Basic Mathematical Operations Research Articles

Performance Analysis of Vedic Multiplier in Hardware Implementation of Biomedical Applications

As technology advances at a rapid pace, there is an increasing need for real-time digital signal processing (DSP) applications that are efficient and swift. DSPs, or digital signal processors, are crucial components of several engineering disciplines. For processes like convolution and Fourier transforms in DSPs, rapid multiplication is essential. Multiplication is one of the basic mathematical operations used by all applications. Many different multiplier designs have been developed to boost their speed. When compared to array and booth multipliers—the products of decades of hard research—vedic multipliers are among the fastest and lowest power multipliers. The sixteen sutras, or algorithms, that the Vedic Multiplier uses are primarily logical procedures. They are the fastest and most effective because several of them have been proposed using the Urdhava Tiryakbhyam sutra. The purpose of this study is to provide an overview of the numerous biomedical applications of Vedic Multiplier in the wide field of digital signal processing, including denoising of Electrocardiogram (ECG) and Electroencephalogram ( EEG) signal. Particular attention is paid to how current Vedic Multiplier designs have been altered to increase speed and performance metrics.

Effectiveness of Using Koin Muatan Teaching Aids to Improve Numeracy Skills

Literacy Numeracy is currently one of the topics in learning mathematics. A person is said to have Numerical Literacy Ability to count, distinguish and process various data symbols, and perform basic mathematical operations to fix the problem. However, the problem that is always faced by students today is the lack of understanding of the basic concepts of mathematics, one of which is integer arithmetic operations, so it won't be easy to understand more abstract mathematical concepts. The low numeracy literacy ability is due to the learning process not applying the suitable model or media. Therefore, it is necessary to have appropriate learning media so that students understand concepts well and can improve Numerical Literacy skills. One of the proper media or teaching aids for learning integer arithmetic operations is Koin Muatan, made with paper as a base material that symbolizes positive and negative charges. The type of research used was experimental research, a one-group pretest-posttest design pre-experimental design on 21 SD GMIT 4 Kefamenanu students. Data collection techniques were observation, tests and documentation. At the same time, the data analysis technique used is descriptive statistical analysis, inferential analysis and N-Gain analysis. The t-test results are used to test the average value before and after being given treatment and whether there is a significant effect. Based on the results of the tests performed, the average pretest and posttest values were 43.51 and 70.79. An N-Gain test was carried out to determine the large increase in numeracy literacy skills so that an N-Gain value of 0.45 was included in the moderate category. This result proves an increase in numeracy literacy skills after students are given the learning treatment using the Koin Muatan teaching aids at SD GMIT 4 Kefamenanu.

Version [1.1]- [Handling decision-making in intuitionistic fuzzy environment: PyIFDM package

The paper introduces the update of the Python Intuitionistic Fuzzy Decision Making (PyIFDM) package, emphasizing its focus on Multi-Criteria Decision Analysis (MCDA) with uncertain data modeled as Intuitionistic Fuzzy Sets (IFS). The update enhances PyIFDM’s capabilities, introducing five new IF-MCDA methods and basic mathematical operations on IFS. The update includes the implementation of Max normalization, a Hausdorff measure-based Euclidean distance, and a module for IFS-similarity measures. The release contributes to a significant library upgrade, providing advanced tools for modeling fuzzy data in and outside the MCDA space. PyIFDM now supports a greater variety of popular IF-MCDA methods, offering flexibility and applicability in decision-making scenarios. The added visualization module facilitates the graphical representation of IFS, aiding the interpretation of complex decision models involving intuitionistic fuzzy data. The enhanced version of the PyIFDM library expands its applicability in research methodologies, making it a more efficient tool for conducting multi-criteria decision analysis in an intuitionistic fuzzy environment.

