Search results for: mathematical row of numbers

Authors: William Wong, Zakaria Alomari, Hon Ching Lai, Zhida Li

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Modern-day information security depends on implementing Diffie-Hellman, which requires the generation of prime numbers. Because the number of primes is infinite, it is impractical to store prime numbers for use, and therefore, primality tests are indispensable in modern-day information security. A primality test is a test to determine whether a number is prime or composite. There are two types of primality tests, which are deterministic tests and probabilistic tests. Deterministic tests are adopting algorithms that provide a definite answer whether a given number is prime or composite. While in probabilistic tests, a probabilistic result would be provided, there is a degree of uncertainty. In this paper, we review three probabilistic tests: the Fermat Primality Test, the Miller-Rabin Test, and the Baillie-PSW Test, as well as one deterministic test, the Agrawal-Kayal-Saxena (AKS) Test. Furthermore, we do an analysis of these tests. All of the reviews discussed are not based on the Elliptic Curve. The analysis demonstrates that, in the majority of real-world scenarios, the Baillie- PSW test’s favorability stems from its typical operational complexity of O(log 3n) and its capacity to deliver accurate results for numbers below 2^64.

Keywords: primality tests, Fermat’s primality test, Miller-Rabin primality test, Baillie-PSW primality test, AKS primality test

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Authors: Johna Bernice Ablaza, Bryan Lim Corpuz, Joanna Marie Estrada, Mary Ann Cristine Olgado, Rhina Recato

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This study aimed to describe the mathematical beliefs and attitudes in relation to the mathematics performance of freshman college students. The descriptive design using the correlational study was used to describe the relationship among mathematical beliefs, attitudes, and performance of freshman college students. This study involved one hundred fifty (150) freshman college students of Philippine Normal University during the third trimester of school year 2015-2016. The research instruments used to gather the information needed in the study are the beliefs about Mathematics Questionnaire, the KIM-Project Questionnaire, and the ACT Compass Mathematics Test. The data gathered were analyzed using the percentages, mean, standard deviation, and Pearson r-moment correlation. The results of this study have shown that although students believe that Mathematics is significant in their lives, the overall result on their beliefs and attitudes are positively low. There is a significant relationship between the students’ mathematical beliefs and mathematics performance. Likewise, their attitudes in mathematics have significant relationship to mathematics performance.

Keywords: attitudes, diligence, interest, mathematical beliefs, mathematical performance, self-confidence

Procedia PDF Downloads 259

Authors: Isaac Benning

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Using technology to expand the learning space is critical for a productive mathematical discourse. This is a case study of two teachers who developed and enacted GeoGebra-based mathematics lessons following their engagement in a two-year professional development. The didactical and semiotic affordance of GeoGebra in widening the learning space for a productive mathematical discourse was explored. The approach of thematic analysis was used for lesson artefact, lesson observation, and interview data. The results indicated that constructing tools in GeoGebra provided a didactical milieu where students used them to explore mathematical concepts with little or no support from their teacher. The prompt feedback from the GeoGebra motivated students to practice mathematical concepts repeatedly in which they privately rethink their solutions before comparing their answers with that of their colleagues. The constructing tools enhanced self-discovery, team spirit, and dialogue among students. With regards to the semiotic construct, the tools widened the physical and psychological atmosphere of the classroom by providing animations that served as virtual concrete to enhance the recording, manipulation, testing of a mathematical idea, construction, and interpretation of geometric objects. These findings advance the discussion of widening the classroom for a productive mathematical discourse within the context of the mathematics curriculum of Ghana and similar Sub-Saharan African countries.

