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Journal articles on the topic 'Operation on integers'

Author: Grafiati

Published: 2 June 2025

Last updated: 31 July 2025

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1

Nurmawati, Nurmawati. "Upaya Meningkatkan Prestasi Belajar Siswa Kelas VII B SMP Negeri 9 Kota Jambi dalam Operasi Hitung Bilangan Bulat Melalui Pemanfaatan Alat Peraga Garis Bilangan." Jurnal Ilmiah Dikdaya 9, no. 1 (2019): 81. http://dx.doi.org/10.33087/dikdaya.v9i1.127.

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An integer counting operation is one of several basic materials in mathematics learning whose applications are used up to college. This shows the importance of understanding counting operations on integers. This study aims to improve student learning achievement in integer counting operation material through the use of number line props. This research is a classroom action research with 3 cycles, in which the research subjects are students of class VII B SMP Negeri 9 Jambi City. The results of the study showed the enthusiasm of students in participating in the learning starting from the first,

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2

Sutiani, Cicih, Linda Herawati, and Redi Hermanto. "PENGEMBANGAN INSTRUMEN TES DIAGNOSTIK UNTUK MENGIDENTIFIKASI MISKONSEPSI PADA MATERI OPERASI BILANGAN BULAT." Jurnal Karya Pendidikan Matematika 11, no. 1 (2024): 70. https://doi.org/10.26714/jkpm.11.1.2024.70-80.

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This study aims to develop a valid and practical diagnostic test instrument so as to identify student misconceptions on integer operation material. Diagnostic tests are developed using a four-tier test format. The research method uses a development method by Tessmer, namely Formative Research which consists of the preliminary stage, self-evaluation stage, prototyping stage (expert review, one to one, small group) and field test stage. The results are diagnostic test instruments that are declared valid and practical by the experts and the students. The results of the student diagnostic test sho

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3

Kurniati, Ratnah, and Fransheine Rumtutuly. "Beach pebbles as a Learning Media: A Case Study of a Prospective Elementary School Teacher." Journal of Education for Sustainability and Diversity 3, no. 2 (2025): 384–97. https://doi.org/10.57142/jesd.v3i2.669.

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This case study examines the understanding of Han (a pseudonym), a prospective elementary school teacher in Universitas Pattimura Southwest Maluku Regency, in three weeks with two two-hour meetings each week. The investigator collected data by giving The Integer Test of Primary Operation and followed by an interview. During the research, it was found that Han's conceptual errors occurred in the addition of positive and negative integers, addition of negative integers, subtraction of positive integers, subtraction of negative integers and subtraction involving both positive and negative integer

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4

Kurniasi, Rima, Nurjanah Nurjanah, and Endang Cahya. "Students’ learning obstacle in operations of integer." Educenter : Jurnal Ilmiah Pendidikan 3, no. 1 (2024): 59–67. http://dx.doi.org/10.55904/educenter.v3i1.1107.

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This study aims to describe the learning obstacles faced by students in the operation of integers. The research method used is a qualitative method with a case study design. The data was taken from 16 students in grade 7, a junior high school in Batang Hari, Jambi. The data collection technique used was triangulation data. There are written tests, interviews with both students and the teacher, and document analysis. The data collection instrument used was a test of integer operations, interview guidelines, and documents (lesson plan and textbook). The results of the research showed that there

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5

Wicaksono, Agung. "PENERAPAN PENDEKATAN PEMBELAJARAN OPEN ENDED UNTUK MENINGKATAKAN PEMAHAMAN SISWA KELAS V AL ANKABUT SDIT AL FAHMI PALU PADA MATERI OPERASI HITUNG BILANGAN BULAT." IBTIDAI'Y DATOKARAMA: JURNAL PENDIDIKAN DASAR 2, no. 1 (2021): 25–36. http://dx.doi.org/10.24239/ibtidaiy.vol2.iss1.24.

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The background of this research is that generally students understand the concept of multiplication and division of integers by memorizing. Basically, the memorization method will be appropriate if you memorize it, you know and understand what you have memorized. So that students do not just memorize alone. However, students really understand what they have memorized, and the teacher in providing material on multiplication and division of integers is only glued to the textbook but does not use other solutions that are easier for students to understand. To improve students' understanding of the

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6

Erlanovna, Temirbekova Zhanerke, Tynymbayev Sakhybay, Abdiakhmetova Zukhra Muratovna, and Turken Gulzat. "Development Paillier's library of fully homomorphic encryption." Indonesian Journal of Electrical Engineering and Computer Science 34, no. 3 (2024): 1989. http://dx.doi.org/10.11591/ijeecs.v34.i3.pp1989-1998.