A Fast Fixed-Point Logarithmic Functions Based on ARM Microprocessor

The fixed-point mathematical library refers to a highly optimized collection of high-precision mathematical functions primarily used for fast and high-precision real-time calculations. It can execute equivalent code written in the C language with floating-point format faster, while maintaining considerable accuracy. Current mainstream fixed-point mathematical libraries face issues such as being non-open source, having unknown models, incomplete basic mathematical operation functions, and insufficient precision. Therefore, designing an open-source, fast, more optimized, and high-precision fixed-point mathematical library will have a groundbreaking impact. It can not only play a crucial role in industrial control algorithms but also eliminate the dependency of domestic fixed-point MCUs on foreign library functions. This paper conducts research on fixed-point arithmetic for logarithmic functions, designs, and improves the implementation of fast logarithmic functions.Taking Q12 as an example, Simulation experiments and MCU experiments show that, in the Q12 format, the highest precision that can be represented by a 32-bit fixed-point number is 0.000244141. From the test results, it can be observed that for 98.15% of the test data, the computational errors of the two mathematical libraries are both smaller than the highest precision value. Both two logarithmic function computations can maintain good computational accuracy within the ARM microprocessor. In terms of computational speeds, the average computation cycle of the fixed-point logarithmic function designed in this paper is reduced by 31.88% compared to the counterpart. This substantial improvement in computational speed, while ensuring computational accuracy, enhances the performance of fixed-point logarithmic operations based on ARM microprocessors.

Calculia: an innovative game to assist individuals with learning difficulties in basic mathematics operations

The educational application entitled “CALCULIA: An innovative game to help people with learning difficulties in basic Mathematics operations” was developed by a multidisciplinary team from the Federal Institute of Education, Science and Technology of Maranhão and Piauí – IFMA and IFPI, together with the Department of Education of the Government of the State of Maranhão – SEDUC-MA, formed by teachers, students and volunteers, to be used in formal and non-formal learning spaces, aiming to teach basic mathematical operations, as well as numerical symbolic understanding, targeting people with dyscalculia. Gamification was inserted as a teaching-learning strategy to acquire mathematical knowledge such as: addition, subtraction, multiplication and division, in addition to understanding mathematical symbols: figures, proportions, concepts and formulas. The methodological path adopted was Applied Behavior Analysis – ABA, for which bibliographical surveys, document analysis, prior search and field research were carried out, followed by the computational steps for the prototyping process, character creation, application development process, creation levels, prototype testing, adjustments and application validation. Its approach focused on verbal and operational dyscalculia with the aim of helping professionals in the field of Education and Health, improving the quality of life of individuals with dyscalculia. The evidence found reinforces the need to expand the project to cover practical, lexical, graphic and ideognostic dyscalculia.

A Comparative Study of BFV and CKKs Schemes to Secure IoT Data Using TenSeal and Pyfhel Homomorphic Encryption Libraries

Internet of things (IoT) devices and applications are on the rise, generating large amounts of sensitive and confidential data that need to be processed securely. Due to resource constraints, the data generated is often stored and processed in the cloud. The drawback of data cloud storage and processing is the fact that it can be hacked, leaked, or sold by cloud companies. Fully homomorphic encryption (FHE) allows computation on encrypted data using basic mathematical operations and has recently been successfully implemented using schemes and libraries with better performance. In this paper, the authors propose a mixture of edge-cloud-based security schemes using FHE to secure IoT data. The authors evaluate the performance of two FHE schemes (BFV and CKKS) based on data: encoding speed, encryption speed, arithmetic operations (addition and multiplication) speed, and decryption decoding speed using two Python libraries (TenSEAL and PyFHEl). The encryption and decryption are done at the edge node using a Raspberry Pi 4, while the processing is done at the cloud node using a laptop.

