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Artykuły w czasopismach na temat „Operations on rational numbers”

Autor: Grafiati

Data publikacji: 2 czerwca 2025

Data aktualizacji: 31 lipca 2025

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1

Christou, Konstantinos P., Courtney Pollack, Jo Van Hoof, and Wim Van Dooren. "Natural number bias in arithmetic operations with missing numbers – A reaction time study." Journal of Numerical Cognition 6, no. 1 (2020): 22–49. http://dx.doi.org/10.5964/jnc.v6i1.228.

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When reasoning about numbers, students are susceptible to a natural number bias (NNB): When reasoning about non-natural numbers they use properties of natural numbers that do not apply. The present study examined the NNB when students are asked to evaluate the validity of algebraic equations involving multiplication and division, with an unknown, a given operand, and a given result; numbers were either small or large natural numbers, or decimal numbers (e.g., 3 × _ = 12, 6 × _ = 498, 6.1 × _ = 17.2). Equations varied on number congruency (unknown operands were either natural or rational number

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Moss, Joan. "Research, Reflection, Practice: Introducing Percents in Linear Measurement to Foster an Understanding of Rational-Number Operations." Teaching Children Mathematics 9, no. 6 (2003): 335–39. http://dx.doi.org/10.5951/tcm.9.6.0335.

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How do we foster computational fluency with rational numbers when this topic is known to pose so many conceptual challenges for young students? How can we help students understand the operations of rational numbers when their grasp of the quantities involved in the rational-number system is often very limited? Traditional instruction in rational numbers focuses on rules and memorization. Teachers often give students instructions such as, “To add fractions, first find a common denominator, then add only the numerators” or “To add and subtract decimal numbers, line up the decimals, then do your

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Schwarzweller, Christoph, and Artur Korniłowicz. "Characteristic of Rings. Prime Fields." Formalized Mathematics 23, no. 4 (2015): 333–49. http://dx.doi.org/10.1515/forma-2015-0027.

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Summary The notion of the characteristic of rings and its basic properties are formalized [14], [39], [20]. Classification of prime fields in terms of isomorphisms with appropriate fields (ℚ or ℤ/p) are presented. To facilitate reasonings within the field of rational numbers, values of numerators and denominators of basic operations over rationals are computed.

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Putra, Zetra Hainul. "Didactic Transposition of Rational Numbers: a Case From a Textbook Analysis and Prospective Elementary Teachers’ Mathematical and Didactic Knowledge." Revija za elementarno izobraževanje 13, no. 4 (2020): 365–94. http://dx.doi.org/10.18690/rei.13.4.365-394.2020.

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This study aims to present a detailed analysis of didactic transposition of rational numbers from knowledge to be taught into taught knowledge occurring in a teacher education institution. The knowledge to be taught of rational numbers is analysed from the mathematics textbook used by prospective elementary teachers in a mathematics education course. The analysis focuses on mathematical praxeology, especially the type of task and technique. Then, the taught knowledge is investigated from 32 prospective elementary teachers’ collaborative work on two hypothetical teacher tasks (HTT) related to o

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Nowlin, Douald. "Division with Fractions." Mathematics Teaching in the Middle School 2, no. 2 (1996): 116–19. http://dx.doi.org/10.5951/mtms.2.2.0116.

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Although operations with fractions have been in the elementary and middle school curriculum for many years, finding examples of practical problems that illustrate the usefulness of division with fractions and mixed numbers is not easy. Most real-world applications of rational numbers involve decimal numerals (Usiskin and Bell 1984), but examples of division with fractions and mixed numbers are often obviously contrived. In addition, many teachers and prospective teachers have difficulty constructing examples and concrete models for the operation of division with fractions (Borko 1992; Ball 198

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Gorbunov, Konstantin, and Vassily Lyubetsky. "Linear Time Additively Exact Algorithm for Transformation of Chain-Cycle Graphs for Arbitrary Costs of Deletions and Insertions." Mathematics 8, no. 11 (2020): 2001. http://dx.doi.org/10.3390/math8112001.

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We propose a novel linear time algorithm which, given any directed weighted graphs a and b with vertex degrees 1 or 2, constructs a sequence of operations transforming a into b. The total cost of operations in this sequence is minimal among all possible ones or differs from the minimum by an additive constant that depends only on operation costs but not on the graphs themselves; this difference is small as compared to the operation costs and is explicitly computed. We assume that the double cut and join operations have identical costs, and costs of the deletion and insertion operations are arb

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Chung, Heewon, and Myungsun Kim. "Encoding of Rational Numbers and Their Homomorphic Computations for FHE-Based Applications." International Journal of Foundations of Computer Science 29, no. 06 (2018): 1023–44. http://dx.doi.org/10.1142/s0129054118500193.

