Search results for: mathematical proof

Authors: Ahmed Tarek, Ahmed Alveed

Abstract:

In the theory of computing, there are a wide variety of direct and indirect proof techniques. However, mathematical induction (MI) stands out to be one of the most powerful proof techniques for proving hypotheses, theorems, and new results. There are variations of mathematical induction-based proof techniques, which are broadly classified into three categories, such as structural induction (SI), weak induction (WI), and strong induction (SI). In this expository paper, several different variants of the mathematical induction techniques are explored, and the specific scenarios are discussed where a specific induction technique stands out to be more advantageous as compared to other induction strategies. Also, the essential difference among the variants of mathematical induction are explored. The points of separation among mathematical induction, recursion, and logical deduction are precisely analyzed, and the relationship among variations of recurrence relations, and mathematical induction are being explored. In this context, the application of recurrence relations, and mathematical inductions are considered together in a single framework for codewords over a given alphabet.

Keywords: alphabet, codeword, deduction, mathematical, induction, recurrence relation, strong induction, structural induction, weak induction

Procedia PDF Downloads 125

Authors: Mohammad Mahmoud Mandurah

Abstract:

The existence of InfoMiracles in scripture is evidence that the scripture has a divine origin. It is also evidence to the existence of God. An InfoMiracle is an information-based miracle. The basic component of an InfoMiracle is a piece of information that could not be obtained by a human except through a divine channel. The existence of a sufficient number of convincing InfoMiracles in a scripture necessitates the existence of the divine source to these InfoMiracles. A mathematical equation is developed to prove that the Qur’an has a divine origin, and hence, prove the existence of God. The equation depends on a single variable only, which is the number of InfoMiracles in the Qur’an. The Qur’an is rich with InfoMiracles. It is shown that the existence of less than 30 InfoMiracles in the Qur’an is sufficient proof to the existence of God and that the Qur’an is a revelation from God.

Keywords: InfoMiracle, God, mathematical proof, miracle, probability

Procedia PDF Downloads 181

Authors: Sakshi Singh, Shampa Chakraverty

Abstract:

One of the essential characteristics of Blockchain is the ability to validate the integrity of new transactions added to the Blockchain. Moreover, one of the essential consensus algorithms, Proof of Work, performs this job. In this work, we implemented the Proof of Work consensus method on the block formed by performing the transaction using Ganache. The primary goal of this implementation is to understand the process and record how Proof of Work works in reality on newly created blocks.

Keywords: proof of work, blockchain, ganache, smart contract

Procedia PDF Downloads 107

Authors: Ayşegül Çabuk, Mine Işıksal

Abstract:

Mathematics is a sense-making activity so that it requires meaningful learning. Hence based on this idea, meaningful mathematical connections are necessary to learn mathematics. At that point, the major question has become that which educational methods can provide opportunities to provide mathematical connections and to understand mathematics. The amalgam of reasoning and proof can be the one of the methods that creates opportunities to learn mathematics in a meaningful way. However, even if reasoning and proof should be included from prekindergarten to grade 12, studies in literature generally include secondary school students and pre-service mathematics teachers. With the light of the idea that the amalgam of reasoning and proof has significant effect on middle school students' mathematical learning, this study aims to investigate middle grade students' tendencies while reasoning the correctness of statements related to numbers. The sample included 272 middle grade students, specifically 69 of them were sixth grade students (25.4%), 101 of them were seventh grade students (37.1%) and 102 of them were eighth grade students (37.5%). Data was gathered through an achievement test including 2 essay types of problems about algebra. The answers of two items were analyzed both quantitatively and qualitatively in terms of students' solutions strategies while reasoning the correctness of the statements. Similar on the findings in the literature, most of the students, in all grade levels, used numerical examples to judge the statements. Moreover the results also showed that the majority of these students appear to believe that providing one or more selected examples is sufficient to show the correctness of the statement. Hence based on the findings of the study, even students in earlier ages have proving and reasoning abilities their reasoning's generally based on the empirical evidences. Therefore, it is suggested that examples and example-based reasoning can be a fundamental role on to generate systematical reasoning and proof insight in earlier ages.