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One of the new areas of cryptography considered-homomorphic cryptography. The article presents the main areas of application of homomorphic encryption. An analysis of existing developments in the field of homomorphic encryption carried out. The analysis showed that existing library implementations only allow processing bits or arrays of bits and do not support division and subtraction operations. However, to solve applied problems, support for performing integer operations are necessary. Because of the analysis, the need to implement the homomorphic division and subtraction operations identifi

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7

Erlanovna, Temirbekova Zhanerke, Tynymbayev Sakhybay, Abdiakhmetova Zukhra Muratovna, and Turken Gulzat. "Development Paillier's library of fully homomorphic encryption." Indonesian Journal of Electrical Engineering and Computer Science 34, no. 3 (2024): 1989–98. https://doi.org/10.11591/ijeecs.v34.i3.pp1989-1998.

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One of the new areas of cryptography considered-homomorphic cryptography. The article presents the main areas of application of homomorphic encryption. An analysis of existing developments in the field of homomorphic encryption carried out. The analysis showed that existing library implementations only allow processing bits or arrays of bits and do not support division and subtraction operations. However, to solve applied problems, support for performing integer operations are necessary. Because of the analysis, the need to implement the homomorphic division and subtraction operations identifi

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8

Aziz, Siti Hanifatul, and Fatkhul Arifin. "Penggunaan Media Colored Stick Untuk Meningkatkan Pemahaman Konsep Operasi Hitung Penjumlahan dan Pengurangan Bilangan Bulat Pada Siswa Sekolah Dasar Kelas III." Elementar : Jurnal Pendidikan Dasar 1, no. 2 (2021): 250–63. http://dx.doi.org/10.15408/elementar.v1i2.21947.

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This study aims to improve the understanding of the concept of arithmetic operations of addition and subtraction of integers in class IV at SDN Jampang 03 through the use of colored stick media. The research method used is Classroom Action Research (CAR), adapting the Kemmis and Mc.Taggart. Subjects in this study consisted of 29 students in class IV at SDN Jampang 03. The results of this study showed that there was an increase in students' conceptual understanding after the application of colored stick learning media in mathematics subjects for arithmetic operations on addition and subtraction

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9

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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10

Putri, Cindy Ade, Baharuddin Paloloang, Pathuddin Pathuddin, and I. Nyoman Murdiana. "PROFIL KESALAHAN SISWA KELAS VII SMP NEGERI 1 DAKO PEMEAN DALAM MENYELESAIKAN SOAL OPERASI HITUNG BILANG BULAT DITINJAU DARI KEMAMPUAN MATEMATIKA." Aksioma 13, no. 1 (2024): 43–50. https://doi.org/10.22487/aksioma.v13i1.4352.

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This study aims to obtain a description of conceptual and procedural the error profiles by seventh grade students of SMP Negeri 1 Dako Pemean in solving integers arithmetic operation problems in terms of mathematical ability. The subjects of this study were students of class VII B SMP Negeri 1 Dako Pemean in the 2023/2024 school year. There are 3 students, 1 student who has low math ability, 1 student who has moderate math ability, and 1 student who has high math ability. The subjects in this study were selected based on the average mathematics score of the students' Midterm Examination (UTS)

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11

Lee, Lee, Maretta Sarkis, Ammar Rawashdeh, and Ahmad Khaldi. "On The 4-Cyclic Refined Neutrosophic Solutions of The Diophantine Equation X^n=1 and m-Cyclic Refined Neutrosophic Modulo Integers." Journal of Neutrosophic and Fuzzy Systems 8, no. 2 (2024): 38–48. http://dx.doi.org/10.54216/jnfs.080205.

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The ring of n-cyclic refined neutrosophic integers is a logical extension of the integer ring Z based on a special multiplication operation defined between the indeterminacy algebraic elements. In this paper, we provide a full description of the 4-cyclic refined neutrosophic integer roots of unity, where we prove that for odd values of n we get exactly two different solutions. For even values of n, we get exactly 15 different solutions. On the other hand, we characterize the m-cyclic refined neutrosophic modulo integers rings and present many of their algebraic properties based on neutrosophic

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12

Isik, Cemalettin. "Analyzing Problems Posed by Prospective Teachers Related to Addition and Subtraction Operations with Integers." Higher Education Studies 8, no. 3 (2018): 1. http://dx.doi.org/10.5539/hes.v8n3p1.

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In this study, it was aimed to analyze the structure of prospective middle school mathematics teachers’ problems posed with regard to given symbolic representation including addition and subtraction operations with integers. The study conducted with 96 last gradeelementary school mathematics teacher candidates studying in Faculty of Education of Erciyes University in Turkey at the beginning of 2018 years. A Problem Posing Task including five items regarding addition and subtraction operations with integers and semi-structured interview forms were used as data gathering tools. Results indicated

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13

Moanoang, Christian, Nurdin Arsyad, and N. Nasrullah. "Desain Pembelajaran Matematika Berbasis Hypothetical Learning Trajectory (HLT) Pada Materi Operasi Bilangan Bulat Siswa Kelas VII SMP Bunda Kasih Sudiang." Issues in Mathematics Education (IMED) 5, no. 2 (2021): 100. http://dx.doi.org/10.35580/imed23842.