Keywords: GeoGebra, theory of didactical situation, semiotic mediation, mathematics laboratory, mathematical discussion

Procedia PDF Downloads 107

Authors: Shanko Chura Aredo, Hailu Jeldie Wodajo, Muktar Jeylan, Kedir Ilka, Abdulnasir Husein

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Toll-free numbers are calling numbers that have unique three or four digit numbers and that don’t require payment from phone lines in order to be called. With the help of these numbers, callers can connect with nearby organizations and/or people without incurring far-reaching fees. Calls to assistance centers are especially popular from toll-free phones. In the past, toll-free services have offered prospective clients and other parties a simple and cost-free means of getting in touch with enterprises. Nevertheless, unless they have an ”unlimited calling” plan, wireless subscribers will be billed for the airtime minutes used during a toll-free call. In Adama, the second largest city in Ethiopia, a call center has been installed as part of smart security system and serving since January 2023 for collection of complaints from different community levels. The call center is situated at the mayor office and has 11 active workers, 4 of these working the night time and the remaining during day time. The information reported in the form of complaints from individuals and groups are illegal constructions, illegal trade, income concealment or hiding, giving and receiving bribe, informing new faces of suspected enemies and exposing individual or group conflicts. This technology has been found to bring a significant outcome in minimizing illegal acts, public safety threats and service delivery problems.

Keywords: smart, safety, crime, call center, security

Procedia PDF Downloads 38

Authors: YongSeok Choi, HwaYoung Seo, InSu Whang, GeogKee Park

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Frankliniella. occidentalis is major pest in chrysanthemum in worldwide. The density of F. occidentalis increased continuously in spite of the periodical chemical control after planting in this study. F. occidentalis began to increase mid-May. The numbers of F. occidentalis collected on a tray with wet paper by heating the flowers of pink, white, and yellow Chrysanthemum standard mums were 18.4, 56.6, and 52.6 in the flowering season. Also, the numbers were 15.2, 45.8, and 41.6 in bud season, but in the case of the leaves, the numbers were 2, 8.8 and 3.4. In the Y-tube olfactometer test, the frequency of F. occidentalis’ visits to one side arm of the Y-tube olfactometer was higher in the odor cue of the white flower than of the yellow, red, and violet flowers, but the frequency was higher in the odor cue of the violet and red flowers than of the yellow without white. In the case of the four-choice olfactometer test, in the same visual cues as the odor cues of the pot mum flowers, the frequency of F. occidentalis was higher in the yellow flower than in the other flowers (white, red, and violet) in all the observation times (10, 15, and 20 minutes).

Keywords: Frankliniella occidentalis, Chrysanthemum, trap plant, control effect

Procedia PDF Downloads 168

Authors: T. Padma, Jayashree S. Pillai

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Random entities are an essential component in any cryptographic application. The suitability of a number theory based novel pseudorandom sequence called Pseudorandom Partial Quotient Sequence (PPQS) generated from the continued fraction expansion of irrational numbers, in cryptographic applications, is analyzed in this paper. An approach to build the algorithm around a hard mathematical problem has been considered. The PQ sequence is tested for randomness and its suitability as a cryptographic key by performing randomness analysis, key sensitivity and key space analysis, precision analysis and evaluating the correlation properties is established.

Keywords: pseudorandom sequences, key sensitivity, correlation, security analysis, randomness analysis, sensitivity analysis

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Authors: Rashmi Tamhankar, Madhav Bapat

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In many projects, we have to use human judgment for determining the duration of the activities which may vary from person to person. Hence, there is vagueness about the time duration for activities in network planning. Fuzzy sets can handle such vague or imprecise concepts and has an application to such network. The vague activity times can be represented by triangular fuzzy numbers. In this paper, a general network with fuzzy activity times is considered and conditions for the critical path are obtained also we compute total float time of each activity. Several numerical examples are discussed.