Chemistry Students' Mathematics Ability and Their Understanding of Buffer Solution

Mathematics's role in solving chemical phenomena has been well known. Basic mathematical operations such as integral, logarithm and differentiations are the tools for communicating chemistry concepts. This paper describes the effect of chemistry students' mathematical ability on understanding buffer solutions. 56 First-year university chemistry students at a public University in Malang, East Java, taking basic chemistry modules involved in this study. The respondents participated on a voluntary basis after getting a piece of comprehensive information about the study. An equivalent basic mathematical skill test (BMST) and Buffer Solution Test (BST) was implemented for data collection. This study found a positive correlation between students' mathematical ability and success in answering relevant buffer solution questions. The contribution of mathematical knowledge in predicting chemistry students' success in answering relevant buffer solution questions was also essentially high.

CODAS extension using novel decomposed Pythagorean fuzzy sets: Strategy selection for IOT based sustainable supply chain system

Decomposed fuzzy sets (DFSs), which have been recently introduced in the field of fuzzy sets are a fuzzy set extension that deals with the membership degree and the non-membership degree of the elements in the set from a functional and dysfunctional point of view in more detail. On the other hand, Pythagorean fuzzy sets (PFSs) are another fuzzy set extension reflecting the hesitancy of decision-makers in a wider area. The main target of this study is to develop a new fuzzy set extension, decomposed Pythagorean fuzzy sets (DPFSs) in order to utilize the properties of DFSs and PFSs together. First, the basic principles and mathematical operators of the DPFSs are developed with their proofs. Then, a new fuzzy multi-criteria decision-making (MCDM) method, DPF- Combinative Distance based Assessment (CODAS) is developed to demonstrate the feasibility and effectiveness of the DPF extension. The developed method is handled in the strategy selection problem for Internet of Things (IoT)-based sustainable supply chain systems. A comprehensive sensitivity analysis is performed on both the criteria weights and the decision makers' weights to verify the stability and effectiveness of the obtained results. In addition, a comparative analysis with decomposed fuzzy Technique for Order Preference by Similarity to Ideal Solution (TOPSIS), Pythagorean fuzzy CODAS and Pythagorean fuzzy TOPSIS methods is presented to show the validity, superiority and advantages of the developed method.

Multiresolution Self-Supervised Feature Integration via Attention Multiple Instance Learning for Histopathology Analysis.

Digital histopathology image analysis of tumor tissue sections has seen great research interest for automating standard diagnostic tasks, but also for developing novel prognostic biomarkers. However, research has mainly been focused on developing uniresolution models, capturing either high-resolution cellular features or low-resolution tissue architectural features. In addition, in the patch-based weakly-supervised training of deep learning models, the features which represent the intratumoral heterogeneity are lost. In this study, we propose a multiresolution attention-based multiple instance learning framework that can capture cellular and contextual features from the whole tissue for predicting patient-level outcomes. Several basic mathematical operations were examined for integrating multiresolution features, i.e. addition, mean, multiplication and concatenation. The proposed multiplication-based multiresolution model performed the best (AUC=0.864), while all multiresolution models outperformed the uniresolution baseline models (AUC=0.669, 0.713) for breast-cancer grading. (Implementation: https://github.com/tsikup/multiresolution-clam).

Rancang Bangun Game Pembelajaran Operasi Dasar Matematika Menggunakan Algoritma Fisher Yattes

One of the lessons regarding basic mathematical operations is found in 2nd grade material of SD Negeri 2 Randusari. In the learning process the teacher has not maximized in utilizing existing technology, especially since grade 2 elementary school. The students still tend to like to play and mathematics is considered a difficult subject. Therefore it is necessary to utilize media to be able to attract students' interest with the learning while playing method. one of them with game media. In this game the researcher applies the Fisher Yattes algorithm to each question that comes out so that students are not monotonous in playing it. The Game Development Life Cycle (GDLC) is a guideline that regulates the process of making this game with development stages including initiation, pre-production, production, alpha testing, beta testing and release. The results of the UAT test on 14 students where this game can be accepted by users by getting an average percentage value of 89.64%. In its application the Fisher Yattes algorithm succeeded in generating random values in the game and no similar questions came out repeatedly at the same level.