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Penelitian ini bertujuan untuk menghasilkan suatu desain pembelajaran berbasis Hypotetical Learning Trajectory (HLT) pada materi operasi bilangan yang dapat membuat siswa kelas VII memahami materi operasi bilangan bulat dan menyelesaikan masalah yang berkaitan dengan operasi bilangan bulat.Jenis penelitian yang digunakan adalah Design Research.Subjek penelitian ini adalah siswa kelas VII.Pada penelitian ini, peneliti membuat HLT sebagai dugaan awal dari aktivitas pembelajaran yang dilakukan dalam dua siklus uji coba hingga didapatkan desain pembelajaran yang diharapkan.Hasil analisis retrospek

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14

Owusu, Alexander, Christopher Saaha Bornaa, Dennis Offei Kwakye, and Abdulai Boare Iddrisu. "Pre-service Mathematics Teachers’ Errors and Misconceptions of Integer Operations." Journal of Statistics and Mathematical Concepts 1, no. 2 (2023): 1–19. http://dx.doi.org/10.58425/jsmc.v1i2.127.

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Purpose: This study investigated common errors and misconceptions made by some pre-service mathematics teachers of the St. Louis College of Education in Ghana about operations on integers. Errors associated with the misconceptions were also explored. Methodology: The study employed mixed-method and sequential explanatory design, Diagnostic test instruments were designed and administered to sixty (60) pre-service mathematics teachers who offer specialized programmes in early grade (EG) and upper primary (UP). Findings: The study identified common errors made by pre-service mathemati

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15

Rohamah, Mamah. "The Use of Number Tower Media to Improve Intelligence Count Operation Ability in Deaf Students." JASSI ANAKKU 21, no. 2 (2021): 131–38. http://dx.doi.org/10.17509/jassi.v21i2.39515.

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The purpose of this study was to determine the use of the Tower of Numbers media in improving the ability to count integer operations for deaf students. The research method used is classroom action research or abbreviated as CAR. The subjects in this study were 4 students with hearing impairments at the Special School, in Subang Indonesia. The results of using the Integer Tower media are very easy and helpful for students in solving math questions in addition and subtraction of integers with results below 15. It can be seen that the average result of the first cycle is 43.75, the second cycle

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16

Bahig, H. M., A. Alghadhban, M. A. Mahdi, K. A. Alutaibi, and H. M. Bahig. "Speeding up the Multiplication Algorithm for Large Integers." Engineering, Technology & Applied Science Research 10, no. 6 (2020): 6533–41. http://dx.doi.org/10.48084/etasr.3932.

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Multiplication is one of the basic operations that influence the performance of many computer applications such as cryptography. The main challenge of the multiplication operation is the cost of the operation as compared to other basic operations such as addition and subtraction, especially when the size of the numbers is large. In this work, we investigate the use of the window strategy for multiplying a sequence of large integers to design an efficient sequential algorithm in order to reduce the number of bit-multiplication operations involved in multiplying a sequence of large integers. In

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Bahig, H. M., A. Alghadhban, M. A. Mahdi, K. A. Alutaibi, and H. M. Bahig. "Speeding up the Multiplication Algorithm for Large Integers." Engineering, Technology & Applied Science Research 10, no. 6 (2020): 6533–41. https://doi.org/10.48084/etasr.3932.

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Multiplication is one of the basic operations that influence the performance of many computer applications such as cryptography. The main challenge of the multiplication operation is the cost of the operation as compared to other basic operations such as addition and subtraction, especially when the size of the numbers is large. In this work, we investigate the use of the window strategy for multiplying a sequence of large integers to design an efficient sequential algorithm in order to reduce the number of bit-multiplication operations involved in multiplying a sequence of large integers. In

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18

Saputri, Juli Pratama. "MENINGKATKAN KEMAMPUAN SISWA PADA PEMBELAJARAN OPERASI HITUNG PENJUMLAHAN DAN PENGURANGAN BILANGAN BULAT MELALUI MEDIA KARTU BILANGAN PADA KELAS V DI SDN 24 TEMMALEBBA KEC. BARA KOTA PALOPO." Pedagogik Journal of Islamic Elementary School 1, no. 2 (2018): 127–38. http://dx.doi.org/10.24256/pijies.v1i2.400.

