing; Luo, Qiu-Ming

2014-01-01

We obtain an expectation formula and give the probabilistic proofs of some summation and transformation formulas of q-series based on our expectation formula. Although these formulas in themselves are not the probability results, the proofs given are based on probabilistic concepts. PMID:24895675

Querying Proofs (Work in Progress)

NASA Technical Reports Server (NTRS)

Aspinall, David; Denney, Ewen; Lueth, Christoph

2011-01-01

We motivate and introduce the basis for a query language designed for inspecting electronic representations of proofs. We argue that there is much to learn from large proofs beyond their validity, and that a dedicated query language can provide a principled way of implementing a family of useful operations.

A Proof Progression for Geometry

ERIC Educational Resources Information Center

Nirode, Wayne

2018-01-01

Twenty years ago when the author was student teaching, he quickly learned what geometry teachers and researchers (e.g., Senk 1985) have long known: High school geometry students struggle with proof. Throughout his career, he has tried to create instructional materials to make proof more accessible to his students. From field-testing materials with…

45 CFR 164.414 - Administrative requirements and burden of proof.

Code of Federal Regulations, 2013 CFR

2013-10-01

... Protected Health Information § 164.414 Administrative requirements and burden of proof. (a) Administrative... 45 Public Welfare 1 2013-10-01 2013-10-01 false Administrative requirements and burden of proof. 164.414 Section 164.414 Public Welfare DEPARTMENT OF HEALTH AND HUMAN SERVICES ADMINISTRATIVE DATA...

45 CFR 164.414 - Administrative requirements and burden of proof.

Code of Federal Regulations, 2012 CFR

2012-10-01

... Protected Health Information § 164.414 Administrative requirements and burden of proof. (a) Administrative... 45 Public Welfare 1 2012-10-01 2012-10-01 false Administrative requirements and burden of proof. 164.414 Section 164.414 Public Welfare DEPARTMENT OF HEALTH AND HUMAN SERVICES ADMINISTRATIVE DATA...

Japanese Logic Puzzles and Proof

ERIC Educational Resources Information Center

Wanko, Jeffrey J.

2009-01-01

An understanding of proof does not start in a high school geometry course. Rather, attention to logical reasoning throughout a student's school experience can help the development of proof readiness. In the spirit of problem solving, the author has begun to use some Japanese logic puzzles other than sudoku to help students develop additional…

33 CFR 20.702 - Burden of proof.

Code of Federal Regulations, 2012 CFR

2012-07-01

... 33 Navigation and Navigable Waters 1 2012-07-01 2012-07-01 false Burden of proof. 20.702 Section 20.702 Navigation and Navigable Waters COAST GUARD, DEPARTMENT OF HOMELAND SECURITY GENERAL RULES OF....702 Burden of proof. (a) Except for an affirmative defense, or as provided by paragraph (b) of this...

33 CFR 20.702 - Burden of proof.

Code of Federal Regulations, 2013 CFR

2013-07-01

... 33 Navigation and Navigable Waters 1 2013-07-01 2013-07-01 false Burden of proof. 20.702 Section 20.702 Navigation and Navigable Waters COAST GUARD, DEPARTMENT OF HOMELAND SECURITY GENERAL RULES OF....702 Burden of proof. (a) Except for an affirmative defense, or as provided by paragraph (b) of this...

33 CFR 20.702 - Burden of proof.

Code of Federal Regulations, 2011 CFR

2011-07-01

... 33 Navigation and Navigable Waters 1 2011-07-01 2011-07-01 false Burden of proof. 20.702 Section 20.702 Navigation and Navigable Waters COAST GUARD, DEPARTMENT OF HOMELAND SECURITY GENERAL RULES OF....702 Burden of proof. (a) Except for an affirmative defense, or as provided by paragraph (b) of this...

33 CFR 20.702 - Burden of proof.

Code of Federal Regulations, 2014 CFR

2014-07-01

... 33 Navigation and Navigable Waters 1 2014-07-01 2014-07-01 false Burden of proof. 20.702 Section 20.702 Navigation and Navigable Waters COAST GUARD, DEPARTMENT OF HOMELAND SECURITY GENERAL RULES OF....702 Burden of proof. (a) Except for an affirmative defense, or as provided by paragraph (b) of this...

33 CFR 20.702 - Burden of proof.

Code of Federal Regulations, 2010 CFR

2010-07-01

... 33 Navigation and Navigable Waters 1 2010-07-01 2010-07-01 false Burden of proof. 20.702 Section 20.702 Navigation and Navigable Waters COAST GUARD, DEPARTMENT OF HOMELAND SECURITY GENERAL RULES OF....702 Burden of proof. (a) Except for an affirmative defense, or as provided by paragraph (b) of this...

6 CFR 27.325 - Burden of proof.

Code of Federal Regulations, 2010 CFR

2010-01-01

... 6 Domestic Security 1 2010-01-01 2010-01-01 false Burden of proof. 27.325 Section 27.325 Domestic Security DEPARTMENT OF HOMELAND SECURITY, OFFICE OF THE SECRETARY CHEMICAL FACILITY ANTI-TERRORISM STANDARDS Orders and Adjudications § 27.325 Burden of proof. The Assistant Secretary bears the initial...

6 CFR 27.325 - Burden of proof.

Code of Federal Regulations, 2011 CFR

2011-01-01

... 6 Domestic Security 1 2011-01-01 2011-01-01 false Burden of proof. 27.325 Section 27.325 Domestic Security DEPARTMENT OF HOMELAND SECURITY, OFFICE OF THE SECRETARY CHEMICAL FACILITY ANTI-TERRORISM STANDARDS Orders and Adjudications § 27.325 Burden of proof. The Assistant Secretary bears the initial...

6 CFR 27.325 - Burden of proof.

Code of Federal Regulations, 2013 CFR

2013-01-01

... 6 Domestic Security 1 2013-01-01 2013-01-01 false Burden of proof. 27.325 Section 27.325 Domestic Security DEPARTMENT OF HOMELAND SECURITY, OFFICE OF THE SECRETARY CHEMICAL FACILITY ANTI-TERRORISM STANDARDS Orders and Adjudications § 27.325 Burden of proof. The Assistant Secretary bears the initial...

6 CFR 27.325 - Burden of proof.

Code of Federal Regulations, 2014 CFR

2014-01-01

... 6 Domestic Security 1 2014-01-01 2014-01-01 false Burden of proof. 27.325 Section 27.325 Domestic Security DEPARTMENT OF HOMELAND SECURITY, OFFICE OF THE SECRETARY CHEMICAL FACILITY ANTI-TERRORISM STANDARDS Orders and Adjudications § 27.325 Burden of proof. The Assistant Secretary bears the initial...

6 CFR 27.325 - Burden of proof.

Code of Federal Regulations, 2012 CFR

2012-01-01

... 6 Domestic Security 1 2012-01-01 2012-01-01 false Burden of proof. 27.325 Section 27.325 Domestic Security DEPARTMENT OF HOMELAND SECURITY, OFFICE OF THE SECRETARY CHEMICAL FACILITY ANTI-TERRORISM STANDARDS Orders and Adjudications § 27.325 Burden of proof. The Assistant Secretary bears the initial...

44 CFR 75.3 - Burden of proof.

Code of Federal Regulations, 2010 CFR

2010-10-01

... 44 Emergency Management and Assistance 1 2010-10-01 2010-10-01 false Burden of proof. 75.3 Section 75.3 Emergency Management and Assistance FEDERAL EMERGENCY MANAGEMENT AGENCY, DEPARTMENT OF HOMELAND... PROPERTIES UNDER SELF-INSURANCE PLAN General § 75.3 Burden of proof. In any application made by a State to...

28 CFR 79.16 - Proof of medical condition.

Code of Federal Regulations, 2011 CFR

2011-07-01

... COMPENSATION ACT Eligibility Criteria for Claims Relating to Leukemia § 79.16 Proof of medical condition. (a... leukemia. Proof that the claimant contracted leukemia must be made either by using the procedure outlined... section. (b) If a claimant was diagnosed as having leukemia in Arizona, Colorado, Nevada, New Mexico, Utah...

21 CFR 1316.60 - Objections; offer of proof.

Code of Federal Regulations, 2010 CFR

2010-04-01

... 21 Food and Drugs 9 2010-04-01 2010-04-01 false Objections; offer of proof. 1316.60 Section 1316.60 Food and Drugs DRUG ENFORCEMENT ADMINISTRATION, DEPARTMENT OF JUSTICE ADMINISTRATIVE FUNCTIONS, PRACTICES, AND PROCEDURES Administrative Hearings § 1316.60 Objections; offer of proof. If any party in the...

21 CFR 1316.56 - Burden of proof.

Code of Federal Regulations, 2010 CFR

2010-04-01

... 21 Food and Drugs 9 2010-04-01 2010-04-01 false Burden of proof. 1316.56 Section 1316.56 Food and Drugs DRUG ENFORCEMENT ADMINISTRATION, DEPARTMENT OF JUSTICE ADMINISTRATIVE FUNCTIONS, PRACTICES, AND PROCEDURES Administrative Hearings § 1316.56 Burden of proof. At any hearing, the proponent for the issuance...

47 CFR 1.359 - Proof of official record; authentication of copy.

Code of Federal Regulations, 2010 CFR

2010-10-01

... 47 Telecommunication 1 2010-10-01 2010-10-01 false Proof of official record; authentication of copy. 1.359 Section 1.359 Telecommunication FEDERAL COMMUNICATIONS COMMISSION GENERAL PRACTICE AND PROCEDURE Hearing Proceedings Evidence § 1.359 Proof of official record; authentication of copy. An official...

28 CFR 79.16 - Proof of medical condition.

Code of Federal Regulations, 2010 CFR

2010-07-01

... COMPENSATION ACT Eligibility Criteria for Claims Relating to Leukemia § 79.16 Proof of medical condition. (a... leukemia. Proof that the claimant contracted leukemia must be made either by using the procedure outlined... section. (b) If a claimant was diagnosed as having leukemia in Arizona, Colorado, Nevada, New Mexico, Utah...

27 CFR 19.188 - Measuring devices and proofing instruments.

Code of Federal Regulations, 2014 CFR

2014-04-01

... 27 Alcohol, Tobacco Products and Firearms 1 2014-04-01 2014-04-01 false Measuring devices and proofing instruments. 19.188 Section 19.188 Alcohol, Tobacco Products and Firearms ALCOHOL AND TOBACCO TAX..., and Security Requirements Measuring and Proofing Equipment Requirements § 19.188 Measuring devices and...

27 CFR 19.188 - Measuring devices and proofing instruments.

Code of Federal Regulations, 2011 CFR

2011-04-01

... 27 Alcohol, Tobacco Products and Firearms 1 2011-04-01 2011-04-01 false Measuring devices and proofing instruments. 19.188 Section 19.188 Alcohol, Tobacco Products and Firearms ALCOHOL AND TOBACCO TAX..., and Security Requirements Measuring and Proofing Equipment Requirements § 19.188 Measuring devices and...

27 CFR 19.188 - Measuring devices and proofing instruments.

Code of Federal Regulations, 2013 CFR

2013-04-01

... 27 Alcohol, Tobacco Products and Firearms 1 2013-04-01 2013-04-01 false Measuring devices and proofing instruments. 19.188 Section 19.188 Alcohol, Tobacco Products and Firearms ALCOHOL AND TOBACCO TAX..., and Security Requirements Measuring and Proofing Equipment Requirements § 19.188 Measuring devices and...

27 CFR 19.188 - Measuring devices and proofing instruments.

Code of Federal Regulations, 2012 CFR

2012-04-01

... 27 Alcohol, Tobacco Products and Firearms 1 2012-04-01 2012-04-01 false Measuring devices and proofing instruments. 19.188 Section 19.188 Alcohol, Tobacco Products and Firearms ALCOHOL AND TOBACCO TAX..., and Security Requirements Measuring and Proofing Equipment Requirements § 19.188 Measuring devices and...

25 CFR 75.11 - Proof of relationship.

Code of Federal Regulations, 2011 CFR

2011-04-01

... 25 Indians 1 2011-04-01 2011-04-01 false Proof of relationship. 75.11 Section 75.11 Indians BUREAU OF INDIAN AFFAIRS, DEPARTMENT OF THE INTERIOR TRIBAL GOVERNMENT REVISION OF THE MEMBERSHIP ROLL OF THE EASTERN BAND OF CHEROKEE INDIANS, NORTH CAROLINA § 75.11 Proof of relationship. If the applicant's...

46 CFR 13.505 - Proof of service for tankerman-engineer endorsement.

Code of Federal Regulations, 2014 CFR

2014-10-01

... 46 Shipping 1 2014-10-01 2014-10-01 false Proof of service for tankerman-engineer endorsement. 13... SEAMEN CERTIFICATION OF TANKERMEN Requirements for Tankerman-Engineer Endorsement § 13.505 Proof of service for tankerman-engineer endorsement. (a) Service must be proved by a letter on company letterhead...

14 CFR 23.641 - Proof of strength.

Code of Federal Regulations, 2011 CFR

2011-01-01

... 14 Aeronautics and Space 1 2011-01-01 2011-01-01 false Proof of strength. 23.641 Section 23.641 Aeronautics and Space FEDERAL AVIATION ADMINISTRATION, DEPARTMENT OF TRANSPORTATION AIRCRAFT AIRWORTHINESS....641 Proof of strength. The strength of stressed-skin wings must be proven by load tests or by combined...

14 CFR 23.641 - Proof of strength.

Code of Federal Regulations, 2010 CFR

2010-01-01

... 14 Aeronautics and Space 1 2010-01-01 2010-01-01 false Proof of strength. 23.641 Section 23.641 Aeronautics and Space FEDERAL AVIATION ADMINISTRATION, DEPARTMENT OF TRANSPORTATION AIRCRAFT AIRWORTHINESS....641 Proof of strength. The strength of stressed-skin wings must be proven by load tests or by combined...

45 CFR 672.16 - Objections and offers of proof.

Code of Federal Regulations, 2010 CFR

2010-10-01

... 45 Public Welfare 3 2010-10-01 2010-10-01 false Objections and offers of proof. 672.16 Section 672.16 Public Welfare Regulations Relating to Public Welfare (Continued) NATIONAL SCIENCE FOUNDATION... brief statement describing the nature of the evidence excluded. The offer of proof for excluded...

"Future Proofing" Faculty: The Struggle To Create Technical Lifelong Learners.

ERIC Educational Resources Information Center

Nay, Fred W.; Malm, Loren D.; Malone, Bobby G.; Oliver, Brad E.; Saunders, Nancy G.; Thompson, Jay C., Jr.

College faculty can avoid investing valuable time and resources in inappropriate technologies by staying in step with technological progress. A "future proof" approach to technology recognizes and welcomes small failures, considering them part of the ongoing process of absorbing technology into the learning process. Future proofing attempts to…

Empowering Students' Proof Learning through Communal Engagement

ERIC Educational Resources Information Center

Ko, Yi-Yin; Yee, Sean P.; Bleiler-Baxter, Sarah K.; Boyle, Justin D.

2016-01-01

This article describes the authors' three-component instructional sequence--a before-class activity, a during-class activity, and an after-class activity--which supports students in becoming self-regulated proof learners by actively developing class-based criteria for proof. All four authors implemented this sequence in their classrooms, and the…

49 CFR 8.21 - Burden of proof.

Code of Federal Regulations, 2010 CFR

2010-10-01

... Office of the Secretary of Transportation CLASSIFIED INFORMATION: CLASSIFICATION/DECLASSIFICATION/ACCESS Classification/Declassification of Information § 8.21 Burden of proof. For the purpose of determinations to be made under §§ 8.13, 8.15, and 8.17, the burden of proof is on the originating Departmental agency to...

49 CFR 8.21 - Burden of proof.

Code of Federal Regulations, 2011 CFR

2011-10-01

... Office of the Secretary of Transportation CLASSIFIED INFORMATION: CLASSIFICATION/DECLASSIFICATION/ACCESS Classification/Declassification of Information § 8.21 Burden of proof. For the purpose of determinations to be made under §§ 8.13, 8.15, and 8.17, the burden of proof is on the originating Departmental agency to...

29 CFR 1926.97 - Electrical protective equipment.

Code of Federal Regulations, 2014 CFR

2014-07-01

... glove. (2) Electrical requirements. (i) Equipment shall be capable of withstanding the ac proof-test voltage specified in Table E-1 or the dc proof-test voltage specified in Table E-2. (A) The proof test shall reliably indicate that the equipment can withstand the voltage involved. (B) The test voltage...

21 CFR 1315.58 - Burden of proof.

Code of Federal Regulations, 2011 CFR

2011-04-01

... 21 Food and Drugs 9 2011-04-01 2011-04-01 false Burden of proof. 1315.58 Section 1315.58 Food and Drugs DRUG ENFORCEMENT ADMINISTRATION, DEPARTMENT OF JUSTICE IMPORTATION AND PRODUCTION QUOTAS FOR EPHEDRINE, PSEUDOEPHEDRINE, AND PHENYLPROPANOLAMINE Hearings § 1315.58 Burden of proof. (a) At any hearing...

21 CFR 1315.58 - Burden of proof.

Code of Federal Regulations, 2013 CFR

2013-04-01

... 21 Food and Drugs 9 2013-04-01 2013-04-01 false Burden of proof. 1315.58 Section 1315.58 Food and Drugs DRUG ENFORCEMENT ADMINISTRATION, DEPARTMENT OF JUSTICE IMPORTATION AND PRODUCTION QUOTAS FOR EPHEDRINE, PSEUDOEPHEDRINE, AND PHENYLPROPANOLAMINE Hearings § 1315.58 Burden of proof. (a) At any hearing...

21 CFR 1315.58 - Burden of proof.

Code of Federal Regulations, 2012 CFR

2012-04-01

... 21 Food and Drugs 9 2012-04-01 2012-04-01 false Burden of proof. 1315.58 Section 1315.58 Food and Drugs DRUG ENFORCEMENT ADMINISTRATION, DEPARTMENT OF JUSTICE IMPORTATION AND PRODUCTION QUOTAS FOR EPHEDRINE, PSEUDOEPHEDRINE, AND PHENYLPROPANOLAMINE Hearings § 1315.58 Burden of proof. (a) At any hearing...

21 CFR 1315.58 - Burden of proof.

Code of Federal Regulations, 2014 CFR

2014-04-01

... 21 Food and Drugs 9 2014-04-01 2014-04-01 false Burden of proof. 1315.58 Section 1315.58 Food and Drugs DRUG ENFORCEMENT ADMINISTRATION, DEPARTMENT OF JUSTICE IMPORTATION AND PRODUCTION QUOTAS FOR EPHEDRINE, PSEUDOEPHEDRINE, AND PHENYLPROPANOLAMINE Hearings § 1315.58 Burden of proof. (a) At any hearing...

21 CFR 1315.58 - Burden of proof.

Code of Federal Regulations, 2010 CFR

2010-04-01

... 21 Food and Drugs 9 2010-04-01 2010-04-01 false Burden of proof. 1315.58 Section 1315.58 Food and Drugs DRUG ENFORCEMENT ADMINISTRATION, DEPARTMENT OF JUSTICE IMPORTATION AND PRODUCTION QUOTAS FOR EPHEDRINE, PSEUDOEPHEDRINE, AND PHENYLPROPANOLAMINE Hearings § 1315.58 Burden of proof. (a) At any hearing...