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This work addresses a basic problem of security systems that operate on very sensitive information. Specifically, we are interested in the problem of privately handling numeric data represented by rational numbers (e.g., medical records). Fully homomorphic encryption (FHE) is one of the natural and powerful tools for ensuring privacy of sensitive data, while allowing complicated computations on the data. However, because the native plaintext domain of known FHE schemes is restricted to a set of quite small integers, it is not easy to obtain efficient algorithms for encrypted rational numbers i

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8

Yakes, Christopher. "Rational Number Operations on the Number Line." Mathematics Enthusiast 14, no. 1-3 (2017): 309–24. http://dx.doi.org/10.54870/1551-3440.1400.

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Jay, Ar I. Laranang Edd, En Jay B. Santiago Prince, Louise Oca Danielle, and Vincent T. Bongon Patrick. "Math SCRABBLE (Strengthening Critical Thinking and Problem-Solving, Reinforcing Rational Numbers and Integers, Applying Basic Operations for Building Learner's Excellence in Mathematics)." International Journal of Social Science and Education Research Studies 05, no. 05 (2025): 435–44. https://doi.org/10.5281/zenodo.15469834.

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Abstract : This action research explores the impact of an innovative game-based intervention entitled “Math SCRABBLE (Strengthening Critical Thinking and Problem-Solving, Reinforcing Rational Numbers and Integers, Applying Basic Operations for Building Learner’s Excellence in Mathematics),” on the academic performance of grade 7 students at Mount Carmel College of Casiguran, Inc., academic year 2024-2025. The research employs a quasi-experimental design with purposive sampling consisting of an experimental and control group, wherein the experimental group undergoes the interv

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10

Carvalho, Alexia Bezerra de, Rita de Cássia da Costa Guimarães, William Vieira, Emanoel Fabiano Menezes Pereira, and Roberto Seidi Imafuku. "Sobre dificuldades de ingressantes no ensino médio na compreensão de números racionais." ForScience 9, no. 1 (2021): e00878. http://dx.doi.org/10.29069/forscience.2021v9n1.e878.

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Apresenta-se, neste artigo, uma análise da resolução de uma questão sobre números racionais, exposta por estudantes ingressantes no Ensino Médio. O objetivo foi identificar as principais dificuldades e erros apresentados pelos participantes sobre o conceito e operações de números racionais. Para isso, realizou-se uma análise de erros das resoluções apresentadas pelos participantes. A interação de aspectos algorítmicos, intuitivos e formais é o referencial teórico adotado nas análises. Verificou-se que os estudantes não possuem clareza sobre o conceito de número racional e apresentam, em decorr

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11

Bergstra, Jan A. "Most General Algebraic Specifications for an Abstract Datatype of Rational Numbers." Scientific Annals of Computer Science XXX, no. 1 (2020): 1–24. https://doi.org/10.7561/SACS.2020.1.1.

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The notion of a most general algebraic specification of an arithmetical datatype of characteristic zero is introduced.Three examples of such specifications are given. A preference is formulated for a specification by means of infinitely many equations which can be presented via a finite number of so-called schematic equations phrased in terms of an infinite signature. On the basis of the latter specification three topics are discussed: (i) fracterm decomposition operators and the numerator paradox,  (ii) foundational specifications of arithmetical datatypes, and  (iii) poly-infix ope

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12

Azim, Diane. "Understanding Multiplication as One Operation." Mathematics Teaching in the Middle School 7, no. 8 (2002): 466–71. http://dx.doi.org/10.5951/mtms.7.8.0466.

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Some of the wonder of numbers becomes apparent when we use numbers to perform calculations. Understanding multiplication with positive rational numbers is not a simple process. It requires reconceptualizing the meanings of multiplication with whole numbers to include numbers that are less than 1 or are mixed numbers. (Numbers in this article are all non-negative numbers.) To learn how multiplication works with fractions is to experience a whole new meaning for multiplication.

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13

LINES, DANIEL. "KNOTS WITH UNKNOTTING NUMBER ONE AND GENERALISED CASSON INVARIANT." Journal of Knot Theory and Its Ramifications 05, no. 01 (1996): 87–100. http://dx.doi.org/10.1142/s0218216596000072.

