Concept Of Proof Research Articles

On Mathematical Proving

Abstract 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.

Upconverting core-shell nanocrystals with high quantum yield under low irradiance: On the role of isotropic and thick shells

Colloidal upconverter nanocrystals (UCNCs) that convert near-infrared photons to higher energies are promising for applications ranging from life sciences to solar energy harvesting. However, practical applications of UCNCs are hindered by their low upconversion quantum yield (UCQY) and the high irradiances necessary to produce relevant upconversion luminescence. Achieving high UCQY under practically relevant irradiance remains a major challenge. The UCQY is severely limited due to non-radiative surface quenching processes. We present a rate equation model for migration of the excitation energy to show that surface quenching does not only affect the lanthanide ions directly at the surface but also many other lanthanide ions quite far away from the surface. The average migration path length is on the order of several nanometers and depends on the doping as well as the irradiance of the excitation. Using Er3+-doped β-NaYF4 UCNCs, we show that very isotropic and thick (∼10 nm) β-NaLuF4 inert shells dramatically reduce the surface-related quenching processes, resulting in much brighter upconversion luminescence at simultaneously considerably lower irradiances. For these UCNCs embedded in poly(methyl methacrylate), we determined an internal UCQY of 2.0% ± 0.2% using an irradiance of only 0.43 ± 0.03 W/cm2 at 1523 nm. Normalized to the irradiance, this UCQY is 120× higher than the highest values of comparable nanomaterials in the literature. Our findings demonstrate the important role of isotropic and thick shells in achieving high UCQY at low irradiances from UCNCs. Additionally, we measured the additional short-circuit current due to upconversion in silicon solar cell devices as a proof of concept and to support our findings determined using optical measurements.

Proof of violation for response time auditing in cloud systems

In this paper we propose to employ the concept of proof of violation (POV) for the response time auditing in the cloud. A POV scheme enables a user or a service provider to produce a precise proof of either the occurrence of the violation of properties or the innocence of the service provider. POV schemes are solutions for obtaining mutual nonrepudiation between users and the service provider in the cloud. To the best of our knowledge, it is the first scheme that can perform response time auditing according to cryptographic evidences without the need of a delivery agent. Experimental results are presented that demonstrate the feasibility of the proposed scheme. Service providers can use the proposed scheme to provide a mutual nonrepudiation guarantee for response time in their service-level agreements.

Transforming Perceptions of Proof: A Four-Part Instructional Sequence

Mathematics teachers are expected to engage their students in critiquing and constructing viable arguments. These classroom expectations are necessary, given that proof is a central mathematical activity. However, mathematics teachers have been provided limited opportunities as learners to construct arguments and critique the reasoning of others, and hence have developed perceptions of proof as an object that must follow a strict format. In this article, we describe a four-part instructional sequence designed to broaden and deepen teachers' perception of the nature of proof. We analyzed participants' reflections on the instructional sequence in order to gain insight into (a) the differences between this instructional sequence and participants' previous proof learning opportunities and (b) the ways this activity was influential in transforming participants' perceptions of proof. Participants' previous learning experiences were focused on memorizing and reproducing textbook or instructor proofs, and our sequence was different because it actively and collaboratively engaged participants in constructing their own arguments, critiquing others' reasoning, and creating criteria for what counts as proof. Participants found these activities transformative as they became more clear about what counts as proof, began to view proof as socially negotiated, and expanded their conception of proof beyond a rigid structure or format.

STUDI PEMAHAMAN BUKTI DAN PEMBUKTIAN DALAM GEOMETRI EUCLID MAHASISWA JURUSAN TADRIS MATEMATIKA IAIN TULUNGAGUNG

One of the problems to be solved in mathematics is a proof. At the college level, proving to be more important than the previous levels. When someone has a hunch about something (theorem), one of the most appropriate way to ensure that something (theorem) is true is by proving mathematically valid (formally). That is, the truth of the theorem is based on logical statements. However, proof of this is a problem when introduced during the learning. Not only the beginning students, final year students, moreover those already graduated are still experiencing difficulties in proving. This study attempts to describe the understanding of the concept of proof in mathematics and describes the ability of students in validating and compiling of proof in mathematics, particularly in Euclidean geometry using qualitative research approach, the type of case studies.