Keywords: PERT, CPM, triangular fuzzy numbers, fuzzy activity times

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Authors: Lei Zhang, Jean-Michel Ghidaglia, Anela Kumbaro

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This work focuses on numerical simulation of two-phase flows based on the bi-fluid six-equation model widely used in many industrial areas, such as nuclear power plant safety analysis. A pressure-based numerical method is adopted in our studies due to the fact that in two-phase flows, it is common to have a large range of Mach numbers because of the mixture of liquid and gas, and density-based solvers experience stiffness problems as well as a loss of accuracy when approaching the low Mach number limit. This work extends the semi-implicit pressure solver in the nuclear component CUPID code, where the governing equations are solved on unstructured grids with co-located variables to accommodate complicated geometries. A conservative version of the solver is developed in order to capture exactly the shock in one-phase flows, and is extended to two-phase situations. An inter-facial pressure term is added to the bi-fluid model to make the system hyperbolic and to establish a well-posed mathematical problem that will allow us to obtain convergent solutions with refined meshes. The ability of the numerical method to treat phase appearance and disappearance as well as the behavior of the scheme at low Mach numbers will be demonstrated through several numerical results. Finally, inter-facial mass and heat transfer models are included to deal with situations when mass and energy transfer between phases is important, and associated industrial numerical benchmarks with tabulated EOS (equations of state) for fluids are performed.

Keywords: two-phase flows, numerical simulation, bi-fluid model, unstructured grids, phase appearance and disappearance

Procedia PDF Downloads 377

Authors: Ric Joseph R. Murillo, Edna N. Gueco, Dennis I. Merino

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Let F be C or R, where C and R are the set of complex numbers and real numbers, respectively, and n be a natural number. An n-by-n matrix A over the field F is called an α-involutory matrix or an α-involution if there exists an α in the field such that the square of the matrix is equal to αI, where I is the n-by-n identity matrix. If α is a complex number or a nonnegative real number, then an n-by-n matrix A over the field F can be written as a sum of n-by-n α-involutory matrices over the field F if and only if the trace of that matrix is an integral multiple of the square root of α. Meanwhile, if α is a negative real number, then a 2n-by-2n matrix A over R can be written as a sum of 2n-by-2n α-involutory matrices over R if and only the trace of the matrix is zero. Some other properties of α-involutory matrices are also determined

Keywords: α-involutory Matrices, sum of α-involutory Matrices, Trace, Matrix Theory

Procedia PDF Downloads 170

Authors: A. Torokhti

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A new method of mathematical modeling of the distributed nonlinear system is developed. The system is represented by a combination of the set of spatially distributed sensors and the fusion center. Its mathematical model is obtained from the iterative procedure that converges to the model which is optimal in the sense of minimizing an associated cost function.

Keywords: mathematical modeling, non-linear system, spatially distributed sensors, fusion center

Procedia PDF Downloads 367

Authors: Gohar Marikyan

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This article is about investigating how to effectively use visuals in teaching introductory mathematics. The analysis showed the use of visuals in teaching introductory mathematics can be an effective tool for enhancing students’ learning and engagement in mathematics. The use of visuals was particularly effective for teaching concepts of numbers, operations with whole numbers, and properties of operations. The analysis also provides strong evidence that the effectiveness of visuals varied depending on the way the visuals are used. Furthermore, the analysis revealed that the use of visuals in mathematics instruction had a positive impact on student’s attitudes toward mathematics, with students showing higher levels of motivation and enjoyment in mathematics classes.

Keywords: analytical thinking skills, instructional strategies with visuals, introductory mathematics, student engagement and motivation

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Authors: Parisa Khoshvaght, Mehdi Hosseinzadeh

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During the past few years, the Residue Number System (RNS) has been receiving considerable interest due to its parallel and fault-tolerant properties. This system is a useful tool for Digital Signal Processing (DSP) since it can support parallel, carry-free, high-speed and low power arithmetic. One of the drawbacks of Residue Number System is the fractional numbers, that is, the corresponding circuit is very hard to realize in conventional CMOS technology. In this paper, we propose a method in which the numbers of transistors are significantly reduced. The related delay is extremely diminished, in the first glance we use this method to solve concerning problem of one decimal functional number some how this proposition can be extended to generalize the idea. Another advantage of this method is the independency on the kind of moduli.