Using Computer-Assisted Multiple Representations in Learning Geometry Proofs

ERIC Educational Resources Information Center

Wong, Wing-Kwong; Yin, Sheng-Kai; Yang, Hsi-Hsun; Cheng, Ying-Hao

2011-01-01

Geometry theorem proving involves skills that are difficult to learn. Instead of working with abstract and complicated representations, students might start with concrete, graphical representations. A proof tree is a graphical representation of a formal proof, with each node representing a proposition or given conditions. A computer-assisted…

25 CFR 75.11 - Proof of relationship.

Code of Federal Regulations, 2010 CFR

2010-04-01

... 25 Indians 1 2010-04-01 2010-04-01 false Proof of relationship. 75.11 Section 75.11 Indians BUREAU OF INDIAN AFFAIRS, DEPARTMENT OF THE INTERIOR TRIBAL GOVERNMENT REVISION OF THE MEMBERSHIP ROLL OF THE EASTERN BAND OF CHEROKEE INDIANS, NORTH CAROLINA § 75.11 Proof of relationship. If the applicant's...

Impact of Proof Validation on Proof Writing in Abstract Algebra

ERIC Educational Resources Information Center

Powers, Robert A.; Craviotto, Cathleen; Grassl, Richard M.

2010-01-01

Many undergraduate students have difficulty writing mathematical proofs even though this skill is important for the development of future teachers and those who may be involved in instruction or training as a graduate student or supervisor. In addition, research indicates that mathematics majors and secondary education mathematics majors possess…

Values and Norms of Proof for Mathematicians and Students

ERIC Educational Resources Information Center

Dawkins, Paul Christian; Weber, Keith

2017-01-01

In this theoretical paper, we present a framework for conceptualizing proof in terms of mathematical values, as well as the norms that uphold those values. In particular, proofs adhere to the values of establishing a priori truth, employing decontextualized reasoning, increasing mathematical understanding, and maintaining consistent standards for…

Three Styles Characterising Mathematicians' Pedagogical Perspectives on Proof

ERIC Educational Resources Information Center

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…

Expert and Novice Approaches to Reading Mathematical Proofs

ERIC Educational Resources Information Center

Inglis, Matthew; Alcock, Lara

2012-01-01

A comparison of the proof validation behavior of beginning undergraduate students and research-active mathematicians is explored. Participants' eye movements were recorded as they validated purported proofs. The main findings are that (a) contrary to previous suggestions, mathematicians sometimes appear to disagree about the validity of even short…

Proof Constructions and Evaluations

ERIC Educational Resources Information Center

Stylianides, Andreas J.; Stylianides, Gabriel J.

2009-01-01

In this article, we focus on a group of 39 prospective elementary (grades K-6) teachers who had rich experiences with proof, and we examine their ability to construct proofs and evaluate their own constructions. We claim that the combined "construction-evaluation" activity helps illuminate certain aspects of prospective teachers' and presumably…

Putting time into proof outlines

NASA Technical Reports Server (NTRS)

Schneider, Fred B.; Bloom, Bard; Marzullo, Keith

1991-01-01

A logic for reasoning about timing of concurrent programs is presented. The logic is based on proof outlines and can handle maximal parallelism as well as resource-constrained execution environments. The correctness proof for a mutual exclusion protocol that uses execution timings in a subtle way illustrates the logic in action.

5 CFR 843.206 - Designation of beneficiary-proof of receipt.

Code of Federal Regulations, 2010 CFR

2010-01-01

... 5 Administrative Personnel 2 2010-01-01 2010-01-01 false Designation of beneficiary-proof of receipt. 843.206 Section 843.206 Administrative Personnel OFFICE OF PERSONNEL MANAGEMENT (CONTINUED) CIVIL... One-time Payments § 843.206 Designation of beneficiary—proof of receipt. (a) Upon receipt of a...

44 CFR 75.3 - Burden of proof.

Code of Federal Regulations, 2014 CFR

2014-10-01

... 44 Emergency Management and Assistance 1 2014-10-01 2014-10-01 false Burden of proof. 75.3 Section 75.3 Emergency Management and Assistance FEDERAL EMERGENCY MANAGEMENT AGENCY, DEPARTMENT OF HOMELAND... PROPERTIES UNDER SELF-INSURANCE PLAN General § 75.3 Burden of proof. In any application made by a State to...

All-versus-nothing proofs with n qubits distributed between m parties

NASA Astrophysics Data System (ADS)

Cabello, Adán; Moreno, Pilar

2010-04-01

All-versus-nothing (AVN) proofs show the conflict between Einstein, Podolsky, and Rosen’s elements of reality and the perfect correlations of some quantum states. Given an n-qubit state distributed between m parties, we provide a method with which to decide whether this distribution allows an m-partite AVN proof specific for this state using only single-qubit measurements. We apply this method to some recently obtained n-qubit m-particle states. In addition, we provide all inequivalent AVN proofs with less than nine qubits and a minimum number of parties.

Micro environmental sensing device

DOEpatents

Polosky, Marc A.; Lukens, Laurance L.

2006-05-02

A microelectromechanical (MEM) acceleration switch is disclosed which includes a proof mass flexibly connected to a substrate, with the proof mass being moveable in a direction substantially perpendicular to the substrate in response to a sensed acceleration. An electrode on the proof mass contacts one or more electrodes located below the proof mass to provide a switch closure in response to the sensed acceleration. Electrical latching of the switch in the closed position is possible with an optional latching electrode. The MEM acceleration switch, which has applications for use as an environmental sensing device, can be fabricated using micromachining.

Proceedings of the 1989 Structural Integrity Program Conference Held in San Antonio, Texas on 5-7 Dec 1989

DTIC Science & Technology

1990-04-01

selected for this study because of the availability of MSD crackgrowth data pertinent to the type of situation for which the proof test had been proposed...proof and maximum service pressures. A range of proof pressure was studied , not only for the effect on post-test safe crack growth interval, but also...to investigate the potential for stable crack extension during the test itself. 30 The study author recommended 1.5P as the optimum proof pressure, the

Construction of state-independent proofs for quantum contextuality

NASA Astrophysics Data System (ADS)

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.

Preparation of Drug-loaded Chitosan Microspheres and Its Application in Paper-based PVC Wallpaper

NASA Astrophysics Data System (ADS)

Lin, Hui; Chen, Lihui; Yan, Guiyang; Chen, Feng; Huang, Liulian

2018-03-01

By screening through test, it was found that the drug-loaded chitosan microspheres with the average particle size of 615 nm may be prepared with NaF as the mold-proof drug, chitosan as the drug carrier and sodium tripolyphosphate as the cross-linking agent; and they can improve the aspergillus niger-proof effect if loaded onto the base paper surface of the paper-based PVC wallpaper. The results show that NaF and chitosan have mold-proof synergistic effects; the mold-proof effect of the wallpaper may be improved by increasing the dose of chitosan; when the mass ratio of NaF, sodium tripolyphosphate and chitosan was 2:7:28, the paper-based PVC wallpaper with good mold-proof property can be prepared.

On the proof of the C 0-inextendibility of the Schwarzschild spacetime

NASA Astrophysics Data System (ADS)

Sbierski, Jan

2018-02-01

This article presents a streamlined version of the author’s original proof of the C 0-inextendibility of the maximal analytic Schwarzschild spacetime. Firstly, we deviate from the original proof by using the result, recently established in collaboration with Galloway and Ling, that given a C 0-extension of a globally hyperbolic spacetime, one can find a timelike geodesic that leaves this spacetime. This result much simplifies the proof of the inextendibility through the exterior region of the Schwarzschild spacetime. Secondly, we give a more flexible and shorter argument for the inextendibility through the interior region. Furthermore, we present a small new structural result for the boundary of a globally hyperbolic spacetime within a C 0-extension which serves as a new and simpler starting point for the proof.

Exploring Logical Reasoning and Mathematical Proof in Grade 6 Elementary School Students

ERIC Educational Resources Information Center

Flegas, Konstantinos; Charalampos, Lemonidis

2013-01-01

Research and classroom experience reveal that the construction of mathematical proofs is difficult for all students. While many contemporary mathematics curricula recognize the importance of teaching reasoning and proof, in Greece these concepts are introduced at the secondary education level. In this study, we will attempt to investigate a group…

Proof of a new colour decomposition for QCD amplitudes

DOE PAGES

Melia, Tom

2015-12-16

Recently, Johansson and Ochirov conjectured the form of a new colour decom-position for QCD tree-level amplitudes. This note provides a proof of that conjecture. The proof is based on ‘Mario World’ Feynman diagrams, which exhibit the hierarchical Dyck structure previously found to be very useful when dealing with multi-quark amplitudes.

77 FR 64829 - Notice of Filing of Proposed Settlement Agreement Resolving Bankruptcy Proofs of Claim Relating...

Federal Register 2010, 2011, 2012, 2013, 2014

2012-10-23

... DEPARTMENT OF JUSTICE Notice of Filing of Proposed Settlement Agreement Resolving Bankruptcy Proofs of Claim Relating to the Breslube-Penn Superfund Site On October 17, 2012, a proposed Settlement... in March 2012. The proposed Settlement Agreement resolves these proofs of claims by providing for an...

31 CFR 346.4 - Proof of purchase.

Code of Federal Regulations, 2010 CFR

2010-07-01

... 31 Money and Finance: Treasury 2 2010-07-01 2010-07-01 false Proof of purchase. 346.4 Section 346.4 Money and Finance: Treasury Regulations Relating to Money and Finance (Continued) FISCAL SERVICE... RETIREMENT BONDS § 346.4 Proof of purchase. At the time an Individual Retirement Bond is issued, the issuing...

28 CFR 79.14 - Proof of initial exposure prior to age 21.

Code of Federal Regulations, 2011 CFR

2011-07-01

... 28 Judicial Administration 2 2011-07-01 2011-07-01 false Proof of initial exposure prior to age 21. 79.14 Section 79.14 Judicial Administration DEPARTMENT OF JUSTICE (CONTINUED) CLAIMS UNDER THE RADIATION EXPOSURE COMPENSATION ACT Eligibility Criteria for Claims Relating to Leukemia § 79.14 Proof of...

77 FR 69548 - Price for the 2012 Limited Edition Silver Proof SetTM

Federal Register 2010, 2011, 2012, 2013, 2014

2012-11-19

... DEPARTMENT OF THE TREASURY United States Mint Price for the 2012 Limited Edition Silver Proof Set TM AGENCY: United States Mint, Department of the Treasury. ACTION: Notice. SUMMARY: The United States Mint is announcing a price of $149.95 for the 2012 Limited Edition Silver Proof Set TM . FOR FURTHER...

Families of Functions and Functions of Proof

ERIC Educational Resources Information Center

Landman, Greisy Winicki

2002-01-01

This article describes an activity for secondary school students that may constitute an appropriate opportunity to discuss with them the idea of proof, particularly in an algebraic context. During the activity the students may experience and understand some of the roles played by proof in mathematics in addition to verification of truth:…

77 FR 4000 - Privacy Act of 1974; Altered System of Records

Federal Register 2010, 2011, 2012, 2013, 2014

2012-01-26

..., citizenship, proof of relationship, and limited use for genealogical purposes. The first change updates the... the 15 CFR part 50 and in accordance with 13 U.S.C. 8 to provide proof of age, citizenship, proof of... electronic media. Paper copies, digital media, and electronic media that contain sensitive information are...

26 CFR 1.871-4 - Proof of residence of aliens.

Code of Federal Regulations, 2011 CFR

2011-04-01

... 26 Internal Revenue 9 2011-04-01 2011-04-01 false Proof of residence of aliens. 1.871-4 Section 1... (CONTINUED) INCOME TAXES (CONTINUED) Nonresident Aliens and Foreign Corporations § 1.871-4 Proof of residence of aliens. (a) Rules of evidence. The following rules of evidence shall govern in determining whether...

26 CFR 1.871-4 - Proof of residence of aliens.

Code of Federal Regulations, 2012 CFR

2012-04-01

... 26 Internal Revenue 9 2012-04-01 2012-04-01 false Proof of residence of aliens. 1.871-4 Section 1... (CONTINUED) INCOME TAXES (CONTINUED) Nonresident Aliens and Foreign Corporations § 1.871-4 Proof of residence of aliens. (a) Rules of evidence. The following rules of evidence shall govern in determining whether...

26 CFR 1.871-4 - Proof of residence of aliens.

Code of Federal Regulations, 2014 CFR

2014-04-01

... 26 Internal Revenue 9 2014-04-01 2014-04-01 false Proof of residence of aliens. 1.871-4 Section 1... (CONTINUED) INCOME TAXES (CONTINUED) Nonresident Aliens and Foreign Corporations § 1.871-4 Proof of residence of aliens. (a) Rules of evidence. The following rules of evidence shall govern in determining whether...

26 CFR 1.871-4 - Proof of residence of aliens.

Code of Federal Regulations, 2013 CFR

2013-04-01

... 26 Internal Revenue 9 2013-04-01 2013-04-01 false Proof of residence of aliens. 1.871-4 Section 1... (CONTINUED) INCOME TAXES (CONTINUED) Nonresident Aliens and Foreign Corporations § 1.871-4 Proof of residence of aliens. (a) Rules of evidence. The following rules of evidence shall govern in determining whether...

28 CFR 79.14 - Proof of initial exposure prior to age 21.

Code of Federal Regulations, 2010 CFR

2010-07-01

... 28 Judicial Administration 2 2010-07-01 2010-07-01 false Proof of initial exposure prior to age 21. 79.14 Section 79.14 Judicial Administration DEPARTMENT OF JUSTICE (CONTINUED) CLAIMS UNDER THE RADIATION EXPOSURE COMPENSATION ACT Eligibility Criteria for Claims Relating to Leukemia § 79.14 Proof of...

A Framework for Identifying and Classifying Undergraduate Student Proof Errors

ERIC Educational Resources Information Center

Strickland, S.; Rand, B.

2016-01-01

This paper describes a framework for identifying, classifying, and coding student proofs, modified from existing proof-grading rubrics. The framework includes 20 common errors, as well as categories for interpreting the severity of the error. The coding scheme is intended for use in a classroom context, for providing effective student feedback. In…

46 CFR 178.320 - Intact stability requirements-non-sailing vessels.

Code of Federal Regulations, 2012 CFR

2012-10-01

... following vessels may undergo the simplified stability proof test detailed in § 178.330 of this part, in the... this part, a self-propelled pontoon vessel may undergo the pontoon simplified stability proof test... deck cargo, and is otherwise eligible to undergo the simplified stability proof test detailed in § 178...

46 CFR 178.320 - Intact stability requirements-non-sailing vessels.

Code of Federal Regulations, 2014 CFR

2014-10-01

... following vessels may undergo the simplified stability proof test detailed in § 178.330 of this part, in the... this part, a self-propelled pontoon vessel may undergo the pontoon simplified stability proof test... deck cargo, and is otherwise eligible to undergo the simplified stability proof test detailed in § 178...

46 CFR 178.320 - Intact stability requirements-non-sailing vessels.

Code of Federal Regulations, 2013 CFR

2013-10-01

... following vessels may undergo the simplified stability proof test detailed in § 178.330 of this part, in the... this part, a self-propelled pontoon vessel may undergo the pontoon simplified stability proof test... deck cargo, and is otherwise eligible to undergo the simplified stability proof test detailed in § 178...

46 CFR 178.320 - Intact stability requirements.

Code of Federal Regulations, 2010 CFR

2010-10-01

... stability proof test in accordance with § 178.330 of this part in the presence of a Coast Guard marine inspector. (b) A pontoon vessel operating on protected waters must undergo a simplified stability proof test... cognizant OCMI may dispense with the simplified stability proof test in § 178.330 for a vessel carrying not...

77 FR 6584 - RR Donnelley & Sons, Inc., Premedia Services Division, Including On-Site Leased Workers From...

Federal Register 2010, 2011, 2012, 2013, 2014

2012-02-08

... related to the production of digital photography, printed proofs and digital files. The initial... digital photography, printed proofs and digital files (or like or directly competitive articles) in 2009... imports of digital photography, printed proofs and digital files (or like or directly competitive articles...

37 CFR 2.96 - Issue; burden of proof.

Code of Federal Regulations, 2010 CFR

2010-07-01

... 37 Patents, Trademarks, and Copyrights 1 2010-07-01 2010-07-01 false Issue; burden of proof. 2.96... COMMERCE RULES OF PRACTICE IN TRADEMARK CASES Interferences and Concurrent Use Proceedings § 2.96 Issue; burden of proof. The issue in an interference between applications is normally priority of use, but the...

Semantic Contamination and Mathematical Proof: Can a Non-Proof Prove?

ERIC Educational Resources Information Center

Mejia-Ramos, Juan Pablo; Inglis, Matthew

2011-01-01

The way words are used in natural language can influence how the same words are understood by students in formal educational contexts. Here we argue that this so-called semantic contamination effect plays a role in determining how students engage with mathematical proof, a fundamental aspect of learning mathematics. Analyses of responses to…

Bridging Algebra & Geometry with "n"-Gram Proofs

ERIC Educational Resources Information Center

Craven, Joshua D.

2010-01-01

For many students, geometry is the first course in which mathematical proof takes center stage. To help ease students into writing proofs, the author tries to create lessons and activities throughout the year that challenge students to prove their own conjectures by using tools learned in previous mathematics courses. Teachers cannot get all…

41 CFR 60-30.19 - Objections; exceptions; offer of proof.

Code of Federal Regulations, 2011 CFR

2011-07-01

... 41 Public Contracts and Property Management 1 2011-07-01 2009-07-01 true Objections; exceptions; offer of proof. 60-30.19 Section 60-30.19 Public Contracts and Property Management Other Provisions... EXECUTIVE ORDER 11246 Hearings and Related Matters § 60-30.19 Objections; exceptions; offer of proof. (a...

41 CFR 60-30.19 - Objections; exceptions; offer of proof.

Code of Federal Regulations, 2010 CFR

2010-07-01

... 41 Public Contracts and Property Management 1 2010-07-01 2010-07-01 true Objections; exceptions; offer of proof. 60-30.19 Section 60-30.19 Public Contracts and Property Management Other Provisions... EXECUTIVE ORDER 11246 Hearings and Related Matters § 60-30.19 Objections; exceptions; offer of proof. (a...

26 CFR 41.6001-2 - Proof of payment for State registration purposes.

Code of Federal Regulations, 2010 CFR

2010-04-01

... section, the vehicle identification number of the vehicle being registered must appear on the Schedule 1... of the vehicles (or their vehicle identification numbers) is not required as part of such proof of... not include a list of vehicle identification numbers is submitted as proof of payment for the...

26 CFR 41.6001-2 - Proof of payment for State registration purposes.

Code of Federal Regulations, 2011 CFR

2011-04-01

... section, the vehicle identification number of the vehicle being registered must appear on the Schedule 1... of the vehicles (or their vehicle identification numbers) is not required as part of such proof of... not include a list of vehicle identification numbers is submitted as proof of payment for the...