TRACTABLE FALSIFIABILITY

Abstract:We propose to strengthen Popper’s notion of falsifiability by adding the requirement that when an observation is inconsistent with a theory, there must be a ‘short proof’ of this inconsistency. We model the concept of a short proof using tools from computational complexity, and provide some examples of economic theories that are falsifiable in the usual sense but not with this additional requirement. We consider several variants of the definition of ‘short proof’ and several assumptions about the difficulty of computation, and study their different implications on the falsifiability of theories.

Daily Life and Mathematic: Student and Content Constructions of the Concepts of Proposition, Theorem, and Proof

The aim of this study is to explore mathematics teaching department students’ perceptions on the concepts ofproposition, theorem, and proof which are very important for daily life, mathematical literacy and studyingmathematics; the common mathematical content used in constructing these concepts; and whether these constructionsand content construction match each other. A survey model was used for fulfilling the aim. The data was taken from329 first-grade mathematics teaching department students’ examination papers. The students were enrolled to anEducation Faculty of a state university located in the Eastern Anatolia Region of Turkey and the data was collected inthe first semesters of academic years 2009-2010, 2010-2011, 2011-2012, 2012–2013 and 2013–2014. The numericaldistribution of the participants across years was, respectively, 82, 46, 52, 42 and 107. The data was descriptivelyanalysed. It was found out that the students better structured the concept of proposition (when compared to theconcepts of proof and theorem) in accordance with the content construction of concepts and the mathematicalexpressions used in construction of the concepts of theorem and proof by the students were far away from themathematical expressions used in the content of these concepts.

Hydrogen-bond-mediated in situ fabrication of AgNPs/agar/PAN electrospun nanofibers as reproducible SERS substrates.

Reproducibility in surface enhanced Raman scattering (SERS) measurements is a challenge. This work developed a facile way to make highly dispersed uniform silver nanoparticles (AgNPs) loaded in the agar/polyacrylonitrile (PAN) nanofibers by the coupling the electrospinning technology from metal complex-containing polymer solution and in situ photoreductive technique. Agar, as hydrophilic component, was introduced into the electrospinning solution considering that its abundant hydroxyl group sites could greatly improve the contents of silver ions in the polymers because of the rich silver ion chelated with the hydroxyl group, whereas hydrophilic agar was integrated with hydrophobic PAN by -OH···N≡C- hydrogen bonds as a bridge. Meanwhile, the in situ photoreductive reaction was made under different light irradiations such as desk lamp, 365 nm UV-lamp, and 254 nm UV-lamp. High yield of stable AgNPs with highly uniform and dispersion are available in the agar/PAN nanofibers after the in situ photoreductive reaction, supplying the possibility of reproducible SERS signals. To identify that concept of proof, a facile approach for the determination of malachite green (MG) in three environmental practical samples was demonstrated by using the composite nanofibrous material irradiated by 365 nm UV-lamp, giving the minimum detection concentration of MG as low as 0.1 μmol/L with a good linear response ranging from 0.1-100 μmol/L (R(2) = 0.9960).