Keywords: computer arithmetic, residue number system, number system, one-Hot, VLSI

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Authors: Ketan Naik, P. H. Bhathawala

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The purpose of this work is to develop a mathematical model of Human Cardiovascular System using lumped parameter method. The model is divided in three parts: Systemic Circulation, Pulmonary Circulation and the Heart. The established mathematical model has been simulated by MATLAB software. The innovation of this study is in describing the system based on the vessel diameters and simulating mathematical equations with active electrical elements. Terminology of human physical body and required physical data like vessel’s radius, thickness etc., which are required to calculate circuit parameters like resistance, inductance and capacitance, are proceeds from well-known medical books. The developed model is useful to understand the anatomic of human cardiovascular system and related syndromes. The model is deal with vessel’s pressure and blood flow at certain time.

Keywords: cardiovascular system, lumped parameter method, mathematical modeling, simulation

Procedia PDF Downloads 322

Authors: Nidal F. Shilbayeh, Remah W. Al-Khatib, Sameer A. Nooh

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Arabic offline handwriting recognition systems are considered as one of the most challenging topics. Arabic Handwritten Numeral Strings are used to automate systems that deal with numbers such as postal code, banking account numbers and numbers on car plates. Segmentation of connected numerals is the main bottleneck in the handwritten numeral recognition system.  This is in turn can increase the speed and efficiency of the recognition system. In this paper, we proposed algorithms for automatic segmentation and feature extraction of Arabic handwritten numeral strings based on Watershed approach. The algorithms have been designed and implemented to achieve the main goal of segmenting and extracting the string of numeral digits written by hand especially in a courtesy amount of bank checks. The segmentation algorithm partitions the string into multiple regions that can be associated with the properties of one or more criteria. The numeral extraction algorithm extracts the numeral string digits into separated individual digit. Both algorithms for segmentation and feature extraction have been tested successfully and efficiently for all types of numerals.

Keywords: handwritten numerals, segmentation, courtesy amount, feature extraction, numeral recognition

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Authors: P. Mendes, H. Stel, R. E. M. Morales

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This article presents a numerical and experimental study of turbulent flow in corrugated pipes with helically “d-type" grooves, for Reynolds numbers between 7500 and 100,000. The ANSYS-CFX software is used to solve the RANS equations with the BSL two equation turbulence model, through the element-based finite-volume method approach. Different groove widths and helix angles are considered. Numerical results are validated with experimental pressure drop measurements for the friction factor. A correlation for the friction factor is also proposed considering the geometric parameters and Reynolds numbers evaluated.

Keywords: turbulent flow, corrugated pipe, helical, numerical, experimental, friction factor, correlation

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Authors: Amir B. Khoshnevis, Morteza Mirhosseini

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The paper deals with a sub-part of an extensive research program on the wake survey method in various Reynolds numbers and angles of attack. This research experimentally investigates the wake flow characteristics behind S823 and S822 airfoils in which designed for small wind turbines. Velocity measurements determined by using hot-wire anemometer. Data acquired in the wake of the airfoil at locations(c is the chord length): 0.01c - 3c. Reynolds number increased due to increase of free stream velocity. Results showed that mean velocity profiles depend on the angle of attack and location of data collections. Data acquired at the low Reynolds numbers (smaller than 10^5). Effects of Reynolds numbers on the mean velocity profiles are more significant in near locations the trailing edge and these effects decrease by taking distance from trailing edge toward downstream. Mean velocity profiles region increased by increasing the angle of attack, except for 7°, and also the maximum velocity deficit (velocity defect) increased. The difference of mean velocity in and out of the wake decreased by taking distance from trailing edge, and mean velocity profile become wider and more uniform.

