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Journal articles on the topic 'Calculus Mathematics Mathematical analysis'

Author: Grafiati

Published: 4 June 2021

Last updated: 5 February 2022

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1

Altenbach, H. "Some remarks on the paper ‘A unified tensor approach to the analysis of mechanical systems’ by A. A. Fogarasy and M. R. Smith." Proceedings of the Institution of Mechanical Engineers, Part C: Journal of Mechanical Engineering Science 223, no. 1 (December 1, 2008): 143–55. http://dx.doi.org/10.1243/09544062jmes1141.

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The tensor calculus is a powerful mathematical tool in the analysis of mechanical problems (or generally, of problems in physics). The aim of Fogarasy and Smith's ‘A unified tensor approach to the analysis of mechanical systems’ is to demonstrate this fact considering a problem of dynamical analysis of mechanisms. Fogarasy and Smith are applying the traditional approach in tensor calculus, which comes originally from the mathematics. This implies the a priori introduction of coordinates, which is usual in the analysis of mechanisms. Later the tensor calculus is used for the discussion of the basic equations and their mathematical handling. In this sense, the results obtained by Fogarasy and Smith are mathematically correct, and the interested reader can now have many fruitful and stimulating ideas.

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Пушкарский, Анатолий. "BOUT GEORGE BOOLE’S CALCULUS OF LOGIC." Логико-философские штудии, no. 3 (March 16, 2021): 267–75. http://dx.doi.org/10.52119/lphs.2021.55.34.004.

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Проводится разбор и анализ небольшой статьи Джорджа Буля, опубликованной на следующий год после выхода его знаменитой работы «Математический анализ логики». Исследуется вопрос о том, насколько ее можно рассматривать как адекватный и репрезентативный обзор его логической концепции. Также исследуются математические, экстралогические и философские основания логики Буля. Указывается, что математическим основанием его логической системы послужили его исследования в области линейных дифференциальных уравнений. Кроме того, в основании его пионерских открытий лежали произвольные философско-методологическим допущения, которые напрямую не относились к области логики и математики. Такими допущениями следует признать некоторую оригинальную психологическую теорию сознания, его философию математики, предполагающую существование универсального математического исчисления, и некоторые положения логико-философской концепции И. Канта In the present paper, the small article by George Boole, published the next year after the publication of his famous work The Mathematical Analysis of Logic, is analyzed. We discuss to what extent it can be considered as an adequate and representative overview of his logical views. The mathematical, extralogical and philosophical foundations of Boole’s logic are explored. It is pointed out that the mathematical basis of his logical system was his research in the field of linear differential equations. Moreover, his pioneering discoveries were based on arbitrary philosophical and methodological assumptions that were not directly related to the field of logic and mathematics. Some of the original psychological theory of mind, its philosophy of mathematics, which presupposes the existence of a universal mathematical calculus, and some provisions of Immanuel Kant’s logico-philosophical doctrine should be recognized as such assumptions.

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G.A, Mahayukti, Dantes N, Candiasa I.M, and Marhaeni A.A.I.N. "The effectiveness of using portfolio assessment in lecture by controlling mathematical logical intelligence." SHS Web of Conferences 42 (2018): 00081. http://dx.doi.org/10.1051/shsconf/20184200081.

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The purpose of this research aims to examine the effectiveness of using portfolio assessment in the integral calculus lecture after logical mathematical intelligence is controlled. The population of this research are all students in the department of mathematics education who program integral calculus courses on the 2015/2016 academic year. Samples in this research are 88 students, who were selected randomly. The data were analyzed by one-way covariance analysis. The result of this research showed that student’s learning outcomes of Integral Calculus who were taught Integral Calculus with portfolio assessment, was higher than those of the students who were tought with essay assessment. The findings of this study show that using portfolio assessment is effective to improve student’s learning outcomes of Integral Calculus.

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Jadhav, Ashish A., Abhijeet D. Kalamkar, Pritish A. Gaikwad, Vishwesh Vyawahare, and Navin Singhaniya. "Analysis of GPU Computation of Parabolic, Bessel, Wright and Riemann Zeta Functions." ITM Web of Conferences 40 (2021): 02005. http://dx.doi.org/10.1051/itmconf/20214002005.

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This paper deals with GPU computing of special mathematical functions that are used in Fractional Calculus. The graphics processing unit (GPU) has grown to be an integral part of nowadays’s mainstream computing structures. The special mathematical functions are an integral part of Fractional Calculus. This paper deals with a novel parallel approach for computing special mathematical functions used in Fractional Calculus. NVIDIA’s GPU hardware is used to speed up the parallel algorithm. A comparison of the sequential code, vectorized code and GPU code is performed. We have successfully reduced the computation time of special mathematical functions using the parallel computing capabilities of GPU.