Four New Techniques of Addition and Subtraction of any Two Numbers

The addition and subtraction operations are some of the most basic mathematical arithmetic operations. The arithmetic operation in the form of addition and subtraction in integer is a basic arithmetic operation that elementary school students must master from an early stage. In fact, there are some students who have difficulty in adding up numbers with existing techniques, namely the saving technique for addition and borrowing technique for subtraction. The problem happened because students forgot that they had saved or borrowed numbers. Eventhough the technique was done correctly, the answer was still incorrect. Therefore, researchers developed several addition and subtraction techniques without saving and borrowing. There were four techniques that had been developed in this research namely multi-level, box, and stacking and table techniques. These new techniques had advantages in making students easier to solve addition and subtraction problems.

Analisis Kesalahan Hasil Belajar Mahasiswa pada Operasi Matriks Mata Kuliah Aljabar Linear dan Matriks

In solving math problems, students including many students experience difficulties, so there is a high probability of experiencing errors in answering questions. This study aims to analyze student errors in solving mathematical problems in matrix material, linear algebra and matrix courses and describe student learning outcomes errors in linear algebra and matrix courses, then identify factors that affect student learning outcomes errors in linear algebra and matrix courses. This type of research is qualitative descriptive research with a case study method. Sampling was done using purposive sampling technique with tests and interviews. The sample of this study consisted of 37 4th semester students who had an average that was still below the limit of completeness in mathematics courses in the previous semester. The results showed that the factors that influence student learning outcomes errors are a) less careful in understanding the problem, b) lack of time management when working on problems, c) lack of focus when working, d) lack of mastery of concepts, formulas and calculation procedures in matrix operations, e) lack of mastery of basic mathematical operations, f) lack of caution and thoroughness.

Opportunities of using rural areas for recreational purposes: The case of the Karacabey District, Bursa Province

Objective: Empty and wide areas, including settlements outside the city center, are rural areas. These areas have great importance in recreational use in terms of their natural and cultural landscape values. Within the scope of the study, it aims to calculate the potential of the Karacabey district of Bursa, one of these areas, in terms of recreational use. Material and Methods: The main material of the study consists of 64 villages located in the Karacabey district of Bursa province. The method of the study is based on the principle of assigning weighted points to five items of recreation areas. After scoring, calculations were made with basic mathematical operations, and the obtained quantitative data were interpreted. Results: As a result of the study, it was determined that there are no villages in the Karacabey district with very low recreation potential (30%>); 40 villages are low (30-45%), 17 villages are medium (45-60%), 5 villages are high (61-75%) and 2 villages were also found to have a very high (75%<) recreational potential. Conclusion: Within the scope of the study, it has been determined that the existing natural and cultural landscape values and infrastructure facilities add great value to the villages with high recreation potential. Therefore, various recreation types in which these values will be protected and used have been evaluated within this framework and new proposals have been developed.

An Overview of Mental Calculation Strategies and the Frequency of Their Application

The paper aims to explore mental calculation strategies and the frequency of their application in tasks. In the paper, we categorized mental calculation strategies related to four basic mathematical operations, looked at several different strategies used by students in a test containing mental calculation tasks, and presented an overview of the interview results. We also analyzed age-related differences in the number of strategies applied by participants. It was found that Mathematics in school does not always contribute to the development of and flexibility in the use of mental calculation strategies. One apparent reason is student preference for previously acquired written algorithms.

Machine Learning Techniques to Enhance the Mental Age of Down Syndrome Individuals: A Detailed Review