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We extend the classical notion of unknotting operation to include operations on rational tangles. We recall the “classical” conditions (on the signature, linking form etc.) for a knot to have integral (respectively rational) unknotting number one. We show that the generalised Casson invariant of the twofold branched cover of the knot gives a further necessary condition. We apply these results to some Montesinos knots and to knots with less than nine crossings.

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14

Lin, Xi. "Difficulties in Learning and Teaching Numbers: A Literature Review on the Obstacles and Misconceptions of Learners and Instructors." Journal of Contemporary Educational Research 6, no. 6 (2022): 111–18. http://dx.doi.org/10.26689/jcer.v6i6.4073.

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This paper attempts to summarize a number of research studies on numbers. The purpose of this study was to investigate and identify the obstacles encountered by students when they are dealing with number reasoning (whole numbers, integers, and rational numbers) and the difficulties faced by pre-service teachers in teaching arithmetic, including their misconceptions and weaknesses when they teach arithmetic and operations. There are two main sections in this paper: students’ cognitive obstacles for number reasoning, and pre-service teachers’ misconceptions of arithmetic. With the summarized mis

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15

Egamnazarov, B. B. "ШОЛИЧИЛИК КЛАСТЕРИ БОШ МОДЕЛИ ВА МАШИНА ПАРКИ ТАРКИБИНИ АСОСЛАШ". Journal of Science and Innovative Development 6, № 3 (2023): 106–14. http://dx.doi.org/10.36522/2181-9637-2023-3-11.

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This article presents the results of a study on the development of a general model of the rice cluster and the determination of the composition, types and quantity of the required machine park. The concept of “General model of a rice-growing cluster” is introduced and its definition is given. The general model for sown area is substantiated by the following sequence: regional rice clusters are grouped according to the values of sown area; clusters with the largest sown areas were selected from the groups and the corresponding variational series of numbers was formed; the upper limit of the mat

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16

Fabulya, Zoltán. "Designing an Excel VBA function to recognize more important irrational numbers." Analecta Technica Szegedinensia 16, no. 1 (2022): 62–70. http://dx.doi.org/10.14232/analecta.2022.1.62-70.

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Calculations typically performed on a calculator or computer show the result as a decimal fraction if it is not an integer. It would be easier to interpret the result if a value could be expressed with integers and operations, such as the root subtraction operation. This article shows how this can be done with a developed algorithm in Microsoft Excel, which recognizes the most famous irrational numbers and displays them in text form together with the character of the operation sign. For example, “5√3/2” is given for 4.330127019. It is also useful to display irrational numbers with integers bec

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17

Ramírez, Juan. "A New Set Theory for Analysis." Axioms 8, no. 1 (2019): 31. http://dx.doi.org/10.3390/axioms8010031.

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We provide a canonical construction of the natural numbers in the universe of sets. Then, the power set of the natural numbers is given the structure of the real number system. For this, we prove the co-finite topology, C o f ( N ) , is isomorphic to the natural numbers. Then, we prove the power set of integers, 2 Z , contains a subset isomorphic to the non-negative real numbers, with all its defining structures of operations and order. We use these results to give the power set, 2 N , the structure of the real number system. We give simple rules for calculating addition, multiplication, subtr

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18

Siegler, Robert S., and Hugues Lortie-Forgues. "Hard Lessons: Why Rational Number Arithmetic Is So Difficult for So Many People." Current Directions in Psychological Science 26, no. 4 (2017): 346–51. http://dx.doi.org/10.1177/0963721417700129.

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Fraction and decimal arithmetic pose large difficulties for many children and adults. This is a serious problem because proficiency with these skills is crucial for learning more advanced mathematics and science and for success in many occupations. This review identifies two main classes of difficulties that underlie poor understanding of rational number arithmetic: inherent and culturally contingent. Inherent sources of difficulty are ones that are imposed by the task of learning rational number arithmetic, such as complex relations among fraction arithmetic operations. They are present for a

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19

Abbasi, F., and T. Allahviranloo. "Fuzzy reliability estimation using the new operations of transmission average on Rational-linear patchy fuzzy numbers." Soft Computing 23, no. 10 (2018): 3383–96. http://dx.doi.org/10.1007/s00500-017-2996-6.

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Schneider, Gregory R. "Foliated compressing discs for Legendrian rational tangles." Journal of Knot Theory and Its Ramifications 25, no. 06 (2016): 1650029. http://dx.doi.org/10.1142/s0218216516500292.