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5

Wang, Long-Fei, Xiao-Jun Yang, Dumitru Baleanu, Carlo Cattani, and Yang Zhao. "Fractal Dynamical Model of Vehicular Traffic Flow within the Local Fractional Conservation Laws." Abstract and Applied Analysis 2014 (2014): 1–5. http://dx.doi.org/10.1155/2014/635760.

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6

Guce, Ive K. "Mathematical Writing Errors in Expository Writings of College Mathematics Students." International Journal of Evaluation and Research in Education (IJERE) 6, no. 3 (September 1, 2017): 233. http://dx.doi.org/10.11591/ijere.v6i3.8549.

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<p>Despite the efforts to confirm the effectiveness of writing in learning mathematics, analysis on common errors in mathematical writings has not received sufficient attention. This study aimed to provide an account of the students’ procedural explanations in terms of their commonly committed errors in mathematical writing. Nine errors in mathematical writing were pre-defined namely, misuse of mathematical terms, misuse of mathematical symbols, incorrect notation, incorrect grammar, incorrect capitalization, no or incorrect punctuation, vague term, incorrect term, and lack of term or phrase. This study used qualitative method of research to keep a record of errors in mathematical writing. Conducted in the College of Education Arts and Sciences of De La Salle Lipa, the study involved twelve BS Mathematics students enrolled in Advanced Calculus 1 class as respondents. Results revealed that the most committed errors done in mathematical writing are incorrect grammar and misuse of mathematical symbols. Certainly, intervention programs on mathematics writing will bring favorable outcomes. Language courses in the students’ curriculum which tackle proper grammar usage may be integrated with writing about mathematics as part of the student activities. Such will provide the students with writing experiences fitted to their discipline.</p><p> </p>

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7

Rusyda, N. A., D. Ahmad, R. Rusdinal, and F. Dwina. "Analysis of students’ mathematical communication skill in calculus course." Journal of Physics: Conference Series 1554 (May 2020): 012043. http://dx.doi.org/10.1088/1742-6596/1554/1/012043.

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8

Siddiqui, Nida. "Mathematical Intuition: impact on non-math major undergraduates." Bolema: Boletim de Educação Matemática 35, no. 70 (May 2021): 727–44. http://dx.doi.org/10.1590/1980-4415v35n70a09.

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Abstract The research question being investigated in this paper is how to improve the learning of calculus for non-math major students whose interests are primarily non mathematical. The study explores the impact of an intuitive approach applied to the concepts of limits and integration. The survey was carried on 1st year engineering students taking the Calculus-1 course. The students had already had a brief encounter with the topics in high school. They were surveyed about their outlook towards the concepts of limits and integration using the same pre and post inquiry form. The post analysis was conducted after introducing both the topics through an intuitive approach. The survey was analyzed for statistical significance using the Mc Nemar’s statistical test, which studies the impact of an intervention. Survey analysis indicated an improved understanding for the students and a positive change in their approach towards the topics.

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Pujilestari, Pujilestari, and Yuntawati Yuntawati. "PENGARUH PEMBELAJARAN PROBLEM POSING TERHADAP KOMUNIKASI MATEMATIKA MAHASISWA." Media Pendidikan Matematika 6, no. 2 (December 30, 2018): 50. http://dx.doi.org/10.33394/mpm.v6i2.1690.

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Type of this research is experimental research which aims to determine the effect of problem posing learning on mathematical communication of students prospective mathematics teacher at IKIP Mataram by calculus I module. This module developed by a problem posing approach that meets the criteria of being feasible, practical, and effective. The experimental design used was the type of Quasi Experimental Design and the design used was Nonequivalent Control Group Design. Data collection instruments included tests of mathematical communication skills, student response questionnaires, and lecturer response questionnaires. Based on the results of the hypothesis test analysis obtained a value with a significantlevel or is . So that it is rejected and accepted. So it can be concluded that Problem Posing Learning by using problem posing based I calculus module influences student mathematics communication and is effectively used in lectures

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Volkova, Elena Sergeevna, and Vladimir Borisovich Gisin. "On the assessment of formation of the system of main concepts of mathematical analysis." Современное образование, no. 2 (February 2020): 12–27. http://dx.doi.org/10.25136/2409-8736.2020.2.32942.

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The object of this research is the results of experimental use of the test for inventory of the concepts of mathematical analysis (Calculus Concept Inventory, CCI), which is aimed at assessment of the key concepts of mathematical analysis, such as function, limit and derivative. The test was conducted in the period from 2016 to 2020 and involved Bachelor’s degree students of Financial University under the Government of the Russian Federation on the discipline “Applied Mathematics and Informatics”. “Mathematical Analysis” is one of the key disciplines in formation of mathematical competencies of students majoring “Applied Mathematics and Informatics”. Test was developed by the leading experts from the United States in the area of mathematics and teaching mathematics in the universities, and was implemented in Russian practice for the first time. For quality assessment of the test was applied Cronbach's alpha coefficient, and the results were evaluated based on the Item Response Theory. Although in universities of the United States the implementation of this test showed relatively low effectiveness, for the students of Financial University the coefficient values were significantly higher and allow making an unequivocal conclusion on the informativeness of results. The article also applies the values of discriminant coefficient. Their fluctuation allows using the test not only for assessing the achievement in learning mathematical analysis of students in groups, but also individual results. The results demonstrate that the traditional approach in teaching the principles of mathematical analysis that is widely recognized in the Russian universities is ineffective, which underlines the need to rearrange the content and methods of teaching mathematical analysis in a university.