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The study aims to 1) Knowing whether the use of number card media can inprove students ability on the subject matter of counting and reducting analysis of 5th grade integers at SDN 24 Temmalebba. 2) To know the improvement of students ability on material count arithmetic operation and reduction of integer through media of number card in class V/A at SDN 24 Temmalebba. This research is a classroom action research conducted in class V/A. Data collection tecnique which in conducted observation method, documentation, interview and test. Data analysis conducted in this research is decriptive analys

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Peñafiel, John Mark, and Sharon Apohen. "The Effect of Algebra Tiles in the Operations of Integers and Polynomials to the Academic Performance of Grade 7 Students." Psychology and Education: A Multidisciplinary Journal 30, no. 9 (2025): 1442–52. https://doi.org/10.5281/zenodo.14652507.

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The study determined the effects of algebra tiles in the operations of integers and polynomials to the academic performance of Grade 7 students of Gil Montilla National High School- Camindangan Extension enrolled in the academic year 2023-2024. A standardized questionnaire based on the Enhanced Regional Unified Numeracy Test (ERUNT) of DepEd Region VI for the operations on integers and based on the self-learning modules published by the Schools Division of Pasig City for the operations of polynomials were used in gathering the data. There are 80 participants in determining the pre-test and pos

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Hikmah, Shofaul. "Teknik Friendly Match Man to Man Untuk Menyelesaikan Operasi Hitung Penjumlahan Dan Pengurangan Bilangan Bulat." Jurnal Edutrained : Jurnal Pendidikan dan Pelatihan 4, no. 1 (2020): 27–34. http://dx.doi.org/10.37730/edutrained.v4i1.53.

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The Man to Man Friendly Match Technique is a new breakthrough created to help Madrasah Ibtidaiyah students complete the operation of adding and subtracting integers. This technique emerged as a result of the writer's concern as one of the subjects of Mathematics in Madrasah Ibtidaiyah who saw the low interest and learning outcomes of students in the material operations of calculating the addition and subtraction of integers. Man to Man Friendly Match Technique is a technique that combines the game as an activity that is very closely related to the daily lives of students with the concept of ar

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Wu, Guang Wen, Xiang Sheng Huang, and Wen Long Hu. "A Novel Method for Solution of the Division Operation on ARM7 Microcontroller." Advanced Materials Research 718-720 (July 2013): 2418–21. http://dx.doi.org/10.4028/www.scientific.net/amr.718-720.2418.

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Before architecture V7, the hardware of ARM microcontroller family does not support division operation. Although it is easy to program on ARM processors with C language which can implement division operation with library functions, the procedure has much trouble and the efficiency is lower when the function code written in C language is called in assembly program. This paper introduces an algorithm for the division operation on ARM7 processor and also gives corresponding subroutines which can be used directly in assembly program design. The algorithm is similar to the operation theory of the d

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Miftahudin, Rifqi Aulia, and Harry Dwi Putra. "Systematic Literature Review: Analysis Of Middle School Students' Difficulties In Solving Integer Problems." Mathline : Jurnal Matematika dan Pendidikan Matematika 10, no. 1 (2025): 17–28. https://doi.org/10.31943/mathline.v10i1.680.

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Middle school students often encounter dificulties in solving integer operation problems, such as understanding concepts like positive and negative integers and correctly applying arithmetic symbols. This study utilizes a Systematic Literature Review (SLR) approach to analyze these difficulties, searching academic databases like Google Scholar, ResearchGate, and Sinta for relevant articles published from 2019 to 2023 and included articles published in 2024 . Articles were selected based on criteria assessing their relevance to the research topic, methodological rigor, and contribution to under

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23

Harun, Nurul Ain, Kyrille Grace Cuevas, Olivia Asakil, Jayson Alviar, and Leo Jay Solon. "Assessing Students’ Mastery and Misconceptions in the Fundamental Operations on Integers." International Journal of Science, Technology, Engineering and Mathematics 3, no. 3 (2023): 36–55. http://dx.doi.org/10.53378/353000.

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One of the common misconceptions affecting mathematics performance of high school students involves operating integers. Evidently, students who were exposed to modular learning demonstrate poor mastery of the pre-requisite skills. This study aimed to assess the mastery level and misconceptions of the Grade 7 students involving operations on integers. A descriptive research design was used with a total of sixty-two (62) conveniently chosen Grade 7 students were twenty-nine (29) were males and thirty-three (33) were females. The Mean Percentage Scores (MPS) per operation on integers were calcula

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24

Maizora, Syafdi, and Rizky Rosjanuardi. "Konsepsi siswa kelas tiga sekolah dasar tentang bilangan bulat." Pythagoras: Jurnal Pendidikan Matematika 15, no. 2 (2021): 201–15. http://dx.doi.org/10.21831/pg.v15i2.37645.

