Journal articles on the topic 'High performances calculus'
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1
Nicola, Marcel, and Claudiu-Ionel Nicola. "Sensorless Fractional Order Control of PMSM Based on Synergetic and Sliding Mode Controllers." Electronics 9, no. 9 (September 11, 2020): 1494. http://dx.doi.org/10.3390/electronics9091494.
Abstract:
The field oriented control (FOC) strategy of the permanent magnet synchronous motor (PMSM) includes all the advantages deriving from the simplicity of using PI-type controllers, but inherently the control performances are limited due to the nonlinear model of the PMSM, the need for wide-range and high-dynamics speed and load torque control, but also due to the parametric uncertainties which occur especially as a result of the variation of the combined rotor-load moment of inertia, and of the load resistance. Based on the fractional calculus for the integration and differentiation operators, this article presents a number of fractional order (FO) controllers for the PMSM rotor speed control loops, and id and iq current control loops in the FOC-type control strategy. The main contribution consists of proposing a PMSM control structure, where the controller of the outer rotor speed control loop is of FO-sliding mode control (FO-SMC) type, and the controllers for the inner control loops of id and iq currents are of FO-synergetic type. Superior performances are obtained by using the control system proposed, even in the case of parametric variations. The performances of the proposed control system are validated both by numerical simulations and experimentally, through the real-time implementation in embedded systems.
2
Bârsan, Ghiţă, Silviu Mihai Petrişor, and Luminiţa Giurgiu. "Validation of the Mathematical and Numerical Models for Artillery Barrels Autofrettage Based on Hydrostatic Procedure." Applied Mechanics and Materials 186 (June 2012): 58–69. http://dx.doi.org/10.4028/www.scientific.net/amm.186.58.
Abstract:
The research of advanced gun barrels focuses on materials or the combination between advanced materials and new innovative processes that enable the increase of the life cycle and performances of all calibers cannons. In addition to the investigation of new materials, considerable efforts were made for developing new techniques. The paper describes a theoretical framework validated with the experimental tests for increasing mechanical properties of thick-walled tubes subjected to high interior pressure loads. The theoretical model established a mathematical model of calculus for non-linear environments in the case of self-hooping or autofrettaging of the thick-walled tubes. The mathematical model was validated with experimental tests performed in the Mechanical Engineering Laboratory of the Military Technical Academy in Bucharest on a standard tension test specimens collected from the abutment barrel made out of alloyed steel. Finally, the present paper introduces some theoretical guidelines of hydrostatic procedure in the field of artillery barrels manufacturing, as well as experimental data obtained after using the autofrettage procedure.
3
Tenreiro Machado, José A., and António M. Lopes. "Fractional-order kinematic analysis of biomechanical inspired manipulators." Journal of Vibration and Control 26, no. 1-2 (October 16, 2019): 102–11. http://dx.doi.org/10.1177/1077546319877703.
Abstract:
Present-day mechanical manipulators reveal limited performances when compared with the human arm. Joint-driven manipulators are sub-optimal due to the high actuator requirements imposed by the transients of the operational space tasks. Muscle-actuated arms are superior because the anatomic structures adapt the task requirements to the driving linear actuators. However, the advantages of muscle actuation are difficult to unravel using the standard integer-order kinematics based on the integer derivatives, namely the positions, velocities and accelerations. This paper investigates the human arm and evaluates the influence of biomechanics upon the driving actuators by means of a new method of kinematic analysis and visualisation. The proposed method uses the tools of fractional calculus for computing the continuous propagation of the signals between positions and accelerations. The behaviour of the variables is compared in the joint and muscle spaces, using both the kinematics in the time domain and the describing function method. In this line of thought, the classical integer-order kinematics, with three discrete levels of visualisation, is generalised to a continuous description represented by the fractional-order kinematics.
4
Wang, Jin, Xiancong Wu, Qiang Li, and Jian Zhao. "First Order Plus Dead Time (FOPDT) Model Approximation and Proportional-Integral-Derivative Controllers Tuning for Multi-Volume Process." Journal of Nanoelectronics and Optoelectronics 17, no. 3 (March 1, 2022): 474–88. http://dx.doi.org/10.1166/jno.2022.3223.
Abstract:
Analysis and controller design for the FOPDT model is widely used because of its simpleness and convenience. In this paper, the problem of the multi-volume process (MVP) being approximated to first order plus dead time (FOPDT) model, as well as its proportional-integral-derivative (PID) controller arguments tuning is studied. These have been heavily studied in recent years and the methods developed for its optimal design rely on the idea of including several robust performance specifications in the objective function the method presents fast convergence and consists of mentioning a desired closed-loop transfer function. Particle swarm optimization (PSO) algorithm and performance index of the integral of the time-weighted absolute error (ITAE) minimum is presented to determine the approximate FOPDT model coefficients of MVP processes, where the order is from two to fifteen. In addition, the approximate FOPDT model is used to design the PID controller, which is used to control MVP. A large number of tuning methods are provided to analyze and compare the closed-loop control performances. At the end of the paper, two simulation examples illustrate the superiority and effectiveness of the PID controller design based on the proposed model reduction method. The simulation results show that the reduced-order controller can control a high-order system well, but the process of order reduction is complicated and it needs a long computation time. The FOPID is a generalization of the conventional PID controller. This is based on an extension calculus. A new method for approximating MVP to the FOPDT model is presented in this paper with more effectiveness.
5
Wang, Jin, Xiancong Wu, Qiang Li, and Jian Zhao. "First Order Plus Dead Time Model Approximation and Proportional-Integral-Derivative Controllers Tuning for Multi-Volume Process." Journal of Nanoelectronics and Optoelectronics 17, no. 5 (May 1, 2022): 794–808. http://dx.doi.org/10.1166/jno.2022.3253.
Abstract:
Analysis and controller design for the FOPDT model is widely used because of its simpleness and convenience. In this paper, the problem of the multi-volume process (MVP) being approximated to first order plus dead time (FOPDT) model, as well as its proportional-integral-derivative (PID) controller arguments tuning is studied. These have been heavily studied in recent years and the methods developed for its optimal design rely on the idea of including several robust performance specifications in the objective function the method presents fast convergence and consists of mentioning a desired closed-loop transfer function. Particle swarm optimization (PSO) algorithm and performance index of the integral of the time-weighted absolute error (ITAE) minimum is presented to determine the approximate FOPDT model coefficients of MVP processes, where the order is from two to fifteen. In addition, the approximate FOPDT model is used to design the PID controller, which is used to control MVP. A large number of tuning methods are provided to analyze and compare the closed-loop control performances. At the end of the paper, two simulation examples illustrate the superiority and effectiveness of the PID controller design based on the proposed model reduction method. The simulation results show that the reduced-order controller can control a high-order system well, but the process of order reduction is complicated and it needs a long computation time. The FOPID is a generalization of the conventional PID controller. This is based on an extension calculus. A new method for approximating MVP to the FOPDT model is presented in this paper with more effectiveness.