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Yang, Xiao-Jun, Jordan Hristov, H. M. Srivastava, and Bashir Ahmad. "Modelling Fractal Waves on Shallow Water Surfaces via Local Fractional Korteweg-de Vries Equation." Abstract and Applied Analysis 2014 (2014): 1–10. http://dx.doi.org/10.1155/2014/278672.

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A mathematical model of fractal waves on shallow water surfaces is developed by using the concepts of local fractional calculus. The derivations of linear and nonlinear local fractional versions of the Korteweg-de Vries equation describing fractal waves on shallow water surfaces are obtained.

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12

Tenreiro Machado, J. A. "Fractional Coins and Fractional Derivatives." Abstract and Applied Analysis 2013 (2013): 1–5. http://dx.doi.org/10.1155/2013/205097.

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This paper discusses the fundamentals of negative probabilities and fractional calculus. The historical evolution and the main mathematical concepts are discussed, and several analogies between the two apparently unrelated topics are established. Based on the new conceptual perspective, some experiments are performed shading new light into possible future progress.

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13

Буль, Джордж. "The Calculus of Logic." Логико-философские штудии, no. 3 (March 16, 2021): 276–91. http://dx.doi.org/10.52119/lphs.2021.99.42.005.

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14

Gondran, Michel, Abdelouahab Kenoufi, and Alexandre Gondran. "Complex variational calculus with mean of (min, +)-analysis." TEMA (São Carlos) 18, no. 3 (January 10, 2018): 385. http://dx.doi.org/10.5540/tema.2017.018.03.385.

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One develops a new mathematical tool, the complex (min, +)-analysis which permits to define a new variational calculus analogous to the classical one (Euler-Lagrange and Hamilton Jacobi equations), but which is well-suited for functions defined from C^n to C. We apply this complex variational calculus to Born-Infeld theory of electromagnetism and show why it does not exhibit nonlinear effects.

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15

Sikora, Ryszard, and Stanislaw Pawłowski. "Fractional derivatives and the laws of electrical engineering." COMPEL - The international journal for computation and mathematics in electrical and electronic engineering 37, no. 4 (July 2, 2018): 1384–91. http://dx.doi.org/10.1108/compel-08-2017-0347.

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Purpose This paper aims to evaluate the possibilities of fractional calculus application in electrical circuits and magnetic field theories. Design/methodology/approach The analysis of mathematical notation is used for physical phenomena description. The analysis aims to challenge or prove the correctness of applied notation. Findings Fractional calculus is sometimes applied correctly and sometimes erroneously in electrical engineering. Originality/value This paper provides guidelines regarding correct application of fractional calculus in description of electrical circuits’ phenomena. It can also inspire researchers to find new applications for fractional calculus in the future.

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Aristika, Ayu, Darhim, Dadang Juandi, and Kusnandi. "The Effectiveness of Hybrid Learning in Improving of Teacher-Student Relationship in Terms of Learning Motivation." Emerging Science Journal 5, no. 4 (August 1, 2021): 443–56. http://dx.doi.org/10.28991/esj-2021-01288.

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The Advanced Mathematical Thinking (AMT) ability is one of the prioritized mathematical abilities needed to be developed in learning mathematics during tertiary education. The present study sought to test the effectiveness of hybrid learning in improving students' advanced mathematical thinking. The research used a quasi-experimental design with a non-equivalent control group design. The subject of this study was students of a mathematics education study program at a university in Bandung who attended lecture for the multi-variable in a calculus course. The sampling technique used was purposive sampling. Of the many variable calculus classes consisting of 2 classes, one class was chosen as the experiment group and the other class as the control group. The sample consists of 40 people for each group. Data analysis used the MANOVA test with normality and homogeneity tests as a prerequisite test. The results showed a difference in AMT's significance between the hybrid learning and conventional groups, where hybrid learning had a higher AMT. Other than that, there is a difference in the significance of AMT between the high motivation group and the low motivation group, where high motivation has a higher AMT, and there is an interaction of learning models and motivational factors to increase AMT. Doi: 10.28991/esj-2021-01288 Full Text: PDF

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17

Elizar, Elizar, and Cut Khairunnisak. "AN INTRODUCTION TO THE RASCH MEASUREMENT MODEL: A CASE OF MATHEMATICS EDUCATION STUDENTS COMPREHENSIVE TEST." Kalamatika: Jurnal Pendidikan Matematika 5, no. 1 (April 30, 2020): 51–60. http://dx.doi.org/10.22236/kalamatika.vol5no1.2020pp51-60.