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Artikel ini menggambarkan konsepsi salah seorang siswa kelas 3 Sekolah Dasar di Kota Bengkulu tentang bilangan bulat di luar pembelajaran formal. Siswa ini mengalami banyak intervensi tanpa skenario dalam pembelajarannya, di antaranya dari keluarga (kakak kelas 8 yang memiliki prestasi baik dalam matematika, kedua orang tua pengajar matematika) dan pelatihan sempoa. Konsepsi yang digali adalah arti bilangan negatif, bilangan bulat, serta operasi penjumlahan dan pengurangan pada bilangan bulat. Jenis penelitian ini adalah penelitian kualitatif dengan pendekatan studi kasus. Subjek diberikan beb

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Bingham, Aram. "Ternary arithmetic, factorization, and the class number one problem." Revista Colombiana de Matemáticas 55, no. 2 (2022): 149–66. http://dx.doi.org/10.15446/recolma.v55n2.102612.

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Ordinary multiplication of natural numbers can be generalized to a ternary operation by considering discrete volumes of lattice hexagons. With this operation, a natural notion of ‘3-primality’ -primality with respect to ternary multiplication- is defined, and it turns out that there are very few 3-primes. They correspond to imaginary quadratic fields Q(√-n), n > 0, with odd discriminant and whose ring of integers admits unique factorization. We also describe how to determine representations of numbers as ternary products and related algorithms for usual primality testing and integer factori

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Al-Harere, Manal Naji, and Ahmed Abed Ali Omran. "On binary operation graphs." Boletim da Sociedade Paranaense de Matemática 38, no. 7 (2019): 59–67. http://dx.doi.org/10.5269/bspm.v38i7.44282.

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A graph labeling is an assignment of integers to the vertices, edges, or to both, and it is subject to certain conditions. In this paper, a new concept of graph labeling called binary operation labeling is introduced. The graph is said to be a binary operation graph if admits a binary operation labeling. Some results for this new type of labeling are contributed.

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Munagi, Augustine O., and Francisco Javier de de Vega. "An Extension of Sylvester’s Theorem on Arithmetic Progressions." Symmetry 15, no. 6 (2023): 1276. http://dx.doi.org/10.3390/sym15061276.

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Sylvester’s theorem states that every number can be decomposed into a sum of consecutive positive integers except powers of 2. In a way, this theorem characterizes the partitions of a number as a sum of consecutive integers. The first generalization we propose of the theorem characterizes the partitions of a number as a sum of arithmetic progressions with positive terms. In addition to synthesizing and rediscovering known results, the method we propose allows us to state a second generalization and characterize the partitions of a number into parts whose differences between consecutive parts f

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SAMOSHCHENKO, Oleksandr. "ADDITION AND SUBTRACTION OF INTEGERS WITH SHIFTED ENCODING A NEGATIVE ZERO." cientific papers of Donetsk National Technical University. Series: Informatics, Cybernetics and Computer Science 2, no. 39 (2024): 12–17. https://doi.org/10.31474/1996-1588-2024-2-39-12-17.

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Computer codes of integers are proposed to be formed in the system of shifted codes with a negative zero. It is proposed to use the converted code based on the result of inverting the high-order bit of the operand for the addend in the addition operation and the decrement in the subtraction operation. It is mathematically confirmed that the computer implementation of operations of addition and subtraction with operands in the coding system with a negative zero ensures the formation of the correct shifted code in the area of definition of shifted operands. It shows the range of changes in the t

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C. Dela Rosa, Mark Gil, Princes Joy O. Rosete, Katelyn Joy N. Maggay, Joanna Rose M. Mego, Mel Jan D. Rivas, and Reina Mae E. Elegido. "DISCOVERING THE ERRORS AND MISCONCEPTION IN OPERATION ON INTEGERS." International Journal of Applied Science and Research 06, no. 06 (2023): 01–07. http://dx.doi.org/10.56293/ijasr.2023.5601.

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Dodo, Arista Ina, Yulius Keremata Lede, and Samuel Rex M. Making. "Analisis Pemecahan Masalah Siswa dalam Operasi Hitung Penjumlahan Bilangan Bulat Siswa SMP Negeri 1 Kota Tambolaka." Indo-MathEdu Intellectuals Journal 4, no. 3 (2023): 2861–72. http://dx.doi.org/10.54373/imeij.v4i3.604.

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The purpose of the research is to the determine students, problem solving in the operation of calculating of integers for students at SMP Negeri 1 Tambolaka City. This type of research is descriptive qualitative. The subject of this research are all students in class VIIB of SMP Neger 1 Tambolaka City, totaling thirty-six students. The object of a research in the aritmatic operation of adding integers to students SMP Negeri 1 Tambolaka City . The data colection techniques used were written test, interviews, and documentation. Based on the research above, it can be conluded that problem solving

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Merdekawati, Sanni. "Enhancing Students’ Understanding of Operation in Integers through Joyful Learning with GeoGebra™ Applet." Southeast Asian Mathematics Education Journal 12, no. 2 (2022): 161–70. http://dx.doi.org/10.46517/seamej.v12i2.165.