Keywords: reasoning, mathematics learning, middle grade students

Procedia PDF Downloads 387

Authors: Frode van der Laak

Abstract:

The paper contributes to the feasibility of using a 5G mobile connection as a node for a Proof of Authority (PoA) blockchain, which is used for microtransactions at the same time. It uses the phone number identity of the users that are linked to the crypto wallet address. It also proposed a consensus protocol based on Proof-of-Authority (PoA) blockchain; PoA is a permission blockchain where consensus is achieved through a set of designated authority rather than through mining, as is the case with a Proof of Work (PoW) blockchain. This report will first explain the concept of a PoA blockchain and how it works. It will then discuss the potential benefits and challenges of using a 5G mobile connection as a node in such a blockchain, and finally, the main open problem statement and proposed solutions with the requirements.

Keywords: 5G, mobile, connection, node, PoA, blockchain, microtransaction

Procedia PDF Downloads 56

Authors: Ying Yi Wu

Abstract:

In this paper, we present a proof of the fact that a finite morphism is proper. We show that a finite morphism is universally closed and of finite type, which are the conditions for properness. Our proof is based on the theory of schemes and involves the use of the projection formula and the base change theorem. We first show that a finite morphism is of finite type and then proceed to show that it is universally closed. We use the fact that a finite morphism is also an affine morphism, which allows us to use the theory of coherent sheaves and their modules. We then show that the map induced by a finite morphism is flat and that the module it induces is of finite type. We use these facts to show that a finite morphism is universally closed. Our proof is constructive, and we provide details for each step of the argument.

Keywords: finite, morphism, schemes, projection.

Procedia PDF Downloads 63

Authors: Rahmayanti, Theresia Simatupang, Ronald H. Sianturi

Abstract:

Corruption criminal act develops rapidly since in the transition era there is weakness in law. Consequently, there is an opportunity for a few people to do fraud and illegal acts and to misuse their positions and formal functions in order to make them rich, and the criminal acts are done systematically and sophisticatedly. Some people believe that legal provisions which specifically regulate the corruption criminal act; namely, Law No. 31/1999 in conjunction with Law No. 20/2001 on the Eradication of Corruption Criminal Act are not effective any more, especially in onus probandi (the burden of proof) on corruptors. The research was a descriptive analysis, a research method which is used to obtain description on a certain situation or condition by explaining the data, and the conclusion is drawn through some analyses. The research used judicial normative approach since it used secondary data as the main data by conducting library research. The system of the burden of proof, which follows the principles of reversal of the burden of proof stipulated in Article 12B, paragraph 1 a and b, Article 37A, and Article 38B of Law No. 20/2001 on the Amendment of Law No. 31/1999, is used only as supporting evidence when the principal case is proved. Meanwhile, how to maximize the implementation of the burden of proof on the perpetrators of corruption criminal act in which the public prosecutor brings a corruption case to Court, depends upon the nature of the case and the type of indictment. The system of burden of proof can be used to eradicate corruption in the Court if some policies and general principles of justice such as independency, impartiality, and legal certainty, are applied.

Keywords: burden of proof, perpetrator, corruption criminal act

Procedia PDF Downloads 282

Authors: Yingxu Wang

Abstract:

The base 6 structure and properties of mirror primes are discovered in this work towards the proof of Goldbach Conjecture. This paper reveals a fundamental pattern on pairs of mirror primes adjacent to any even number nₑ > 2 with symmetrical distances on both sides determined by a methodology of Mirror Prime Decomposition (MPD). MPD leads to a formal proof of the Goldbach conjecture, which states that the conjecture holds because any pivot even number, nₑ > 2, is a sum of at least an adjacent pair of primes divided by 2. This work has not only revealed the analytic pattern of base 6 primes but also proven the infinitive validation of the Goldbach conjecture.

Keywords: number theory, primes, mirror primes, double recursive patterns, Goldbach conjecture, formal proof, mirror-prime decomposition, applications

Procedia PDF Downloads 11

Authors: Feng-Hisang Lai

Abstract:

CFD(Computational Fluid Dynamics) is conducted to numerically study the flow and heat transfer features of a two-pole, 6,080HP, 60Hz, 3,150V open drip-proof (ODP) motor. The stator and rotor cores in this high voltage induction motor are segmented with the use of spacers for cooling purposes, which leads to difficulties in meshing when the entire system is to be simulated. The system is divided into 4 parts, meshed separately and then combined using interfaces. The deviation between the CFD and experimental results in temperature and flow rate is less than 10%. The internal flow is further examined and a final design is proposed to reduce the winding temperature by 10 degrees.