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Mathematics assessments should be designed for all students, regardless of their background or gender. Rasch analysis, developed based on Item Response Theory (IRT), is one of the primary tools to analyse the inclusiveness of mathematics assessment. However, the mathematics test development has been dominated by Classical Test Theory (CTT). This study is a preliminary study to evaluate the mathematics comprehensive test. This study aims to demonstrate the use of Rasch analysis by assessing the appropriateness of the mathematics comprehensive test to measure students' mathematical understanding. Data were collected from one cycle of mathematics comprehensive test involving 48 undergraduate students of mathematics education department. Rasch analysis was conducted using ACER Conquest 4 software to assess the item difficulty and differential item functioning (DIF). The findings show that the item related to geometry is the easiest question for students, while item concerning calculus as the hardest question. The test is viable to measure students’ mathematical understanding as it shows no evidence of Differential Item Functioning (DIF). Gender has been drawn for each of the test items. The assessment showed that the test was inclusive. More application of Rasch analysis should be conducted to create a thorough and robust mathematics assessment.

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18

Kotiah, Thoddi C. T. "Correlation analysis in calculus." International Journal of Mathematical Education in Science and Technology 23, no. 5 (September 1992): 671–82. http://dx.doi.org/10.1080/0020739920230505.

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Amevor, Godfred, Anass Bayaga, and Michael J. Bosse. "Analysis of Rural-Based Pre-Service Teachers Spatial-Visualisation Skills in Problem Solving in Vector Calculus Using MATLAB." International Journal of Emerging Technologies in Learning (iJET) 16, no. 10 (May 25, 2021): 125. http://dx.doi.org/10.3991/ijet.v16i10.19269.

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In science, technology, engineering and mathematics (STEM) for instance, interdisciplinary studies have noted positive correlation between spatial-visualization (SV skills) and mathematical problem solving. The majority of these studies sharing a link between SV skills and problem solving were contextualized in urban settings and only a few in rural settings. This investigation analyses how rural-based pre-service teachers apply their SV skills in problem-solving in a South African university, in the context of vector calculus. One hundred rural-based pre-service teachers in a second year vector calculus class at University of Zululand (UNIZULU) were randomly selected into control and experimental groups. MATLAB was used as a dynamic visual tool to analyse how research participants applied their SV skills. A mixed method approach was employed in data collection (quantitative and qualitative). Our findings revealed that the rural-based pre-service teachers’ SV skills correlate with their problem-solving skills in vector calculus.

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Kolman, Vojtěch. "Hegel’s ‘Bad Infinity’ as a Logical Problem." Hegel Bulletin 37, no. 2 (September 14, 2016): 258–80. http://dx.doi.org/10.1017/hgl.2016.18.

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AbstractThe paper analyses the concept of ‘bad infinity’ in connection with Hegel’s critique of infinitesimal calculus and with the belittling of Hegel’s mathematical notions by the representatives of modern logic and the foundations of mathematics. The main line of argument draws on the observation that Hegel’s difference is only derivatively a mathematical one and is primarily of a broadly logico-epistemological nature. Because of this, the concept of bad infinity can be fruitfully utilized, by way of inversion, in an analysis of the conceptual shortcomings of the most prominent foundational attempts at dealing with infinite quanta, such as Cantor’s set theory and Hilbert’s axiomatism. As such, the paper is an attempt at reconstructing Hegel’s philosophy of mathematics and its role in his philosophical system and, more importantly, as a contribution to logic in the more general and radical sense of the word.

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Pu, Yi-Fei, Ji-Liu Zhou, Patrick Siarry, Ni Zhang, and Yi-Guang Liu. "Fractional Partial Differential Equation: Fractional Total Variation and Fractional Steepest Descent Approach-Based Multiscale Denoising Model for Texture Image." Abstract and Applied Analysis 2013 (2013): 1–19. http://dx.doi.org/10.1155/2013/483791.

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The traditional integer-order partial differential equation-based image denoising approaches often blur the edge and complex texture detail; thus, their denoising effects for texture image are not very good. To solve the problem, a fractional partial differential equation-based denoising model for texture image is proposed, which applies a novel mathematical method—fractional calculus to image processing from the view of system evolution. We know from previous studies that fractional-order calculus has some unique properties comparing to integer-order differential calculus that it can nonlinearly enhance complex texture detail during the digital image processing. The goal of the proposed model is to overcome the problems mentioned above by using the properties of fractional differential calculus. It extended traditional integer-order equation to a fractional order and proposed the fractional Green’s formula and the fractional Euler-Lagrange formula for two-dimensional image processing, and then a fractional partial differential equation based denoising model was proposed. The experimental results prove that the abilities of the proposed denoising model to preserve the high-frequency edge and complex texture information are obviously superior to those of traditional integral based algorithms, especially for texture detail rich images.