Keywords: angle of attack, Reynolds number, velocity deficit, separation

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Authors: Jaroslav Krutil, František Pochylý, Simona Fialová, Vladimír Habán

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A mathematical model of the additional effects of the liquid in the hydrodynamic gap is presented in the paper. An in-compressible viscous fluid is considered. Based on computational modeling are determined the matrices of mass, stiffness and damping. The mathematical model is experimentally verified.

Keywords: computational modeling, mathematical model, hydrodynamic gap, matrices of mass, stiffness and damping

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Authors: Paula Verdugo-Hernandez, Patricio Cumsille

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We analyze a first-class on the convergence of real number sequences, named hereafter sequences, to foster exploration and discovery of concepts through graphical representations before engaging students in proving. The main goal was to differentiate between sequences and continuous functions-of-a-real-variable and better understand concepts at an initial stage. We applied the analytic frame of mathematical working spaces, which we expect to contribute to extending to sequences since, as far as we know, it has only developed for other objects, and which is relevant to analyze how mathematical work is built systematically by connecting the epistemological and cognitive perspectives, and involving the semiotic, instrumental, and discursive dimensions.

Keywords: convergence, graphical representations, mathematical working spaces, paradigms of real analysis, real number sequences

Procedia PDF Downloads 131

Authors: Song Hyok Choe

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This study presented a method to determine the optimum design parameters based on a mathematical model of the operating process in a manual electromagnetic hammer using solenoid electromagnets. The operating process of the electromagnetic hammer depends on the circuit scheme of the power controller. Mathematical modeling of the operating process was carried out by considering the energy transfer process in the forward and reverse windings and the electromagnetic force acting on the impact and brake pistons. Using the developed mathematical model, the initial design data of a manual electromagnetic hammer proposed in this paper are encoded and analyzed in Matlab. On the other hand, a measuring experiment was carried out by using a measurement device to check the accuracy of the developed mathematical model. The relative errors of the analytical results for measured stroke distance of the impact piston, peak value of forward stroke current and peak value of reverse stroke current were −4.65%, 9.08% and 9.35%, respectively. Finally, it was shown that the mathematical model of the operating process of an electromagnetic hammer is relatively accurate, and it can be used to determine the design parameters of the electromagnetic hammer. Therefore, the design parameters that can provide the required impact energy in the manual electromagnetic hammer were determined using a mathematical model developed. The proposed method will be used for the further design and development of the various types of percussion rock drills.

Keywords: solenoid electromagnet, electromagnetic hammer, stone processing, mathematical modeling

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Authors: N. Ibrahim-Rassoul, A. Kessi, E. K. Si-Ahmed, N. Djilali, J. Legrand

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The static and dynamic formation of liquid water bridges is analyzed using a combination of visualization experiments in a microchannel with a mathematical model. This paper presents experimental and theoretical findings of water plug/capillary bridge formation in a 250 μm squared microchannel. The approach combines mathematical and numerical modeling with experimental visualization and measurements. The generality of the model is also illustrated for flow conditions encountered in manipulation of polymeric materials and formation of liquid bridges between patterned surfaces. The predictions of the model agree favorably the observations as well as with the experimental recordings.

Keywords: green energy, mathematical modeling, fuel cell, water plug, gas diffusion layer, surface of revolution

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Authors: Zahid Ullah, Atlas Khan