6
Niederle, Muriel, and Lise Vesterlund. "Explaining the Gender Gap in Math Test Scores: The Role of Competition." Journal of Economic Perspectives 24, no. 2 (May 1, 2010): 129–44. http://dx.doi.org/10.1257/jep.24.2.129.
Abstract:
The mean and standard deviation in performance on math test scores are only slightly larger for males than for females. Despite minor differences in mean performance, many more boys than girls perform at the right tail of the distribution. This gender gap has been documented for a series of math tests including the AP calculus test, the mathematics SAT, and the quantitative portion of the Graduate Record Exam (GRE). The objective of this paper is not to discuss whether the mathematical skills of males and females differ, be it a result of nurture or nature. Rather we argue that the reported test scores do not necessarily match the gender differences in math skills. We will present results that suggest that the evidence of a large gender gap in mathematics performance at high percentiles in part may be explained by the differential manner in which men and women respond to competitive test-taking environments. The effects in mixed-sex settings range from women failing to perform well in competitions, to women shying away from environments in which they have to compete. We find that the response to competition differs for men and women, and in the examined environment, gender difference in competitive performance does not reflect the difference in noncompetitive performance. We argue that the competitive pressures associated with test taking may result in performances that do not reflect those of less-competitive settings. Of particular concern is that the distortion is likely to vary by gender and that it may cause gender differences in performance to be particularly large in mathematics and for the right tail of the performance distribution. Thus the gender gap in math test scores may exaggerate the math advantage of males over females.
7
Chiu, Singa Wang, Liang-Wei You, Tsu-Ming Yeh, and Tiffany Chiu. "The Collective Influence of Component Commonality, Adjustable-Rate, Postponement, and Rework on Multi-Item Manufacturing Decision." Mathematics 8, no. 9 (September 11, 2020): 1570. http://dx.doi.org/10.3390/math8091570.
Abstract:
The present study explores the collective influence of component commonality, adjustable-rate, postponement, and rework on the multi-item manufacturing decision. In contemporary markets, customer demand trends point to fast-response, high-quality, and diversified merchandise. Hence, to meet customer expectations, modern manufacturers must plan their multiproduct fabrication schedule in the most efficient and cost-saving way, especially when product commonality exists in a series of end products. To respond to the above viewpoints, we propose a two-stage multiproduct manufacturing scheme, featuring an adjustable fabrication rate in stage one for all needed common parts, and manufacturing diversified finished goods in stage two. The rework processes are used in both stages to repair the inevitable, nonconforming items and ensure the desired product quality. We derive the cost-minimized rotation cycle decision through modeling, formulation, cost analysis, and differential calculus. Using a numerical illustration, we reveal the collective and individual influence of adjustable-rate, rework, and postponement strategies on diverse critical system performances (such as uptime of the common part and/or end products, utilization, individual cost factor, and total system cost). Our decision-support model offers in-depth managerial insights for manufacturing and operations planning in a wide variety of contemporary industries, such as household merchandise, clothing, and automotive.
8
Padernal, Rogie E., and Crispina V. Diego. "Academic Performance of Senior High School Students in Pre-Calculus." Philippine Social Science Journal 3, no. 2 (November 12, 2020): 69–70. http://dx.doi.org/10.52006/main.v3i2.185.
Abstract:
Knowledge in Pre-Calculus depends on students' understanding of Algebra and Trigonometry. The result of the Program for International Students Assessment (PISA) in 2018 disclosed that the Philippines ranked the second-lowest in Mathematics assessment and indicated low performance in advanced subjects such as Calculus. Hence, the paper described the level of academic performance of senior high school students in a maritime school in Bacolod City during the school year 2019-2020. Likewise, it aimed to determine the relationship between the students' demographics and the level of academic performance in Pre-Calculus. Furthermore, it is intended to test the correlation and predictive capability of the school of origin and entrance examination scores in the academic performance of students in Pre-Calculus.
9
King, Nancy T. "Calculus & Technology: Calculus Reform for High School Teachers." Journal of Educational Technology Systems 23, no. 2 (December 1994): 183–95. http://dx.doi.org/10.2190/5q4b-p4db-m7n8-rxw3.
Abstract:
Technology has changed our lives. It affects how we work, play, handle business transactions, and even how and when we die. The fact that it influences our daily activities is undebatable. That technology would be used to enhance the teaching of mathematics was inevitable. While technology is not the only component of the Calculus Reform movement, it is the central focus of the movement. It is what separates this movement from reform movements of years past. Mathematicians and math educators are changing how we teach calculus. Critics may question the role of calculators and computers in the classroom, but the opportunities provided by technology will make it virtually impossible to ignore this medium of delivering classroom instructions. It is gernerally accepted that the problems associated with poor mathematics performance in this country must be solved in the institutions of higher education [1]. CAL-TECH is the beginning of Texas Southern University's contribution to the solution.
10
Sadler, Philip, and Gerhard Sonnert. "The Path to College Calculus: The Impact of High School Mathematics Coursework." Journal for Research in Mathematics Education 49, no. 3 (May 2018): 292–329. http://dx.doi.org/10.5951/jresematheduc.49.3.0292.
Abstract:
This study addresses a longstanding question among high school mathematics teachers and college mathematics professors: Which is the best preparation for college calculus—(a) a high level of mastery of mathematics considered preparatory for calculus (algebra, geometry, precalculus) or (b) taking calculus itself in high school? We used a data set of 6,207 students of 216 professors at 133 randomly selected U.S. colleges and universities, and hierarchical models controlled for differences in demography and background. Mastery of the mathematics considered preparatory for calculus was found to have more than double the impact of taking a high school calculus course on students' later performance in college calculus, on average. However, students with weaker mathematics preparation gained the most from taking high school calculus.
11
Agua, Breix Michael Grande, Merlyn Lingo, and Junar Lingo. "A multiple linear regression model of students’ performance in calculus in the new normal." Journal of Research, Policy & Practice of Teachers & Teacher Education 13, no. 1 (June 27, 2023): 103–17. http://dx.doi.org/10.37134/jrpptte.vol13.1.8.2023.