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Osmolovskii, Nikolai P., and Vladimir M. Veliov. "On the strong subregularity of the optimality mapping in mathematical programming and calculus of variations." Journal of Mathematical Analysis and Applications 500, no. 1 (August 2021): 125077. http://dx.doi.org/10.1016/j.jmaa.2021.125077.

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23

Rchid Sidi Ammi, Moulay, and Mostafa Tahiri. "Analysis of the spread of COVID-19 in Morocco based on a SEIR epidemic model." General Letters in Mathematics 10, no. 2 (June 2021): 72–78. http://dx.doi.org/10.31559/glm2021.10.2.8.

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Fractional calculus has been widely used in mathematical modeling of evolutionary systems with memory effect on dynamics. In order to illustrate the efficiency of this non-integer order calculus, we employ SEIR models to model the dynamics, with and without memory, of the spread of Covid-19 in Morocco country.

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Brown, Jennifer L., Glennelle Halpin, and Gerald Halpin. "Relationship between High School Mathematical Achievement and Quantitative GPA." Higher Education Studies 5, no. 6 (October 28, 2015): 1. http://dx.doi.org/10.5539/hes.v5n6p1.

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<p>The demand for STEM graduates has increased, but the number of incoming freshmen who declare a STEM major has remained stagnant. High school courses, such as calculus, can open or close the gate for students interested in careers in STEM. The purpose of this study was to determine if high school mathematics preparation was a significant prerequisite for success in the pre-engineering curriculum at the post-secondary level. The College Freshman Survey was administered to a sample of 2,328 incoming freshman students, then their survey responses were matched with the grades and standardized test scores provided by the university’s institutional research office. A multiple regression analysis was conducted to predict quantitative pre-engineering GPA. The most significant predictor of quantitative GPA was adjusted ACT math score. Other significant contributors to the models were calculus, algebra II, trigonometry, and algebra I grades. The results suggest that high school preparation in specific mathematics subjects does have a positive impact on success in pre-engineering education.</p>

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Steen, Lynn Arthur. "From the 2000s: Facing Facts: Achieving Balance in High School Mathematics." Mathematics Teacher 100, no. 5 (December 2006): 86–95. http://dx.doi.org/10.5951/mt.100.5.0086.

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This article from 2005 presents comprehensive analysis of the state of mathematics education since launching of soviet Sputnik till now concluding that despite extraordinary efforts today's typical 17-year-old knows no more mathematics than his or her grandparents at the same age. After the analysis of the problem author proposes two recommendations balancing interests of different stakeholders. He concludes that due to the extraordinary recent expansion of mathematical applications a new strategy may be used. He believes that the unique power of mathematics that the current curriculum provides for a minority of calculus-bound students, such as reasoning, abstraction, generalization, can extended to a substantial majority of students through a more diverse curriculum designed to offer breadth, balance, utility, and coherence.

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Steen, Lynn Arthur. "From the 2000s: Facing Facts: Achieving Balance in High School Mathematics." Mathematics Teacher 100, no. 5 (December 2006): 86–95. http://dx.doi.org/10.5951/mt.100.5.0086.

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This article from 2005 presents comprehensive analysis of the state of mathematics education since launching of soviet Sputnik till now concluding that despite extraordinary efforts today's typical 17-year-old knows no more mathematics than his or her grandparents at the same age. After the analysis of the problem author proposes two recommendations balancing interests of different stakeholders. He concludes that due to the extraordinary recent expansion of mathematical applications a new strategy may be used. He believes that the unique power of mathematics that the current curriculum provides for a minority of calculus-bound students, such as reasoning, abstraction, generalization, can extended to a substantial majority of students through a more diverse curriculum designed to offer breadth, balance, utility, and coherence.

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Yi, Li Feng, Kai Ru Zhang, and Jun Liu. "Fractional Order Modeling and Analysis of Buck-Boost Converter." Applied Mechanics and Materials 789-790 (September 2015): 842–48. http://dx.doi.org/10.4028/www.scientific.net/amm.789-790.842.

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Considered the theoretical foundation of fractional order, the fractional mathematical model of the Buck-Boost converter in continuous conduction mode operation is built and analyzed in theory. Based on the improved Oustaloup fractional calculus for filter algorithm, the simulation model is framed by using the Matlab/Simulink software. And the simulation results are compared with that of integer order. It proves the correctness of the fractional order mathematical model and the theoretical analysis.

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Lubich, Ch. "Discretized Fractional Calculus." SIAM Journal on Mathematical Analysis 17, no. 3 (May 1986): 704–19. http://dx.doi.org/10.1137/0517050.

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Bangerezako, Gaspard. "Variational q-calculus." Journal of Mathematical Analysis and Applications 289, no. 2 (January 2004): 650–65. http://dx.doi.org/10.1016/j.jmaa.2003.09.004.