Keywords: CFD, open drip proof, induction motor, cooling

Procedia PDF Downloads 153

Authors: Rabinder Singh Bharj, Sandeep Kumar

Abstract:

This investigation presents preparation of sample and analysis of results of ballistic impact test as per EN 1063 on the size, thickness, number, position, and type of the bonding interlayer Polyvinyl Butyral, Poly Carbonate and Poly Urethane on bullet proof glass. It was observed that impact energy absorbed by bullet proof glass increases with the increase of the total thickness from 33mm to 42mm to 51mm for all the three samples respectively. Absorption impact energy is greater for samples with more number of bonding interlayers than with the number of glass layers for uniform increase in total sample thickness. There is no effect on the absorption impact energy with the change in position of the bonding interlayer.

Keywords: absorbed energy, bullet proof glass, laminated glass, safety glass

Procedia PDF Downloads 349

Authors: Gyoutae Park, Seungho Han, Byungduk Kim, Youngdo Jo, Yongsop Shim, Yeonjae Lee, Sangguk Ahn, Hiesik Kim, Jungil Park

Abstract:

In this paper, we presented not only development technology of an explosion proof type and portable combustible gas leak detector but also algorithm to improve accuracy for measuring gas concentrations. The presented techniques are to apply the flame-proof enclosure and intrinsic safe explosion proof to an infrared gas leak detector at first in Korea and to improve accuracy using linearization recursion equation and Lagrange interpolation polynomial. Together, we tested sensor characteristics and calibrated suitable input gases and output voltages. Then, we advanced the performances of combustible gaseous detectors through reflecting demands of gas safety management fields. To check performances of two company's detectors, we achieved the measurement tests with eight standard gases made by Korea Gas Safety Corporation. We demonstrated our instruments better in detecting accuracy other than detectors through experimental results.

Keywords: accuracy improvement, IR gas sensor, gas leak, detector

Procedia PDF Downloads 355

Authors: Mirza Amin Ul Haq

Abstract:

Purpose – the purpose of conducting this research is to check the impact of nudges constructs, whether they create an encouragement factor with consumer brand loyalty and relating of word-of-mouth power have some kind of effect with all independent variables. Desin/Methodology/Approach – this study adopted the four constructs (i.e., Digital Nudge, Social Proof Nudge, Trust, and the mediator Word of Mouth) and explore its effect and connection with Brand Loyalty. A total of 390 respondents were selected for self-administrated questionnaire to obtain the finding of the research. Findings – the impact and cause between the constructs were done through structural equation modeling. The findings show a positive impact of social proof nudge and word of mouth whereas, digital nudge and trust have the weaker influence on the consumer choices when talk about brand loyalty. Originality/Value – Further implication for research and its marketing strategies in the field of clothing industry creating brand loyalty with customer.

Keywords: nudge, digital nudge, social proof, online buying, brand loyalty, trust, word of mouth

Procedia PDF Downloads 74

Authors: Fahad Alsharari, Mohd Salmi Md. Noorani

Abstract:

A Motzkin shift is a mathematical model for constraints on genetic sequences. In terms of the theory of symbolic dynamics, the Motzkin shift is nonsofic, and therefore, we cannot use the Perron-Frobenius theory to calculate its topological entropy. The Motzkin shift M(M,N) which comes from language theory, is defined to be the shift system over an alphabet A that consists of N negative symbols, N positive symbols and M neutral symbols. For an x in the full shift AZ, x is in M(M,N) if and only if every finite block appearing in x has a non-zero reduced form. Therefore, the constraint for x cannot be bounded in length. K. Inoue has shown that the entropy of the Motzkin shift M(M,N) is log(M + N + 1). In this paper, we find a new method of calculating the topological entropy of the Motzkin shift M(M,N) without any measure theoretical discussion.