Down syndrome individuals are known as intellectually disabled people. Their intellectual ability is classified into four categories known as mild, moderate, severe, and profound. These individuals have significant limitations in learning and adapting skills. Psychologists evaluate mental capability of such individuals using conventional intellectual quotient method instead of using any technology. The research matrix shows most of research has been carried out on analyzing neuroimaging, antenatal screening, and hearing impairment of individuals. But there is still an obvious gap of evaluating mental age using artificial intelligence. We have proposed an artificial neural network model, which supervises how software is used to obtain dataset using Knowledge Base Decision Support System. In a survey (N = 120) individuals examined by psychiatrist, medical expert, and a teacher to assess the presence of Down’s syndrome by analyzing their physical and facial appearances, and communication skills. Only (N = 62) individuals declared as Down syndrome. Selected individuals invited to perform mental ability assessment using Interactive Mental Learning Software. The results of mental age of Down syndrome with a raise in IQ from severe to moderate (20% to 35%), moderate to mild (35% to 75%) severity were carried out with the help of assessing the interactive series of software opinion polls based on comparison, logic, and basic mathematical operations using initial IQ (iIQ), and enhanced IQ (eIQ) variables input and output parameters.

ENHANCEMENT OF MATHEMATICAL APTITUDE OF GRADE SEVEN STUDENTS THROUGH VEDIC MATHEMATICAL TECHNIQUES

In today’s competitive world every student wants to score highest mark, for scoring highest mark he needs to master the basic mathematical operations. After completion of his elementary education, a child has optioned for choosing his career in any stream. Mathematics is the subject, which is used in our day- to-day life even an illiterate person should know basic operations of mathematics. At primary and upper primary schooling stage, learning of the mathematic necessary and this is proper stage when students’ mathematical aptitude should be enhanced. For this purpose, Vedic mathematic technique is useful, because it is based on 16 main sutras and 13 sub-sutras. By using Vedic mathematic techniques, we can enhance mathematical aptitude of upper primary school students. And can remove their mathematic phobia and anxiety. Researcher developed a mathematical aptitude test and done a pilot study on upper primary school students. This paper high lights the effect of Vedic mathematic techniques on the student ability to do mathematical operation fastly. Hence enhancing their mathematical aptitude.

MATHEMATICAL VERBS IN POLISH AND ENGLISH PHRASEOLOGY: A COMPARATIVE STUDY

The use of mathematical vocabulary in phraseology is a topic of numerous papers as numbers indicate not only quantity but may also have a cultural connotation. In the paper, Polish and English phraseological units with the verbs indicating basic mathematical operations are analysed. The study shows the common phraseological expressions containing these verbs in Polish and English and if there is equivalence between the languages in question.

VTUFileHandler: A VTU library in the Julia language that implements an algebra for basic mathematical operations on VTU data

Bittens, M., (2022). VTUFileHandler: A VTU library in the Julia language that implements an algebra for basic mathematical operations on VTU data. Journal of Open Source Software, 7(73), 4300, https://doi.org/10.21105/joss.04300

VTUFileHandler: A VTU library in the Julia language that implements an algebra for basic mathematical operations on VTU data

VTUFileHandler: A VTU library in the Julia language that implements an algebra for basic mathematical operations on VTU data

Teaching Soft Skill and Basic Mathematical Operations to SDN Kedungmlati Students Using the PERIODIK Teaching Aid

SDN Kedungmlati is the only public elementary school in Kedungmlati village. The school lacks the infrastructure to support the teaching and learning process. They do not have adequate teaching aids to help the students learn abstract concepts in mathematics. We carried out this community service to introduce the PERIODIK teaching aid to respond to their needs. PERIODIK teaching aids are aids in learning basic mathematical operations, which include addition, subtraction, multiplication, and division of integers. This activity, conducted in the academic year of 2019/2020, aimed to increase the students' soft skills in using the PERIODIK teaching aid and thus develop their understanding of basic mathematical operations. The soft skills we expected the students to gain include the skills to use the teaching aid, be persistent, and be able to cooperate with others. This activity was carried out in three stages: preparation, implementation, and reporting, and evaluated using two instruments: a questionnaire and a written test. The questionnaire was distributed to the students before and after the training, whereas the written test was conducted only at the end of the activity. We used paired samples t-test to measure the students’ soft skills and independent samples t-test to examine whether the students had reached achieved the minimum score of 80. The results show that teaching aids can improve students' soft skills and understanding of the four basic mathematical operations. The PERIODIK then became an inventory of SDN Kedungmlati for learning mathematics.