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Sumargiyani, Sumargiyani, and Bidayatun Nafi'ah. "Analysis of the Mathematical Communication Ability of Pre-Service Mathematics Teachers through Online Learning during the Covid-19 Pandemic." Hipotenusa : Journal of Mathematical Society 2, no. 2 (November 8, 2020): 98–119. http://dx.doi.org/10.18326/hipotenusa.v2i2.98-119.

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During the current Covid-19 pandemic, the learning system in all educational institution is shifted from face to face to online learning, including universities. This study aims to describe the results of the mathematical communication skills of class B students of Mathematics Education from Ahmad Dahlan University for the 2019/2020 academic year during online learning during the Covid-19 pandemic and to examine students' mistakes in solving differential calculus problems regarding the minimum, maximum material. This study employed descriptive qualitative research. The research instrument used is a test and interview guide. The data are collected using tests and interviews. The research subjects were selected by stratified random sampling technique so that 6 students are classified into high, medium and low categories. The questions are in the form of a description of one question with six questions. The results showed that students' mathematical communication skills on indicators (1) restating information was done appropriately, (2) writing down ideas or problem-solving steps clearly and precisely, some were not thorough, (3) presenting information using graphic images again. There are still things that they couldn't understand and (4) Writing down the answers according to what is known and are asked using mathematical formulas, some are still wrong because they are not accurate.

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Abbas, Marat M., and Vladimir A. Zakharov. "Even Simple Processes of π-calculus are Hard for Analysis." Modeling and Analysis of Information Systems 25, no. 6 (December 19, 2018): 589–606. http://dx.doi.org/10.18255/1818-1015-2018-6-589-606.

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Mathematical models of distributed computations, based on the calculus of mobile processes (π-calculus) are widely used for checking the information security properties of cryptographic protocols. Since π-calculus is Turing-complete, this problem is undecidable in general case. Therefore, the study is carried out only for some special classes of π-calculus processes with restricted computational capabilities, for example, for non-recursive processes, in which all runs have a bounded length, for processes with a bounded number of parallel components, etc. However, even in these cases, the proposed checking procedures are time consuming. We assume that this is due to the very nature of the π -calculus processes. The goal of this paper is to show that even for the weakest model of passive adversary and for relatively simple protocols that use only the basic π-calculus operations, the task of checking the information security properties of these protocols is co-NP-complete.

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Vivas-Cortez, Miguel, Thabet Abdeljawad, Pshtiwan Othman Mohammed, and Yenny Rangel-Oliveros. "Simpson’s Integral Inequalities for Twice Differentiable Convex Functions." Mathematical Problems in Engineering 2020 (June 27, 2020): 1–15. http://dx.doi.org/10.1155/2020/1936461.

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Integral inequality is an interesting mathematical model due to its wide and significant applications in mathematical analysis and fractional calculus. In the present research article, we obtain new inequalities of Simpson’s integral type based on the φ-convex and φ-quasiconvex functions in the second derivative sense. In the last sections, some applications on special functions are provided and shown via two figures to demonstrate the explanation of the readers.

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Yerizon, Siti Fatimah, and Fridgo Tasman. "Development of a GeoGebra-Assisted Calculus Worksheet to Enhance Students’ Understanding." International Journal of Information and Education Technology 11, no. 10 (2021): 456–63. http://dx.doi.org/10.18178/ijiet.2021.11.10.1550.

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The goal of this study is to develop a GeoGebra-assisted worksheet to enhance students' understanding of calculus. Many studies report that students have difficulty understanding calculus. GeoGebra provides an alternative method to overcome the difficulties associated with calculus. The Plomp development model consists of three phases: specifically, preliminary analysis, prototype development and an assessment was used in this study. The subjects of this study were 37 students. The results of this study are valid in terms of content, presentation, linguistics and graphics and practical in terms of implementation, time, ease of use and effective in terms of its potential impact on students' mathematical understanding. The GeoGebra-assisted worksheet can help students rediscover the given concept, while the use of visualization of the calculus concept can significantly enhance students’ mathematical understanding. Likewise, GeoGebra-assisted worksheets can be used to enhance students’ understanding of calculus. Teachers are suggested using GeoGebra in order to build students’ understanding on calculus subject.

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Pomini, Mario. "ECONOMIC DYNAMICS AND THE CALCULUS OF VARIATIONS IN THE INTERWAR PERIOD." Journal of the History of Economic Thought 40, no. 1 (February 15, 2018): 57–79. http://dx.doi.org/10.1017/s1053837217000116.