Keywords: entropy, Motzkin shift, mathematical model, theory

Procedia PDF Downloads 425

Authors: Yingxu Wang

Abstract:

This work presents basic research on the recursive structures and dual sequential patterns of primes for the formal proof of the Twin-Prime Conjecture (TPC). A rigorous methodology of Twin-Prime Decomposition (TPD) is developed in MATLAB to inductively verify potential twins in the dual sequences of primes. The key finding of this basic study confirms that the dual sequences of twin primes are not only symmetric but also infinitive in the unique base 6 cycle, except a limited subset of potential pairs is eliminated by the lack of dual primality. Both theory and experiments have formally proven that the infinity of twin primes stated in TPC holds in the P x P space.

Keywords: number theory, primes, twin-prime conjecture, dual primes (P x P), twin prime decomposition, formal proof, algorithm

Procedia PDF Downloads 17

Authors: M. Rodionov, Z. Dedovets

Abstract:

The article describes the theoretical concept of teaching secondary school students proof demonstration skills in mathematics. It describes in detail different levels of mastery of the concept of proof-which correspond to Piaget’s idea of there being three distinct and progressively more complex stages in the development of human reflection. Lessons for each level contain a specific combination of the visual-figurative components and deductive reasoning. It is vital at the transition point between levels to carefully and rigorously recalibrate teaching to reflect the development of more complex reflective understanding. This can apply even within the same age range, since students will develop at different speeds and to different potential. The authors argue that this requires an aware and adaptive approach to lessons to reflect this complexity and variation. The authors also contend that effective teaching which enables students to properly understand the implementation of proof arguments must develop specific competences. These are: understanding of the importance of completeness and generality in making a valid argument; being task focused; having an internalised locus of control and being flexible in approach and evaluation. These criteria must be correlated with the systematic application of corresponding methodologies which are best likely to achieve success. The particular pedagogical decisions which are made to deliver this objective are illustrated by concrete examples from the existing secondary school mathematics courses. The proposed theoretical concept formed the basis of the development of methodological materials which have been tested in 47 secondary schools.

Keywords: education, teaching of mathematics, proof, deductive reasoning, secondary school

Procedia PDF Downloads 210

Authors: Sangguk Ahn, Youngyu Kim, Jaheon Gu, Gyoutae Park

Abstract:

In this paper, we developed a dual gas leak instrument to detect Hydrocarbon (HC) and Monoxide (CO) gases. To two kinds of gases, it is necessary to design compact structure for sensors. And then it is important to draw sensing circuits such as measuring, amplifying and filtering. After that, it should be well programmed with robust, systematic and module coding methods. In center of them, improvement of accuracy and initial response time are a matter of vital importance. To manufacture distinguished gas leak detector, we applied intrinsically safe explosion-proof structure to lithium ion battery, main circuits, a pump with motor, color LCD interfaces and sensing circuits. On software, to enhance measuring accuracy we used numerical analysis such as Lagrange and Neville interpolation. Performance test result is conducted by using standard Methane with seven different concentrations with three other products. We want raise risk prevention and efficiency of gas safe management through distributing to the field of gas safety. Acknowledgment: This study was supported by Small and Medium Business Administration under the research theme of ‘Commercialized Development of a portable intrinsically safe explosion-proof type dual gas leak detector’, (task number S2456036).

Keywords: gas leak, dual gas detector, intrinsically safe, explosion proof

Procedia PDF Downloads 200

Authors: A. Giniatoulline

Abstract:

A model of the mathematical fluid dynamics which describes the motion of a three-dimensional viscous rotating fluid in a homogeneous gravitational field with the consideration of the salinity and heat transfer is considered in a vertical finite layer. The model is a generalization of the linearized Navier-Stokes system with the addition of the Coriolis parameter and the equations for changeable density, salinity, and heat transfer. An explicit solution is constructed and the proof of the existence and uniqueness theorems is given. The localization and the structure of the spectrum of inner waves is also investigated. The results may be used, in particular, for constructing stable numerical algorithms for solutions of the considered models of fluid dynamics of the Atmosphere and the Ocean.

Keywords: Fourier transform, generalized solutions, Navier-Stokes equations, stratified fluid

Procedia PDF Downloads 215

Authors: Jaemyoung Lee

Abstract:

We propose a stable laser scanning leveler transmitter scheme. In the proposed scheme, the transmitter has a right angled mirror which can eliminates the mechanical up and down vibration from scanning the mirror of the transmitter. In this paper, the mathematical proof for the proposed scheme which is not disturbed by the swivel movement of the right angled mirror is derived.