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We establish a new framework for diagramming both Legendrian rational tangles in the standard contact structure on [Formula: see text] and the signed characteristic foliations of their associated compressing discs, as well as the technical means by which these diagrams can be used to study Legendrian isotopies of such tangles. We then establish a number of results that represent new progress in the ongoing effort to classify Legendrian rational tangles under a pair of operations known as Legendrian flypes. These operations, while topologically isotopies, are known to produce distinct Legendria

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Zhou, Meijun, Jiayu Qin, Gang Mei, and John C. Tipper. "Simple and Robust Boolean Operations for Triangulated Surfaces." Mathematics 11, no. 12 (2023): 2713. http://dx.doi.org/10.3390/math11122713.

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Boolean operations on geometric models are important in numerical simulation and serve as essential tools in the fields of computer-aided design and computer graphics. The accuracy of these operations is heavily influenced by finite precision arithmetic, a commonly employed technique in geometric calculations, which introduces numerical approximations. To ensure robustness in Boolean operations, numerical methods relying on rational numbers or geometric predicates have been developed. These methods circumvent the accumulation of rounding errors during computation, thus preserving accuracy. Non

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22

Li, Wan Qing, Zhe Zhao, and Ling Yu Meng. "Approach for Setting Project Buffer with Engineering Materials Based on the Theory of Unascertained Rational Number." Advanced Materials Research 459 (January 2012): 364–67. http://dx.doi.org/10.4028/www.scientific.net/amr.459.364.

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The paper proposes an approach for setting the size of project buffer based on the theory of unascertained rational numbers and critical chain management. This method applies the optimistic time into programming schedule plan and using the addition operation of unascertained rational numbers to obtain the unascertained schedule plan, to finish and generate cumulative reliability. This technique is applied to calculate the buffer time by using the optimistic construction period and total project period when finishing reliability is 90%. This feasibility of the model has been proved by an exampl

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Trümper, Manfred. "The Collatz Problem in the Light of an Infinite Free Semigroup." Chinese Journal of Mathematics 2014 (April 30, 2014): 1–21. http://dx.doi.org/10.1155/2014/756917.

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The Collatz (or 3m+1) problem is examined in terms of a free semigroup on which suitable diophantine and rational functions are defined. The elements of the semigroup, called T-words, comprise the information about the Collatz operations which relate an odd start number to an odd end number, the group operation being the concatenation of T-words. This view puts the concept of encoding vectors, first introduced in 1976 by Terras, in the proper mathematical context. A method is described which allows to determine a one-parameter family of start numbers compatible with any given T-word. The resul

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Kärki, Tomi, Jake McMullen, and Erno Lehtinen. "Improving rational number knowledge using the NanoRoboMath digital game." Educational Studies in Mathematics 110, no. 1 (2021): 101–23. http://dx.doi.org/10.1007/s10649-021-10120-6.

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AbstractRational number knowledge is a crucial feature of primary school mathematics that predicts students’ later mathematics achievement. Many students struggle with the transition from natural number to rational number reasoning, so novel pedagogical approaches to support the development of rational number knowledge are valuable to mathematics educators worldwide. Digital game-based learning environments may support a wide range of mathematics skills. NanoRoboMath, a digital game-based learning environment, was developed to enhance students’ conceptual and adaptive rational number knowledge

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Picciarelli, V., M. Di Gennaro, A. Loconsole, and R. Stella. "Development in mastering of rational number concepts and rational number operations: the role of gender, cognitive style and intellectual skills." International Journal of Mathematical Education in Science and Technology 26, no. 3 (1995): 407–16. http://dx.doi.org/10.1080/0020739950260309.

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Talambutsa, Alexey Leonidovich, and Tobias Hartnick. "Efficient computations with counting functions on free groups and free monoids." Sbornik: Mathematics 214, no. 10 (2023): 1458–99. http://dx.doi.org/10.4213/sm9683e.

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We present efficient algorithms to decide whether two given counting functions on nonabelian free groups or monoids are at bounded distance from each other and to decide whether two given counting quasimorphisms on nonabelian free groups are cohomologous. We work in the multi-tape Turing machine model with nonconstant-time arithmetic operations. In the case of integer coefficients we construct an algorithm of linear time complexity (assuming that the rank is at least $3$ in the monoid case). In the case of rational coefficients we prove that the time complexity is $O(N\log N)$, where $N$ denot

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27

Rahayuningsih, Sri, Ade Eka Anggriani, Mardhatillah, et al. "Examining natural number bias processes in elementary school students: A case study in Indonesia." Multidisciplinary Science Journal 7, no. 8 (2025): 2025381. https://doi.org/10.31893/multiscience.2025381.