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This paper demonstrates a teacher-as-researcher intervention study by utilizing GeoGebra™ activities in the teaching and learning of arithmetical operations with integers. The researcher evaluated how the applet can elevate students understanding of the concepts of arithmetic integer operations. The data was collected through recordings of students’ worksheets and communications in a virtual classroom. The teacher monitored students’ progress and provided immediate suggestions and assistance via several methods. As a result, students could communicate and interact with each other and the teach

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Lancia, Giuseppe, and Marcello Dalpasso. "FASTSET: A Fast Data Structure for the Representation of Sets of Integers." Algorithms 12, no. 5 (2019): 91. http://dx.doi.org/10.3390/a12050091.

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We describe a simple data structure for storing subsets of { 0 , … , N − 1 } , with N a given integer, which has optimal time performance for all the main set operations, whereas previous data structures are non-optimal for at least one such operation. We report on the comparison of a Java implementation of our structure with other structures of the standard Java Collections.

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Whittle, Geoff. "Duality in Polymatroids and Set Functions." Combinatorics, Probability and Computing 1, no. 3 (1992): 275–80. http://dx.doi.org/10.1017/s0963548300000304.

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Notions of deletion and contraction for the class of set functions from finite sets into the integers are defined. An operation on a subclass of such set functions is a function from the subclass into itself that preserves ground sets and respects isomorphism. The operations on set functions that interchange deletion and contraction are characterised, as are those with the further property of being involutary. Similar results are given for polymatroids. There is a unique involutary operation on the class of k-polymatroids that interchanges deletion and contraction. The results generalise those

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Alan, Kübra, and Elif Ertem Akbaş. "Examining the Effect of Elementary School 5th Grade Subject of Extraction on Readiness for Integers." World Journal of Education 13, no. 1 (2023): 14. http://dx.doi.org/10.5430/wje.v13n1p14.

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The concept of number sense first appeared theoretically in the report published by NCTM in 1989. Although it is an important concept that includes the meaning of numbers and the relationship between numbers, it is very difficult to make a clear definition of it. This could also be true for the concept of integer, which we cannot place in our world of meaning in daily life or which we have difficulty in finding an equivalent for. For integers that have an abstract world of meaning, a misconception may occur between the integer sign and the sign used for operation. In this respect, this study a

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Nisa, Thoiffatul K., Evangelista LW Palupi, Mayang Purbaningrum, Sylvana Novilia Sumarto, and Viky H. Putra. "Development of Rujuku Mobile Learning Apps on Integer Operation Material as Alternative Media." Jurnal Gantang 7, no. 1 (2022): 1–9. http://dx.doi.org/10.31629/jg.v7i1.4478.

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Since the Covid-19 pandemic in early 2020, Indonesia has implemented distance education by optimizing the use of technology. Therefore, the researcher developed the Rujuku Mobile Learning Apps Development on Integer Operation Material in Class VII SMP/MTs to support the implementation of distance learning during the pandemic. This study aimed to develop the RUJUKU application and determine student responses in learning after using the developed media. This development research uses the ADDIE method. The data collection technique used a questionnaire with data processing techniques analyzed usi

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Wang, Xingbo. "Densification of Witnesses for Randomized Algorithm Design." Journal of Advances in Mathematics and Computer Science 38, no. 10 (2023): 44–69. http://dx.doi.org/10.9734/jamcs/2023/v38i101823.

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This paper investigates the densification of witnesses for randomized algorithm design and its application in factoring integers. By defining a set operation named with Cartesian subtraction on two countable sets and proving several properties of the operation, it is shown that the Cartesian subtraction can densify certain elements in a countable set so as to promote the abundance of witnesses for the randomized algorithm design. It is also proven that the Cartesian subtraction of two sets containing consecutive integers can form a triangular lattice zone that has a higher density of witnesses

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Rodiyana, R., E. Santoso, W. Dwi Puspitasari, and H. Miko. "The Effect of Multimedia in Increasing the Integers Operation Ability." Journal of Physics: Conference Series 1477 (March 2020): 042057. http://dx.doi.org/10.1088/1742-6596/1477/4/042057.

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Nurmayani, Nurmayani, Geovani Sembiring Meliala, and Geovani Sembiring Meliala. "PENGEMBANGAN MEDIA PEMBELAJARAN DOMINO MINUS DAN PLUS BERBASIS IT MATERI OPERASI HITUNG BILANGAN BULAT PESERTA DIDIK KELAS IV SEKOLAH DASAR." Jurnal Guru Kita PGSD 6, no. 2 (2022): 93. http://dx.doi.org/10.24114/jgk.v6i2.33435.