수학 교사의 증명과 증명 지도에 대한 인식 - 대학원에 재학 중인 교사를 중심으로 -

수학 교사의 증명과 증명 지도에 대한 인식 - 대학원에 재학 중인 교사를 중심으로 -

Supramolecular curcumin–barium prodrugs for formulating with ceramic particles

A simple and stable curcumin–ceramic combined formulation was developed with an aim to improve curcumin stability and release profile in the presence of reactive ceramic particles for potential dental and orthopedic applications. For that, curcumin was complexed with barium (Ba2+) to prepare curcumin–barium (BaCur) complex. Upon removal of the unbound curcumin and Ba2+ by dialysis, a water-soluble BaCur complex was obtained. The complex was showing [M+1]+ peak at 10,000–20,000 with multiple fractionation peaks of MALDI-TOF-MS studies, showed that the complex was a supramolecular multimer. The 1H NMR and FTIR studies revealed that, divalent Ba2+ interacted predominantly through di-phenolic groups of curcumin to form an end-to-end complex resulted in supramolecular multimer. The overall crystallinity of the BaCur was lower than curcumin as per XRD analysis. The complexation of Ba2+ to curcumin did not degrade curcumin as per HPLC studies. The fluorescence spectrum was blue shifted upon Ba2+ complexation with curcumin. Monodisperse nanoparticles with size less than 200dnm was formed, out of the supramolecular complex upon dialysis, as per DLS, and upon loading into pluronic micelles the size was remaining in similar order of magnitude as per DLS and AFM studies. Stability of the curcumin was improved greater than 50% after complexation with Ba2+ as per UV/Vis spectroscopy. Loading of the supramloecular nanoparticles into pluronic micelles had further improved the stability of curcumin to approx. 70% in water. These BaCur supramolecule nanoparticles can be considered as a new class of prodrugs with improved solubility and stability. Subsequently, ceramic nanoparticles with varying chemical composition were prepared for changing the material surface reactivity in terms of the increase in, degradability, surface pH and protein adsorption. Further, these ceramic particles were combined with curcumin prodrug formulations and optimized the curcumin release properties in the combined formulations. Our proof concept study shows that, the conversion of curcumin to a metal-organic supramolecular prodrug improved the solubility, stability and release profile of curcumin. The prodrug approach with the micellisation strategy appears to be more appropriate to deliver intact curcumin in the presence of ceramic particles of varying surface reactivity.

Investigating Mathematics Trainee Teachers’ Conceptions of Proof Writing in Algebra: A Case of One College of Education in Zambia

This paper investigates mathematics trainee teachers’ conceptions of proof writing in algebra at Copperbelt College of Education in Zambia. The ability to construct proofs seems to be an important skill for all mathematicians and those who have interest in mathematics education. However, literature shows that proof is widely acknowledged to be one of the most difficult aspects in the mathematics curriculum. The sample comprised of 35 male and 15 female third year mathematics trainee teachers. Data was collected by means of a self-administered questionnaire, a written diagnostic test and oral interviews. The three instruments were used to provide multiple views to triangulate the data. The results show that students seem to understand proof as a verification and confirmation tool. Many of them applied empirical approaches in their written proofs. They did not have sufficient knowledge of the right set of accepted statements such as axioms and could not identify which statements required proofs in mathematics. These findings suggest that students’ conceptions of proof were underdeveloped hence affecting their ability to produce valid proofs. These findings will assist in guiding curricula designers and teachers of proof related knowledge. DOI: 10.5901/mjss.2014.v5n14p331

Design and implementation of a malware detection system based on network behavior

AbstractWith the increasing of new malicious software attacks, the host‐based malware detection methods cannot always detect the latest unknown malware. Intrusion detection system does not focus on malware detection, whereas the behavior‐based detection methods still have some difficulties in being deployed in the network layer. This paper presents a malware detection method based on network behavior evidence chains. The proposed new method will detect the specific network behavior characteristics on three different stages as connection establishment, operating control, and connection maintenance. Then a final detection decision will be concluded according to the results detected in the different stages before. A system prototype is implemented to proof concept the proposed malware detection methods. Copyright © 2014 John Wiley & Sons, Ltd.

Soldiering Archaeology: Pitt Rivers and ‘Militarism’

This paper initially explores the impact of the military on the development of British archaeology generally. It then focuses on the career of General Pitt Rivers, whose army background – especially his work in ordnance and when serving as legal prosecutor – fundamentally informed his archaeology, providing the basis for his concept of proof and the adjudication of evidence. Pitt Rivers was an active member of, and contributed to, the collections of the ‘lost’ museum of the Royal United Services Institute. His particular interest was in the study of Primitive Warfare , and he demonstrated its evolution through his ‘typological’ collections of weapons. Finally, given the breadth of military experience and the diverse participation of its members within the discipline, critique is made of Wheeler’s singular formulation of an ‘army-influenced archaeology’.