Abstract:
The Philippines launched an educational reform in 2012, adding two years of senior high schools (SHS) with strands that aim to prepare students for work or pursue college degrees. The STEM strand was designed for those wishing to enroll in Science, Technology, Engineering, and Mathematics-related degree programs. This study investigates the performance in Calculus and the University admission examination of a random sample of 234 enrolled students for the First Semester of 2021-2022 at Caraga State University taking Differential Calculus. It tries to identify the socio-economic predictors of students' performance in Calculus. Results revealed that age, gender, SHS strand, enhancement program, and admission scores in English, Mathematics, and Abstract Reasoning correlate with students' Calculus performance. Also, the students who graduated from the SHS strand performed better in Calculus than those who did not. Nonetheless, Calculus student performance is regardless of the type of community, SHS type, and family monthly income. Among the socio-economic correlates, the SHS strand and calculus enhancement program are the main predictors of student performance in Calculus using multiple linear regression. Other significant predictors of Calculus student performance are the students' admission scores in Mathematics and Abstract Reasoning. This means that students who performed well in the Mathematics and Abstract Reasoning admission scores, along with SHS STEM strand enrolment and provision of the Calculus enhancement program, are indicators of students' performance in Calculus, implying the importance of mathematics interventions for the students' performance. Furthermore, an appropriate senior high school strand for college degree program preference is a necessary pre-requisite.
12
Leomarich F. Casinillo and Ma. Rachel Kim L. Aure. "Econometric Evidence on Academic Performance in Basic Calculus of Science, Technology, Engineering and Mathematics (STEM) Senior High Students." Journal of Educational and Human Resource Development (JEHRD) 6 (December 28, 2018): 238–49. http://dx.doi.org/10.61569/8qd7sc65.
Abstract:
Low academic performance in high school mathematics is a deeply-rooted concern in the Philippine education system. With the implementation of the K to 12 Education program, this has drawn more concern in the academe, most especially in mathematics. Basic Calculus is a mathematics course that usually serves as requisite to different collegiate courses which may hopefully be useful in their respective major fields. This study was conducted to evaluate the different factors affecting the academic performance in Basic Calculus of all senior high schools enrolled in SY 2017-2018. Using a mixed-method research approach, this paper employed Grade 11 STEM students enrolled from the time of the study. A structured questionnaire on students’ perception towards Basic Calculus served as instrument to gather information. Descriptive measures were used to summarize the different factors and regression modelling was undertaken to identify the significant factors influencing the academic performance of the students. Results of the study revealed that in order for the students to perform well in Basic Calculus they must first understand the basic skills in Pre-calculus. The students may perform well when they highly favor the said subject. Furthermore, students’ academic performance in Basic Calculus may still remain to be limited by knowledge, interest, and capability. Hence, academic performance of the said subject was not derived from socio-demographic profile of students, economic resources, and student’s perception to teacher but to their past knowledge and interest in mathematics.
13
Lu, Shizhou, Wei Liu, Chenyu Zhu, Qiang Zhai, and Renshui Cao. "Precision Displacement Control of a Diamond-shaped Amplifying Mechanism Driven by Piezoelectric Actuator Based on Fuzzy Fractionalorder PIλDμ Controller." Current Nanoscience 15, no. 6 (October 11, 2019): 596–605. http://dx.doi.org/10.2174/1573413715666181212141714.
Abstract:
Background: As a high-performance functional material, stacked piezoelectric actuator can produce a displacement under the effect of changing voltage. Its advantages of fast response and easy operation make it to be widely applied in the precision structure field. However, its small displacement stroke and hysteresis nonlinearity affect the accuracy of the output. : In the next step, some experiments were undertaken based on the constructed platform. Methods: In order to enlarge the displacement of piezoelectric actuator and reduce the influence of hysteresis, this study designs a diamond-shaped amplifying mechanism to amplify the output of the piezoelectric actuator, and then develops a self-tuning fuzzy fractional-order PIλDμ controller for the high precision displacement control of the proposed amplifying mechanism. After analyzing the working principle and modeling the amplifying mechanism, the fractional-order PIλDμ control model of the proposed mechanism was built and discretized according to the theoretical base of the fractional calculus in the time domain. Moreover, the fuzzy control algorithm was also introduced to achieve self-turning of parameters. Besides, the amplifying mechanism was also adopted for a microdroplet jetting dispenser to verify the practicability of the mechanism and control strategy. In the next step, some experiments were undertaken based on the constructed platform. Results: Experiments show that the displacement overshoots, the times of reaching a steady state of the traditional integer-order controller and the fractional-order controller are 5.08%, 1.17% and 17.25 s, 12.00 s, respectively. However, the fuzzy PIλDμ controller lowers the overshoot and the time of reaching a steady state to 0.95% and 9.00 s, respectively. The control algorithm can not only improve the follow-ability of the output displacement of the proposed mechanism, but also maintain the deviation within the range of 0.4% after the displacement stroke is stable and reduce the entering time of the mechanism up to 47.8%. In actual application, the droplet volume of micro-droplet jetting dispenser under fuzzy fractional-order PID control method is more stable, and its repeatability accuracy can reach up to 1.6475%. Conclusion: Experimental results indicate that the self-tuning fuzzy fractional-order PIλDμ controller can significantly improve the tracking performances of the PID and the integer-order PID with regard to the amplifying mechanism with the advantages of good dynamic character and regulation precision. Furthermore, the diamond-shaped amplification mechanism and control strategy can be applied for some micro-droplet jetting dispensers used in microelectronic packaging, life science and 3D printing fields.
14
Dzafic, Izudin, Rabih A. Jabr, and Tarik Hrnjic. "High Performance Distribution Network Power Flow Using Wirtinger Calculus." IEEE Transactions on Smart Grid 10, no. 3 (May 2019): 3311–19. http://dx.doi.org/10.1109/tsg.2018.2824018.
15
Q. Quimson, Jerrie-Marie. "STEM Students' Engagement in Horizontal Transfer from Calculus to Physics and their Difficulties." International Journal on Research in STEM Education 3, no. 1 (May 29, 2021): 36–46. http://dx.doi.org/10.31098/ijrse.v3i1.503.