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Abstract : Development of Domino Minus and Plus Learning Media Based on It Operation Material Counting Integers Grade IV Elementary School Students. The problems in this study are the lack of use of learning media in the teaching and learning process, the lack of teacher skills in making IT-based learning media, the learning methods used in the learning process are still conventional, the students' mathematics learning outcomes in the arithmetic operations material of integer addition and subtraction are still is low. The purpose of this research is to develop learning media for IT-based domin

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Nuraida, Elis Muslimah, and Ratu Ilma Indra Putri. "THE CONTEXT OF ARCHIPELAGO TRADITIONAL CAKE TO EXPLORE STUDENTS’ UNDERSTANDING IN INTEGERS DIVISION CLASS VII." Jurnal Pendidikan Matematika 14, no. 1 (2019): 91–100. http://dx.doi.org/10.22342/jpm.14.1.7400.91-100.

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This study aims to explore the students’ mathematical understanding in integer division operation through the context of archipelago traditional cakes in class VII. This research is related to the Indonesian Realistic Mathematics Approach (PMRI) as a learning approach used. The methodology used in this study is Design Research consisting of three stages: preliminary design, experimental design, and retrospective analysis. The study was conducted on VII grade students of Palembang 1 Junior High School. The learning path (Hypothetical Learning Trajectory) in design research plays an important ro

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MIASNIKOV, ALEXEI G., ALEXANDER USHAKOV, and DONG WOOK WON. "POWER CIRCUITS, EXPONENTIAL ALGEBRA, AND TIME COMPLEXITY." International Journal of Algebra and Computation 22, no. 06 (2012): 1250047. http://dx.doi.org/10.1142/s0218196712500476.

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Motivated by algorithmic problems from combinatorial group theory we study computational properties of integers equipped with binary operations +, -, z = x ⋅ 2y, z = x ⋅ 2-y (the former two are partial) and predicates < and =. Notice that in this case very large numbers, which are obtained as n towers of exponentiation in the base 2 can be realized as n applications of the operation x ⋅ 2y, so working with such numbers given in the usual binary expansions requires super exponential space. We define a new compressed representation for integers by power circuits (a particular type of straight

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Vinay, S. Iyengar. "A Novel Approach for Cryptography Technique on Perturbed Data for Distributed Environment." International Journal on Cryptography and Information Security (IJCIS) 2, no. 3 (2019): 57–66. https://doi.org/10.5281/zenodo.3401274.

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Efficient and secure public-key cryptosystems are essential in today’s age of rapidly growing Internet communications. Elliptic curve scalar multiplication in particular, which refers to the operation of multiplying a large integer by a point on an elliptic curve, is crucial for both data encryption technology as well as testing the security of cryptographic systems. The purpose of this project was to design and implement an elliptic curve scalar multiplication algorithm 10% faster than one of the best algorithms currently used: the binary double-add algorithm. The algorithm designed was

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Vinay, S. Iyengar. "Novel Elliptic Curve Scalar Multiplication Algorithms for Faster and Safer Public-Key Cryptosystems." International Journal on Cryptography and Information Security (IJCIS) 2, no. 3 (2019): 57–66. https://doi.org/10.5281/zenodo.3549467.

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Efficient and secure public-key cryptosystems are essential in today’s age of rapidly growing Internet communications. Elliptic curve scalar multiplication in particular, which refers to the operation of multiplying a large integer by a point on an elliptic curve, is crucial for both data encryption technology as well as testing the security of cryptographic systems. The purpose of this project was to design and implement an elliptic curve scalar multiplication algorithm 10% faster than one of the best algorithms currently used: the binary double-add algorithm. The algorithm designed was

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BARBÉ, ANDRÉ, HEINZ-OTTO PEITGEN, and GENCHO SKORDEV. "AUTOMATICITY OF COARSE-GRAINING INVARIANT ORBITS OF ONE-DIMENSIONAL LINEAR CELLULAR AUTOMATA." International Journal of Bifurcation and Chaos 09, no. 01 (1999): 67–95. http://dx.doi.org/10.1142/s0218127499000043.

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We consider one-dimensional linear cellular automata whose states are the integers modulo a prime power pd and their orbital patterns. We are particulary interested in initial states and their orbital patterns which are invariant under a certain coarse-graining operation. We show that these coarse-graining invariant initial states are p-automatic. The relationship between the solutions of a certain family of coarse-graining invariant problems concerning linear cellular automata over the integers modulo pn is investigated.

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Xia, Shu, and Xiaolin Ge. "The Optimized Operation of Gas Turbine Combined Heat and Power Units Oriented for the Grid-Connected Control." International Journal of Emerging Electric Power Systems 17, no. 2 (2016): 143–50. http://dx.doi.org/10.1515/ijeeps-2015-0167.