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Elementary, middle, and college students often encounter difficulties in grasping rational numbers and their properties. This qualitative study utilized a case study approach to examine the cognitive processes of elementary students affected by natural number bias, contributing to the advancement of cognitive theories in mathematics instruction. Non-random purposive sampling was employed to select participants, with 171 fifth-grade students in Malang undergoing a paper-and-pencil exam. After screening, only seven students qualified as research participants. Data collection involved mathematica

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Feliu, Elisenda. "A chain morphism for Adams operations on rational algebraic K-theory." Journal of K-Theory 5, no. 2 (2009): 349–402. http://dx.doi.org/10.1017/is009010016jkt085.

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AbstractFor any regular noetherian scheme X and every k ≥ 1, we define a chain morphism ψk between two chain complexes whose homology with rational coefficients is isomorphic to the algebraic K-groups of X tensored by ℚ. It is shown that the morphisms ψk induce in homology the Adams operations defined by Gillet and Soulé or the ones defined by Grayson.

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Masáková, Z., J. Patera, and E. Pelantová. "Exceptional algebraic properties of the three quadratic irrationalities observed in quasicrystals." Canadian Journal of Physics 79, no. 2-3 (2001): 687–96. http://dx.doi.org/10.1139/p01-003.

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There are only three irrationalities directly related to experimentally observed quasicrystals, namely, those which appear in extensions of rational numbers by Ö5, Ö2, Ö3. In this article, we demonstrate that the algebraically defined aperiodic point sets with precisely these three irrational numbers play an exceptional role. The exceptional role stems from the possibility of equivalent characterization of these point sets using one binary operation. PACS Nos.: 61.90+d, 61.50-f

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Belinska, A., O. Varankina, O. Bliznjuk, N. Masalitina, and L. Krichkovska. "CONTROL AND OPERATIONS MANAGEMENT OF EXTRACTION PROCESS IN INDUSTRIAL BIOTECHNOLOGY OF BETA-CAROTINE FROM BLAKESLEA TRISPORA." Integrated Technologies and Energy Saving, no. 3 (November 9, 2021): 46–56. http://dx.doi.org/10.20998/2078-5364.2021.3.05.

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The technological parameters, namely temperature and duration of β-carotene extraction process from the biomass of filamentous fungus Blakeslea trispora with vegetable oils of various fatty acid compositions and with various contents of natural antioxidants (refined deodorized sunflower, viso-oleic sunflower, corn and sesame) have been investigated. Statistical models of dependences of β-carotene, as well as analytical numbers, characterizing the content of free fatty acids (acid number) and primary products of lipid oxidation (peroxide number) content, in oil extracts of the specified refined

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Norton, Anderson, and Jesse L. M. Wilkins. "The Splitting Group." Journal for Research in Mathematics Education 43, no. 5 (2012): 557–83. http://dx.doi.org/10.5951/jresematheduc.43.5.0557.

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Piagetian theory describes mathematical development as the construction and organization of mental operations within psychological structures. Research on student learning has identified the vital roles of two particular operations–splitting and units coordination–play in students' development of advanced fractions knowledge. Whereas Steffe and colleagues (e.g., Steffe, 2001; Steffe & Olive, 2010) describe these knowledge structures in terms of fractions schemes, Piaget introduced the possibility of modeling students' psychological structures with formal mathematical structures, such as al

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Asadi, Mohammadali, Alexander Brandt, Robert H. C. Moir, and Marc Moreno Maza. "Algorithms and Data Structures for Sparse Polynomial Arithmetic." Mathematics 7, no. 5 (2019): 441. http://dx.doi.org/10.3390/math7050441.

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We provide a comprehensive presentation of algorithms, data structures, and implementation techniques for high-performance sparse multivariate polynomial arithmetic over the integers and rational numbers as implemented in the freely available Basic Polynomial Algebra Subprograms (BPAS) library. We report on an algorithm for sparse pseudo-division, based on the algorithms for division with remainder, multiplication, and addition, which are also examined herein. The pseudo-division and division with remainder operations are extended to multi-divisor pseudo-division and normal form algorithms, re

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Tang, Shujue. "A TODIM Method Based on 2- Tuple Linguistic Neutrosophic Numbers and Its Application." Journal of Innovation and Development 2, no. 3 (2023): 78–83. http://dx.doi.org/10.54097/jid.v2i3.7280.