Abstract:
Majority of science students are facing different problems in applying their calculus knowledge to physics courses. Researchers started to develop an integrated approach to address this problem however, many schools are still teaching calculus and physics as two separate subjects. Moreover, there has been no significant research on senior high school students' transfer of learning and difficulties in calculus-based physics subjects. It is crucial because this is when the students first experience applying calculus in a physics context. Hence, the study investigated the engagement of senior high school STEM students to horizontal transfer from Basic Calculus to General Physics subjects and the difficulties they experience in solving calculus-based-physics problems. A correlational study research design was employed to explore the relationship between the students’ physics and calculus performance using a physics worksheet. Both qualitative and quantitative methods were also employed to determine the difficulties of the students in calculus-based-physics problems. The Pearson correlation revealed that there is a significant positive correlation between the students’ physics and calculus performance. Although this could not serve as strong evidence of transfer, this strong correlation implies that senior high school STEM students were able to construct the similarities between the calculus-based physics problems and their calculus schema. As revealed in the questionnaire and the students’ responses in the worksheet and interview, students have difficulty in solving calculus-based physics problems in terms of identifying the variable that needs to be integrated, setting-up the limits of integration, evaluating the limits of integral, and identifying the appropriate rules of integration and applying it in solving the physics problem. These difficulties are rooted in the fact that students have little experience applying calculus in word problems, especially in the physics context.
16
Capinding, Andie Tangonan. "REVOLUTIONIZING PRE-CALCULUS EDUCATION: PHOTOMATH'S AI-POWERED MATHEMATICS TUTORSHIP." Problems of Education in the 21st Century 81, no. 6 (December 18, 2023): 758–75. http://dx.doi.org/10.33225/pec/23.81.758.
Abstract:
Mathematics plays a vital role in education; however, Filipino students encounter difficulties, evident in their performance on both national and international assessments. However, current literature suggests that leveraging technology, such as calculators and AI, in mathematics education can enhance students' proficiency, particularly in the pre-calculus domain. Thus, this research study examined the effectiveness of Photomath in enhancing Filipino students' self-reliance, interest, and performance in pre-calculus. A quasi-experimental one-group pretest-posttest design was used, with 49 Grade 11 students from NEUST Laboratory High School participating. Descriptive and inferential statistical analyses were performed to examine the pre-and post-intervention data. Results revealed a significant increase in students' self-reliance, interest, and performance in pre-calculus following the use of Photomath. The mean scores on all three measures increased significantly from the pretest to the posttest. The results of the t-tests further confirmed the effectiveness of Photomath in enhancing students' self-reliance, interest, and performance in pre-calculus. These results suggest that Photomath can be a valuable tool for educators to incorporate into pre-calculus teaching to enhance students' confidence and interest, foster intrinsic motivation, and ultimately improve their performance. Keywords: Photomath, students’ interest, students’ self-reliance, performance in pre-calculus
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Etcuban, Jonathan, Cirilo Daculara, Jr., Mayette Cutab, Suzette Lapiña, and Bell Campanilla. "Attitudes and Performance of Grade 11 Students in Pre-Calculus Using Strategic Intervention Material." Journal of Mathematics and Statistics Studies 5, no. 2 (May 18, 2024): 01–12. http://dx.doi.org/10.32996/jmss.2024.5.2.1.
Abstract:
Strategic Intervention Material (SIM) served as instructional support to help students review key ideas and techniques to help them master a competency-based ability they could not achieve during routine class discussions. This study aimed to determine the attitudes and the performance of Grade 11 students in Pre-Calculus using SIM at the three-identified public national high schools in Cebu, Philippines. It employed the descriptive-correlational method to collect data from 97 samples using two questionnaires (A standardized Attitudinal Test by Fennema-Sherman and researchers-made Performance Test in Equations of Circles). The Chi-square test, t-test, frequency, simple percentage, mean, standard deviation, and attitude toward success were used to analyze the respondents' attitudes about pre-calculus regarding confidence in learning, attitude toward success, mathematics as a male domain, and usefulness. The findings demonstrated that SIMs were appropriate for the respondents' needs, with more excellent knowledge gained from the SIM leading to a better understanding of Pre-Calculus, specifically Equations of Circles, which is beneficial when SIM is used as a teaching tool. The study concluded that using SIM in Pre-Calculus as instructional support significantly affected the student's performance in Pre-Calculus, which is effective in learning the subject. The proposed intervention plan was recommended to be implemented, monitored, and evaluated to boost the math performance of the Grade 11 senior high schools.
18
Jamian, Nurul Husna, Najihan Awang Ali, and Muhammad Aslam Mohd Safari. "Exploring Pre-Calculus (MAT133) Final Assessment Marks Between Gender Using Principal Component Analysis: A Case In UiTM Tapah." Mathematical Sciences and Informatics Journal 2, no. 2 (November 30, 2021): 57–66. http://dx.doi.org/10.24191/mij.v2i2.15934.
Abstract:
Pre-Calculus covers additional algebraic and trigonometric, where the students are encouraged to become proficient in those topics to prepare for an in-depth calculus learning. In Universiti Teknologi Mara (UiTM), practically every semester the issue of Pre-Calculus’ high failure rate is commonly reported. One of the ways to measure the students' understanding of this subject is through the final assessment performance. Besides, gender significance is one of the most notable studies in mathematics performance. Therefore, this study aims to compare the performance of part 1 diploma students who registered Pre-Calculus in UiTM Tapah in in accordance to their gender. To analyze the results, this study performed Descriptive and Principal Component Analysis using R statistical software. It was found that the students faced problems in answering Question 2, but scored more marks for Question 5. This revealed that most of the students faced difficulties in handling sketches of parabolas and circles. It was also discovered that the female students outperformed the males in this course.
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González-López, Verónica Andrea, Marina Capelari Piovesana, and Nícolas Romano. "Tail conditional probabilities to predict academic performance." 4open 2 (2019): 18. http://dx.doi.org/10.1051/fopen/2019012.
Abstract:
In this paper, we estimate tail conditional probabilities by incorporating copula models and adopting a Bayesian estimation process for the copula’s parameter. Based on the records of student’s classifications in (a) Mathematics and (b) Natural Sciences/Physics (of the entrance exam to the University of Campinas, from 2013 to 2015), by means of tail conditional probabilities we predict the performance, of the same students, in Calculus I which is a mandatory subject of the undergraduate course of Statistics, and we compare the conditional probabilities year after year. We see that (a), (b) and Calculus I show maximal trivariate correlations in tail events given by classifications which are jointly high/low in the three subjects. We compare the evolution of the tail conditional probabilities from 2013 to 2015 and, according to our results there has been an improvement (from 2013 to 2015) of at most 12%. This improvement being more incisive in the settings with conditional events given by jointly high classifications in comparison with settings with conditional events given by jointly lower classifications.
20
Yu, Bo, Yifei Pu, Qiuyan He, and Xiao Yuan. "Circuit Implementation of Variable-Order Scaling Fractal-Ladder Fractor with High Resolution." Fractal and Fractional 6, no. 7 (July 12, 2022): 388. http://dx.doi.org/10.3390/fractalfract6070388.