Argumentation and Inference: A Unified Approach

We propose in this paper to use Ludics as a unified framework for the analysis of dialogue and the reasoning system. Not only is Ludics a logical theory, but it may also be built by means of concepts of game theory. We first present the main concepts of Ludics. A design is an abstraction and a generalization of the concept of proof. Interaction between designs is equivalent to cut elimination or modus ponens in logical theories. It appears to be a natural means for representing dialogues and also for reasoning. A design is a set of sequences of alternate actions, similar to a move in game theory. We apply Ludics to argumentative dialogues. We discuss how to model the speech acts of argumentative dialogues in terms of dialogue acts. A dialogue act is given by a Ludics action together with the expression that reveals the action in a turn of speech. We show also how arguments may be stored in a commitment state used for reasoning. Finally we revisit an example of juridical dialogue that has been analyzed by Prakken in a different framework.

Abstract 2137: Development of CAST (cancer stromal targeting) therapy.

Abstract Although many monoclonal antibodies (mAbs) have been already approved for the therapy of cancer, they are usually used in the combination with anticancer agents (ACAs) because of limited anti-tumor activity as single agent. Antibody-drug conjugate (ADC), a next generation of therapeutic antibody, is the promising strategy to enhance the cytotoxic effect. Most human solid tumors, however, possess abundant stroma that hinders the distribution of ADC. Moreover, conventional ADC is depending on the enzymatic cleavage following internalization into the cytoplasm or lysosome. But the process of cell-uptake would be disturbed by stromal barrier. Heterogeneity of the tumor cells also prevents development of the ADC therapy based on cell-specific antigen. To overcome this drawback, we have created a unique type of ADC, namely CAST (Cancer stromal targeting) therapy, utilizes dense stroma as scaffold for the drug delivery. It was composed of ACAs conjugated to stroma targeting mAb (anti-collagen 4 or anti-fibrin mAb) via PEGylated ester-bond linker. We considered mAb was one of ideal DDS carriers, because IgG in size range from 10 to 20nm had stronger EPR (Enhanced permeability and retention) effect as passive tumor targeting activity than albumin being used in clinics as a carrier. Moreover, our ADC bound to the tumor stroma from which ACAs were control-released gradually and distributed throughout the tumor, resulting in the arrest of tumor growth due to induced damage to both tumor cells and tumor vessels. In addition to xenograft model, spontaneous mouse cancer models having dense stroma, remarkable fibrin deposition and abundant collagen e.g. chemically-induced cutaneous cancer or pancreatic cancer from genetic engineered mouse were used for the proof concept study of CAST therapy. We also made full use of imaging technology (fluorescence, PET/CT) for the evaluation of the biodistribution property and tumor stroma specificity of our anti-stroma mAbs. We will present the CAST therapy and discuss our development strategy for the clinical use. [1] Matsumura Y, Maeda H. A new concept for macromolecular therapeutics in cancer chemotherapy: mechnism of tumoritropic accumulation of proteins and antitumor agent smancs. Cancer Res. 46:6387-92. 1986. [2] Yasunaga M, Manabe S, Matsumura Y. New concept of cytotoxic immunoconjugate therapy cancer-induced fibrin clots. Cancer Sci. 102:1396-1402, 2011. [3] Yasuanga M, Manabe S, Tarin D, Matsumura Y. Cancer-stroma targeting therapy by cytotoxic immunoconjugate bound to the collagen 4 network in the tumor tissue. Bioconjugate Chem.22:1776-1783, 2011. [4] Yasuanga M, Manabe S, Tarin D, Matsumura Y. Tailored immunoconjugate therapy depending on a quantity of tumor stroma. Cancer Sci. 2012. [Epub ahead of print] [5] Matsumura Y. Cancer stromal targeting (CAST) therapy.Adv Drug Deliv Rev. 64:710-719, 2012. Citation Format: Masahiro Yasunaga, Takashi Sugino, Atsushi Tsuji, Tsuneo Saga, Shino Manabe, Yasuhiro Matsumura. Development of CAST (cancer stromal targeting) therapy. [abstract]. In: Proceedings of the 104th Annual Meeting of the American Association for Cancer Research; 2013 Apr 6-10; Washington, DC. Philadelphia (PA): AACR; Cancer Res 2013;73(8 Suppl):Abstract nr 2137. doi:10.1158/1538-7445.AM2013-2137