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This paper proposes a TODIM method based on 2-Tuple Linguistic Neutrosophic Numbers for the decision-making problem of bounded rational online shopping consumers. Firstly, the definition of 2- Tuple Linguistic Neutrosophic sets, normalized Hamming distance and the operation method of traditional TODIM method are introduced. Then the paper puts forward the operation steps of TODIM method based on 2-Tuple Linguistic Neutrosophic Numbers. Finally, an actual example analysis application is carried out to illustrate the operability and rationality of the method. Suggestions on recommendation functi

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Matczak, K., A. Mućka, and A. B. Romanowska. "Duality for dyadic intervals." International Journal of Algebra and Computation 29, no. 01 (2019): 41–60. http://dx.doi.org/10.1142/s0218196718500625.

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In an earlier paper, Romanowska, Ślusarski and Smith described a duality between the category of (real) polytopes (finitely generated real convex sets considered as barycentric algebras) and a certain category of intersections of hypercubes, considered as barycentric algebras with additional constant operations. This paper is a first step in finding a duality for dyadic polytopes, analogues of real convex polytopes, but defined over the ring [Formula: see text] of dyadic rational numbers instead of the ring of reals. A dyadic [Formula: see text]-dimensional polytope is the intersection with th

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Улитенко, Ю. А., та О. В. Кислов. "МЕТОД ОБҐРУНТУВАННЯ СХЕМИ ТА ВИБОРУ ПАРАМЕТРІВ СИЛОВОЇ УСТАНОВКИ ЛІТАЛЬНОГО АПАРАТУ ДЛЯ ШВИДКОСТЕЙ ПОЛЬОТУ МП = 0…5". Aerospace Technic and Technology, № 7 (7 липня 2017): 5–9. http://dx.doi.org/10.32620/aktt.2017.7.01.

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In this article, we briefly review the main aspects of the method of justifying the choice of the circuit and the parameters of the power plant of an aircraft with flight speeds from 0 to 5 Mach numbers in the early stages of design. The analysis of existing methods is carried out. The algorithm for performing operations for determining the optimum composition and parameters of the power plant, as well as the size of the aircraft depending on the mass of the payload, is stated and justified. Application of the obtained results will allow to shorten the terms of creation of competitive engines

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Campit, Marvin Nonoy B., Cristine A. Enomis, Desiree T. Castillo, and Jane C. Tuan. "Addressing Learning Loss in Mathematics: A Research-Based Intervention." Jurnal Pendidikan Indonesia Gemilang 4, no. 1 (2024): 75–88. https://doi.org/10.53889/jpig.v4i1.348.

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This study aimed to investigate the "learning loss" resulting from recent academic disruptions. This study used a classroom action research, utilizing peer tutoring as the primary intervention amidst various psychological factors. The pretest identifies ten least-mastered mathematics skills, including simplifying numerical expressions, operations on integers, converting fractions to decimals, ordering rational numbers, and solving word problems. Challenges are also noted in approximating volume and area, understanding angles, and interpreting graphical data. Focus group discussions highlight t

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Marei, Sa'ida Tawfiq, and Khalid Muhammad Abo Loum. "The Effect of the Realistic Mathematics Education Approach (RME) in Improving the Conceptual and Operational Level of Proportional Thinking among the Classroom Teacher’s Students." Jordanian Educational Journal 9, no. 3 (2024): 403–27. https://doi.org/10.46515/jaes.v9i3.901.

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This study aimed to reveal the effect of the Realistic Mathematics Education approach (RME) in improving the conceptual and operational level in proportional thinking among the students of the classroom teacher’s students at the Hashemite University. Intentionally choosing two groups who registered the subject of numbers and operations on it, and one of the two groups was randomly assigned as an experimental group, and their number was (39) who were taught using the (RME), and (39) as a control group who were taught through using traditional way. To achieve the objectives of the study, the res

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Cherchi, Gianmarco, Fabio Pellacini, Marco Attene, and Marco Livesu. "Interactive and Robust Mesh Booleans." ACM Transactions on Graphics 41, no. 6 (2022): 1–14. http://dx.doi.org/10.1145/3550454.3555460.

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Boolean operations are among the most used paradigms to create and edit digital shapes. Despite being conceptually simple, the computation of mesh Booleans is notoriously challenging. Main issues come from numerical approximations that make the detection and processing of intersection points inconsistent and unreliable, exposing implementations based on floating point arithmetic to many kinds of degeneracy and failure. Numerical methods based on rational numbers or exact geometric predicates have the needed robustness guarantees, that are achieved at the cost of increased computation times tha

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Cheng, Harry H. "Handling of Complex Numbers in the CHProgramming Language." Scientific Programming 2, no. 3 (1993): 77–106. http://dx.doi.org/10.1155/1993/427160.