Abstract:
Extensive research has been conducted on the scaling fractal fractor using various structures. The development of high-resolution emulator circuits to achieve a variable-order scaling fractal fractor with high resolution is a major area of interest. We present a scaling fractal-ladder circuit for achieving high-resolution variable-order fractor based on scaling expansion theory using a high-resolution multiplying digital-to-analog converter (HMDAC). Firstly, the circuit configuration of variable-order scaling fractal-ladder fractor (VSFF) is designed. A theoretical demonstration proves that VSFF exhibits the operational characteristics of variable-order fractional calculus. Secondly, a programmable resistor–capacitor series circuit and universal electronic component emulators are developed based on the HMDAC to adjust the resistance and capacitance in the circuit configuration. Lastly, the model, component parameters, approximation performance, and variable-order characteristics are analyzed, and the circuit is physically implemented. The experimental results demonstrate that the circuit exhibits variable-order characteristics, with an operational order ranging from −0.7 to −0.3 and an operational frequency ranging from 7.72Hz to 4.82kHz. The peak value of the input signal is 10V. This study also proposes a novel method for variable-order fractional calculus based on circuit theory. This study was the first attempt to implement feasible high-resolution continuous variable-order fractional calculus hardware based on VSFF.
21
Ullah, Nasim, Wakeel Khan, and Shaoping Wang. "High Performance Direct Torque Control of Electrical Aerodynamics Load Simulator using Fractional Calculus." Acta Polytechnica Hungarica 11, no. 10 (2014): 59–78. http://dx.doi.org/10.12700/aph.11.10.2014.10.4.
22
Bekene Bedada, Tola, and M. F. Machaba. "The Effect of GeoGebra on Students’ Abilities to Study Calculus." Education Research International 2022 (August 11, 2022): 1–14. http://dx.doi.org/10.1155/2022/4400024.
Abstract:
The study aimed to investigate the effect of GeoGebra on students’ ability to learn calculus. Calculus can be a challenging subject to teach. Moreover, students have problems, especially in connecting the concepts of calculus with the real world. Concerning gender, the study looked at the impact of utilizing GeoGebra Mathematical software on students’ calculus proficiency and ability to utilize GeoGebra software to learn calculus. The study developed a cycle model that posits nine steps to promote the teaching and learning process with the help of GeoGebra to improve the learning process. A quantitative research methodology was employed to achieve the goal of the study. A quasi-experiment with a pretest and posttest design was used in the quantitative part of the study. Students learning calculus were the subjects of the study, which took place at a university in Ethiopia. The quantitative data were analyzed using SPSS version 27. The results show that there is a significant difference between pretest and posttest in students’ performance (ability) when using GeoGebra mathematics software, indicating that students performed better after the intervention (F (1,64) = 10.495, p = 0.002 < 0.05). The treatment benefited both high- and low-ability pupils in their brain-based learning, although students in the experimental group, both female and male, outperformed those in the control group. While the GeoGebra-oriented learning approach to calculus has the potential to improve competency, it is still necessary that it be structured (cycle model) to address a specific deficiency.
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Sami, Irfan, Shafaat Ullah, Shafqat Ullah, Syed Sabir Hussain Bukhari, Naseer Ahmed, Muhammad Salman, and Jong-Suk Ro. "A Non-Integer High-Order Sliding Mode Control of Induction Motor with Machine Learning-Based Speed Observer." Machines 11, no. 6 (May 24, 2023): 584. http://dx.doi.org/10.3390/machines11060584.
Abstract:
The induction motor (IM) drives are prone to various uncertainties, disturbances, and non-linear dynamics. A high-performance control system is essential in the outer loop to guarantee the accurate convergence of speed and torque to the required value. Super-twisting sliding mode control (ST-SMC) and fractional-order calculus have been widely used to enhance the sliding mode control (SMC) performance for IM drives. This paper combines the ST-SMC and fractional-order calculus attributes to propose a novel super-twisting fractional-order sliding mode control (ST-FOSMC) for the outer loop speed control of the model predictive torque control (MPTC)-based IM drive system. The MPTC of the IM drive requires some additional sensors for speed control. This paper also presents a novel machine learning-based Gaussian Process Regression (GPR) framework to estimate the speed of IM. The GPR model is trained using the voltage and current dataset obtained from the simulation of a three-phase MPTC based IM drive system. The performance of the GPR-based ST-FOSMC MPTC drive system is evaluated using various test cases, namely (a) electric fault incorporation, (b) parameter perturbation, and (c) load torque variations in Matlab/Simulink environment. The stability of ST-FOSMC is validated using a fractional-order Lyapunov function. The proposed control and estimation strategy provides effective and improved performance with minimal error compared to the conventional proportional integral (PI) and SMC strategies.
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Casinillo, Leomarich F., and Ginna F. Tavera. "ON THE DARK SIDE OF LEARNING CALCULUS: EVIDENCE FROM AGRIBUSINESS STUDENTS." IJIET (International Journal of Indonesian Education and Teaching) 5, no. 1 (January 25, 2021): 52–60. http://dx.doi.org/10.24071/ijiet.v5i1.2825.
Abstract:
This study focused on evaluating the agribusiness students negative experiences in learning Calculus. The study employed 121 agribusiness students in the first semester of school year 2019-2020 in Visayas State University, Baybay City, Leyte, Philippines. A selected secondary data from the study of Casinillo and Casinillo (2020a) was utilized in this study. With the aid of correlational research approach, this study stresses to explain the nature and characteristics of negative effects of learning calculus which is very helpful for improving the level of achievement of students and modifying the strategy of mathematics teachers. Results showed that most of the agribusiness students dont have enough background in pre-calculus topics since there are only 9% of them took a STEM strand during senior high school. Seemingly, it is revealed that students are experiencing extreme stress, natural emotional exhaustion and frustration, and average absenteeism, somatic burden and laziness in learning Calculus. It is found out that the negative experiences of these agribusiness students are significantly related to each other. This suggest that these negative experiences are inter-correlated and dependent to each other which is wearisome to their studies and leads to poor academic performance. However, these students are driven to pursue studying calculus since its part to their requirements in their degree program. Hence, by proper motivation and appropriate teaching strategy in Calculus, these students can progress their level of achievement.
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Casinillo, Leomarich F., and Emily L. Casinillo. "Econometric Evidence on Self-Determination Theory in Learning Calculus Among Agribusiness Students." Indonesian Journal of Social Studies 3, no. 1 (July 15, 2020): 1. http://dx.doi.org/10.26740/ijss.v3n1.p1-12.