An Agent-Based Wellness Indicator

A personal wellness indicator is a software system that can give people a better understanding of their wellness conditions and can help them improve their wellness levels. The personal wellness indicator is a decision-support system for healthcare professionals. An agent-based wellness visualization system was developed as the proof concept. The agent-based system is constructed from the operational wellness model, the authors developed. The agent-based wellness visualization system is simple, expandable, modular, and its results are appropriate for two types of users with different requirements and backgrounds. This research also developed a framework for evaluating a wellness visualization system. The framework contains both technical evaluations and user studies. The proof of concept obtained positive feedbacks in various aspects. However, there are limitations found during the evaluations. This paper presents the analyzed results obtained from the proof of concept, recommended solutions to the limitations found, and future directions.

Otto Hölder’s Interpretation of David Hilbert’s Axiomatic Method*

In this paper I provide a brief reconstruction of Otto Hölder’s conception of proof. My reconstruction focuses on Hölder’s critical assessment of David Hilbert’s account of axiomatics in general, and of Hilbert’s conception of metamathematics in particular. I argue that Hölder’s analysis of Hilbert’s general methodological ideas and, more importantly, Hölder’s analysis of the logical structure of the proofs provided by Hilbert in his Grundlagen der Geometrie of 1899 are helpful in reaching a clearer understanding of van der Waerden’s claim linking Hölder’s conception of proof to the tradition established by Kurt Gödel.

Toward a wiki guide for obstetrics and gynecology trainees in Ireland

BackgroundThe present paper describes the implementation of a novel, web-based, comprehensive national information hub for trainees in obstetrics and gynecology in Ireland. This was a unique development in the context of an entire medical specialty and was aligned with the communication strategy of the governing professional body. To date, trainee doctors working in Ireland undergo an incoherent and inconsistent new-staff induction and handover. In the healthcare setting, staff integration can have a major impact on the quality of patient care. MethodsA free wiki software platform (PBworks) was used for the website, and freely available software (Google Analytics) was used to determine user interaction and level of engagement. ResultsIn the first year, 442 user visits were recorded. The average duration of site visits was 4minutes 39seconds, which compared favorably with the 4-minute duration for visits to Wikipedia. ConclusionThe project was successful as a proof concept and in practice. Other medical faculties have expressed an interest in adopting the concept and developing it for their trainees. The concept is widely applicable to other countries, with the negligible cost relevant to resource-poor areas.

Aristotle on Circular Proof

Abstract In Posterior Analytics 1.3, Aristotle advances three arguments against circular proof. The third argument relies on his discussion of circular proof in Prior Analytics 2.5. This is problematic because the two chapters seem to deal with two rather disparate conceptions of circular proof. In Posterior Analytics 1.3, Aristotle gives a purely propositional account of circular proof, whereas in Prior Analytics 2.5 he gives a more complex, syllogistic account. My aim is to show that these problems can be solved, and that Aristotle’s third argument in 1.3 is successful. I argue that both chapters are concerned with the same conception of circular proof, namely the propositional one. Contrary to what is often thought, the syllogistic conception provides an adequate analysis of the internal deductive structure of the propositional one. Aristotle achieves this by employing a kind of multiple-conclusion logic.

A novel multifunctional coupler: the concept of coupling and proof of principle

A multifunctional coupler with an ethylene carbonate- and a thiolactone ring was synthesized. As proof of principle the coupler was reacted with four low-molecular weight building blocks to form a multifunctional molecule. The reactivity/selectivity of the coupler towards amines, acrylates and acyl halides was evaluated.