Keywords: leveler, right angled mirror, sweeping, laser

Procedia PDF Downloads 338

Authors: Yoshio Kurosawa

Abstract:

To reduce the interior noise of cars in high-frequency region, sound proof materials are laminated with the body panels and the interior trims. Therefore, sound proof properties of the laminates play an important role for the efficient acoustical design. A program code which predicts both sound absorption properties and sound insulation properties of the laminates are developed. This program code is used for transfer matrix method by Biot theory. This report described the outline of this program code, and the calculation results almost agreed with the experimental results.

Keywords: porous media, transmission loss, Biot theory, transfer matrix method

Procedia PDF Downloads 241

Authors: Konstancja Syller

Abstract:

International law and European regulations remain hardly silent about the admissibility of evidence obtained illegally in a criminal trial. However, Article 6 of the European Convention on Human Rights guarantees the right to a fair trial, it does not normalise a proceeding status of specified sources or means of proof outright. Therefore, it is the preserve of national legislation and national law enforcement authorities to decide on this matter. In most countries, especially in Germany and Poland, a rather complex normative approach to the issue of proof obtained in violation of the right to privacy is evident, which pursues in practise to many interpretive doubts. In Germany the jurisprudence has a significant impact within the range of the matter mentioned above. The Constitutional Court and the Supreme Court of Germany protect the right to privacy quite firmly - they ruled on inadmissibility of obtaining a proof in the form of a diary or a journal as a protection measure of constitutional guaranteed right. At the same time, however, the Supreme Court is not very convinced with reference to the issue of whether materials collected as a result of an inspection, call recordings or listening to the premises, which were carried out in breach of law, can be used in a criminal trial. Generally speaking, German courts indicate a crucial importance of the principle of Truth and the principle of proportionality, which both enable a judgement to be made as to the possibility of using an evidence obtained unlawfully. Comparing, in Poland there is almost no jurisprudence of the Constitutional Tribunal relating directly to the issue of illegal evidence. It is somehow surprising, considering the doctrinal analysis of the admissibility of using such proof in a criminal trial is performed in relation to standards resulted from the Constitution. Moreover, a crucial de lega lata legal provision, which enables allowing a proof obtained in infringement of the provisions in respect of criminal proceedings or through a forbidden act, is widely criticised within the legal profession ant therefore many courts give it their own interpretation at odds with legislator’s intentions. The comparison of two civil law legal systems’ standards regarding to the admissibility of an evidence obtained in contravention of the right to privacy in a criminal trial, taking also into account EU legislation and judicature, is the conclusive aim of this article.

Keywords: criminal trial, evidence, Germany, right to privacy, Poland

Procedia PDF Downloads 121

Authors: A. Giniatoulline

Abstract:

A nonlinear model of the mathematical fluid dynamics which describes the motion of an incompressible viscous rotating fluid in a homogeneous gravitational field is considered. The model is a generalization of the known Navier-Stokes system with the addition of the Coriolis parameter and the equations for changeable density. An explicit algorithm for the solution is constructed, and the proof of the existence and uniqueness theorems for the strong solution of the nonlinear problem is given. For the linear case, the localization and the structure of the spectrum of inner waves are also investigated.

Keywords: Galerkin method, Navier-Stokes equations, nonlinear partial differential equations, Sobolev spaces, stratified fluid

Procedia PDF Downloads 272

Authors: S. A. Sadegh Zadeh, C. Kambhampati

Abstract:

Mathematical and computational modellings are the necessary tools for reviewing, analysing, and predicting processes and events in the wide spectrum range of scientific fields. Therefore, in a field as rapidly developing as neuroscience, the combination of these two modellings can have a significant role in helping to guide the direction the field takes. The paper combined mathematical and computational modelling to prove a weakness in a very precious model in neuroscience. This paper is intended to analyse all-or-none principle in Hodgkin-Huxley mathematical model. By implementation the computational model of Hodgkin-Huxley model and applying the concept of all-or-none principle, an investigation on this mathematical model has been performed. The results clearly showed that the mathematical model of Hodgkin-Huxley does not observe this fundamental law in neurophysiology to generating action potentials. This study shows that further mathematical studies on the Hodgkin-Huxley model are needed in order to create a model without this weakness.