Abstract:
Self-determination theory is a study of individual interest and motivation which plays a vital role in good and productive performance in learning. This study focus on the agribusiness students’ motivation in learning Calculus as part of their curriculum. Using econometric models, this study identified some statistically significant factors of motivation. The study employed 121 agribusiness students as respondents using stratified random sampling in the first semester of SY 2019-2020. Results revealed that most of the agribusiness students are motivated in learning calculus. Female student is more likely motivated compared to male students. Females are more focusing on their studies while males are affected by online games. The study revealed that learning attitude and health are significant factors of motivation in learning. Also, students’ experience in calculus makes them creative in the classroom which positively contributes to their interest. Perhaps, this students makes or invents new ideas in the learning environment. Results documented that problems encountered in the classroom does not affects their interest in learning. Furthermore, results showed that their perception to their calculus teacher is relatively high which is a significant factor to their motivation. In fact, their teachers are the most important factor that contributes to their level of achievement in Calculus, more important than any other school resources.
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Lin, Hong, Jeremy Kemp, and Padraic Gilbert. "Computing Gamma Calculus on Computer Cluster." International Journal of Technology Diffusion 1, no. 4 (October 2010): 42–52. http://dx.doi.org/10.4018/jtd.2010100104.
Abstract:
Gamma Calculus is an inherently parallel, high-level programming model, which allows simple programming molecules to interact, creating a complex system with minimum of coding. Gamma calculus modeled programs were written on top of IBM’s TSpaces middleware, which is Java-based and uses a “Tuple Space” based model for communication, similar to that in Gamma. A parser was written in C++ to translate the Gamma syntax. This was implemented on UHD’s grid cluster (grid.uhd.edu), and in an effort to increase performance and scalability, existing Gamma programs are being transferred to Nvidia’s CUDA architecture. General Purpose GPU computing is well suited to run Gamma programs, as GPU’s excel at running the same operation on a large data set, potentially offering a large speedup.
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Nunez, Maria Merlinda A., Alberto D. Yazon, Sherwin B. Sapin, Victoria E. Tamban, and Karen A. Manaig. "Improving high school students' performance in basic calculus using the Enhancing Mastery & Expertise in Mathematics supplementary material." Applied Quantitative Analysis 3, no. 1 (June 30, 2023): 42–54. http://dx.doi.org/10.31098/quant.1597.
Abstract:
Preparing K-12 students to gear up for higher mathematics and sciences, and to be more mathematically college-ready, teachers were given the essential role in bridging the learning gaps. One way to address this was the utilization of modules. The researcher developed Enhancing Mastery & Expertise in Mathematics (EM&EM) module in Basic Calculus. The objective of this quasi-experimental research was to evaluate the effectiveness of the EM&EM module in improving students' performance about the theorems of differentiation. The experimental and comparison groups comprised forty-six (46) Grade 11 students who used the EM&EM module and the DepEd module, respectively. The instruments used in the study were the pretest, formative tests, and posttest found in the EM&EM module. Mean and standard deviation were used to describe student performance in these assessments. To see if a significant difference existed, the formative test and posttest scores between the two groups were analyzed using an independent t-test, while the pretest and posttest scores within each group were analyzed using a paired sample t-test. The findings showed that the experimental and comparison groups' formative tests and posttest scores did not differ significantly, although the former generally performed better when their mean scores were compared. However, there was a significant difference between the two groups' pretest and posttest scores, and that had a large positive effect on their improvement. Therefore, just like the DepEd module, the EM&EM module was effective in facilitating the learning process. Overall, the EM&EM module significantly and substantially enhanced students' learning of Basic Calculus.
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Cabuquin, Jomar C. "Examining Multiple Intelligences and Performance of Science, Technology, Engineering, and Mathematics (STEM) Students in the Specialized Subjects." European Journal of Education and Pedagogy 3, no. 5 (September 26, 2022): 55–60. http://dx.doi.org/10.24018/ejedu.2022.3.5.426.
Abstract:
This study generally examined the multiple intelligences of the Senior high school (SHS) students under the Science, Technology, Engineering, and Mathematics (STEM) strand and their performance in the specialized subjects. Descriptive and comparative research designs were utilized to measure the variation among the identified study variables. It involved 193 STEM students (composed of 94 males and 99 females) who were selected using complete enumeration sampling. Secondary data on students' performance in the specialized subjects and an adopted Multiple Intelligence Inventory survey questionnaire were employed to collect the data. The T-test for two independent samples was likewise used to examine the significant difference between the performance in the specialized subjects of students with STEM strand as their preferred choice and those who do not prefer STEM. Based on the results, interpersonal intelligence was shown to be the most dominant intelligence type among STEM students, whereas logical intelligence was determined to be the least dominant. On the specialized subjects’ performance, the students demonstrated very good to superior performance in pre-calculus, general biology, and basic calculus subjects. Meanwhile, the study indicated no significant difference in the specialized subjects’ performance between students with STEM strand as their preferred choice and those who do not prefer STEM. Career guidance orientation for students must be reinforced so that they can be advised on what career track or stand to take in senior high school. Future related studies are suggested to further substantiate the results.
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Granger-Serrano, Angela, and Alexander Villarraga-Orjuela. "Peer Effects on First-Year University Students’ Results: The Role of Classmates’ Academic Performance and Socioeconomic Status." Mathematics 9, no. 23 (December 3, 2021): 3115. http://dx.doi.org/10.3390/math9233115.
Abstract:
Peer effects in the context of higher education have lately received increased attention. Higher diversity in the composition of new cohorts of students, generated mainly in countries where public and institutional policies have enabled access to students from low socioeconomic conditions and races who unusually attend postsecondary education, make these effects even more relevant. This research estimates and analyzes the effect of peers’ academic performance and course composition by socioeconomic origin on students’ academic achievement at a private Colombian university between 2008 and 2019. The estimates, by Ordinary Least Squares and Multilevel models, support the existence of significant peer effects. There was a positive effect of peers’ performance on Calculus I academic results, principally of medium and high-performance peers, and a null effect of the socioeconomic level in Calculus I, but a significant effect in Communication Skills I, although with a limited impact. By introducing heterogeneities, it is evident that students perceived a greater benefit from performance improvements from peers who are in the same performance category or socioeconomic level. These results provide evidence of the existence, direction, and magnitude of peer effects in Colombian higher education. Additionally, they suggest that the most relevant characteristic of classmates is their academic performance and not their socioeconomic origin.