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The handling of complex numbers in the CHprogramming language will be described in this paper. Complex is a built-in data type in CH. The I/O, arithmetic and relational operations, and built-in mathematical functions are defined for both regular complex numbers and complex metanumbers of ComplexZero, Complexlnf, and ComplexNaN. Due to polymorphism, the syntax of complex arithmetic and relational operations and built-in mathematical functions are the same as those for real numbers. Besides polymorphism, the built-in mathematical functions are implemented with a variable number of arguments that

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ZHANG, WEI, MARK YEARY, J. Q. TRELEWICZ, and MONTE TULL. "EFFICIENT COMPUTATION OF MULTIPLIERLESS FILTERS IN EMBEDDED SYSTEMS EMPLOYING AN OPTIMAL APPROXIMATION METHOD." International Journal of Computational Methods 03, no. 02 (2006): 177–204. http://dx.doi.org/10.1142/s0219876206000801.

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An integerization technique for creating fixed integer transforms with computationally optimal representations is presented, and the improved performance in embedded systems by employing these integerized implementations is explored. This technique uses an optimal approximation algorithm that finds the lowest-length fractional representation of the rational numbers. The integer transform approximation allows multiplication to be replaced by shift-and-add operations in hardware systems; where multiplication can take several cycles, shifts and adds take one or fewer cycles each. The multiplierle

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Potgieter, Petrus H. "Computability of sets in Euclidean space." Pure Mathematics and Applications 30, no. 3 (2022): 65–77. http://dx.doi.org/10.2478/puma-2022-0025.

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Abstract We consider several concepts of computability (recursiveness) for sets in Euclidean space. A list of four ideal properties for such sets is proposed and it is shown in a very elementary way that no notion can satisfy all four desiderata. Most notions introduced here are essentially based on separability of ℝ n and this is natural when thinking about operations on an actual digital computer where, in fact, rational numbers are the basis of everything. We enumerate some properties of some naïve but practical notions of recursive sets and contrast these with others, including the widely

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Ural, Alattin. "A Classification of Mathematical Modeling Problems of Prospective Mathematics Teachers." Journal of Educational Issues 6, no. 1 (2020): 98. http://dx.doi.org/10.5296/jei.v6i1.16566.

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The purpose of this research is to classify the mathematical modelling problems produced by pre-service mathematics teachers in terms of the number of variables and to determine the mathematical modelling skills and mathematical skills used in solving the problems in each class. The current study is a qualitative research and the data was analyzed using descriptive analysis. The data of the study was obtained from the mathematical modelling problem written by 59 senior mathematics teachers. They were given a 1-week period to write the problems and solutions. The participants took mathematical

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Shiu, Daniel, та Peter Shiu. "A poor person's approximation to π". Mathematical Gazette 96, № 537 (2012): 408–14. http://dx.doi.org/10.1017/s0025557200005027.

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Suppose that we have a computing machine that can only deal with the operations of addition, subtraction and multiplication, but not division, of integers. Can such a machine be used to find the decimal expansion of a given real number α to an arbitrary length? The answer is ‘yes’, at least in the sense that α is the limit of a sequence of rational numbers, and one can obtain the decimal expansion of a positive rational number a/b without division. For example, for any positive k, we try all non-negative c < b and d < 10ka, and see if 10ka = db + c. There will be success because all we a

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Okada, Isamu. "Evolution of cooperative study." Impact 2020, no. 8 (2020): 76–78. http://dx.doi.org/10.21820/23987073.2020.8.76.

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Associate Professor Isamu Okada is based at the Department of Business Administration, Faculty of Business Administration, Soka University in Japan, as well as a visiting professor of Department of Information Systems and Operations, Vienna University of Economics and Business in Austria. Okada has dedicated his career to understanding more about the evolution of cooperation which is a strand of thought that falls under evolutionary biology. Academics around the world have long considered the issues relating to the evolution of cooperation. In these studies, cooperation is taken to mean provid

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Volodymyr, Kudin, Onotskyi Viacheslav, Al-Ammouri Ali, and Shkvarchuk Lyudmyla. "ADVANCEMENT OF A LONG ARITHMETIC TECHNOLOGY IN THE CONSTRUCTION OF ALGORITHMS FOR STUDYING LINEAR SYSTEMS." Eastern-European Journal of Enterprise Technologies 1, no. 4 (97) (2019): 14–22. https://doi.org/10.15587/1729-4061.2019.157521.