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Analogies with rational mechanics played a pivotal role in the search for formal models in economics. In the period between the two world wars, a small group of mathematical economists tried to extend this view from statics to dynamics. The main result was the extensive application of calculus of variations to obtain a dynamic representation of economic variables. This approach began with the contributions put forward by Griffith C. Evans, a mathematician who, in the first phase of his scientific career, published widely in economics. Evans’s research was further developed by his student Charles Roos. At the international level, this dynamic approach found its main followers in Italy, within the Paretian tradition. During the 1930s, Luigi Amoroso, the leading exponent of the Paretian School, made major contributions, along with his student Giulio La Volpe, that anticipated the concept of temporary equilibrium. The analysis of the application of the calculus of variations to economic dynamics in the interwar period raises a set of questions on the application of mathematics designed to study mechanics and physics to economics.

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Torczynski, J. R. "Dimensional Analysis and Calculus Identities." American Mathematical Monthly 95, no. 8 (October 1988): 746. http://dx.doi.org/10.2307/2322258.

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Nigmatullin, Raoul R., Paolo Lino, and Guido Maione. "“Fuzzy” calculus: The link between quantum mechanics and discrete fractional operators." Fractional Calculus and Applied Analysis 23, no. 3 (June 25, 2020): 764–86. http://dx.doi.org/10.1515/fca-2020-0038.

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AbstractIn this paper, based on the “fuzzy” calculus covering the continuous range of operations between two couples of arithmetic operations (+, –) and (×, :), a new form of the fractional integral is proposed occupying an intermediate position between the integral and derivative of the first order. This new form of the fractional integral satisfies the C1 criterion according to the Ross classification. The new calculus is tightly related to the continuous values of the continuous spin S = 1 and can generalize the expression for the fractional values of the shifting discrete index. This calculus can be interpreted as the appearance of the hidden states corresponding to unobservable values of S = 1. Many well-known formulas can be generalized and receive a new extended interpretation. In particular, one can factorize any rectangle matrix and receive the “perfect” filtering formula that allows transforming any (deterministic or random) function to another arbitrary function and vice versa. This transformation can find unexpected applications in data transmission, cryptography and calibration of different gadgets and devices. One can also receive the hybrid (”centaur”) formula for the Fourier (F-) transformation unifying both expressions for the direct and inverse F-transformations in one mathematical unit. The generalized Dirichlet formula, which is obtained in the frame of the new calculus to allow selecting the desired resonance frequencies, will be useful in discrete signals processing, too. The basic formulas are tested numerically on mimic data.

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Fan, Jie, Xue Yang, and Yong Liu. "Fractal calculus for analysis of wool fiber: Mathematical insight of its biomechanism." Journal of Engineered Fibers and Fabrics 14 (January 2019): 155892501987220. http://dx.doi.org/10.1177/1558925019872200.

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Wool fiber has a complex hierarchic inner structure. However, like most of the natural things, wool fiber does not have an exactly strict self-similar fractal feature. Here, we calculate the fractal dimension of each hierarchic level of wool fiber using the two-scale dimension method. The obtained fractal dimension of wool fiber in different hierarchic level ranges between 1.37 and 1.47, which is close to that obtained according to the traditional fractal geometry. Thermal property of wool fiber is investigated based on the fractal feature of wool fiber. The result shows that the temperature gradient and the rate of the temperature gradient along the fiber is very slow, suggesting that wool fiber has a good thermal retention property.

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Tang, Dongchun. "Development of Extreme Thoughts in Calculus and Its Application in Mathematical Analysis." Journal of Physics: Conference Series 1650 (October 2020): 032204. http://dx.doi.org/10.1088/1742-6596/1650/3/032204.

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Rajasekhar P and Babu T Jose. "Influence of Mathematical and Astronomical Developments in Medieval Kerala on Vāstuśāstra." Mathematical Journal of Interdisciplinary Sciences 7, no. 2 (March 6, 2019): 111–16. http://dx.doi.org/10.15415/mjis.2019.72014.

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The contribution in the field of mathematics is unparalleled. The concept of zero and the place value system is alone sufficed to place India in a high pedestal. Historians were generally under the impression that Indian supremacy in Mathematics came to an end with Bhaskaracharya (1114–1185) who is also known as Bhaskara II.Recent researches and publications of books like ‘Crest of the peacock’ written by George Gheverghese Joseph, has brought out the marvelous achievements of Southern India, especially Kerala region after the period of Bhaskaracharya which produced many results surpassing the Europeans in its indigenous style till the advent of Western Education system in early 19th Cent. This medieval contribution includes mathematical analysis and first steps in Calculus and many outstanding discoveries in astronomy. These contributions in Mathematics as well as in Astronomy are now grouped and studied under the title “Kerala School”. Accordingly, Sangamagrama Madhava (14th Cent.), doyen of Kerala School, is recognized as the ‘Father of infinitesimal Analysis’.In this paper the attempt is made to analyse the influence of Kerala School in the development of traditional building science and architecture. This branch of knowledge is generally categorized under the term ‘Vāstuśāstra’.`

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Harmini, Triana, Aziz Musthofa, and Shoffin Nahwa Utama. "Mathematical thinking ability of informatics students based on gender in calculus course." International Journal on Teaching and Learning Mathematics 2, no. 1 (June 29, 2019): 7. http://dx.doi.org/10.18860/ijtlm.v2i1.8337.