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Rif'at, Mohamad, and Nurfadilah Siregar. "RETHINKING TEACHERS’ PROFESSIONAL DEVELOPMENT: LESSON FROM EVALUATION IN MASTER PROGRAM OF MATHEMATICS EDUCATION." Jurnal Pendidikan Matematika dan IPA 13, no. 2 (July 16, 2022): 231. http://dx.doi.org/10.26418/jpmipa.v13i2.49370.
Abstract:
This research is based on the results of the evaluation of the last ten years related to the development of studies in the Mathematics Education Master Program, Tanjungpura University, through a partnership model to develop and implement national and international comparative studies on mathematics teacher education. The aims are to describe the methodology used in the national level study of teacher education through the Teacher Professional Education Program or Pendidikan Profesi Guru (PPG)- Teacher Education and Development of Studies in Mathematics and share key findings related to mathematics preparation for future teachers. The research applied a quantitative approach with cross-sectional survey method with students of the master program of mathematics education class of 2019/2022 and 2020/2021. The results of the study show that future teacher performance: (1) has less opportunity to learn than high achievers in geometry, functions, calculus, and groups with mastery of linear algebra, number theory, analytic geometry, introduction to probability, and statistics and (2) has less opportunity for those who study school mathematics in data representation, calculus compared to linear algebra, analytic geometry, introduction to calculus, calculus, probability, and statistics. Thus, it can be concluded that attention and emphasis are needed on the type and depth of learning materials given to future teachers who continue their studies at the master's level. This pattern represents an extension to better future secondary school teachers.
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Mehta, U., R. Prasad, and K. Kothari. "VARIOUS ANALYTICAL MODELS FOR SUPERCAPACITORS: A MATHEMATICAL STUDY." Resource-Efficient Technologies, no. 1 (May 9, 2020): 1–15. http://dx.doi.org/10.18799/24056537/2020/1/218.
Abstract:
Supercapacitors (SCs) are used extensively in high-power potential energy applications like renewable energy systems, electric vehicles, power electronics, and many other industrial applications. This is due to SCs containing high-power density and the ability to respond spontaneously with fast charging and discharging demands. Advancements in material and fabrication techniques have induced a scope for research to improve the application of SCs. Many researchers have studied various SC properties and their effects on energy storage and management performance. In this paper, various fractional calculus-based SC models are summarized, with emphasis on analytical studies from derived classical SC models. Study prevails such parameterized resistor–capacitor networks have simplified the representation of electrical behavior of SCs to deal with the complicated internal structure. Fractional calculus has been used to develop SC models with the aim of understanding their complicated structure. Finally, the properties of different SC models utilized by various researchers to understand the behavior of SCs are listed using an equivalent circuit.
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Zeitoun, Eman, Zuhrieh Shana, Azhar Shater, Khadijeh Naser, and Ziad Mukattash. "Does flipping the classroom with videos and notetaking promote high school students’ performance in mathematics?" Eurasia Journal of Mathematics, Science and Technology Education 19, no. 6 (June 1, 2023): em2274. http://dx.doi.org/10.29333/ejmste/13200.
Abstract:
Using a quasi-experiment with the pre-/post-test control group design, the present study investigated whether flipping an advanced pre-calculus class would lead to a statistically significant gain in the learning of conic sections for high school students. The subjects were 50 11th graders (n=50), who were equally divided into two groups. The treatment group (n=25) learned conic sections via the flipped classroom model, while the control group (n=25) was taught the same topic traditionally via the didactic approach. The intervention comprised flipping mathematics class with four video-assisted lessons and notetaking. All subjects were pre-tested on their prior knowledge on conic sections before starting the experiment and post-tested after intervention. The results of the post-test indicated statistically significant difference between the mean score of the treatment group and that of the control group, reflecting the effectiveness of the flipped instruction. Participants enjoyed the intervention.
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Yu, Wan Neng, Su Wen Li, and Min Ying Zheng. "The Filtering Mechanism Modeling and Simulation of Passive Power Filter Based on Differentiator Circuit." Advanced Materials Research 430-432 (January 2012): 1593–96. http://dx.doi.org/10.4028/www.scientific.net/amr.430-432.1593.
Abstract:
Traditional continuous-time filters are of integer order which the power loss of passive power filter is general very much. However, using fractional calculus, filters may also be represented by the more general fractional-order differential equations. In this work, firstly, the passive elements were described with fractional-order differential equations depending on the introduction of fractional calculus application research. Secondly, the mathematical model of fractional-order filters was derived and discussed which includes high impedance at a certain frequency and low impedance at others, and the integer-order filters are only a tight subset of fractional-order filters that are testified. At last, the filter design idea to the fractional-order domain is developed and the better filter performance of the fractional-order passive power filter is validated by the mathematical model analysis and simulation results.
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Evardo Jr, Orville Jardinico, and Estela Corro Itaas. "Enhancing students’ performance on least taught topics in basic calculus through Moodle-based courseware package." Journal of Mathematics and Science Teacher 4, no. 2 (April 1, 2024): em060. http://dx.doi.org/10.29333/mathsciteacher/14310.
Abstract:
This study utilized the developmental research design to identify the least taught topics in basic calculus and design and investigate the effectiveness of a Moodle-based courseware package. Data were collected from seven basic calculus teachers and five academic administrators through survey questionnaires, interviews, and validation sheets. The quasi-experimental phase of the study used a pre-/post-test control group design with a sample of 69 students, 34 students in the experimental group and 35 students in the control group. The experimental group received instruction using an asynchronous Moodle-based courseware package, while the control group received instruction through lecture notes. Results showed that the least taught topics include infinite limits, limits at infinity, and limits of trigonometric, exponential, and logarithmic functions. These topics were least taught due to time constraints, students’ capacity, scheduling, complexity, and relatability. Validation of the courseware package showed a very high validity. It was found that the use of Moodle-based courseware package and lecture notes effectively increased the students’ performance. However, one-way analysis of covariance results showed that the experimental group gained considerably greater than those in the control group. It was recommended that teachers continue to update their knowledge of different teaching methodologies to develop an encouraging and dynamic learning environment.
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Duan, Qiang, Xinghe Li, and Linjie Zhang. "Network Calculus-Based Delay Analysis for QoS Provision in Buffered Crossbar Switch." Journal of Interconnection Networks 04, no. 02 (June 2003): 131–46. http://dx.doi.org/10.1142/s0219265903000787.