Keywords: all-or-none, computational modelling, mathematical model, transmembrane voltage, action potential

Procedia PDF Downloads 575

Authors: Elizabeth Chinyere Amadi

Abstract:

Yeast (sacchoromyces cerevisiae) was isolated from the fermenting sap of raffia palm (Raphia hookeri) wine. Different concerntrations of the yeast isolate were used to produce bread samples – B, C, D, E, F containing (2, 3, 4, 5, 6) g of yeast isolate respectively, other ingredients were kept constant. Sample A, containing 2g of commercial baker yeast served as control. The proof heights, weights, volumes and specific volume of the dough and bread samples were determined. The bread samples were also subjected to sensory evaluation using a 9–point hedonic scale. Results showed that proof height increased with increased concentration of the yeast isolate; that is direct proportion. Sample B with the least concentration of the yeast isolate had the least loaf height and volume of 2.80c m and 200 cm³ respectively but exhibited the highest loaf weight of 205.50g. However, Sample A, (commercial bakers’ yeast) had the highest loaf height and volume of 5.00 cm and 400 cm³ respectively. The sensory evaluation results showed sample D compared favorably with sample A in all the organoleptic attributes-(appearance, taste, crumb texture, crust colour and overall acceptability) tested for (P< 0.05). It was recommended that 4g compressed yeast isolate per 100g flour could be used to proof dough as a substitute for commercial bakers’ yeast and produce acceptable bread loaves.

Keywords: isolation of yeast, performance evaluation of yeast, Raffia palm wine, used at different concentrations, proofing of bread dough

Procedia PDF Downloads 275

Authors: Sam Ng, Lewis Leighton, Sam Atkinson, Carson Yan, Landan Hu, Leslie Cheung, Brian Yap, Kent Lung, Ketat Sarakune

Abstract:

This paper introduces a method for verifying cryptocurrency reserves that balances the need for both transparency and data confidentiality. Our methodology employs cryptographic techniques, including Merkle Trees, Bulletproof, and zkSnark, to verify that total assets equal or exceed total liabilities, represented by customer funds. Importantly, this verification is achieved without disclosing sensitive information such as the total asset value, customer count, or cold wallet addresses. We delve into the construction and implementation of this methodology. While the system is robust and scalable, we also identify areas for potential enhancements to improve its efficiency and versatility. As the digital asset landscape continues to evolve, our approach provides a solid foundation for ensuring continued trust and security in digital asset platforms.

Keywords: cryptocurrency, crypto-currency, proof-of-reserve, por, zero-knowledge, ZKP

Procedia PDF Downloads 31

Authors: Kun-Peng Jin, Jin Liang, Ti-Jun Xiao

Abstract:

In this work, we are concerned with the dynamic behaviors of solutions to some coupled systems with infinite memory, which consist of two partial differential equations where only one partial differential equation has damping. Such coupled systems are good mathematical models to describe the deformation and stress characteristics of some viscoelastic materials affected by temperature change, external forces, and other factors. By using the theory of operator semigroups, we give wellposedness results for the Cauchy problem for these coupled systems. Then, with the help of some auxiliary functions and lemmas, which are specially designed for overcoming difficulties in the proof, we show that the solutions of the coupled systems decay to zero in a strong way under a few basic conditions. The results in this dynamic analysis of coupled systems are generalizations of many existing results.

Keywords: dynamic analysis, coupled system, infinite memory, damping.

Procedia PDF Downloads 180

Authors: Hashem Sazegar

Abstract:

In 1937, Vinograd of Russian Mathematician proved that each odd large number can be shown by three primes. In 1973, Chen Jingrun proved that each odd number can be shown by one prime plus a number that has maximum two primes. In this article, we state one proof for Goldbach’conjecture. Introduction: Bertrand’s postulate state for every positive integer n, there is always at least one prime p, such that n < p < 2n. This was first proved by Chebyshev in 1850, which is why postulate is also called the Bertrand-Chebyshev theorem. Legendre’s conjecture states that there is a prime between n2 and (n+1)2 for every positive integer n, which is one of the four Landau’s problems. The rest of these four basic problems are; (i) Twin prime conjecture: There are infinitely many primes p such that p+2 is a prime. (ii) Goldbach’s conjecture: Every even integer n > 2 can be written asthe sum of two primes. (iii) Are there infinitely many primes p such that p−1 is a perfect square? Problems (i), (ii), and (iii) are open till date.