77 FR 15457 - Pricing for the 2012 American Eagle Silver Proof Coin

Federal Register 2010, 2011, 2012, 2013, 2014

2012-03-15

... DEPARTMENT OF THE TREASURY United States Mint Pricing for the 2012 American Eagle Silver Proof Coin AGENCY: United States Mint, Department of the Treasury. ACTION: Notice. SUMMARY: The United States Mint is announcing the price of the 2012 American Eagle Silver Proof Coin. The coins will be offered...

76 FR 65563 - Pricing for 2011 American Eagle Silver Proof and Uncirculated Coins

Federal Register 2010, 2011, 2012, 2013, 2014

2011-10-21

... DEPARTMENT OF THE TREASURY United States Mint Pricing for 2011 American Eagle Silver Proof and Uncirculated Coins AGENCY: United States Mint, Department of the Treasury. ACTION: Notice. SUMMARY: The United States Mint is announcing the re-pricing of the 2011 American Eagle Silver Proof and Uncirculated Coins...

76 FR 53717 - Pricing for the 2011 American Eagle Silver Proof Coin

Federal Register 2010, 2011, 2012, 2013, 2014

2011-08-29

... DEPARTMENT OF THE TREASURY United States Mint Pricing for the 2011 American Eagle Silver Proof Coin AGENCY: United States Mint, Department of the Treasury. ACTION: Notice. SUMMARY: The United States Mint is announcing the re-pricing of the 2011 American Eagle Silver Proof Coin. The price of the coins...

76 FR 33026 - Pricing for the 2011 American Eagle Silver Proof Coin

Federal Register 2010, 2011, 2012, 2013, 2014

2011-06-07

... DEPARTMENT OF THE TREASURY United States Mint Pricing for the 2011 American Eagle Silver Proof Coin AGENCY: United States Mint, Department of the Treasury. ACTION: Notice. SUMMARY: The United States Mint is announcing the price of the 2011 American Eagle Silver Proof Coin. The coin will be offered for...

29 CFR 1919.33 - Proof tests-wire rope.

Code of Federal Regulations, 2010 CFR

2010-07-01

... 29 Labor 7 2010-07-01 2010-07-01 false Proof tests-wire rope. 1919.33 Section 1919.33 Labor Regulations Relating to Labor (Continued) OCCUPATIONAL SAFETY AND HEALTH ADMINISTRATION, DEPARTMENT OF LABOR... Persons § 1919.33 Proof tests—wire rope. Wire rope, except as provided in § 1919.14(b), shall be tested by...

29 CFR 1919.33 - Proof tests-wire rope.

Code of Federal Regulations, 2011 CFR

2011-07-01

... 29 Labor 7 2011-07-01 2011-07-01 false Proof tests-wire rope. 1919.33 Section 1919.33 Labor Regulations Relating to Labor (Continued) OCCUPATIONAL SAFETY AND HEALTH ADMINISTRATION, DEPARTMENT OF LABOR... Persons § 1919.33 Proof tests—wire rope. Wire rope, except as provided in § 1919.14(b), shall be tested by...

43 CFR 2524.3 - Time extended to make final proof.

Code of Federal Regulations, 2012 CFR

2012-10-01

... 43 Public Lands: Interior 2 2012-10-01 2012-10-01 false Time extended to make final proof. 2524.3 Section 2524.3 Public Lands: Interior Regulations Relating to Public Lands (Continued) BUREAU OF LAND... Entries Within a Reclamation Project § 2524.3 Time extended to make final proof. When the time for...

43 CFR 2524.3 - Time extended to make final proof.

Code of Federal Regulations, 2013 CFR

2013-10-01

... 43 Public Lands: Interior 2 2013-10-01 2013-10-01 false Time extended to make final proof. 2524.3 Section 2524.3 Public Lands: Interior Regulations Relating to Public Lands (Continued) BUREAU OF LAND... Entries Within a Reclamation Project § 2524.3 Time extended to make final proof. When the time for...

43 CFR 2524.3 - Time extended to make final proof.

Code of Federal Regulations, 2011 CFR

2011-10-01

... 43 Public Lands: Interior 2 2011-10-01 2011-10-01 false Time extended to make final proof. 2524.3 Section 2524.3 Public Lands: Interior Regulations Relating to Public Lands (Continued) BUREAU OF LAND... Entries Within a Reclamation Project § 2524.3 Time extended to make final proof. When the time for...

43 CFR 2524.3 - Time extended to make final proof.

Code of Federal Regulations, 2014 CFR

2014-10-01

... 43 Public Lands: Interior 2 2014-10-01 2014-10-01 false Time extended to make final proof. 2524.3 Section 2524.3 Public Lands: Interior Regulations Relating to Public Lands (Continued) BUREAU OF LAND... Entries Within a Reclamation Project § 2524.3 Time extended to make final proof. When the time for...

28 CFR 79.14 - Proof of initial exposure prior to age 21.

Code of Federal Regulations, 2013 CFR

2013-07-01

... 28 Judicial Administration 2 2013-07-01 2013-07-01 false Proof of initial exposure prior to age 21. 79.14 Section 79.14 Judicial Administration DEPARTMENT OF JUSTICE (CONTINUED) CLAIMS UNDER THE RADIATION EXPOSURE COMPENSATION ACT Eligibility Criteria for Claims Relating to Leukemia § 79.14 Proof of...

28 CFR 79.14 - Proof of initial exposure prior to age 21.

Code of Federal Regulations, 2014 CFR

2014-07-01

... 28 Judicial Administration 2 2014-07-01 2014-07-01 false Proof of initial exposure prior to age 21. 79.14 Section 79.14 Judicial Administration DEPARTMENT OF JUSTICE (CONTINUED) CLAIMS UNDER THE RADIATION EXPOSURE COMPENSATION ACT Eligibility Criteria for Claims Relating to Leukemia § 79.14 Proof of...

28 CFR 79.14 - Proof of initial exposure prior to age 21.

Code of Federal Regulations, 2012 CFR

2012-07-01

... 28 Judicial Administration 2 2012-07-01 2012-07-01 false Proof of initial exposure prior to age 21. 79.14 Section 79.14 Judicial Administration DEPARTMENT OF JUSTICE (CONTINUED) CLAIMS UNDER THE RADIATION EXPOSURE COMPENSATION ACT Eligibility Criteria for Claims Relating to Leukemia § 79.14 Proof of...

Using Dynamic Geometry to Expand Mathematics Teachers' Understanding of Proof

ERIC Educational Resources Information Center

de Villiers, Michael

2004-01-01

This paper gives a broad descriptive account of some activities that the author has designed using Sketchpad to develop teachers' understanding of other functions of proof than just the traditional function of 'verification'. These other functions of proof illustrated here are those of explanation, discovery and systematization (in the context of…

18 CFR 385.911 - Burden of proof (Rule 911).

Code of Federal Regulations, 2014 CFR

2014-04-01

... 18 Conservation of Power and Water Resources 1 2014-04-01 2014-04-01 false Burden of proof (Rule 911). 385.911 Section 385.911 Conservation of Power and Water Resources FEDERAL ENERGY REGULATORY... Remedial Orders § 385.911 Burden of proof (Rule 911). (a) The Secretary has the burden of going forward and...

18 CFR 385.911 - Burden of proof (Rule 911).

Code of Federal Regulations, 2012 CFR

2012-04-01

... 18 Conservation of Power and Water Resources 1 2012-04-01 2012-04-01 false Burden of proof (Rule 911). 385.911 Section 385.911 Conservation of Power and Water Resources FEDERAL ENERGY REGULATORY... Remedial Orders § 385.911 Burden of proof (Rule 911). (a) The Secretary has the burden of going forward and...

18 CFR 385.911 - Burden of proof (Rule 911).

Code of Federal Regulations, 2013 CFR

2013-04-01

... 18 Conservation of Power and Water Resources 1 2013-04-01 2013-04-01 false Burden of proof (Rule 911). 385.911 Section 385.911 Conservation of Power and Water Resources FEDERAL ENERGY REGULATORY... Remedial Orders § 385.911 Burden of proof (Rule 911). (a) The Secretary has the burden of going forward and...

18 CFR 385.911 - Burden of proof (Rule 911).

Code of Federal Regulations, 2010 CFR

2010-04-01

... 18 Conservation of Power and Water Resources 1 2010-04-01 2010-04-01 false Burden of proof (Rule 911). 385.911 Section 385.911 Conservation of Power and Water Resources FEDERAL ENERGY REGULATORY... Remedial Orders § 385.911 Burden of proof (Rule 911). (a) The Secretary has the burden of going forward and...

18 CFR 385.911 - Burden of proof (Rule 911).

Code of Federal Regulations, 2011 CFR

2011-04-01

... 18 Conservation of Power and Water Resources 1 2011-04-01 2011-04-01 false Burden of proof (Rule 911). 385.911 Section 385.911 Conservation of Power and Water Resources FEDERAL ENERGY REGULATORY... Remedial Orders § 385.911 Burden of proof (Rule 911). (a) The Secretary has the burden of going forward and...

26 CFR 20.2014-5 - Proof of credit.

Code of Federal Regulations, 2010 CFR

2010-04-01

... 26 Internal Revenue 14 2010-04-01 2010-04-01 false Proof of credit. 20.2014-5 Section 20.2014-5 Internal Revenue INTERNAL REVENUE SERVICE, DEPARTMENT OF THE TREASURY (CONTINUED) ESTATE AND GIFT TAXES ESTATE TAX; ESTATES OF DECEDENTS DYING AFTER AUGUST 16, 1954 Credits Against Tax § 20.2014-5 Proof of...

38 CFR 6.4 - Proof of age, relationship and marriage.

Code of Federal Regulations, 2012 CFR

2012-07-01

... 38 Pensions, Bonuses, and Veterans' Relief 1 2012-07-01 2012-07-01 false Proof of age, relationship and marriage. 6.4 Section 6.4 Pensions, Bonuses, and Veterans' Relief DEPARTMENT OF VETERANS....4 Proof of age, relationship and marriage. Whenever it is necessary for a claimant to prove age...

38 CFR 6.4 - Proof of age, relationship and marriage.

Code of Federal Regulations, 2014 CFR

2014-07-01

... 38 Pensions, Bonuses, and Veterans' Relief 1 2014-07-01 2014-07-01 false Proof of age, relationship and marriage. 6.4 Section 6.4 Pensions, Bonuses, and Veterans' Relief DEPARTMENT OF VETERANS....4 Proof of age, relationship and marriage. Whenever it is necessary for a claimant to prove age...

38 CFR 6.4 - Proof of age, relationship and marriage.

Code of Federal Regulations, 2013 CFR

2013-07-01

... 38 Pensions, Bonuses, and Veterans' Relief 1 2013-07-01 2013-07-01 false Proof of age, relationship and marriage. 6.4 Section 6.4 Pensions, Bonuses, and Veterans' Relief DEPARTMENT OF VETERANS....4 Proof of age, relationship and marriage. Whenever it is necessary for a claimant to prove age...

21 CFR 1310.07 - Proof of identity.

Code of Federal Regulations, 2011 CFR

2011-04-01

... 21 Food and Drugs 9 2011-04-01 2011-04-01 false Proof of identity. 1310.07 Section 1310.07 Food... CHEMICALS AND CERTAIN MACHINES § 1310.07 Proof of identity. (a) Each regulated person who engages in a... be accomplished by having the other party present documents which would verify the identity, or...

21 CFR 1310.07 - Proof of identity.

Code of Federal Regulations, 2014 CFR

2014-04-01

... 21 Food and Drugs 9 2014-04-01 2014-04-01 false Proof of identity. 1310.07 Section 1310.07 Food... CHEMICALS AND CERTAIN MACHINES § 1310.07 Proof of identity. (a) Each regulated person who engages in a... be accomplished by having the other party present documents which would verify the identity, or...

21 CFR 1310.07 - Proof of identity.

Code of Federal Regulations, 2012 CFR

2012-04-01

... 21 Food and Drugs 9 2012-04-01 2012-04-01 false Proof of identity. 1310.07 Section 1310.07 Food... CHEMICALS AND CERTAIN MACHINES § 1310.07 Proof of identity. (a) Each regulated person who engages in a... be accomplished by having the other party present documents which would verify the identity, or...

21 CFR 1310.07 - Proof of identity.

Code of Federal Regulations, 2013 CFR

2013-04-01

... 21 Food and Drugs 9 2013-04-01 2013-04-01 false Proof of identity. 1310.07 Section 1310.07 Food... CHEMICALS AND CERTAIN MACHINES § 1310.07 Proof of identity. (a) Each regulated person who engages in a... be accomplished by having the other party present documents which would verify the identity, or...

The Notion of Proof in the Context of Elementary School Mathematics

ERIC Educational Resources Information Center

Stylianides, Andreas J.

2007-01-01

Despite increased appreciation of the role of "proof" in students' mathematical experiences across "all" grades, little research has focused on the issue of understanding and characterizing the notion of proof at the elementary school level. This paper takes a step toward addressing this limitation, by examining the characteristics of four major…

14 CFR 23.307 - Proof of structure.

Code of Federal Regulations, 2010 CFR

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...

Pre-Service Classroom Teachers' Proof Schemes in Geometry: A Case Study of Three Pre-Service Teachers

ERIC Educational Resources Information Center

Oflaz, Gülcin; Bulut, Neslihan; Akcakin, Veysel

2016-01-01

Problem Statement: Recent research and evaluation reports show that students are not learning geometry efficiently. One identifier of student understanding related to geometry is teachers' knowledge structures. Understanding what a proof is and writing proofs are essential for success in mathematics. Thus, school mathematics should include proving…

47 CFR 1.254 - Nature of the hearing; burden of proof.

Code of Federal Regulations, 2010 CFR

2010-10-01

... 47 Telecommunication 1 2010-10-01 2010-10-01 false Nature of the hearing; burden of proof. 1.254 Section 1.254 Telecommunication FEDERAL COMMUNICATIONS COMMISSION GENERAL PRACTICE AND PROCEDURE Hearing Proceedings Hearing and Intermediate Decision § 1.254 Nature of the hearing; burden of proof. Any hearing upon...

47 CFR 1.254 - Nature of the hearing; burden of proof.

Code of Federal Regulations, 2013 CFR

2013-10-01

... 47 Telecommunication 1 2013-10-01 2013-10-01 false Nature of the hearing; burden of proof. 1.254 Section 1.254 Telecommunication FEDERAL COMMUNICATIONS COMMISSION GENERAL PRACTICE AND PROCEDURE Hearing Proceedings Hearing and Intermediate Decision § 1.254 Nature of the hearing; burden of proof. Any hearing upon...

47 CFR 1.254 - Nature of the hearing; burden of proof.

Code of Federal Regulations, 2014 CFR

2014-10-01

... 47 Telecommunication 1 2014-10-01 2014-10-01 false Nature of the hearing; burden of proof. 1.254 Section 1.254 Telecommunication FEDERAL COMMUNICATIONS COMMISSION GENERAL PRACTICE AND PROCEDURE Hearing Proceedings Hearing and Intermediate Decision § 1.254 Nature of the hearing; burden of proof. Any hearing upon...

47 CFR 1.254 - Nature of the hearing; burden of proof.

Code of Federal Regulations, 2011 CFR

2011-10-01

... 47 Telecommunication 1 2011-10-01 2011-10-01 false Nature of the hearing; burden of proof. 1.254 Section 1.254 Telecommunication FEDERAL COMMUNICATIONS COMMISSION GENERAL PRACTICE AND PROCEDURE Hearing Proceedings Hearing and Intermediate Decision § 1.254 Nature of the hearing; burden of proof. Any hearing upon...

47 CFR 1.254 - Nature of the hearing; burden of proof.

Code of Federal Regulations, 2012 CFR

2012-10-01

... 47 Telecommunication 1 2012-10-01 2012-10-01 false Nature of the hearing; burden of proof. 1.254 Section 1.254 Telecommunication FEDERAL COMMUNICATIONS COMMISSION GENERAL PRACTICE AND PROCEDURE Hearing Proceedings Hearing and Intermediate Decision § 1.254 Nature of the hearing; burden of proof. Any hearing upon...

Euler's Theorem under the Microscope

ERIC Educational Resources Information Center

Tennant, Geoff

2010-01-01

"Proofs and refutations: the logic of mathematical discovery" by Imre Lakatos was published posthumously in 1976. This is a fascinating, if somewhat hard to access, book which calls into question many of the assumptions that people make about proof--one may start reading with a clear sense of what mathematical proof is, but almost certainly will…

Open Textbook Proof-of-Concept via Connexions

ERIC Educational Resources Information Center

Baker, Judy; Thierstein, Joel; Fletcher, Kathi; Kaur, Manpreet; Emmons, Jonathan

2009-01-01

To address the high cost of textbooks, Rice University's Connexions and the Community College Open Textbook Project (CCOTP) collaborated to develop a proof-of-concept free and open textbook. The proof-of-concept served to document a workflow process that would support adoption of open textbooks. Open textbooks provide faculty and students with a…

Sharing Data between Mobile Devices, Connected Vehicles and Infrastructure Task 8 : D2X Hub Proof-of-Concept Test Evaluation Report.

DOT National Transportation Integrated Search

2017-10-25

The Task 8 D2X Hub Proof-of-Concept Test Evaluation Report provides results of the experimental data analysis performed in accordance with the experimental plan for the proof-of-concept version of the prototype system. The data set analyzed includes ...

Proof of a new colour decomposition for QCD amplitudes

DOE Office of Scientific and Technical Information (OSTI.GOV)

Melia, Tom

Recently, Johansson and Ochirov conjectured the form of a new colour decom-position for QCD tree-level amplitudes. This note provides a proof of that conjecture. The proof is based on ‘Mario World’ Feynman diagrams, which exhibit the hierarchical Dyck structure previously found to be very useful when dealing with multi-quark amplitudes.

43 CFR 3742.3-4 - Proof of publication.

Code of Federal Regulations, 2012 CFR

2012-10-01

... 43 Public Lands: Interior 2 2012-10-01 2012-10-01 false Proof of publication. 3742.3-4 Section... DEVELOPMENT Procedures Under the Act § 3742.3-4 Proof of publication. After the period of newspaper publication has expired, the person requesting publication shall obtain from the office of the newspaper of...

43 CFR 3712.2-5 - Proof of publication.

Code of Federal Regulations, 2012 CFR

2012-10-01

... 43 Public Lands: Interior 2 2012-10-01 2012-10-01 false Proof of publication. 3712.2-5 Section... Proceedings Under the Act § 3712.2-5 Proof of publication. After the period of newspaper publication has expired, the department or agency requesting the publication shall obtain from the office of the newspaper...

43 CFR 3742.3-4 - Proof of publication.

Code of Federal Regulations, 2011 CFR

2011-10-01

... 43 Public Lands: Interior 2 2011-10-01 2011-10-01 false Proof of publication. 3742.3-4 Section... DEVELOPMENT Procedures Under the Act § 3742.3-4 Proof of publication. After the period of newspaper publication has expired, the person requesting publication shall obtain from the office of the newspaper of...

43 CFR 3712.2-5 - Proof of publication.

Code of Federal Regulations, 2011 CFR

2011-10-01

... 43 Public Lands: Interior 2 2011-10-01 2011-10-01 false Proof of publication. 3712.2-5 Section... Proceedings Under the Act § 3712.2-5 Proof of publication. After the period of newspaper publication has expired, the department or agency requesting the publication shall obtain from the office of the newspaper...