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We have advanced the application of algorithms within a method of basic matrices, which are equipped with the technology of long arithmetic to improve the precision of performing the basic operations in the course of studying the ill-conditioned linear systems, specifically, the systems of linear algebraic equations (SLAE). Identification of the fact of ill-conditionality of a system is a rather time-consuming computational procedure. The possibility to control computations entering the state of incorrectness and the impossibility of accumulating calculation errors, which is a desirable proper

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Hill, Heather C. "The Nature and Predictors of Elementary Teachers' Mathematical Knowledge for Teaching." Journal for Research in Mathematics Education 41, no. 5 (2010): 513–45. http://dx.doi.org/10.5951/jresematheduc.41.5.0513.

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This article explores elementary school teachers' mathematical knowledge for teaching and the relationship between such knowledge and teacher characteristics. The Learning Mathematics for Teaching project administered a multiple-choice assessment covering topics in number and operation to a nationally representative sample of teachers (n = 625) and at the same time collected information on teacher and student characteristics. Performance did not vary according to mathematical topic (e.g., whole numbers or rational numbers), and items categorized as requiring specialized knowledge of mathematic

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Frič, Roman, and Martin Papčo. "Upgrading Probability via Fractions of Events." Communications in Mathematics 24, no. 1 (2016): 29–41. http://dx.doi.org/10.1515/cm-2016-0004.

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Abstract The influence of “Grundbegriffe” by A. N. Kolmogorov (published in 1933) on education in the area of probability and its impact on research in stochastics cannot be overestimated. We would like to point out three aspects of the classical probability theory “calling for” an upgrade: (i) classical random events are black-and-white (Boolean); (ii) classical random variables do not model quantum phenomena; (iii) basic maps (probability measures and observables { dual maps to random variables) have very different “mathematical nature”. Accordingly, we propose an upgraded probability theory

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Gaibyldaev, Zhanybek, Zhamalbek Ashimov, Damirbek Abibillaev, and Fuat Kocyigit. "Survival analysis of renal patients underwent transplantation in Kyrgyz Republic and various countries by 10 years follow-up." Heart, Vessels and Transplantation 3, Issue 4 (2019): 243. http://dx.doi.org/10.24969/hvt.2019.168.

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In our study we conducted survival analysis of 204 patients visited Scientific-Research Institute of Heart Surgery and Organs transplantation and who underwent renal transplantation in Kyrgyzstan and other Eurasian countries between 2005 and 2016 years (age range: 9-71 years, mean: 38.21 (12.74) years, median: 34.0 (0.89) years; gender: 142 male (69.6%)). During follow-up period, mortality event was observed in 16 (7.84%) patients. Survival function probabilities of patients and rational risk factors of survival functions were evaluated by Kaplan-Meier and Cox regression analyses, respectively

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Moxness, Vidar Weidemann, Knut Gåseidnes, and Harald Asheim. "Skimmer Capacity for Viscous Oil." SPE Journal 16, no. 01 (2010): 155–61. http://dx.doi.org/10.2118/118701-pa.

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Summary When a skimmer removes oil locally, oil floating further away will flow toward it. The maximum flow rate toward the skimmer defines its natural capacity. Traditional skimmer-capacity modeling considers flow driven by height potential and resisted by inertial forces but neglects viscosity. On the basis of theory and experiments, this paper claims that high oil viscosity may govern the skimmer capacity. It is shown that viscous resistance relates to a dimensionless quantity called the Goose number, representing the ratio of inertial to viscous forces. At high Goose numbers, viscosity may

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Strauss, D. F. M. "Philosophical tendencies in the genesis of our understanding of physical nature." Suid-Afrikaanse Tydskrif vir Natuurwetenskap en Tegnologie 25, no. 2 (2006): 93–110. http://dx.doi.org/10.4102/satnt.v25i2.150.

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The rise of a long-standing legacy of natural scientific thought is found in ancient Greece – the well-spring of Western civilization and the source of articulated rational reflection. The earliest phase of Greek culture already gave birth to theoretical thinking about the universe. The Pythagoreans are first of all famous for their emphasis on number as a mode of explanation. However, in their thesis that everything is number they solely acknowledged rational numbers (fractions) and this approach eventually stranded on the discovery of irrational numbers that led to the geometrization of Gree

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