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The rapid advancements in data collection, storage, and processing capabilities have led to an explosion of data in various domains. In this era of big data, mathematical sciences play a crucial role in uncovering valuable insights and driving informed decision-making through data analytics. The purpose of this abstract is to present the latest advances in mathematical sciences and their application in harnessing the power of data analytics. This abstract highlights the interdisciplinary nature of data analytics, showcasing how mathematics intersects with statistics, computer science, and other related fields to develop cutting-edge methodologies. It explores key mathematical techniques such as optimization, mathematical modeling, network analysis, and computational algorithms that underpin effective data analysis and interpretation. The abstract emphasizes the role of mathematical sciences in addressing real-world challenges across different sectors, including finance, healthcare, engineering, social sciences, and beyond. It showcases how mathematical models and statistical methods extract meaningful insights from complex datasets, facilitating evidence-based decision-making and driving innovation. Furthermore, the abstract emphasizes the importance of collaboration and knowledge exchange among researchers, practitioners, and industry professionals. It recognizes the value of interdisciplinary collaborations and the need to bridge the gap between academia and industry to ensure the practical application of mathematical advancements in data analytics. The abstract highlights the significance of ongoing research in mathematical sciences and its impact on data analytics. It emphasizes the need for continued exploration and innovation in mathematical methodologies to tackle emerging challenges in the era of big data and digital transformation. In summary, this abstract sheds light on the advances in mathematical sciences and their pivotal role in unveiling the power of data analytics. It calls for interdisciplinary collaboration, knowledge exchange, and ongoing research to further unlock the potential of mathematical methodologies in addressing complex problems and driving data-driven decision-making in various domains.

Keywords: mathematical sciences, data analytics, advances, unveiling

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Authors: Anthony Overmars, Sitalakshmi Venkatraman

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This paper presents a method for determining all of the co-prime right angle triangles in the Euclidean field by looking at the intersection of the Pythagorean and Platonic right angle triangles and the corresponding lattice that this produces. The co-prime properties of each lattice point representing a unique right angle triangle are then considered. This paper proposes a conjunction between these two ancient disparaging theorists. This work has wide applications in information security where cryptography involves improved ways of finding tuples of prime numbers for secure communication systems. In particular, this paper has direct impact in enhancing the encryption and decryption algorithms in cryptography.

Keywords: Pythagorean triples, platonic triples, right angle triangles, co-prime numbers, cryptography

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Authors: Bathmajaa Muralisankar

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As much as railway station infrastructure designs and ticket-booking norms have been changed to facilitate use by differently abled persons, the railway train compartments themselves have not been made user-friendly for differently abled persons. Owing to safety concerns, dependency on others for their travel, and fear of isolation, differently abled people do not prefer travelling by train. Rather than including a dedicated compartment open only to the differently abled, including the latter with others in the normal compartment (with the proposed modifications discussed here) will make them feel secure and make for an enhanced travel experience for them. This approach also represents the most practical way to include a particular category of people in the mainstream society. Lowering the height of the compartment doors and providing a wider entrance with a ramp will provide easy entry for those using wheelchairs. As well, removing the first two alternate rows and the first two side seats will not only widen the passage and increase seating space but also improve wheelchair turning radius. This will help them travel without having to depend on others. Seating arrangements may be done to accommodate their family members near them instead of isolating the differently abled in a separate compartment. According to present ticket-booking regulations of the Indian Railways, three to four disabled persons may travel without their family or one to two along with their family, and the numbers may be added or reduced. To help visually challenged and hearing-impaired persons, in addition to the provision of special instruments, railings, and textured footpaths and flooring, the seat numbers above the seats may be set in metal or plastic as an outward projection so the visually impaired can touch and feel the numbers. Braille boards may be included at the entrance to the compartment along with seat numbers in the aforementioned projected manner. These seat numbers may be designed as buttons, which when pressed results in an announcement of the seat number in the applicable local language as well as English. Emergency buttons, rather than emergency chains, within the easy reach of disabled passengers will also help them.

Keywords: dependency, differently abled, inclusion, mainstream society

Procedia PDF Downloads 240

Authors: Mohammed Abubakar Ndanusa, A. A. Hassan, R. W. Gimba, A. M. Alfa, M. T. Abari