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Abstract In this study, according to various grid-connected demands, the optimization scheduling models of Combined Heat and Power (CHP) units are established with three scheduling modes, which are tracking the total generation scheduling mode, tracking steady output scheduling mode and tracking peaking curve scheduling mode. In order to reduce the solution difficulty, based on the principles of modern algebraic integers, linearizing techniques are developed to handle complex nonlinear constrains of the variable conditions, and the optimized operation problem of CHP units is converted into a m

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Tereshchenko, Andrii, and Valeriy Zadiraka. "Implementation of Multidigit Multiplication Basing on Discrete Cosine and Sine Transforms." Cybernetics and Computer Technologies, no. 4 (December 30, 2021): 61–79. http://dx.doi.org/10.34229/2707-451x.21.4.7.

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Introduction. The emergence of new parallel computing systems such as multi-core processors, clusters, distributed systems, due to the solution of various applications in different spheres. Among such problems are the calculation of systems of linear algebraic equations with the number of unknown 33-35 million, the calculation of nuclear reactor shells, modeling of physical and chemical processes, aerodynamics, hydrodynamics, information security, and so on. This greatly expands the use of multidigit arithmetic, due to the fact that ignoring rounding errors leads to the fact that sometimes com

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Safonov, Ilia, Anton Kornilov, and Daria Makienko. "An Approach for Matrix Multiplication of 32-Bit Fixed Point Numbers by Means of 16-Bit SIMD Instructions on DSP." Electronics 12, no. 1 (2022): 78. http://dx.doi.org/10.3390/electronics12010078.

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Matrix multiplication is an important operation for many engineering applications. Sometimes new features that include matrix multiplication should be added to existing and even out-of-date embedded platforms. In this paper, an unusual problem is considered: how to implement matrix multiplication of 32-bit signed integers and fixed-point numbers on DSP having SIMD instructions for 16-bit integers only. For examined tasks, matrix size may vary from several tens to two hundred. The proposed mathematical approach for dense rectangular matrix multiplication of 32-bit numbers comprises decompositio

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Ate, Dekriati. "Analisis Jawaban Siswa pada Operasi Hitung Campuran Melalui Penerapan Pendekatan Metakognitif-Diskursif." Jurnal Penelitian dan Pengkajian Ilmu Pendidikan: e-Saintika 1, no. 2 (2018): 66. http://dx.doi.org/10.36312/e-saintika.v1i2.103.

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[Title: Analysis of Student Answers on Mixed Calculation Operations Through the Implementation of Metacognitive-Discursive Approach] Mixed calculation operations are one of the important topics in mathematics but there are still many students who have difficulty performing mixed calculation operations and are unable to give the right reasons. This research aims to determine the effect of the use of teaching materials that have been designed by didactic mathematicians and have been tested in several schools using a metacognitive-discursive approach. This study was a design study which consisted

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Guzhov, Vladimir I., Ilya O. Marchenko, Ekaterina E. Trubilina, and Dmitry S. Khaidukov. "Comparison of numbers and analysis of overflow in modular arithmetic." Analysis and data processing systems, no. 3 (September 30, 2021): 75–86. http://dx.doi.org/10.17212/2782-2001-2021-3-75-86.

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The method of modular arithmetic consists in operating not with a number, but with its remainders after division by some integers. In the modular number system or the number system in the residual classes, a multi-bit integer in the positional number system is represented as a sequence of several positional numbers. These numbers are the remainders (residues) of dividing the original number into some modules that are mutually prime integers. The advantage of the modular representation is that it is very simple to perform addition, subtraction and multiplication operations. In parallel executio

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Elita, Elita. "The Implementation Of Direct Learning Model By Using Props Beads At The Material Operations In Addition And Subtraction Of Integers At The Iva Class In Sd Negeri 002 Tualang." Jurnal Ilmiah Pendidikan Scholastic 2, no. 1 (2018): 140–49. http://dx.doi.org/10.36057/jips.v2i1.318.

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Mathematics is a very important lesson so that math needs to be given to all learners starting from elementary school.It aims to equip learners with the ability to think logically, analytically, systematically, critically and creatively as well as the ability to work together.Competence is required for learners have the ability to obtain, manage and utilize information.In line with one of the goals of mathematics in the Education Unit Level Curriculum (SBC) that have properties appreciate the usefulness of mathematics in life is curiosity, concern and interest in studying mathematics, as well

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Dassow, Jürgen. "Operational Accepting State Complexity: The Unary and Finite Case." International Journal of Foundations of Computer Science 30, no. 06n07 (2019): 959–78. http://dx.doi.org/10.1142/s0129054119400240.

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Let [Formula: see text] be the minimal number of accepting states which is sufficient for deterministic finite automata to accept [Formula: see text]. For a number [Formula: see text] and an [Formula: see text]-ary regularity preserving operation ∘, we define [Formula: see text] as the set of all integers [Formula: see text] such that there are [Formula: see text] languages [Formula: see text], [Formula: see text], with [Formula: see text] In this paper, we study these sets for the operations union, catenation, star, complement, set-subtraction, and intersection where we restrict to unary or f

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