27 CFR 19.773 - Daily record of wholesale liquor dealer and taxpaid storeroom operations.

Code of Federal Regulations, 2010 CFR

2010-04-01

... the receipt and disposition of distilled spirits and wines shall contain all data necessary... distilled spirits involved (proof and proof gallons if in packages, wine gallons or liters and proof if in bottles); (6) The package identification or serial numbers of packages involved; (7) The name of the...

Words to Argue By

ERIC Educational Resources Information Center

Pourciau, Bruce

2018-01-01

In a first proof-oriented mathematics course, students will often ask questions--for example, "What is this problem asking me to do?" or "What would a proof of this even look like"--that have more to do with logic than mathematics. The logical structure of a proof is a dance involving those basic logical forms--such as "p…

Geometry: A Flow Proof Approach.

ERIC Educational Resources Information Center

McMurray, Robert

The inspiration for this text was provided by an exposure to the flow proof approach to a proof format as opposed to the conventional two-column approach. Historical background is included, to provide a frame of reference to give the student an appreciation of the subject. The basic constructions are introduced early and briefly, to aid the…

Proof in Algebra: Reasoning beyond Examples

ERIC Educational Resources Information Center

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…

Synthesizing Safety Conditions for Code Certification Using Meta-Level Programming

NASA Technical Reports Server (NTRS)

Eusterbrock, Jutta

2004-01-01

In code certification the code consumer publishes a safety policy and the code producer generates a proof that the produced code is in compliance with the published safety policy. In this paper, a novel viewpoint approach towards an implementational re-use oriented framework for code certification is taken. It adopts ingredients from Necula's approach for proof-carrying code, but in this work safety properties can be analyzed on a higher code level than assembly language instructions. It consists of three parts: (1) The specification language is extended to include generic pre-conditions that shall ensure safety at all states that can be reached during program execution. Actual safety requirements can be expressed by providing domain-specific definitions for the generic predicates which act as interface to the environment. (2) The Floyd-Hoare inductive assertion method is refined to obtain proof rules that allow the derivation of the proof obligations in terms of the generic safety predicates. (3) A meta-interpreter is designed and experimentally implemented that enables automatic synthesis of proof obligations for submitted programs by applying the modified Floyd-Hoare rules. The proof obligations have two separate conjuncts, one for functional correctness and another for the generic safety obligations. Proof of the generic obligations, having provided the actual safety definitions as context, ensures domain-specific safety of program execution in a particular environment and is simpler than full program verification.

Opportunities to Learn Reasoning and Proof in High School Mathematics Textbooks

ERIC Educational Resources Information Center

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…

42 CFR 1005.15 - The hearing and burden of proof.

Code of Federal Regulations, 2014 CFR

2014-10-01

... respondent or petitioner, as applicable, bears the burden of going forward and the burden of persuasion with... forward and the burden of persuasion with respect to all other issues. (c) Burden of proof in all other... allocate the burden of proof as the ALJ deems appropriate. (d) The burden of persuasion will be judged by a...

42 CFR 1005.15 - The hearing and burden of proof.

Code of Federal Regulations, 2011 CFR

2011-10-01

... respondent or petitioner, as applicable, bears the burden of going forward and the burden of persuasion with... forward and the burden of persuasion with respect to all other issues. (c) Burden of proof in all other... allocate the burden of proof as the ALJ deems appropriate. (d) The burden of persuasion will be judged by a...

42 CFR 1005.15 - The hearing and burden of proof.

Code of Federal Regulations, 2013 CFR

2013-10-01

... respondent or petitioner, as applicable, bears the burden of going forward and the burden of persuasion with... forward and the burden of persuasion with respect to all other issues. (c) Burden of proof in all other... allocate the burden of proof as the ALJ deems appropriate. (d) The burden of persuasion will be judged by a...

42 CFR 1005.15 - The hearing and burden of proof.

Code of Federal Regulations, 2012 CFR

2012-10-01

... respondent or petitioner, as applicable, bears the burden of going forward and the burden of persuasion with... forward and the burden of persuasion with respect to all other issues. (c) Burden of proof in all other... allocate the burden of proof as the ALJ deems appropriate. (d) The burden of persuasion will be judged by a...

42 CFR 1005.15 - The hearing and burden of proof.

Code of Federal Regulations, 2010 CFR

2010-10-01

... respondent or petitioner, as applicable, bears the burden of going forward and the burden of persuasion with... forward and the burden of persuasion with respect to all other issues. (c) Burden of proof in all other... allocate the burden of proof as the ALJ deems appropriate. (d) The burden of persuasion will be judged by a...

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

ERIC Educational Resources Information Center

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…

17 CFR 12.105 - Submission of proof only in documentary or tangible form.

Code of Federal Regulations, 2014 CFR

2014-04-01

... 17 Commodity and Securities Exchanges 1 2014-04-01 2014-04-01 false Submission of proof only in documentary or tangible form. 12.105 Section 12.105 Commodity and Securities Exchanges COMMODITY FUTURES TRADING COMMISSION RULES RELATING TO REPARATIONS Rules Applicable to Voluntary Decisional Proceedings § 12.105 Submission of proof only in...

17 CFR 12.105 - Submission of proof only in documentary or tangible form.

Code of Federal Regulations, 2013 CFR

2013-04-01

... 17 Commodity and Securities Exchanges 1 2013-04-01 2013-04-01 false Submission of proof only in documentary or tangible form. 12.105 Section 12.105 Commodity and Securities Exchanges COMMODITY FUTURES TRADING COMMISSION RULES RELATING TO REPARATIONS Rules Applicable to Voluntary Decisional Proceedings § 12.105 Submission of proof only in...

17 CFR 12.105 - Submission of proof only in documentary or tangible form.

Code of Federal Regulations, 2011 CFR

2011-04-01

... 17 Commodity and Securities Exchanges 1 2011-04-01 2011-04-01 false Submission of proof only in documentary or tangible form. 12.105 Section 12.105 Commodity and Securities Exchanges COMMODITY FUTURES TRADING COMMISSION RULES RELATING TO REPARATIONS Rules Applicable to Voluntary Decisional Proceedings § 12.105 Submission of proof only in...

17 CFR 12.105 - Submission of proof only in documentary or tangible form.

Code of Federal Regulations, 2010 CFR

2010-04-01

... 17 Commodity and Securities Exchanges 1 2010-04-01 2010-04-01 false Submission of proof only in documentary or tangible form. 12.105 Section 12.105 Commodity and Securities Exchanges COMMODITY FUTURES TRADING COMMISSION RULES RELATING TO REPARATIONS Rules Applicable to Voluntary Decisional Proceedings § 12.105 Submission of proof only in...

17 CFR 12.105 - Submission of proof only in documentary or tangible form.

Code of Federal Regulations, 2012 CFR

2012-04-01

... 17 Commodity and Securities Exchanges 1 2012-04-01 2012-04-01 false Submission of proof only in documentary or tangible form. 12.105 Section 12.105 Commodity and Securities Exchanges COMMODITY FUTURES TRADING COMMISSION RULES RELATING TO REPARATIONS Rules Applicable to Voluntary Decisional Proceedings § 12.105 Submission of proof only in...

29 CFR 1919.28 - Unit proof tests-cranes and gear accessory thereto.

Code of Federal Regulations, 2011 CFR

2011-07-01

... 29 Labor 7 2011-07-01 2011-07-01 false Unit proof tests-cranes and gear accessory thereto. 1919.28... Loads; Heat Treatment; Competent Persons § 1919.28 Unit proof tests—cranes and gear accessory thereto. (a) Except as noted in paragraph (e) of this section, cranes and other hoisting machines, together...

77 FR 43662 - Price for the 2012 American Eagle Silver Proof Coin

Federal Register 2010, 2011, 2012, 2013, 2014

2012-07-25

... DEPARTMENT OF THE TREASURY United States Mint Price for the 2012 American Eagle Silver Proof Coin... is lowering the price of the 2012 American Eagle Silver Proof Coin. The product will now be offered for sale at a price of $54.95. FOR FURTHER INFORMATION CONTACT: B. B. Craig, Associate Director for...

The Harmonic Series Diverges Again and Again

ERIC Educational Resources Information Center

Kifowit, Steven J.; Stamps, Terra A.

2006-01-01

The harmonic series is one of the most celebrated infinite series of mathematics. A quick glance at a variety of modern calculus textbooks reveals that there are two very popular proofs of the divergence of the harmonic series. In this article, the authors survey these popular proofs along with many other proofs that are equally simple and…

26 CFR 1.871-4 - Proof of residence of aliens.

Code of Federal Regulations, 2010 CFR

2010-04-01

... 26 Internal Revenue 9 2010-04-01 2010-04-01 false Proof of residence of aliens. 1.871-4 Section 1... (CONTINUED) INCOME TAXES Nonresident Aliens and Foreign Corporations § 1.871-4 Proof of residence of aliens... alien within the United States has acquired residence therein for purposes of the income tax. (b...

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

ERIC Educational Resources Information Center

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…

34 CFR 34.14 - Burden of proof.

Code of Federal Regulations, 2010 CFR

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...

6 CFR 13.30 - The hearing and burden of proof.

Code of Federal Regulations, 2010 CFR

2010-01-01

... 6 Domestic Security 1 2010-01-01 2010-01-01 false The hearing and burden of proof. 13.30 Section 13.30 Domestic Security DEPARTMENT OF HOMELAND SECURITY, OFFICE OF THE SECRETARY PROGRAM FRAUD CIVIL REMEDIES § 13.30 The hearing and burden of proof. (a) The ALJ will conduct a hearing on the record in order...

22 CFR 51.40 - Burden of proof.

Code of Federal Regulations, 2010 CFR

2010-04-01

... 22 Foreign Relations 1 2010-04-01 2010-04-01 false Burden of proof. 51.40 Section 51.40 Foreign Relations DEPARTMENT OF STATE NATIONALITY AND PASSPORTS PASSPORTS Evidence of U.S. Citizenship or Nationality § 51.40 Burden of proof. The applicant has the burden of proving that he or she is a U.S. citizen...

22 CFR 51.44 - Proof of resumption or retention of U.S. citizenship.

Code of Federal Regulations, 2013 CFR

2013-04-01

... 22 Foreign Relations 1 2013-04-01 2013-04-01 false Proof of resumption or retention of U.S. citizenship. 51.44 Section 51.44 Foreign Relations DEPARTMENT OF STATE NATIONALITY AND PASSPORTS PASSPORTS Evidence of U.S. Citizenship or Nationality § 51.44 Proof of resumption or retention of U.S. citizenship...

22 CFR 51.44 - Proof of resumption or retention of U.S. citizenship.

Code of Federal Regulations, 2012 CFR

2012-04-01

... 22 Foreign Relations 1 2012-04-01 2012-04-01 false Proof of resumption or retention of U.S. citizenship. 51.44 Section 51.44 Foreign Relations DEPARTMENT OF STATE NATIONALITY AND PASSPORTS PASSPORTS Evidence of U.S. Citizenship or Nationality § 51.44 Proof of resumption or retention of U.S. citizenship...

22 CFR 51.40 - Burden of proof.

Code of Federal Regulations, 2011 CFR

2011-04-01

... 22 Foreign Relations 1 2011-04-01 2011-04-01 false Burden of proof. 51.40 Section 51.40 Foreign Relations DEPARTMENT OF STATE NATIONALITY AND PASSPORTS PASSPORTS Evidence of U.S. Citizenship or Nationality § 51.40 Burden of proof. The applicant has the burden of proving that he or she is a U.S. citizen...

22 CFR 51.40 - Burden of proof.

Code of Federal Regulations, 2014 CFR

2014-04-01

... 22 Foreign Relations 1 2014-04-01 2014-04-01 false Burden of proof. 51.40 Section 51.40 Foreign Relations DEPARTMENT OF STATE NATIONALITY AND PASSPORTS PASSPORTS Evidence of U.S. Citizenship or Nationality § 51.40 Burden of proof. The applicant has the burden of proving that he or she is a U.S. citizen...

22 CFR 51.40 - Burden of proof.

Code of Federal Regulations, 2013 CFR

2013-04-01

... 22 Foreign Relations 1 2013-04-01 2013-04-01 false Burden of proof. 51.40 Section 51.40 Foreign Relations DEPARTMENT OF STATE NATIONALITY AND PASSPORTS PASSPORTS Evidence of U.S. Citizenship or Nationality § 51.40 Burden of proof. The applicant has the burden of proving that he or she is a U.S. citizen...

22 CFR 51.44 - Proof of resumption or retention of U.S. citizenship.

Code of Federal Regulations, 2014 CFR

2014-04-01

... 22 Foreign Relations 1 2014-04-01 2014-04-01 false Proof of resumption or retention of U.S. citizenship. 51.44 Section 51.44 Foreign Relations DEPARTMENT OF STATE NATIONALITY AND PASSPORTS PASSPORTS Evidence of U.S. Citizenship or Nationality § 51.44 Proof of resumption or retention of U.S. citizenship...

22 CFR 51.44 - Proof of resumption or retention of U.S. citizenship.

Code of Federal Regulations, 2010 CFR

2010-04-01

... 22 Foreign Relations 1 2010-04-01 2010-04-01 false Proof of resumption or retention of U.S. citizenship. 51.44 Section 51.44 Foreign Relations DEPARTMENT OF STATE NATIONALITY AND PASSPORTS PASSPORTS Evidence of U.S. Citizenship or Nationality § 51.44 Proof of resumption or retention of U.S. citizenship...

22 CFR 51.40 - Burden of proof.

Code of Federal Regulations, 2012 CFR

2012-04-01

... 22 Foreign Relations 1 2012-04-01 2012-04-01 false Burden of proof. 51.40 Section 51.40 Foreign Relations DEPARTMENT OF STATE NATIONALITY AND PASSPORTS PASSPORTS Evidence of U.S. Citizenship or Nationality § 51.40 Burden of proof. The applicant has the burden of proving that he or she is a U.S. citizen...

22 CFR 51.44 - Proof of resumption or retention of U.S. citizenship.

Code of Federal Regulations, 2011 CFR

2011-04-01

... 22 Foreign Relations 1 2011-04-01 2011-04-01 false Proof of resumption or retention of U.S. citizenship. 51.44 Section 51.44 Foreign Relations DEPARTMENT OF STATE NATIONALITY AND PASSPORTS PASSPORTS Evidence of U.S. Citizenship or Nationality § 51.44 Proof of resumption or retention of U.S. citizenship...

Simple Proof of Jury Test for Complex Polynomials

NASA Astrophysics Data System (ADS)

Choo, Younseok; Kim, Dongmin

Recently some attempts have been made in the literature to give simple proofs of Jury test for real polynomials. This letter presents a similar result for complex polynomials. A simple proof of Jury test for complex polynomials is provided based on the Rouché's Theorem and a single-parameter characterization of Schur stability property for complex polynomials.

Pre-Service Middle School Mathematics Teachers' Evaluations of Discussions: The Case of Proof by Contradiction

ERIC Educational Resources Information Center

Demiray, Esra; Isiksal Bostan, Mine

2017-01-01

The purposes of this study are to investigate whether pre-service middle school mathematics teachers evaluate discussions in the cases regarding proof by contradiction correctly, to what extent they explain their correct evaluations by referring to proof by contradiction, and the reasons of their misinterpretations of discussions in the cases…

Using Hip-Hop Music and Music Videos to Teach Aristotle's Three Proofs

ERIC Educational Resources Information Center

Sciullo, Nick J.

2014-01-01

Aristotle's three proofs remain central to students' understanding of argumentation and persuasion. They are fundamental for those just beginning rhetorical study, as well as being of interest to experienced scholars. Investing time in learning the proofs supports students' future practice and study of rhetoric. Unfortunately, the…

26 CFR 1.534-1 - Burden of proof as to unreasonable accumulations generally.

Code of Federal Regulations, 2010 CFR

2010-04-01

... (CONTINUED) INCOME TAX (CONTINUED) INCOME TAXES (CONTINUED) Corporations Used to Avoid Income Tax on Shareholders § 1.534-1 Burden of proof as to unreasonable accumulations generally. For purposes of applying the... under section 535(c)(1), the burden of proof with respect to an allegation by the Commissioner that all...

Who Wants Proof?

ERIC Educational Resources Information Center

Ball, Derek

2002-01-01

People are inclined to desire proof of theories if they have developed a certain philosophical style when they are quite young. It is a style that questions the authority for things, so that they can hold fast to what is good. Regarding mathematical proof, this author argues that it is only those who are prepared to take their own authority for…

How Can the Relationship between Argumentation and Proof Be Analysed?

ERIC Educational Resources Information Center

Pedemonte, Bettina

2007-01-01

The paper presents a characterisation about argumentation and proof in mathematics. On the basis of contemporary linguistic theories, the hypothesis that proof is a special case of argumentation is put forward and Toulmin's model is proposed as a methodological tool to compare them. This model can be used to detect and analyse the structure of an…

26 CFR 301.7454-2 - Burden of proof in foundation manager, etc. cases.

Code of Federal Regulations, 2010 CFR

2010-04-01

... 26 Internal Revenue 18 2010-04-01 2010-04-01 false Burden of proof in foundation manager, etc... Actions by the United States § 301.7454-2 Burden of proof in foundation manager, etc. cases. (a) Foundation manager. In any proceeding involving the issue whether a foundation manager as defined in section...

47 CFR 76.1700 - Records to be maintained by cable system operators.

Code of Federal Regulations, 2011 CFR

2011-10-01

... programming); § 76.1704 (proof-of-performance test data); and § 76.1706 (signal leakage logs and repair... children's programming); § 76.1704 (proof-of-performance test data); and § 76.1706 (signal leakage logs and... programming); § 76.1704 (proof-of-performance test data); and § 76.1706 (signal leakage logs and repair...

A Production Network Model and Its Diffusion Approximation.

DTIC Science & Technology

1982-09-01

ordinary Riemann-Stieltjes integrals. Proof. By making minor changes in the proof of the Kunita-Watanabe [91 change of variable formula it can be shown...n.) converges meakly to I, where X Is a Brownian motion wlth drift p and covarlance mtrx A - (ajj) djj b I! (41) aij 2 f Puj(a) do The proof of Lemna

Analysis of the Mathematical Proof Skills of Students of Science Teaching

ERIC Educational Resources Information Center

Gökkt, Burçin; Soylu, Yasin; Sahin, Ömer

2014-01-01

Mathematics and proof are two closely related concepts. Mathematics not only shows what is right or wrong, but it also teaches that it is not enough to know the latest formulas and results should be explained with causality. In this context, students learn the underlying meaning behind what mathematicians do by way of proofs. Accordingly, this…

75 FR 10345 - Pricing for 2010 United States Mint America the Beautiful Quarters Proof Set, etc.

Federal Register 2010, 2011, 2012, 2013, 2014

2010-03-05

... DEPARTMENT OF THE TREASURY United States Mint Pricing for 2010 United States Mint America the.... SUMMARY: The United States Mint is announcing the prices of the 2010 United States Mint America the Beautiful Quarters Proof Set; 2010 United States Mint America the Beautiful Quarters Silver Proof Set; 2010...