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This study investigated the Impact of Mathematical Modeling on Mathematics Achievement, Attitude and Interest of Pre-Service Teachers in Niger States, Nigeria. It was an attempt to ease students’ difficulties in comprehending mathematics. The study used randomized pretest, posttest control group design. Two Colleges of Education were purposively selected from Niger State with a sample size of eighty-four 84 students. Three research instruments used are Mathematical Modeling Achievement Test (MMAT), Attitudes Towards Mathematical Modeling Questionnaire (ATMMQ) and Mathematical Modeling Students Interest Questionnaire (MMSIQ). Pearson Product Moment Correlation (PPMC) formula was used for MMAT and Alpha Cronbach was used for ATMMQ and MMSIQ to determine their reliability coefficient and the values the following values were obtained respectively 0.76, 0.75 and 0.73. Independent t-test statistics was used to test hypothesis One while Mann Whitney U-test was used to test hypothesis Two and Three. Findings revealed that students taught Mathematics using Mathematical Modeling performed better than their counterparts taught using lecture method. However, there was a significant difference in the attitude and interest of pre-service mathematics teachers after being exposed to mathematical modeling. The strategy, therefore, was recommended to be used by Mathematics teachers with a view to improving students’ attitude and interest towards Mathematics. Also, modeling should be taught at NCE level in order to prepare pre-service teachers towards real task in the field of Mathematics.

Keywords: achievement, attitude, interest, mathematical modeling, pre-service teachers

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Authors: Chang He, Hiroshi Tamura, Hiroshi Katsuchi, Jiaqi Wang

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In this study, the aim is to infer the slip limit (static friction limit) of contact interfaces in bolt friction joints by analyzing other bolt friction joints with the same contact surface but in a different shape. By using the Weibull distribution to deal with microelements on the contact surface statistically, the slip limit of a certain type of bolt joint was predicted from other types of bolt joint with the same contact surface. As a result, this research succeeded in predicting the slip limit of bolt joins with different numbers of contact surfaces and with different numbers of bolt rows.

Keywords: bolt joints, slip coefficient, finite element method, Weibull distribution

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Authors: Felicitas Pielsticker, Christoph Pielsticker, Ingo Witzke

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Neurological findings provide foundational results for many different disciplines. In this article we want to discuss these with a special focus on mathematics education. The intention is to make neuroscience research useful for the description of cognitive mathematical learning processes. A key issue of mathematics education is that students often behave as if their mathematical knowledge is constructed in isolated compartments with respect to the specific context of the original learning situation; supporting students to link these compartments to form a coherent mathematical society of mind is a fundamental task not only for mathematics teachers. This aspect goes hand in hand with the question if there is such a thing as abstract general mathematical knowledge detached from concrete reality. Educational Neuroscience may give answers to the question why students develop their mathematical knowledge in isolated subjective domains of experience and if it is generally possible to think in abstract terms. To address these questions, we will provide examples from different fields of mathematics education e.g. students’ development and understanding of the general concept of variables or the mathematical notion of universal proofs. We want to discuss these aspects in the reflection of functional studies which elucidate the role of specific brain regions in mathematical learning processes. In doing this the paper addresses concept formation processes of students in the mathematics classroom and how to support them adequately considering the results of (educational) neuroscience.

Keywords: brain regions, concept formation processes in mathematics education, proofs, teaching-learning processes