Keywords: Bertrand-Chebyshev theorem, Landau’s problems, twin prime, Legendre’s conjecture, Oppermann’s conjecture

Procedia PDF Downloads 357

Authors: Maarten J. Van der Burgt

Abstract:

A universe containing matter and antimatter can only exist when matter and antimatter repel each other. Such a system, where like attracts like and like repels unlike, will always expand. Calculations made for such a symmetric universe demonstrate that the expansion is consistent with Hubble’s law, the observed increase in the expansion velocity with time, the initial high acceleration and the foam structure of the universe. Conversely, these observations can be considered as proof for a symmetrical universe and for antimatter possessing a negative gravitational mass. A second proof can be found by reinterpreting the behavior of relativistic moving charged particles. Attributing their behavior to a charge defect of √(1-v2/c2) instead of to a mass defect of 1/√(1-v2/c2) makes it plausible that gravitation is an electromagnetic force, as already suggested by Feynman. This would automatically imply that antimatter has a negative gravitational mass. These proofs underpin the untenability of the Weak Equivalence Principle which states that in a gravitational field all structure less point-like particles follow the same path.

Keywords: celestial mechanics, cosmology, gravitation astrophysics, origin of structure, miscellaneous (matter and antimatter)

Procedia PDF Downloads 194

Authors: Agarana Michael C., Akinlabi Esther T., Pule Kholopane

Abstract:

Innovation in manufacturing process technologies and associated product design affects the prospects for manufacturing today and in near future. In this study some theoretical methods, useful as tools in advanced manufacturing, are considered. In particular, some basic Mathematical, Operational Research, Heuristic, and Statistical techniques are discussed. These techniques/methods are very handy in many areas of advanced manufacturing processes, including process planning optimization, modelling and analysis. Generally the production rate requires the application of Mathematical methods. The Emerging Trends Processes in Advanced Manufacturing can be enhanced by using Mathematical Modelling and Optimization techniques.

Keywords: mathematical modelling, optimization, emerging trends, advanced manufacturing

Procedia PDF Downloads 254

Authors: Rizky Oktaviana

Abstract:

The main purpose of studying lies in improving students’ understanding. Teachers usually use written test to measure students’ understanding about learning material especially mathematical learning material. This common method actually has a lack point, such that in mathematics content, written test only show procedural steps to solve mathematical problems. Therefore, teachers unable to see whether students actually understand about mathematical concepts and the relation between concepts or not. One of the best tools to observe students’ understanding about the mathematical concepts is concept map. The goal of this research is to describe junior high school students understanding about mathematical concepts through Concept Maps based on the difference of mathematical ability. There were three steps in this research; the first step was choosing the research subjects by giving mathematical ability test to students. The subjects of this research are three students with difference mathematical ability, high, intermediate and low mathematical ability. The second step was giving concept mapping training to the chosen subjects. The last step was giving concept mapping task about the function to the subjects. Nodes which are the representation of concepts of function were provided in concept mapping task. The subjects had to use the nodes in concept mapping. Based on data analysis, the result of this research shows that subject with high mathematical ability has formal understanding, due to that subject could see the connection between concepts of function and arranged the concepts become concept map with valid hierarchy. Subject with intermediate mathematical ability has relational understanding, because subject could arranged all the given concepts and gave appropriate label between concepts though it did not represent the connection specifically yet. Whereas subject with low mathematical ability has poor understanding about function, it can be seen from the concept map which is only used few of the given concepts because subject could not see the connection between concepts. All subjects have instrumental understanding for the relation between linear function concept, quadratic function concept and domain, co domain, range.

Keywords: concept map, concept mapping, mathematical concepts, understanding

Procedia PDF Downloads 237

Authors: Yoon Suh Song

Abstract:

Though music education can broaden one’s capacity for mathematical performance, many countries lag behind in music education. Little empirical evidence is found to identify the connection between math and music. Therefore, this research was set out to explore what music-related variables are associated with mathematical performance. The result of our analysis is as follows: A Pearson's Correlation analysis revealed that PISA math score is strongly correlated with students' Intelligence Quotient (IQ). This lays the foundation for further research as to what factors in students’ IQ lead to a better performance in math.

Keywords: music education, mathematical performance, education, IQ

Procedia PDF Downloads 173