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

ERIC Educational Resources Information Center

Padula, Janice

2011-01-01

The study of Kurt Godel's proof of the "incompleteness" of a formal system such as "Principia Mathematica" is a great way to stimulate students' thinking and creative processes and interest in mathematics and its important developments. This article describes salient features of the proof together with ways to deal with potential difficulties for…

Proof and Reasoning in Secondary School Algebra Textbooks

ERIC Educational Resources Information Center

Dituri, Philip

2013-01-01

The purpose of this study was to determine the extent to which the modeling of deductive reasoning and proof-type thinking occurs in a mathematics course in which students are not explicitly preparing to write formal mathematical proofs. Algebra was chosen because it is the course that typically directly precedes a student's first formal…

Protecting Privacy and Securing the Gathering of Location Proofs - The Secure Location Verification Proof Gathering Protocol

NASA Astrophysics Data System (ADS)

Graham, Michelle; Gray, David

As wireless networks become increasingly ubiquitous, the demand for a method of locating a device has increased dramatically. Location Based Services are now commonplace but there are few methods of verifying or guaranteeing a location provided by a user without some specialised hardware, especially in larger scale networks. We propose a system for the verification of location claims, using proof gathered from neighbouring devices. In this paper we introduce a protocol to protect this proof gathering process, protecting the privacy of all involved parties and securing it from intruders and malicious claiming devices. We present the protocol in stages, extending the security of this protocol to allow for flexibility within its application. The Secure Location Verification Proof Gathering Protocol (SLVPGP) has been designed to function within the area of Vehicular Networks, although its application could be extended to any device with wireless & cryptographic capabilities.

A Generic Software Safety Document Generator

NASA Technical Reports Server (NTRS)

Denney, Ewen; Venkatesan, Ram Prasad

2004-01-01

Formal certification is based on the idea that a mathematical proof of some property of a piece of software can be regarded as a certificate of correctness which, in principle, can be subjected to external scrutiny. In practice, however, proofs themselves are unlikely to be of much interest to engineers. Nevertheless, it is possible to use the information obtained from a mathematical analysis of software to produce a detailed textual justification of correctness. In this paper, we describe an approach to generating textual explanations from automatically generated proofs of program safety, where the proofs are of compliance with an explicit safety policy that can be varied. Key to this is tracing proof obligations back to the program, and we describe a tool which implements this to certify code auto-generated by AutoBayes and AutoFilter, program synthesis systems under development at the NASA Ames Research Center. Our approach is a step towards combining formal certification with traditional certification methods.

Studies on proofing of yeasted bread dough using near- and mid-infrared spectroscopy.

PubMed

Sinelli, Nicoletta; Casiraghi, Ernestina; Downey, Gerard

2008-02-13

Dough proofing is the resting period after mixing during which fermentation commences. Optimum dough proofing is important for production of high quality bread. Near- and mid-infrared spectroscopies have been used with some success to investigate macromolecular changes during dough mixing. In this work, both techniques were applied to a preliminary study of flour doughs during proofing. Spectra were collected contemporaneously by NIR (750-1100 nm) and MIR (4000-600 cm(-1)) instruments using a fiberoptic surface interactance probe and horizontal ATR cell, respectively. Studies were performed on flours of differing baking quality; these included strong baker's flour, retail flour, and gluten-free flour. Following principal component analysis, changes in the recorded spectral signals could be followed over time. It is apparent from the results that both vibrational spectroscopic techniques can identify changes in flour doughs during proofing and that it is possible to suggest which macromolecular species are involved.

Boudot's Range-Bounded Commitment Scheme Revisited

NASA Astrophysics Data System (ADS)

Cao, Zhengjun; Liu, Lihua

Checking whether a committed integer lies in a specific interval has many cryptographic applications. In Eurocrypt'98, Chan et al. proposed an instantiation (CFT Proof). Based on CFT, Boudot presented a popular range-bounded commitment scheme in Eurocrypt'2000. Both CFT Proof and Boudot Proof are based on the encryption E(x, r)=g^xh^r mod n, where n is an RSA modulus whose factorization is unknown by the prover. They did not use a single base as usual. Thus an increase in cost occurs. In this paper, we show that it suffices to adopt a single base. The cost of the modified Boudot Proof is about half of that of the original scheme. Moreover, the key restriction in the original scheme, i.e., both the discrete logarithm of g in base h and the discrete logarithm of h in base g are unknown by the prover, which is a potential menace to the Boudot Proof, is definitely removed.

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

NASA Astrophysics Data System (ADS)

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.

The challenge of computer mathematics.

PubMed

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.

Proponents of Creationism but Not Proponents of Evolution Frame the Origins Debate in Terms of Proof

ERIC Educational Resources Information Center

Barnes, Ralph M.; Church, Rebecca A.

2013-01-01

In Study 1, 72 internet documents containing creationism, ID (intelligent design), or evolution content were selected for analysis. All instances of proof cognates (the word "proof" and related terms such as "proven", "disproof", etc.) contained within these documents were identified and labeled in terms of the manner in which the terms were used.…

28 CFR 79.15 - Proof of onset of leukemia more than two years after first exposure.

Code of Federal Regulations, 2011 CFR

2011-07-01

... 28 Judicial Administration 2 2011-07-01 2011-07-01 false Proof of onset of leukemia more than two...) CLAIMS UNDER THE RADIATION EXPOSURE COMPENSATION ACT Eligibility Criteria for Claims Relating to Leukemia § 79.15 Proof of onset of leukemia more than two years after first exposure. The Program will presume...

27 CFR 30.61 - Table 1, showing the true percent of proof spirit for any indication of the hydrometer at...

Code of Federal Regulations, 2010 CFR

2010-04-01

... percent of proof spirit for any indication of the hydrometer at temperatures between zero and 100 degrees... true percent of proof spirit for any indication of the hydrometer at temperatures between zero and 100... hydrometer likely to occur in practice at temperatures between zero and 100 degrees Fahrenheit and shall be...

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

ERIC Educational Resources Information Center

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…

28 CFR 79.15 - Proof of onset of leukemia more than two years after first exposure.

Code of Federal Regulations, 2010 CFR

2010-07-01

... 28 Judicial Administration 2 2010-07-01 2010-07-01 false Proof of onset of leukemia more than two...) CLAIMS UNDER THE RADIATION EXPOSURE COMPENSATION ACT Eligibility Criteria for Claims Relating to Leukemia § 79.15 Proof of onset of leukemia more than two years after first exposure. The Program will presume...

What's 2 Got to Do with It? Using Dynamic Geometry Environments to Find Surprising Results and Motivate Proof

ERIC Educational Resources Information Center

Martin, Tami; Cullen, Craig J.; Day, Roger

2011-01-01

Dynamic geometry software (DGS), such as Geometer's Sketchpad[TM], Cabri Geometry[TM], and GeoGebra[TM] has become a widely used classroom technology. The broad availability of DGS has given students the opportunity to engage in many aspects of reasoning and proof, including exploration, conjecture development, and proof, in its many roles. By…

Proof and Proving in the Classroom: Dynamic Geometry Systems as Tools of Semiotic Mediation

ERIC Educational Resources Information Center

Mariotti, Maria Alessandra

2012-01-01

The objective of this paper is to discuss the didactic potential offered by the use of a Dynamic Geometry System (DGS) in introducing students to theoretical thinking and specifically to the practice of proof. Starting from a discussion about what constitutes the general objective in developing students' sense of proof, the notion of Theorem is…

28 CFR 79.15 - Proof of onset of leukemia more than two years after first exposure.

Code of Federal Regulations, 2013 CFR

2013-07-01

... 28 Judicial Administration 2 2013-07-01 2013-07-01 false Proof of onset of leukemia more than two...) CLAIMS UNDER THE RADIATION EXPOSURE COMPENSATION ACT Eligibility Criteria for Claims Relating to Leukemia § 79.15 Proof of onset of leukemia more than two years after first exposure. The Program will presume...

28 CFR 79.15 - Proof of onset of leukemia more than two years after first exposure.

Code of Federal Regulations, 2014 CFR

2014-07-01

... 28 Judicial Administration 2 2014-07-01 2014-07-01 false Proof of onset of leukemia more than two...) CLAIMS UNDER THE RADIATION EXPOSURE COMPENSATION ACT Eligibility Criteria for Claims Relating to Leukemia § 79.15 Proof of onset of leukemia more than two years after first exposure. The Program will presume...

28 CFR 79.15 - Proof of onset of leukemia more than two years after first exposure.

Code of Federal Regulations, 2012 CFR

2012-07-01

... 28 Judicial Administration 2 2012-07-01 2012-07-01 false Proof of onset of leukemia more than two...) CLAIMS UNDER THE RADIATION EXPOSURE COMPENSATION ACT Eligibility Criteria for Claims Relating to Leukemia § 79.15 Proof of onset of leukemia more than two years after first exposure. The Program will presume...

29 CFR 1919.33 - Proof tests-wire rope.

Code of Federal Regulations, 2013 CFR

2013-07-01

... 29 Labor 7 2013-07-01 2013-07-01 false Proof tests-wire rope. 1919.33 Section 1919.33 Labor... Persons § 1919.33 Proof tests—wire rope. Wire rope, except as provided in § 1919.14(b), shall be tested by... acceptable to the Administration on the basis of design, shall not exceed one-fifth of the breaking load of...

29 CFR 1919.33 - Proof tests-wire rope.

Code of Federal Regulations, 2012 CFR

2012-07-01

... 29 Labor 7 2012-07-01 2012-07-01 false Proof tests-wire rope. 1919.33 Section 1919.33 Labor... Persons § 1919.33 Proof tests—wire rope. Wire rope, except as provided in § 1919.14(b), shall be tested by... acceptable to the Administration on the basis of design, shall not exceed one-fifth of the breaking load of...

29 CFR 1919.33 - Proof tests-wire rope.

Code of Federal Regulations, 2014 CFR

2014-07-01

... 29 Labor 7 2014-07-01 2014-07-01 false Proof tests-wire rope. 1919.33 Section 1919.33 Labor... Persons § 1919.33 Proof tests—wire rope. Wire rope, except as provided in § 1919.14(b), shall be tested by... acceptable to the Administration on the basis of design, shall not exceed one-fifth of the breaking load of...

27 CFR 30.61 - Table 1, showing the true percent of proof spirit for any indication of the hydrometer at...

Code of Federal Regulations, 2012 CFR

2012-04-01

... percent of proof spirit for any indication of the hydrometer at temperatures between zero and 100 degrees... true percent of proof spirit for any indication of the hydrometer at temperatures between zero and 100... hydrometer likely to occur in practice at temperatures between zero and 100 degrees Fahrenheit and shall be...

27 CFR 30.61 - Table 1, showing the true percent of proof spirit for any indication of the hydrometer at...

Code of Federal Regulations, 2014 CFR

2014-04-01

... percent of proof spirit for any indication of the hydrometer at temperatures between zero and 100 degrees... true percent of proof spirit for any indication of the hydrometer at temperatures between zero and 100... hydrometer likely to occur in practice at temperatures between zero and 100 degrees Fahrenheit and shall be...

27 CFR 30.61 - Table 1, showing the true percent of proof spirit for any indication of the hydrometer at...

Code of Federal Regulations, 2011 CFR

2011-04-01

... percent of proof spirit for any indication of the hydrometer at temperatures between zero and 100 degrees... true percent of proof spirit for any indication of the hydrometer at temperatures between zero and 100... hydrometer likely to occur in practice at temperatures between zero and 100 degrees Fahrenheit and shall be...

27 CFR 30.61 - Table 1, showing the true percent of proof spirit for any indication of the hydrometer at...

Code of Federal Regulations, 2013 CFR

2013-04-01

... percent of proof spirit for any indication of the hydrometer at temperatures between zero and 100 degrees... true percent of proof spirit for any indication of the hydrometer at temperatures between zero and 100... hydrometer likely to occur in practice at temperatures between zero and 100 degrees Fahrenheit and shall be...

49 CFR 40.385 - Who bears the burden of proof in a PIE proceeding?

Code of Federal Regulations, 2010 CFR

2010-10-01

... 49 Transportation 1 2010-10-01 2010-10-01 false Who bears the burden of proof in a PIE proceeding... TRANSPORTATION WORKPLACE DRUG AND ALCOHOL TESTING PROGRAMS Public Interest Exclusions § 40.385 Who bears the burden of proof in a PIE proceeding? (a) As the proponent of issuing a PIE, the initiating official bears...

29 CFR 102.113 - Methods of service of process and papers by the Agency; proof of service.

Code of Federal Regulations, 2010 CFR

2010-07-01

... 29 Labor 2 2010-07-01 2010-07-01 false Methods of service of process and papers by the Agency; proof of service. 102.113 Section 102.113 Labor Regulations Relating to Labor NATIONAL LABOR RELATIONS... process and papers by the Agency; proof of service. (a) Service of complaints and compliance...

Supporting Students' Participation in Authentic Proof Activities in Computer Supported Collaborative Learning (CSCL) Environments

ERIC Educational Resources Information Center

Oner, Diler

2008-01-01

In this paper, I review both mathematics education and CSCL literature and discuss how we can better take advantage of CSCL tools for developing mathematical proof skills. I introduce a model of proof in school mathematics that incorporates both empirical and deductive ways of knowing. I argue that two major forces have given rise to this…

Factors Influencing Students' Propensity for Semantic and Syntactic Reasoning in Proof Writing: A Case Study

ERIC Educational Resources Information Center

Mejía-Ramos, Juan Pablo; Weber, Keith; Fuller, Evan

2015-01-01

In this paper we present a case study of an individual student who consistently used semantic reasoning to construct proofs in calculus but infrequently used semantic reasoning to produce proofs in linear algebra. We hypothesize that the differences in these reasoning styles can be partially attributed to this student's familiarity with the…

76 FR 15047 - Pricing for 2010 United States Mint America the Beautiful Quarters Silver Proof SetTM

Federal Register 2010, 2011, 2012, 2013, 2014

2011-03-18

... Beautiful Quarters Silver Proof Set. In accordance with 31 U.S.C. 9701(b)(2)(B), the United States Mint is... DEPARTMENT OF THE TREASURY United States Mint Pricing for 2010 United States Mint America the Beautiful Quarters Silver Proof Set\\TM\\, etc. ACTION: Pricing for 2010 United States Mint America the...

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

ERIC Educational Resources Information Center

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…

Diagonalization of the symmetrized discrete i th right shift operator

NASA Astrophysics Data System (ADS)

Fuentes, Marc

2007-01-01

In this paper, we consider the symmetric part of the so-called ith right shift operator. We determine its eigenvalues as also the associated eigenvectors in a complete and closed form. The proposed proof is elementary, using only basical skills such as Trigonometry, Arithmetic and Linear algebra. The first section is devoted to the introduction of the tackled problem. Second and third parts contain almost all the ?technical? stuff of the proofE Afterwards, we continue with the end of the proof, provide a graphical illustration of the results, as well as an application on the polyhedral ?sandwiching? of a special compact of arising in Signal theory.

Generalized Dandelin’s Theorem

NASA Astrophysics Data System (ADS)

Kheyfets, A. L.

2017-11-01

The paper gives a geometric proof of the theorem which states that in case of the plane section of a second-order surface of rotation (quadrics of rotation, QR), such conics as an ellipse, a hyperbola or a parabola (types of conic sections) are formed. The theorem supplements the well-known Dandelin’s theorem which gives the geometric proof only for a circular cone and applies the proof to all QR, namely an ellipsoid, a hyperboloid, a paraboloid and a cylinder. That’s why the considered theorem is known as the generalized Dandelin’s theorem (GDT). The GDT proof is based on a relatively unknown generalized directrix definition (GDD) of conics. The work outlines the GDD proof for all types of conics as their necessary and sufficient condition. Based on the GDD, the author proves the GDT for all QR in case of a random position of the cutting plane. The graphical stereometric structures necessary for the proof are given. The implementation of the structures by 3d computer methods is considered. The article shows the examples of the builds made in the AutoCAD package. The theorem is intended for the training course of theoretical training of elite student groups of architectural and construction specialties.

Proof-test-based life prediction of high-toughness pressure vessels

DOE Office of Scientific and Technical Information (OSTI.GOV)

Panontin, T.L.; Hill, M.R.

1996-02-01

The paper examines the problems associated with applying proof-test-based life prediction to vessels made of high-toughness metals. Two A106 Gr B pipe specimens containing long, through-wall circumferential flaws were tested. One failed during hydrostatic testing and the other during tension-tension cycling following a hydrostatic test. Quantitative fractography was used to verify experimentally obtained fatigue crack growth rates and a variety of LEFM and EPFM techniques were used to analyze the experimental results. The results show that: plastic collapse analysis provides accurate predictions of screened (initial) crack size when the flow stress is determined experimentally; LEFM analysis underestimates the crack sizemore » screened by the proof test and overpredicts the subsequent fatigue life of the vessel when retardation effects are small (i.e., low proof levels); and, at a high proof-test level (2.4 {times} operating pressure), the large retardation effect on fatigue crack growth due to the overload overwhelmed the deleterious effect on fatigue life from stable tearing during the proof test and alleviated the problem of screening only long cracks due to the high toughness of the metal.« less

Verification of fault-tolerant clock synchronization systems. M.S. Thesis - College of William and Mary, 1992

NASA Technical Reports Server (NTRS)

Miner, Paul S.

1993-01-01

A critical function in a fault-tolerant computer architecture is the synchronization of the redundant computing elements. The synchronization algorithm must include safeguards to ensure that failed components do not corrupt the behavior of good clocks. Reasoning about fault-tolerant clock synchronization is difficult because of the possibility of subtle interactions involving failed components. Therefore, mechanical proof systems are used to ensure that the verification of the synchronization system is correct. In 1987, Schneider presented a general proof of correctness for several fault-tolerant clock synchronization algorithms. Subsequently, Shankar verified Schneider's proof by using the mechanical proof system EHDM. This proof ensures that any system satisfying its underlying assumptions will provide Byzantine fault-tolerant clock synchronization. The utility of Shankar's mechanization of Schneider's theory for the verification of clock synchronization systems is explored. Some limitations of Shankar's mechanically verified theory were encountered. With minor modifications to the theory, a mechanically checked proof is provided that removes these limitations. The revised theory also allows for proven recovery from transient faults. Use of the revised theory is illustrated with the verification of an abstract design of a clock synchronization system.

Fool-proofing design and crisis management for customized intelligent physical fitness and healthcare system.

PubMed

Huang, Chung-Chi; Huang, Chung-Lin; Liu, Hsiao-Man

2015-01-01

In recent years, it is quite important to develop a customized system which can enhance physical fitness and health for people. And the system reliability is more important. In the paper, a fool-proofing design and crisis management for customized physical fitness and healthcare system is proposed. It is designed to prevent the failure of the various mechanisms of customized physical fitness and healthcare system, including records, surveillance, assessments, predictions, diagnosis, prescription, and scheduling. It is separated into (1) fool-proofing design module (2) crisis management module. The fool-proofing indexes are set to prevent the failure of the various mechanisms. The states of the various mechanisms are managed by the auto-checked fool-proofing indexes. If mistakes prevention was fail, we have to execute the crisis management for stopping harmful results. The crisis management will find the error level and response the solution by using fuzzy method. By the experiments, we can find the advantages of the fool-proofing design and crisis management for customized physical fitness and healthcare system. And it is effective to prevent the failure of the various mechanisms of intelligent customized physical fitness and healthcare system.