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<p class="ABS-C">This study aimed to analyse the difference in the mathematical thinking abilities of Informatics Engineering students based on gender in Calculus problem-solving. Mathematical thinking ability was measured based on four indicators of the mathematical thinking process, namely specialisation, generalising, conjecturing, and convincing. The instruments in this study were mathematical thinking tests and observation sheets. The test used in this study was composed of four questions by indicators of the mathematical thinking process. The technique of data collection was the test, observation, and interview. Subjects of this study consisted of 35 male students and 22 female students. Data were analysed using the t-test. The results of the analysis showed that there is a significant difference in the mathematical thinking ability of male and female students. Mathematical thinking abilities of female students reached indicators of specialisation, generalising, and conjecturing. On the other hand, mathematical thinking abilities of male students passed the elements of speciality and generalising.</p>

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Nataf, Frèdèric, and Francis Nier. "Convergence of domain decomposition methods via semi-classical calculus semiclassical calculus." Communications in Partial Differential Equations 23, no. 5-6 (January 1998): 1007–59. http://dx.doi.org/10.1080/03605309808821377.

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Hu, Yaozhong, and David Nualart. "Rough path analysis via fractional calculus." Transactions of the American Mathematical Society 361, no. 05 (November 20, 2008): 2689–718. http://dx.doi.org/10.1090/s0002-9947-08-04631-x.

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RAPPAZ, JACQUES, and ADRIAN REIST. "MATHEMATICAL AND NUMERICAL ANALYSIS OF A THREE-DIMENSIONAL FLUID FLOW MODEL IN GLACIOLOGY." Mathematical Models and Methods in Applied Sciences 15, no. 01 (January 2005): 37–52. http://dx.doi.org/10.1142/s0218202505003897.

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The main goal of this article is to analyze a three-dimensional model for stress and velocity fields in grounded glaciers and ice sheets including the role of normal deviatoric stress gradients. This model leads to a nonlinear system of stationary partial differential equations for the velocity with a viscosity depending on the stress–tensor but which is not explicitly depending on the velocity. The existence and uniqueness of a weak solution corresponding to this model is established by using the calculus of variations. The approximation of this model is made by a finite element method with piecewise polynomial functions of degree 1 on a tetrahedral mesh and error analysis is performed. Numerical solutions show that the theoretical results we have obtained are almost optimal.

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Neto, Antônio Francisco. "Matrix Analysis and Omega Calculus." SIAM Review 62, no. 1 (January 2020): 264–80. http://dx.doi.org/10.1137/19m1241362.

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Rota, G. C., and B. D. Taylor. "The Classical Umbral Calculus." SIAM Journal on Mathematical Analysis 25, no. 2 (March 1994): 694–711. http://dx.doi.org/10.1137/s0036141093245616.

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Sun, Xie-Hua. "On Umbral Calculus I." Journal of Mathematical Analysis and Applications 244, no. 2 (April 2000): 279–90. http://dx.doi.org/10.1006/jmaa.1999.6686.

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Verdoodt, Ann. "p-adicq-umbral Calculus." Journal of Mathematical Analysis and Applications 198, no. 1 (February 1996): 166–77. http://dx.doi.org/10.1006/jmaa.1996.0074.

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Agler, Jim, and John E. McCarthy. "Non-commutative functional calculus." Journal d'Analyse Mathématique 137, no. 1 (March 2019): 211–29. http://dx.doi.org/10.1007/s11854-018-0070-7.

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Osborne, M. Scott, and Garth Warner. "On the Dini calculus." Journal of Mathematical Analysis and Applications 118, no. 1 (August 1986): 255–62. http://dx.doi.org/10.1016/0022-247x(86)90307-0.

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Manea, Daniela-Ioana, Emilia Țiţan, Radu R. Șerban, and Mihaela Mihai. "Statistical applications of optimization methods and mathematical programming." Proceedings of the International Conference on Applied Statistics 1, no. 1 (October 1, 2019): 312–28. http://dx.doi.org/10.2478/icas-2019-0028.

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Abstract Optimization techniques perform an important role in different domains of statistic. Examples of parameter estimation of different distributions, correlation analysis (parametric and nonparametric), regression analysis, optimal allocation of resources in partial research, exploration of response surfaces, design of experiments, efficiency tests, reliability theory, survival analysis are the most known methods of statistical analysis in which we find optimization techniques. The paper contains a synthetic presentation of the main statistical methods using classical optimization techniques, numerical optimization methods, linear and nonlinear programming, variational calculus techniques. Also, an example of applying the “simplex” algorithm in making a decision to invest an amount on the stock exchange, using a prediction model..

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