Procedia PDF Downloads 125

Authors: Liang Ming Zhong, Yu Zhong, Wen Zhong, Fei Fei Yin

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Trinary affinity is a description of existence: every object exists as it is known and spoken of, in a system of 2 differences (denoted dif1, dif₂) and 1 similarity (Sim), equivalently expressed as dif₁ / Sim / dif₂ and kn / 0 / tkn (kn = the known, tkn = the 'to be known', 0 = the zero point of knowing). They are mathematically verified and illustrated in this paper by the arrangement of all integers onto 3 columns, where each number exists as a difference in relation to another number as another difference, and the 2 difs as arbitrated by a third number as the Sim, resulting in a trinary affinity or trinity of 3 numbers, of which one is the known, the other the 'to be known', and the third the zero (0) from which both the kn and tkn are measured and specified. Consequently, any number is horizontally specified either as 3n, or as '3n – 1' or '3n + 1', and vertically as 'Cn + c', so that any number seems to occur at the intersection of its X and Y axes and represented by its X and Y coordinates, as any point on Earth’s surface by its latitude and longitude. Technically, i) primes are viewed and treated as progenitors, and composites as descending from them, forming families of composites, each capable of being measured and specified from its own zero called in this paper the realistic zero (denoted 0r, as contrasted to the mathematic zero, 0m), which corresponds to the constant c, and the nature of which separates the composite and prime numbers, and ii) any number is considered as having a magnitude as well as a position, so that a number is verified as a prime first by referring to its descriptive formula and then by making sure that no composite number can possibly occur on its position, by dividing it with factors provided by the composite number formulas. The paper consists of 3 parts: 1) a brief explanation of the trinary affinity of things, 2) the 8 formulas that represent ALL the primes, and 3) families of composite numbers, each represented by a formula. A composite number family is described as 3n + f₁‧f₂. Since there are an infinitely large number of composite number families, to verify the primality of a great probable prime, we have to have it divided with several or many a f₁ from a range of composite number formulas, a procedure that is as laborious as it is the surest way to verifying a great number’s primality. (So, it is possible to substitute planned division for trial division.)

Keywords: trinary affinity, difference, similarity, realistic zero

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Authors: A. A. A. Aboalnour, Ahmed M. Amasaib, Mohammed-Almujtaba A. Mohammed-Farah, Abdelhakam, A. Noreldien

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This paper presents a design and study of Parabolic Trough Solar Collector (PTC). Mathematical models were used in this work to find the direct and reflected solar radiation from the air layer on the surface of the earth per hour based on the total daily solar radiation on a horizontal surface. Also mathematical models had been used to calculate the radiation of the tilted surfaces. Most of the ingredients used in this project as previews data required on several solar energy applications, thermal simulation, and solar power systems. In addition, mathematical models had been used to study the flow of the fluid inside the tube (receiver), and study the effect of direct and reflected solar radiation on the pressure, temperature, speed, kinetic energy and forces of fluid inside the tube. Finally, the mathematical models had been used to study the (PTC) performances and estimate its thermal efficiency.

Keywords: CFD, experimental, mathematical models, parabolic trough, radiation

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Authors: Md Kamruzzaman, Lyazid Djenidi, R. A. Antonia

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This paper reports an experimental investigation of the energy spectrum of turbulent velocity fields at low Reynolds numbers ( Rλ ) in grid turbulence. Hot wire measurements are carried out in grid turbulence with subjected to a 1.36:1 contraction of the wind tunnel. Three different grids are used: (i) large square perforated grid (mesh size 43.75 mm), (ii) small square perforated grid (mesh size 14 and (iii) woven mesh grid (mesh size 5mm). The results indicate that the energy spectrum at small Rλ does not follow Kolmogorov’s universal scaling. It is further found that the critical Reynolds number,Rλ,ϲ below which the scaling breaks down is around 25.

Keywords: energy spectrum, Taylor microscale, Reynolds number, turbulent kinetic energy, decay exponent

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Authors: Benjamin Okike

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There is a need to hide information along the superhighway. Today, information relating to the survival of individuals, organizations, or government agencies is transmitted from one point to another. Adversaries are always on the watch along the superhighway to intercept any information that would enable them to inflict psychological ‘injuries’ to their victims. But with information encryption, this can be prevented completely or at worst reduced to the barest minimum. There is no doubt that so many encryption techniques have been proposed, and some of them are already being implemented. However, adversaries always discover loopholes on them to perpetuate their evil plans. In this work, we propose the enhanced data encryption standard (EDES) that would deploy randomly generated numbers as an encryption method. Each time encryption is to be carried out, a new set of random numbers would be generated, thereby making it almost impossible for cryptanalysts to decrypt any information encrypted with this newly proposed method.

Keywords: encryption, enhanced data encryption, encryption techniques, information security

Procedia PDF Downloads 131