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

ERIC Educational Resources Information Center

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…

90 Minutes on a Sunday Afternoon or: The Proof of the Special MT Issue Is in...

ERIC Educational Resources Information Center

Pinel, Adrian

2002-01-01

This article was written as a result of the author reading "MT177," a special issue dedicated to the teaching of "proof" in mathematics. He used the ideas in this special issue for planning his session "mathematical reasoning and proof," which was part of a weekend course for primary trainees. It consisted of three activities: (1) How many…

Some Comments On: A Historical Note on the Proof of the Area of a Circle

ERIC Educational Resources Information Center

Naidu, Jaideep T.; Sanford, John F.

2011-01-01

In a recent paper by Wilamowsky et al. [6], an intuitive proof of the area of the circle dating back to the twelfth century was presented. They discuss challenges made to this proof and offer simple rebuttals to these challenges. The alternative solution presented by them is simple and elegant and can be explained rather easily to non-mathematics…

Yet another proof of Hawking and Ellis's Lemma 8.5.5

NASA Astrophysics Data System (ADS)

Krasnikov, S.

2014-11-01

The fact that the null generators of a future Cauchy horizon are past-complete was first proved by Hawking and Ellis (1973 The Large Scale Structure of Spacetime (Cambridge: Cambridge University Press)). Then, Budzyński, Kondracki and Królak outlined a proof free from the error found in the original one (2000 New properties of Cauchy and event horizons arXiv:gr-qc/0011033). Now, Minguzzi has published his version of the proof (2014 J. Math. Phys. 55 082503), patching a previously unnoticed hole in the preceding two. I am not aware of any flaws in that last proof, but it is quite difficult. In this note, I present a simpler one.

Mistake proofing: changing designs to reduce error

PubMed Central

Grout, J R

2006-01-01

Mistake proofing uses changes in the physical design of processes to reduce human error. It can be used to change designs in ways that prevent errors from occurring, to detect errors after they occur but before harm occurs, to allow processes to fail safely, or to alter the work environment to reduce the chance of errors. Effective mistake proofing design changes should initially be effective in reducing harm, be inexpensive, and easily implemented. Over time these design changes should make life easier and speed up the process. Ideally, the design changes should increase patients' and visitors' understanding of the process. These designs should themselves be mistake proofed and follow the good design practices of other disciplines. PMID:17142609

Systems of nonlinear algebraic equations with positive solutions.

PubMed

Ciurte, Anca; Nedevschi, Sergiu; Rasa, Ioan

2017-01-01

We are concerned with the positive solutions of an algebraic system depending on a parameter [Formula: see text] and arising in economics. For [Formula: see text] we prove that the system has at least a solution. For [Formula: see text] we give three proofs of the existence and a proof of the uniqueness of the solution. Brouwer's theorem and inequalities involving convex functions are essential tools in our proofs.

20 CFR 404.780 - Evidence of “good cause” for exceeding time limits on accepting proof of support or application...

Code of Federal Regulations, 2010 CFR

2010-04-01

... accepting proof of support or application for a lump-sum death payment. (a) When evidence of good cause is... death payment. You may be asked for evidence of good cause for these delays if— (1) You are the insured... limits on accepting proof of support or application for a lump-sum death payment. 404.780 Section 404.780...

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

ERIC Educational Resources Information Center

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…

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

DTIC Science & Technology

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

Intent v. Impact: The Standard of Proof Necessary to Establish a Prima Facie Case of Race Discrimination under 42 U.S.C. Section 1981.

ERIC Educational Resources Information Center

Heiser, Walter

1979-01-01

Considers action's impact and intent as proof; analyzes language, purpose, and legislative history of civil rights statutes; and concludes that the Supreme Court will likely require proof of intent to sustain a prima facie case of discrimination. Available from San Diego Law Review Association, University of San Diego School of Law, San Diego,…

Simple proof that Gaussian attacks are optimal among collective attacks against continuous-variable quantum key distribution with a Gaussian modulation

DOE Office of Scientific and Technical Information (OSTI.GOV)

Leverrier, Anthony; Grangier, Philippe; Laboratoire Charles Fabry, Institut d'Optique, CNRS, University Paris-Sud, Campus Polytechnique, RD 128, F-91127 Palaiseau Cedex

2010-06-15

In this article, we give a simple proof of the fact that the optimal collective attacks against continuous-variable quantum key distribution with a Gaussian modulation are Gaussian attacks. Our proof, which makes use of symmetry properties of the protocol in phase space, is particularly relevant for the finite-key analysis of the protocol and therefore for practical applications.

A microelectromechanical accelerometer fabricated using printed circuit processing techniques

NASA Astrophysics Data System (ADS)

Rogers, J. E.; Ramadoss, R.; Ozmun, P. M.; Dean, R. N.

2008-01-01

A microelectromechanical systems (MEMS) capacitive-type accelerometer fabricated using printed circuit processing techniques is presented. A Kapton polymide film is used as the structural layer for fabricating the MEMS accelerometer. The accelerometer proof mass along with four suspension beams is defined in the Kapton polyimide film. The proof mass is suspended above a Teflon substrate using a spacer. The deflection of the proof mass is detected using a pair of capacitive sensing electrodes. The top electrode of the accelerometer is defined on the top surface of the Kapton film. The bottom electrode is defined in the metallization on the Teflon substrate. The initial gap height is determined by the distance between the bottom electrode and the Kapton film. For an applied external acceleration (normal to the proof mass), the proof mass deflects toward or away from the fixed bottom electrode due to inertial force. This deflection causes either a decrease or increase in the air-gap height thereby either increasing or decreasing the capacitance between the top and the bottom electrodes. An example PCB MEMS accelerometer with a square proof mass of membrane area 6.4 mm × 6.4 mm is reported. The measured resonant frequency is 375 Hz and the Q-factor in air is 0.52.

A False-name-Proof Double Auction Protocol for Arbitrary Evaluation Values

NASA Astrophysics Data System (ADS)

Sakurai, Yuko; Yokoo, Makoto

We develop a new false-name-proof double auction protocol called the Generalized Threshold Price Double auction (GTPD) protocol. False-name-proofness generalizes strategy-proofness by incorporating the possibility of false-name bids, e.g., bids submitted using multiple e-mail addresses. An existing protocol called TPD protocol is false-name-proof but can handle only the cases where marginal utilities of each agent always decrease, while our new GTPD protocol can handle arbitrary evaluation values. When marginal utilities can increase, some bids cannot be divided into a single unit (e.g., an all-or-nothing bid). Due to the existence of such indivisible bids, meeting supply/demand becomes difficult. Furthermore, a seller/buyer can submit a false-name-bid by pretending to be a potential buyer/seller to manipulate allocations and payments. In the GTPD protocol, the auctioneer is required to absorb the supply-demand imbalance up to a given upper-bound. Also, the GTPD incorporate a new false-name-proof one-sided auction protocol that is guaranteed to sell/buy a certain number of units. Simulation results show that when the threshold price is set appropriately, this protocol can obtain a good social surplus, and the number of absorbed units is much smaller than the given upper-bound.

27 CFR 30.63 - Table 3, for determining the number of proof gallons from the weight and proof of spirituous liquor.

Code of Federal Regulations, 2014 CFR

2014-04-01

... decimal point one place to the left; that for 8 pounds from the column 800 pounds by moving the decimal point two places to the left. Example. A package of spirits at 86 proof weighed 3211/2 pounds net. We... to the left; that for 1 pound from the column 100 pounds by moving the decimal point two places to...

27 CFR 30.63 - Table 3, for determining the number of proof gallons from the weight and proof of spirituous liquor.

Code of Federal Regulations, 2013 CFR

2013-04-01

... decimal point one place to the left; that for 8 pounds from the column 800 pounds by moving the decimal point two places to the left. Example. A package of spirits at 86 proof weighed 3211/2 pounds net. We... to the left; that for 1 pound from the column 100 pounds by moving the decimal point two places to...

27 CFR 30.63 - Table 3, for determining the number of proof gallons from the weight and proof of spirituous liquor.

Code of Federal Regulations, 2011 CFR

2011-04-01

... decimal point one place to the left; that for 8 pounds from the column 800 pounds by moving the decimal point two places to the left. Example. A package of spirits at 86 proof weighed 3211/2 pounds net. We... to the left; that for 1 pound from the column 100 pounds by moving the decimal point two places to...

27 CFR 30.63 - Table 3, for determining the number of proof gallons from the weight and proof of spirituous liquor.

Code of Federal Regulations, 2012 CFR

2012-04-01

... decimal point one place to the left; that for 8 pounds from the column 800 pounds by moving the decimal point two places to the left. Example. A package of spirits at 86 proof weighed 3211/2 pounds net. We... to the left; that for 1 pound from the column 100 pounds by moving the decimal point two places to...

27 CFR 30.63 - Table 3, for determining the number of proof gallons from the weight and proof of spirituous liquor.

Code of Federal Regulations, 2010 CFR

2010-04-01

... decimal point one place to the left; that for 8 pounds from the column 800 pounds by moving the decimal point two places to the left. Example. A package of spirits at 86 proof weighed 3211/2 pounds net. We... to the left; that for 1 pound from the column 100 pounds by moving the decimal point two places to...

Research on Quantum Algorithms at the Institute for Quantum Information

DTIC Science & Technology

2009-10-17

accuracy threshold theorem for the one-way quantum computer. Their proof is based on a novel scheme, in which a noisy cluster state in three spatial...detected. The proof applies to independent stochastic noise but (in contrast to proofs of the quantum accuracy threshold theorem based on concatenated...proved quantum threshold theorems for long-range correlated non-Markovian noise, for leakage faults, for the one-way quantum computer, for postselected

Proof test criteria for thin-walled 2219 aluminum pressure vessels. Volume 1: Program summary and data analysis

NASA Technical Reports Server (NTRS)

Finger, R. W.

1976-01-01

This experimental program was undertaken to investigate the crack growth behavior of deep surface flaws in 2219 aluminum. The program included tests of uniaxially loaded surface flaw and center crack panels at temperatures ranging from 20K (-423 F) to ambient. The tests were conducted on both the base metal and as-welded weld metal material. The program was designed to provide data on the mechanisms of failure by ligament penetration, and the residual cyclic life, after proof-testing, of a vessel which has been subjected to incipient penetration by the proof test. The results were compared and analyzed with previously developed data to develop guidelines for the proof testing of thin walled 2219 pressure vessels.

Wireless Sensors Grouping Proofs for Medical Care and Ambient Assisted-Living Deployment

PubMed Central

Trček, Denis

2016-01-01

Internet of Things (IoT) devices are rapidly penetrating e-health and assisted living domains, and an increasing proportion among them goes on the account of computationally-weak devices, where security and privacy provisioning alone are demanding tasks, not to mention grouping proofs. This paper, therefore, gives an extensive analysis of such proofs and states lessons learnt to avoid possible pitfalls in future designs. It sticks with prudent engineering techniques in this field and deploys in a novel way the so called non-deterministic principle to provide not only grouping proofs, but (among other) also privacy. The developed solution is analyzed by means of a tangible metric and it is shown to be lightweight, and formally for security. PMID:26729131

US NDC Modernization: Service Oriented Architecture Proof of Concept

DOE Office of Scientific and Technical Information (OSTI.GOV)

Hamlet, Benjamin R.; Encarnacao, Andre Villanova; Jackson, Keilan R.

2014-12-01

This report is a progress update on the US NDC Modernization Service Oriented Architecture (SOA) study describing results from a proof of concept project completed from May through September 2013. Goals for this proof of concept are 1) gain experience configuring, using, and running an Enterprise Service Bus (ESB), 2) understand the implications of wrapping existing software in standardized interfaces for use as web services, and 3) gather performance metrics for a notional seismic event monitoring pipeline implemented using services with various data access and communication patterns. The proof of concept is a follow on to a previous SOA performancemore » study. Work was performed by four undergraduate summer student interns under the guidance of Sandia staff.« less

Wireless Sensors Grouping Proofs for Medical Care and Ambient Assisted-Living Deployment.

PubMed

Trček, Denis

2016-01-02

Internet of Things (IoT) devices are rapidly penetrating e-health and assisted living domains, and an increasing proportion among them goes on the account of computationally-weak devices, where security and privacy provisioning alone are demanding tasks, not to mention grouping proofs. This paper, therefore, gives an extensive analysis of such proofs and states lessons learnt to avoid possible pitfalls in future designs. It sticks with prudent engineering techniques in this field and deploys in a novel way the so called non-deterministic principle to provide not only grouping proofs, but (among other) also privacy. The developed solution is analyzed by means of a tangible metric and it is shown to be lightweight, and formally for security.

The Development of Proofs in Analytical Mathematics for Undergraduate Students

NASA Astrophysics Data System (ADS)

Ali, Maselan; Sufahani, Suliadi; Hasim, Nurnazifa; Saifullah Rusiman, Mohd; Roslan, Rozaini; Mohamad, Mahathir; Khalid, Kamil

2018-04-01

Proofs in analytical mathematics are essential parts of mathematics, difficult to learn because its underlying concepts are not visible. This research consists of problems involving logic and proofs. In this study, a short overview was provided on how proofs in analytical mathematics were used by university students. From the results obtained, excellent students obtained better scores compared to average and poor students. The research instruments used in this study consisted of two parts: test and interview. In this way, analysis of students’ actual performances can be obtained. The result of this study showed that the less able students have fragile conceptual and cognitive linkages but the more able students use their strong conceptual linkages to produce effective solutions

UV LED charge control of an electrically isolated proof mass in a Gravitational Reference Sensor configuration at 255 nm

NASA Astrophysics Data System (ADS)

Balakrishnan, Karthik; Sun, Ke-Xun

2012-07-01

Precise control over the potential of an electrically isolated proof mass is necessary for the operation of devices such as a Gravitational Reference Sensor (GRS) and satellite missions such as LISA. We show that AlGaN UV LEDs operating at 255 nm are an effective substitute for Mercury vapor lamps used in previous missions because of their ability to withstand space qualification levels of vibration and thermal cycling. After 27 thermal and thermal vacuum cycles and 9 minutes of 14.07 g RMS vibration, there is less than 3% change in current draw, less than 15% change in optical power, and no change in spectral peak or FWHM (full width at half maximum). We also demonstrate UV LED stimulated photoemission from a wide variety of thin film carbide proof mass coating candidates (SiC, Mo2C, TaC, TiC, ZrC) that were applied using electron beam evaporation on an Aluminum 6061-T6 substrate. All tested carbide films have measured quantum efficiencies of 3.8-6.8*10^-7 and reflectivities of 0.11-0.15, which compare favorably with the properties of previously used gold films. We demonstrate the ability to control proof mass potential on an 89 mm diameter spherical proof mass over a 20 mm gap in a GRS-like configuration. Proof mass potential was measured via a non-contact DC probe, which would allow control without introducing dynamic forcing of the spacecraft. Finally we provide a look ahead to an upcoming technology demonstration mission of UV LEDs and future applications toward charge control of electrically isolated proof masses.

Robust Soft Textile Transfer Case for Contaminated Materials

DTIC Science & Technology

2017-08-28

least thirty-six pounds per square inch; remain leak -proof after a thirty foot drop when filled with water to at least a ninety-eight percent...shipping standards for use require a leak -proof seal without an allowance for pressure relief. While the container would likely never need to be re...after the insertion of the contents; be puncture Attorney Docket No. 300153 3 of 17 resistant; be leak -proof at a hydrostatic pressure of at

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

ERIC Educational Resources Information Center

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…

Study of Solid State Drives performance in PROOF distributed analysis system

NASA Astrophysics Data System (ADS)

Panitkin, S. Y.; Ernst, M.; Petkus, R.; Rind, O.; Wenaus, T.

2010-04-01

Solid State Drives (SSD) is a promising storage technology for High Energy Physics parallel analysis farms. Its combination of low random access time and relatively high read speed is very well suited for situations where multiple jobs concurrently access data located on the same drive. It also has lower energy consumption and higher vibration tolerance than Hard Disk Drive (HDD) which makes it an attractive choice in many applications raging from personal laptops to large analysis farms. The Parallel ROOT Facility - PROOF is a distributed analysis system which allows to exploit inherent event level parallelism of high energy physics data. PROOF is especially efficient together with distributed local storage systems like Xrootd, when data are distributed over computing nodes. In such an architecture the local disk subsystem I/O performance becomes a critical factor, especially when computing nodes use multi-core CPUs. We will discuss our experience with SSDs in PROOF environment. We will compare performance of HDD with SSD in I/O intensive analysis scenarios. In particular we will discuss PROOF system performance scaling with a number of simultaneously running analysis jobs.

Microelectromechanical accelerometer with resonance-cancelling control circuit including an idle state

DOEpatents

Chu, Dahlon D.; Thelen, Jr., Donald C.; Campbell, David V.

2001-01-01

A digital feedback control circuit is disclosed for use in an accelerometer (e.g. a microelectromechanical accelerometer). The digital feedback control circuit, which periodically re-centers a proof mass in response to a sensed acceleration, is based on a sigma-delta (.SIGMA..DELTA.) configuration that includes a notch filter (e.g. a digital switched-capacitor filter) for rejecting signals due to mechanical resonances of the proof mass and further includes a comparator (e.g. a three-level comparator). The comparator generates one of three possible feedback states, with two of the feedback states acting to re-center the proof mass when that is needed, and with a third feedback state being an "idle" state which does not act to move the proof mass when no re-centering is needed. Additionally, the digital feedback control system includes an auto-zero trim capability for calibration of the accelerometer for accurate sensing of acceleration. The digital feedback control circuit can be fabricated using complementary metal-oxide semiconductor (CMOS) technology, bi-CMOS technology or bipolar technology and used in single- and dual-proof-mass accelerometers.

Lunar exploration rover program developments

NASA Technical Reports Server (NTRS)

Klarer, P. R.

1994-01-01

The Robotic All Terrain Lunar Exploration Rover (RATLER) design concept began at Sandia National Laboratories in late 1991 with a series of small, proof-of-principle, working scale models. The models proved the viability of the concept for high mobility through mechanical simplicity, and eventually received internal funding at Sandia National Laboratories for full scale, proof-of-concept prototype development. Whereas the proof-of-principle models demonstrated the mechanical design's capabilities for mobility, the full scale proof-of-concept design currently under development is intended to support field operations for experiments in telerobotics, autonomous robotic operations, telerobotic field geology, and advanced man-machine interface concepts. The development program's current status is described, including an outline of the program's work over the past year, recent accomplishments, and plans for follow-on development work.

Photographic copy of 10” x 15”, black and white, proof ...

Library of Congress Historic Buildings Survey, Historic Engineering Record, Historic Landscapes Survey

Photographic copy of 10” x 15”, black and white, proof photograph. Located loose in oversized box at the National Museum of American History, Smithsonian Institution, Archives Center, Work and Industry Division, Washington, D.C. Photographer, The Billings Studio. PROOF PHOTOGRAPH OF COMPLETED BRIDGE TAKEN FROM WEST BANK LEVEE LOOKING NORTH DOWN RIVER TOWARD EAST BANK. - Huey P. Long Bridge, Spanning Mississippi River approximately midway between nine & twelve mile points upstream from & west of New Orleans, Jefferson, Jefferson Parish, LA

A proof of the conjecture on the twin primes

DOE Office of Scientific and Technical Information (OSTI.GOV)

Zuo-ling, Zhou

2016-06-08

In this short note, we have proved the conjecture on twin primes using some thoughts of the set theory. Firstly, using the original sieve method and a new notation(concept)introduced by myself, the conjecture on twin primes is summed up as an elementary successive limit, afterwards we form a subsequence of positive integers,and using it,we prove that the successive limits are commutative and complete the proof of the conjecture on twin primes We also give a more straightforward proof of the conjecture.

Color aspects of variable data proofing

NASA Astrophysics Data System (ADS)

Beretta, Giordano B.

2005-01-01

The Internet in combination with digital presses has allowed the geographical distribution of manufacturing printed materials. An increasing number of printed pieces is customized for the recipient; when each printed piece is different, conventional proofing fails, because it is impossible to proof the entire print job. One frequent problem in automatically generated pieces is the readability of one page element on top of another element; the color combination can be unreadable or clash. I propose simple algorithms to automatically detect and correct color discriminability problems in variable data printing.

Color aspects of variable data proofing

NASA Astrophysics Data System (ADS)

Beretta, Giordano B.

2004-12-01

The Internet in combination with digital presses has allowed the geographical distribution of manufacturing printed materials. An increasing number of printed pieces is customized for the recipient; when each printed piece is different, conventional proofing fails, because it is impossible to proof the entire print job. One frequent problem in automatically generated pieces is the readability of one page element on top of another element; the color combination can be unreadable or clash. I propose simple algorithms to automatically detect and correct color discriminability problems in variable data printing.

A proof of the theorem regarding the distribution of lift over the span for minimum induced drag

NASA Technical Reports Server (NTRS)

Durand, W F

1931-01-01

The proof of the theorem that the elliptical distribution of lift over the span is that which will give rise to the minimum induced drag has been given in a variety of ways, generally speaking too difficult to be readily followed by the graduate of the average good technical school of the present day. In the form of proof this report makes an effort to bring the matter more readily within the grasp of this class of readers.

Mechanical verification of a schematic Byzantine clock synchronization algorithm

NASA Technical Reports Server (NTRS)

Shankar, Natarajan

1991-01-01

Schneider generalizes a number of protocols for Byzantine fault tolerant clock synchronization and presents a uniform proof for their correctness. The authors present a machine checked proof of this schematic protocol that revises some of the details in Schneider's original analysis. The verification was carried out with the EHDM system developed at the SRI Computer Science Laboratory. The mechanically checked proofs include the verification that the egocentric mean function used in Lamport and Melliar-Smith's Interactive Convergence Algorithm satisfies the requirements of Schneider's protocol.

Another short and elementary proof of strong subadditivity of quantum entropy

NASA Astrophysics Data System (ADS)

Ruskai, Mary Beth

2007-08-01

A short and elementary proof of the joint convexity of relative entropy is presented, using nothing beyond linear algebra. The key ingredients are an easily verified integral representation and the strategy used to prove the Cauchy-Schwarz inequality in elementary courses. Several consequences are proved in a way which allows an elementary proof of strong subadditivity in a few more lines. Some expository material on Schwarz inequalities for operators and the Holevo bound for partial measurements is also included.

27 CFR 19.768 - Gauge record.

Code of Federal Regulations, 2010 CFR

2010-04-01

... or warehouseman; and (j) Gauge data: (1) Package identification, tank number, volumetric or weight... whiskey; (4) Proof gallons per filled package; and (5) Total proof gallons of spirits or wine gallons of...

Quantum Locality?

DOE Office of Scientific and Technical Information (OSTI.GOV)

Stapp, Henry

Robert Griffiths has recently addressed, within the framework of a ‘consistent quantum theory’ (CQT) that he has developed, the issue of whether, as is often claimed, quantum mechanics entails a need for faster-than-light transfers of information over long distances. He argues, on the basis of his examination of certain arguments that claim to demonstrate the existence of such nonlocal influences, that such influences do not exist. However, his examination was restricted mainly to hidden-variable-based arguments that include in their premises some essentially classical-physics-type assumptions that are fundamentally incompatible with the precepts of quantum physics. One cannot logically prove properties ofmore » a system by attributing to the system properties alien to that system. Hence Griffiths’ rejection of hidden-variable-based proofs is logically warranted. Griffiths mentions the existence of a certain alternative proof that does not involve hidden variables, and that uses only macroscopically described observable properties. He notes that he had examined in his book proofs of this general kind, and concluded that they provide no evidence for nonlocal influences. But he did not examine the particular proof that he cites. An examination of that particular proof by the method specified by his ‘consistent quantum theory’ shows that the cited proof is valid within that restrictive framework. This necessary existence, within the ‘consistent’ framework, of long range essentially instantaneous influences refutes the claim made by Griffiths that his ‘consistent’ framework is superior to the orthodox quantum theory of von Neumann because it does not entail instantaneous influences. An added section responds to Griffiths’ reply, which cites a litany of ambiguities that seem to restrict, devastatingly, the scope of his CQT formalism, apparently to buttress his claim that my use of that formalism to validate the nonlocality theorem is flawed. But the vagaries that he cites do not upset the proof in question. It is show here in detail why the precise statement of this theorem justifies the specified application of CQT. It is also shown, in response to his challenge, why a putative proof of locality that he has proposed is not valid.« less

5 CFR 890.1024 - Standard and burden of proof for deciding contests.

Code of Federal Regulations, 2010 CFR

2010-01-01

...) CIVIL SERVICE REGULATIONS (CONTINUED) FEDERAL EMPLOYEES HEALTH BENEFITS PROGRAM Administrative Sanctions Imposed Against Health Care Providers Permissive Debarments § 890.1024 Standard and burden of proof for...

46 CFR 28.845 - General requirements for electrical systems.

Code of Federal Regulations, 2011 CFR

2011-10-01

... liquids. If electrical equipment, such as lighting, is necessary in these spaces, it must be explosion-proof or intrinsically safe. (d) Explosion-proof and intrinsically safe equipment must meet the...

46 CFR 28.845 - General requirements for electrical systems.

Code of Federal Regulations, 2010 CFR

2010-10-01

... liquids. If electrical equipment, such as lighting, is necessary in these spaces, it must be explosion-proof or intrinsically safe. (d) Explosion-proof and intrinsically safe equipment must meet the...

44 CFR 68.10 - Burden of proof.

Code of Federal Regulations, 2013 CFR

2013-10-01

... HOMELAND SECURITY INSURANCE AND HAZARD MITIGATION National Flood Insurance Program ADMINISTRATIVE HEARING PROCEDURES § 68.10 Burden of proof. The burden shall be on appellant(s) to prove that the flood elevation...

44 CFR 68.10 - Burden of proof.

Code of Federal Regulations, 2011 CFR

2011-10-01

... HOMELAND SECURITY INSURANCE AND HAZARD MITIGATION National Flood Insurance Program ADMINISTRATIVE HEARING PROCEDURES § 68.10 Burden of proof. The burden shall be on appellant(s) to prove that the flood elevation...

44 CFR 68.10 - Burden of proof.

Code of Federal Regulations, 2010 CFR

2010-10-01

... HOMELAND SECURITY INSURANCE AND HAZARD MITIGATION National Flood Insurance Program ADMINISTRATIVE HEARING PROCEDURES § 68.10 Burden of proof. The burden shall be on appellant(s) to prove that the flood elevation...

27 CFR 19.618 - Gauge record.

Code of Federal Regulations, 2013 CFR

2013-04-01

... plant number of the producer or warehouseman; and (j) The following gauge data— (1) Package... whiskey; (4) Proof gallons per filled package; and (5) Total proof gallons of spirits or wine gallons of...

27 CFR 19.618 - Gauge record.

Code of Federal Regulations, 2014 CFR

2014-04-01

... plant number of the producer or warehouseman; and (j) The following gauge data— (1) Package... whiskey; (4) Proof gallons per filled package; and (5) Total proof gallons of spirits or wine gallons of...

27 CFR 19.618 - Gauge record.

Code of Federal Regulations, 2011 CFR

2011-04-01

... plant number of the producer or warehouseman; and (j) The following gauge data— (1) Package... whiskey; (4) Proof gallons per filled package; and (5) Total proof gallons of spirits or wine gallons of...

27 CFR 19.618 - Gauge record.

Code of Federal Regulations, 2012 CFR

2012-04-01

... plant number of the producer or warehouseman; and (j) The following gauge data— (1) Package... whiskey; (4) Proof gallons per filled package; and (5) Total proof gallons of spirits or wine gallons of...

27 CFR 30.32 - Determination of proof obscuration.

Code of Federal Regulations, 2010 CFR

2010-04-01

... added to the temperature corrected hydrometer reading will give the true proof. (c) Distillation method... use of a precision hydrometer and thermometer in accordance with the provisions of § 13.23 to the...

29 CFR 1919.29 - Limitations on safe working loads and proof loads.

Code of Federal Regulations, 2013 CFR

2013-07-01

... ADMINISTRATION, DEPARTMENT OF LABOR (CONTINUED) GEAR CERTIFICATION Certification of Vessels: Tests and Proof... pertinent limitations based on stability and/or on structural competence at particular radii. Safe working...

29 CFR 1919.29 - Limitations on safe working loads and proof loads.

Code of Federal Regulations, 2012 CFR

2012-07-01

... ADMINISTRATION, DEPARTMENT OF LABOR (CONTINUED) GEAR CERTIFICATION Certification of Vessels: Tests and Proof... pertinent limitations based on stability and/or on structural competence at particular radii. Safe working...

29 CFR 1919.29 - Limitations on safe working loads and proof loads.

Code of Federal Regulations, 2011 CFR

2011-07-01

... ADMINISTRATION, DEPARTMENT OF LABOR (CONTINUED) GEAR CERTIFICATION Certification of Vessels: Tests and Proof... pertinent limitations based on stability and/or on structural competence at particular radii. Safe working...

29 CFR 1919.29 - Limitations on safe working loads and proof loads.

Code of Federal Regulations, 2010 CFR

2010-07-01

... ADMINISTRATION, DEPARTMENT OF LABOR (CONTINUED) GEAR CERTIFICATION Certification of Vessels: Tests and Proof... pertinent limitations based on stability and/or on structural competence at particular radii. Safe working...

29 CFR 1919.29 - Limitations on safe working loads and proof loads.

Code of Federal Regulations, 2014 CFR

2014-07-01

... ADMINISTRATION, DEPARTMENT OF LABOR (CONTINUED) GEAR CERTIFICATION Certification of Vessels: Tests and Proof... pertinent limitations based on stability and/or on structural competence at particular radii. Safe working...

46 CFR 183.530 - Hazardous areas.

Code of Federal Regulations, 2010 CFR

2010-10-01

... equipment in spaces containing machinery powered by, or fuel tanks for, gasoline or other fuels having a... flammable liquids must be explosion-proof or be part of an intrinsically safe system. (c) Explosion-proof...

46 CFR 183.530 - Hazardous areas.

Code of Federal Regulations, 2014 CFR

2014-10-01

... equipment in spaces containing machinery powered by, or fuel tanks for, gasoline or other fuels having a... flammable liquids must be explosion-proof or be part of an intrinsically safe system. (c) Explosion-proof...

46 CFR 183.530 - Hazardous areas.

Code of Federal Regulations, 2013 CFR

2013-10-01

... equipment in spaces containing machinery powered by, or fuel tanks for, gasoline or other fuels having a... flammable liquids must be explosion-proof or be part of an intrinsically safe system. (c) Explosion-proof...

46 CFR 183.530 - Hazardous areas.

Code of Federal Regulations, 2012 CFR

2012-10-01

... equipment in spaces containing machinery powered by, or fuel tanks for, gasoline or other fuels having a... flammable liquids must be explosion-proof or be part of an intrinsically safe system. (c) Explosion-proof...

1. Bombproof barracks, southwest corner from atop curtain wall, looking ...

Library of Congress Historic Buildings Survey, Historic Engineering Record, Historic Landscapes Survey

1. Bomb-proof barracks, southwest corner from atop curtain wall, looking easterly. Two lightning rods can be seen in background. - Fort Hamilton, Bomb-Proof Barracks, Rose Island, Newport, Newport County, RI

A physical zero-knowledge object-comparison system for nuclear warhead verification

PubMed Central

Philippe, Sébastien; Goldston, Robert J.; Glaser, Alexander; d'Errico, Francesco

2016-01-01

Zero-knowledge proofs are mathematical cryptographic methods to demonstrate the validity of a claim while providing no further information beyond the claim itself. The possibility of using such proofs to process classified and other sensitive physical data has attracted attention, especially in the field of nuclear arms control. Here we demonstrate a non-electronic fast neutron differential radiography technique using superheated emulsion detectors that can confirm that two objects are identical without revealing their geometry or composition. Such a technique could form the basis of a verification system that could confirm the authenticity of nuclear weapons without sharing any secret design information. More broadly, by demonstrating a physical zero-knowledge proof that can compare physical properties of objects, this experiment opens the door to developing other such secure proof-systems for other applications. PMID:27649477

A physical zero-knowledge object-comparison system for nuclear warhead verification.

PubMed

Philippe, Sébastien; Goldston, Robert J; Glaser, Alexander; d'Errico, Francesco

2016-09-20

Zero-knowledge proofs are mathematical cryptographic methods to demonstrate the validity of a claim while providing no further information beyond the claim itself. The possibility of using such proofs to process classified and other sensitive physical data has attracted attention, especially in the field of nuclear arms control. Here we demonstrate a non-electronic fast neutron differential radiography technique using superheated emulsion detectors that can confirm that two objects are identical without revealing their geometry or composition. Such a technique could form the basis of a verification system that could confirm the authenticity of nuclear weapons without sharing any secret design information. More broadly, by demonstrating a physical zero-knowledge proof that can compare physical properties of objects, this experiment opens the door to developing other such secure proof-systems for other applications.

A physical zero-knowledge object-comparison system for nuclear warhead verification

NASA Astrophysics Data System (ADS)

Philippe, Sébastien; Goldston, Robert J.; Glaser, Alexander; D'Errico, Francesco

2016-09-01

Zero-knowledge proofs are mathematical cryptographic methods to demonstrate the validity of a claim while providing no further information beyond the claim itself. The possibility of using such proofs to process classified and other sensitive physical data has attracted attention, especially in the field of nuclear arms control. Here we demonstrate a non-electronic fast neutron differential radiography technique using superheated emulsion detectors that can confirm that two objects are identical without revealing their geometry or composition. Such a technique could form the basis of a verification system that could confirm the authenticity of nuclear weapons without sharing any secret design information. More broadly, by demonstrating a physical zero-knowledge proof that can compare physical properties of objects, this experiment opens the door to developing other such secure proof-systems for other applications.

A physical zero-knowledge object-comparison system for nuclear warhead verification

DOE PAGES

Philippe, Sébastien; Goldston, Robert J.; Glaser, Alexander; ...

2016-09-20

Zero-knowledge proofs are mathematical cryptographic methods to demonstrate the validity of a claim while providing no further information beyond the claim itself. The possibility of using such proofs to process classified and other sensitive physical data has attracted attention, especially in the field of nuclear arms control. Here we demonstrate a non-electronic fast neutron differential radiography technique using superheated emulsion detectors that can confirm that two objects are identical without revealing their geometry or composition. Such a technique could form the basis of a verification system that could confirm the authenticity of nuclear weapons without sharing any secret design information.more » More broadly, by demonstrating a physical zero-knowledge proof that can compare physical properties of objects, this experiment opens the door to developing other such secure proof-systems for other applications.« less

A physical zero-knowledge object-comparison system for nuclear warhead verification

DOE Office of Scientific and Technical Information (OSTI.GOV)

Philippe, Sébastien; Goldston, Robert J.; Glaser, Alexander

Zero-knowledge proofs are mathematical cryptographic methods to demonstrate the validity of a claim while providing no further information beyond the claim itself. The possibility of using such proofs to process classified and other sensitive physical data has attracted attention, especially in the field of nuclear arms control. Here we demonstrate a non-electronic fast neutron differential radiography technique using superheated emulsion detectors that can confirm that two objects are identical without revealing their geometry or composition. Such a technique could form the basis of a verification system that could confirm the authenticity of nuclear weapons without sharing any secret design information.more » More broadly, by demonstrating a physical zero-knowledge proof that can compare physical properties of objects, this experiment opens the door to developing other such secure proof-systems for other applications.« less

Meaning of counterfactual statements in quantum physics

NASA Astrophysics Data System (ADS)

Stapp, Henry P.

1998-10-01

David Mermin suggests that my recent proof pertaining to quantum nonlocality is undermined by an essential ambiguity pertaining to the meaning of counterfactual statements in quantum physics. The ambiguity he cites arises from his imposition of a certain criterion for the meaningfulness of such counterfactual statements. That criterion conflates the meaning of a counterfactual statement with the details of a proof of its validity in such a way as to make the meaning of such a statement dependent upon the context in which it occurs. That dependence violates the normal demand in logic that the meaning of a statement be defined by the words in the statement itself, not by the context in which the statement occurs. My proof conforms to that normal requirement. I describe the context-independent meaning within my proof of the counterfactual statements in question.

On mathematicians' different standards when evaluating elementary proofs.

PubMed

Inglis, Matthew; Mejia-Ramos, Juan Pablo; Weber, Keith; Alcock, Lara

2013-04-01

In this article, we report a study in which 109 research-active mathematicians were asked to judge the validity of a purported proof in undergraduate calculus. Significant results from our study were as follows: (a) there was substantial disagreement among mathematicians regarding whether the argument was a valid proof, (b) applied mathematicians were more likely than pure mathematicians to judge the argument valid, (c) participants who judged the argument invalid were more confident in their judgments than those who judged it valid, and (d) participants who judged the argument valid usually did not change their judgment when presented with a reason raised by other mathematicians for why the proof should be judged invalid. These findings suggest that, contrary to some claims in the literature, there is not a single standard of validity among contemporary mathematicians. Copyright © 2013 Cognitive Science Society, Inc.

Frameworks for Proof-of-Concept Clinical Trials of Interventions That Target Fundamental Aging Processes

PubMed Central

Justice, Jamie; Miller, Jordan D.; Newman, John C.; Hashmi, Shahrukh K.; Halter, Jeffrey; Austad, Steve N.; Barzilai, Nir

2016-01-01

Therapies targeted at fundamental processes of aging may hold great promise for enhancing the health of a wide population by delaying or preventing a range of age-related diseases and conditions—a concept dubbed the “geroscience hypothesis.” Early, proof-of-concept clinical trials will be a key step in the translation of therapies emerging from model organism and preclinical studies into clinical practice. This article summarizes the outcomes of an international meeting partly funded through the NIH R24 Geroscience Network, whose purpose was to generate concepts and frameworks for early, proof-of-concept clinical trials for therapeutic interventions that target fundamental processes of aging. The goals of proof-of-concept trials include generating preliminary signals of efficacy in an aging-related disease or outcome that will reduce the risk of conducting larger trials, contributing data and biological samples to support larger-scale research by strategic networks, and furthering a dialogue with regulatory agencies on appropriate registration indications. We describe three frameworks for proof-of-concept trials that target age-related chronic diseases, geriatric syndromes, or resilience to stressors. We propose strategic infrastructure and shared resources that could accelerate development of therapies that target fundamental aging processes. PMID:27535966

What is Proof of Concept Research and how does it Generate Epistemic and Ethical Categories for Future Scientific Practice?

PubMed

Kendig, Catherine Elizabeth

2016-06-01

"Proof of concept" is a phrase frequently used in descriptions of research sought in program announcements, in experimental studies, and in the marketing of new technologies. It is often coupled with either a short definition or none at all, its meaning assumed to be fully understood. This is problematic. As a phrase with potential implications for research and technology, its assumed meaning requires some analysis to avoid it becoming a descriptive category that refers to all things scientifically exciting. I provide a short analysis of proof of concept research and offer an example of it within synthetic biology. I suggest that not only are there activities that circumscribe new epistemological categories but there are also associated normative ethical categories or principles linked to the research. I examine these and provide an outline for an alternative ethical account to describe these activities that I refer to as "extended agency ethics". This view is used to explain how the type of research described as proof of concept also provides an attendant proof of principle that is the result of decision-making that extends across practitioners, their tools, techniques, and the problem solving activities of other research groups.

Security of six-state quantum key distribution protocol with threshold detectors

PubMed Central

Kato, Go; Tamaki, Kiyoshi

2016-01-01

The security of quantum key distribution (QKD) is established by a security proof, and the security proof puts some assumptions on the devices consisting of a QKD system. Among such assumptions, security proofs of the six-state protocol assume the use of photon number resolving (PNR) detector, and as a result the bit error rate threshold for secure key generation for the six-state protocol is higher than that for the BB84 protocol. Unfortunately, however, this type of detector is demanding in terms of technological level compared to the standard threshold detector, and removing the necessity of such a detector enhances the feasibility of the implementation of the six-state protocol. Here, we develop the security proof for the six-state protocol and show that we can use the threshold detector for the six-state protocol. Importantly, the bit error rate threshold for the key generation for the six-state protocol (12.611%) remains almost the same as the one (12.619%) that is derived from the existing security proofs assuming the use of PNR detectors. This clearly demonstrates feasibility of the six-state protocol with practical devices. PMID:27443610

21 CFR 1311.105 - Requirements for obtaining an authentication credential-Individual practitioners.

Code of Federal Regulations, 2010 CFR

2010-04-01

... Office of Technology Strategy/Division of Identity Management to conduct identity proofing that meets the... assurance level or above. (b) The practitioner must submit identity proofing information to the credential...

Analytic Methods in Investigative Geometry.

ERIC Educational Resources Information Center

Dobbs, David E.

2001-01-01

Suggests an alternative proof by analytic methods, which is more accessible than rigorous proof based on Euclid's Elements, in which students need only apply standard methods of trigonometry to the data without introducing new points or lines. (KHR)

43 CFR 4.1384 - Burdens of proof.

Code of Federal Regulations, 2010 CFR

2010-10-01

... Written Decisions Concerning Ownership Or Control Challenges § 4.1384 Burdens of proof. (a) OSM shall have the burden of going forward to present a prima facie case of the validity of the decision. (b) The...

Circular, explosion-proof lamp provides uniform illumination

NASA Technical Reports Server (NTRS)

1966-01-01

Circular explosion-proof fluorescent lamp is fitted around a TV camera lens to provide shadowless illumination with a low radiant heat flux. The lamp is mounted in a transparent acrylic housing sealed with clear silicone rubber.

5. Bombproof barracks, front elevation at southwest end. Doors and ...

Library of Congress Historic Buildings Survey, Historic Engineering Record, Historic Landscapes Survey

5. Bomb-proof barracks, front elevation at southwest end. Doors and windows covered with plywood. Railway and car stop in foreground. - Fort Hamilton, Bomb-Proof Barracks, Rose Island, Newport, Newport County, RI

Calibration Device Designed for proof ring used in SCC Experiment

NASA Astrophysics Data System (ADS)

Hu, X. Y.; Kang, Z. Y.; Yu, Y. L.

2017-11-01

In this paper, a calibration device for proof ring used in SCC (Stress Corrosion Cracking) experiment was designed. A compact size loading device was developed to replace traditional force standard machine or a long screw nut. The deformation of the proof ring was measured by a CCD (Charge-Coupled Device) during the calibration instead of digital caliper or a dial gauge. The calibration device was verified at laboratory that the precision of force loading is ±0.1% and the precision of deformation measurement is ±0.002mm.

Single-Cycle Versus Multicycle Proof Testing

NASA Technical Reports Server (NTRS)

Hudak, S. J., Jr.; Mcclung, R. C.; Bartlett, M. L.; Fitzgerald, J. H.; Russell, D. A.

1992-01-01

Report compares single-cycle with multiple-cycle mechanical-stress tests of parts under mechanical stresses. Objective of proof testing: to screen out gross manufacturing or material deficiencies and provide additional assurance of quality. Report concludes that changes in distribution of crack sizes during multicycle proof testing depend on initial distribution, number of cycles, relationship between resistance of material and elastic/plastic fracture-mechanics parameter, relationship between load control and displacement control, and magnitude of applied load or displacement. Whether single-cycle or multicycle testing used depends on shape, material, and technique of fabrication of components tested.

Convex Optimization Methods for Graphs and Statistical Modeling

DTIC Science & Technology

2011-06-01

of a set obtained by taking nonnegative linear combinations of elements of the set. The cone TC(x) is the set of directions to points in C from the...Proof. The tangent cone at any signed vector x? with respect to the `∞ ball is a rotation of the nonnegative orthant. Thus we only need to compute the...that ξ(B ?) 1−4ξ(B?)µ(A?) < γ in the second inequality. Sec. A.2. Proofs 167 Proof of Proposition 3.4.2 Based on the Perron - Frobenius theorem [82

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

NASA Astrophysics Data System (ADS)

de Cock Buning, Madeleine; de Bruin, Roeland

2017-07-01

Principle 2 of the EPSRC's principles of robotics (AISB workshop on Principles of Robotics, 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 designed; operated as far as is practicable to comply with existing laws and fundamental rights and freedoms, including privacy by design. It will show that some legal questions arising from autonomous intelligent driving technology can be answered by the technology itself.

Determination of Flaw Growth Characteristics of Ti-6Al-4V Sheet in the Solution-Treated and Aged Condition

NASA Technical Reports Server (NTRS)

Hoeppner, David W.; Pettit, Donald E.; Feddersen, Charles E.; Hyler, Walter S.

1968-01-01

The specific experimental investigation undertaken was designed to answer these questions on Ti-6Al-4V in the solution treated and aged condition. The defect growth and fracture characteristics were studied in parent (unwelded) and welded sheet material. The results of the study indicate that cryogenic proof testing will screen smaller size defects than proof testing at ambient conditions. However some unusual crack growth behavior during the proof test simulation suggests that some further study be made of stress and time duration effects.

Chemical Remote Sensing ’Proof of Concept’,

DTIC Science & Technology

1981-03-31

A122 579 CHEMICAL REMOTE SENSING ;PROOF OF CONCEPT’(U) UTAH 1/I \\ STATE UNIV LOGAN ELECTRO-DYNAMICS LAB BARTSCHI ET AL. 31 MAR 81 SCIENTIFC-8...STANDARDS -I963-A AFGL-TR-81-021 2 CHEMICAL REMOTE SENSING "Proof of Concept" B.Y. Bartschi F. P. DelGreco M. Ahmadjian Electro-Dynamics Laboratories...Applications of remote sensing 2 2.2 Program Development 4 -O 3.1 Optical Layout 6 3.2 Block Diagram of Sensor System 7 3.3 Sensor Facility 10 3.4

RIFs: Procedural Issues and Post-Termination Rights.

ERIC Educational Resources Information Center

Phay, Robert E.

1980-01-01

Reviews the major procedural issues that have been litigated when an employee has challenged a layoff. These areas include timely notice, notice of reason, burden of proof, standard of proof, prior hearing, and impartial hearer. (Author/IRT)

Proof of concept test plan.

DOT National Transportation Integrated Search

2008-06-05

This document is the Proof of Concept (POC) Test Plan and procedures that will be used : to verify that hardware and application functionality meet the requirements of the U.S. : Department of Transportation (USDOT) Next Generation 9-1-1 Initiative (...

29 CFR 1919.27 - Unit proof tests-winches, derricks and gear accessory thereto.

Code of Federal Regulations, 2010 CFR

2010-07-01

..., goosenecks, eye plates, eye bolts, or other attachments), shall be tested with a proof load which shall..., a qualified technical office of an accredited gear certification agency, with the recognition that...

Study on hydraulic characteristics of mine dust-proof water supply network

NASA Astrophysics Data System (ADS)

Deng, Quanlong; Jiang, Zhongan; Han, Shuo; Fu, Enqi

2018-01-01

In order to study the hydraulic characteristics of mine dust-proof water supply network and obtain the change rule of water consumption and water pressure, according to the similarity principle and the fluid continuity equation and energy equation, the similarity criterion of mine dust-proof water supply network is deduced, and a similar model of dust-proof water supply network is established based on the prototype of Kailuan Group, the characteristics of hydraulic parameters in water supply network are studied experimentally. The results show that water pressure at each point is a dynamic process, and there is a negative correlation between water pressure and water consumption. With the increase of water consumption, the pressure of water points show a decreasing trend. According to the structure of the pipe network and the location of the water point, the influence degree on the pressure of each point is different.

Meaning of counterfactual statements in quantum physics

DOE Office of Scientific and Technical Information (OSTI.GOV)

Stapp, H.P.

1998-10-01

David Mermin suggests that my recent proof pertaining to quantum nonlocality is undermined by an essential ambiguity pertaining to the meaning of counterfactual statements in quantum physics. The ambiguity he cites arises from his imposition of a certain criterion for the meaningfulness of such counterfactual statements. That criterion conflates the meaning of a counterfactual statement with the details of a proof of its validity in such a way as to make the meaning of such a statement dependent upon the context in which it occurs. That dependence violates the normal demand in logic that the meaning of a statement bemore » defined by the words in the statement itself, not by the context in which the statement occurs. My proof conforms to that normal requirement. I describe the context-independent meaning within my proof of the counterfactual statements in question. {copyright} {ital 1998 American Association of Physics Teachers.}« less

Acoustic emission testing of 12-nickel maraging steel pressure vessels

NASA Technical Reports Server (NTRS)

Dunegan, H. L.

1973-01-01

Acoustic emission data were obtained from three point bend fracture toughness specimens of 12-nickel maraging steel, and two pressure vessels of the same material. One of the pressure vessels contained a prefabricated flaw which was extended and sharpened by fatigue cycling. It is shown that the flawed vessel had similar characteristics to the fracture specimens, thereby allowing estimates to be made of its nearness to failure during a proof test. Both the flawed and unflawed pressure vessel survived the proof pressure and 5 cycles to the working pressure, but it was apparent from the acoustic emission response during the proof cycle and the 5 cycles to the working pressure that the flawed vessel was very near failure. The flawed vessel did not survive a second cycle to the proof pressure before failure due to flaw extension through the wall (causing a leak).

Definition of mutually optimum NDI and proof test criteria for 2219 aluminum pressure vessels. Volume 1: Methods

NASA Technical Reports Server (NTRS)

Schwartzberg, F. R.; King, R. G.; Todd, P. H., Jr.

1979-01-01

The requirements for proof testing and nondestructive inspection of aluminum pressure vessels were discussed. The following conclusions are (1) lack-of-fusion weld defects are sufficiently tight in the as-welded condition to be considered undetectable; (2) proof-level loads are required to fully open lack-of-fusion weld defects; (3) significant crack opening occurs at subproof levels so that an inspection enhancement loading treatment designed to avoid catastrophic failure is feasible; (4) currently used proof levels for 2219 pressure vessels are adequate for postproof inspection; (5) quantification of defect size and location using collimated ultrasonic pitch-catch techniques appears sufficiently feasible for tankage to warrant developmental work; (6) for short-time single-cycle pressure-vessel applications, postproof inspection is desirable; and (7) for long-term multiple-cycle pressure-vessel applications, postproof inspection is essential for life assurance.

Abstract Datatypes in PVS

NASA Technical Reports Server (NTRS)

Owre, Sam; Shankar, Natarajan

1997-01-01

PVS (Prototype Verification System) is a general-purpose environment for developing specifications and proofs. This document deals primarily with the abstract datatype mechanism in PVS which generates theories containing axioms and definitions for a class of recursive datatypes. The concepts underlying the abstract datatype mechanism are illustrated using ordered binary trees as an example. Binary trees are described by a PVS abstract datatype that is parametric in its value type. The type of ordered binary trees is then presented as a subtype of binary trees where the ordering relation is also taken as a parameter. We define the operations of inserting an element into, and searching for an element in an ordered binary tree; the bulk of the report is devoted to PVS proofs of some useful properties of these operations. These proofs illustrate various approaches to proving properties of abstract datatype operations. They also describe the built-in capabilities of the PVS proof checker for simplifying abstract datatype expressions.

Experimental ladder proof of Hardy's nonlocality for high-dimensional quantum systems

NASA Astrophysics Data System (ADS)

Chen, Lixiang; Zhang, Wuhong; Wu, Ziwen; Wang, Jikang; Fickler, Robert; Karimi, Ebrahim

2017-08-01

Recent years have witnessed a rapidly growing interest in high-dimensional quantum entanglement for fundamental studies as well as towards novel applications. Therefore, the ability to verify entanglement between physical qudits, d -dimensional quantum systems, is of crucial importance. To show nonclassicality, Hardy's paradox represents "the best version of Bell's theorem" without using inequalities. However, so far it has only been tested experimentally for bidimensional vector spaces. Here, we formulate a theoretical framework to demonstrate the ladder proof of Hardy's paradox for arbitrary high-dimensional systems. Furthermore, we experimentally demonstrate the ladder proof by taking advantage of the orbital angular momentum of high-dimensionally entangled photon pairs. We perform the ladder proof of Hardy's paradox for dimensions 3 and 4, both with the ladder up to the third step. Our paper paves the way towards a deeper understanding of the nature of high-dimensionally entangled quantum states and may find applications in quantum information science.

Formal Methods Tool Qualification

NASA Technical Reports Server (NTRS)

Wagner, Lucas G.; Cofer, Darren; Slind, Konrad; Tinelli, Cesare; Mebsout, Alain

2017-01-01

Formal methods tools have been shown to be effective at finding defects in safety-critical digital systems including avionics systems. The publication of DO-178C and the accompanying formal methods supplement DO-333 allows applicants to obtain certification credit for the use of formal methods without providing justification for them as an alternative method. This project conducted an extensive study of existing formal methods tools, identifying obstacles to their qualification and proposing mitigations for those obstacles. Further, it interprets the qualification guidance for existing formal methods tools and provides case study examples for open source tools. This project also investigates the feasibility of verifying formal methods tools by generating proof certificates which capture proof of the formal methods tool's claim, which can be checked by an independent, proof certificate checking tool. Finally, the project investigates the feasibility of qualifying this proof certificate checker, in the DO-330 framework, in lieu of qualifying the model checker itself.

Design, Fabrication and Levitation Experiments of a Micromachined Electrostatically Suspended Six-Axis Accelerometer

PubMed Central

Cui, Feng; Liu, Wu; Chen, Wenyuan; Zhang, Weiping; Wu, Xiaosheng

2011-01-01

A micromachined electrostatically suspended six-axis accelerometer, with a square plate as proof mass housed by a top stator and bottom stator, is presented. The device structure and related techniques concerning its operating principles, such as calculation of capacitances and electrostatic forces/moments, detection and levitation control of the proof mass, acceleration measurement, and structural parameters design, are described. Hybrid MEMS manufacturing techniques, including surface micromachining fabrication of thin film electrodes and interconnections, integration fabrication of thick nickel structures about 500 μm using UV-LIGA by successful removal of SU-8 photoresist mold, DRIE of silicon proof mass in thickness of 450 μm, microassembly and solder bonding, were employed to fabricate this prototype microdevice. A levitation experiment system for the fabricated microaccelerometer chip is introduced, and levitation results show that fast initial levitation within 10 ms and stable full suspension of the proof mass have been successfully demonstrated. PMID:22247662

Dynamic Stability and Gravitational Balancing of Multiple Extended Bodies

NASA Technical Reports Server (NTRS)

Quadrelli, Marco

2008-01-01

Feasibility of a non-invasive compensation scheme was analyzed for precise positioning of a massive extended body in free fall using gravitational forces influenced by surrounding source masses in close proximity. The N-body problem of classical mechanics is a paradigm used to gain insight into the physics of the equivalent N-body problem subject to control forces. The analysis addressed how a number of control masses move around the proof mass so that the proof mass position can be accurately and remotely compensated when exogenous disturbances are acting on it, while its sensitivity to gravitational waves remains unaffected. Past methods to correct the dynamics of the proof mass have considered active electrostatic or capacitive methods, but the possibility of stray capacitances on the surfaces of the proof mass have prompted the investigation of other alternatives, such as the method presented in this paper. While more rigorous analyses of the problem should be carried out, the data show that, by means of a combined feedback and feed-forward control approach, the control masses succeeded in driving the proof mass along the specified trajectory, which implies that the proof mass can, in principle, be balanced via gravitational forces only while external perturbations are acting on it. This concept involves the dynamic stability of a group of massive objects interacting gravitationally under active control, and can apply to drag-free control of spacecraft during missions, to successor gravitational wave space borne sensors, or to any application requiring flying objects to be precisely controlled in position and attitude relative to another body via gravitational interactions only.

Proof Pressure Evaluation of Worn Passenger Car Tire Carcasses

DOT National Transportation Integrated Search

1976-11-01

Test work is described that examines the value of hydrostatic proof pressure testing in screening worn tire carcasses before retreading. Results are given from dynamometer wheel tests on a significant sample of retreaded passenger car tires. Each sam...

An Informal History of Formal Proofs: From Vigor to Rigor?

ERIC Educational Resources Information Center

Galda, Klaus

1981-01-01

The history of formal mathematical proofs is sketched out, starting with the Greeks. Included in this document is a chronological guide to mathematics and the world, highlighting major events in the world and important mathematicians in corresponding times. (MP)

49 CFR 1503.639 - Burden of proof.

Code of Federal Regulations, 2011 CFR

2011-10-01

... Transportation Other Regulations Relating to Transportation (Continued) TRANSPORTATION SECURITY ADMINISTRATION, DEPARTMENT OF HOMELAND SECURITY ADMINISTRATIVE AND PROCEDURAL RULES INVESTIGATIVE AND ENFORCEMENT PROCEDURES... affirmative defense, the burden of proof is on the agency. (b) Except as otherwise provided by statute or rule...

33 CFR 20.701 - Standard of proof.

Code of Federal Regulations, 2012 CFR

2012-07-01

... 33 Navigation and Navigable Waters 1 2012-07-01 2012-07-01 false Standard of proof. 20.701 Section 20.701 Navigation and Navigable Waters COAST GUARD, DEPARTMENT OF HOMELAND SECURITY GENERAL RULES OF... affirmative defense by a preponderance of the evidence. ...