Abstract:
The buffered crossbar switch employs crossbar-based switching fabric architecture with internal buffers and combined input and output queueing scheme. It is promising to achieve high performance without complex implementation. In this paper, we apply network calculus-based analytical technique to study the delay performance of the buffered crossbar switch. We set up a service curve-based model for the traffic control system of buffered crossbar switch. Based on this model, we develop techniques that can determine the end-to-end service curve guaranteed to a flow of traffic and calculate the packet delay upper bound of this flow. Then we analyze the determining factors of this delay bound performance and the relation between the delay bound and the amount of resources (bandwidth and credits) allocated in the switch to a flow.
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Lacy, John H., Gabriel E. Patenotte, Abby C. Kinney, and Protik K. Majumder. "Broadband High-Precision Faraday Rotation Spectroscopy with Uniaxial Single Crystal CeF3 Modulator." Photonics 11, no. 4 (March 26, 2024): 304. http://dx.doi.org/10.3390/photonics11040304.
Abstract:
We present a low-noise (<10 µrad/Hz) broadband Faraday Rotation Spectroscopy method which is feasible for near-ultraviolet through near-infrared wavelengths. We demonstrate this in the context of a high-precision spectroscopy experiment using a heated Pb vapor cell and two different lasers, one in the UV (368 nm) and a second in the IR (1279 nm). A key element of the experimental technique is the use of a uniaxial single crystal CeF3 Faraday modulator with excellent transmission and optical rotation properties across the aforementioned wavelength range. Polarimeter performance is assessed as a function of crystal orientation and alignment, AC modulation amplitude, laser power, and laser wavelength. Crystal-induced distortion of the (6p2)3P0→(6p2)3P1 (1279 nm) and (6p2)3P1→(6p7s)3P0 (368 nm) spectral lines due to misalignment-induced birefringence is discussed and modeled using the Jones calculus.
37
Nohara, B. T., and T. Nishizawa. "An Optimal Working Function Based on the Energetic Cost for Myriapod Robot Systems: How Many Legs Are Optimal for a Centipede?" Journal of Vibration and Control 11, no. 10 (October 2005): 1235–51. http://dx.doi.org/10.1177/1077546305054149.
Abstract:
The objective of this paper is to obtain working functions for the legs of a myriapod robot from a kinetic energy point of view. The realization of the high performance of energy consumption is indispensable in the battery-based robot system. We introduce the cost of transport and reduce to the minimum problem of the cost of transport. The calculus of variations is applied to obtain governing equations and the functions for legs. We obtain optimal functions for legs in an octarupedal robot.
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Irizarry, Yasmiyn. "On Track or Derailed? Race, Advanced Math, and the Transition to High School." Socius: Sociological Research for a Dynamic World 7 (January 2021): 237802312098029. http://dx.doi.org/10.1177/2378023120980293.
Abstract:
Recent scholarship has examined how accelerated math trajectories leading to calculus take shape during middle school. The focus of this study is on advanced math course taking during the critical yet understudied period that follows: the transition to high school. Data from the High School Longitudinal Study of 2009 are used to examine advanced math course taking in ninth grade, including both track persistence among students who took advanced math in middle school and upward mobility among students who took standard math in middle school. Results reveal sizable racial gaps in the likelihood of staying on (and getting on) the accelerated math track, neither of which are fully explained by prior academic performance factors. Interactions with parents and teachers positively predict advanced math course taking. In some cases, interactions with teachers may also reduce inequality in track persistence, whereas interactions with counselors increase such inequality. Implications for research and policy are discussed.
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Vozianov, О. S. "The contact ureterolithotripsy in treatment of ureterolythiasis." Klinicheskaia khirurgiia 87, no. 7-8 (September 30, 2020): 43–46. http://dx.doi.org/10.26779/2522-1396.2020.7-8.43.
Abstract:
Objective. Аnalysis of the treatment results in patients, suffering ureteric calculi, using the contact ureterolithotripsy procedure.
Маterials and methods. In 104 patients with ureteric calculi, in whom ureteroscopy with further laser contact ureterolithotripsy was conducted, symptoms of the disease were analyzed, as well as the diagnostic methods value, peculiarities and efficacy of surgical treatment.
Results. In all the patients endoscopic extraction of calculi have been succeeded. Calculus does not cause significant macroscopic changes in ureter, if symptoms, characteristic for ureterolithiasis, persists up to one week. Local edema is formed, if a calculus persists in ureter longer than a week. Long-term (more than two months) local ureteric persistence of calculi enhances the risk of its intramucosal intraureteric «ingrowth» greatly.
Conclusion. The contact ureterolithotripsy constitutes a highly effective and miniinvasive method of surgical intervention in ureterolithiasis, guaranteeing high level of postoperative “stone free rate”. Prolongation of the calculi ureteric insertion time without a process of a stone discharge causes the ureteric wall changes, complicating performance of miniinvasive interventions (the contact ureterolithotripsy and a distant shock-wave lithotripsy).
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Konopatskiy, E. V., K. V. Ryabinin, and A. A. Bezditnyi. "Visualization of Geometric Models of Faceted Solids in Point Calculus." Scientific Visualization 15, no. 1 (April 2023): 60–70. http://dx.doi.org/10.26583/sv.15.1.05.
Abstract:
The paper considers the case of faceted solids and discusses visualisation of geometric solids in the form of a three-parameter set of points which belongs to a three-dimensional space. To visualize geometric solids, taking advantage of the modern GPU hardware acceleration, the Ray marching method is used. The implementation considers the definition of a signed distance function, which is reduced to the task of determining the set of intersection points of the projection rays with the rendered geometric solid. After that, for each pixel of the screen, its color is determined in accordance with whether the ray passes through the geometric solid or not. The analytical description of geometric solids and the solution of their intersection problem with projecting rays are solved within the framework of the point calculus mathematical apparatus. As a result, it was concluded that the proposed approach justifies itself, providing high rendering performance and the complete absence of visual artifacts when rendering faceted solids.
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Konopatskiy, E. V., and A. A. Bezditnyi. "CONJUGATION OF CURVED LINES IN THE POINT CALCULUS." Vestnik komp'iuternykh i informatsionnykh tekhnologii, no. 216 (June 2022): 3–11. http://dx.doi.org/10.14489/vkit.2022.06.pp.003-011.
Abstract:
The paper implements a general approach to conjugate curves in the point calculus, which includes geometric algorithms for conjugating curves and their analytical description in the form of point equations. This is the mathematical basis for building high-performance computer-aided design systems and providing them with the necessary geometric modeling tools. Geometric algorithms for conjugating planar and spatial curves in general form involving, respectively, two or three free functions continuous and deferential within the parameter variation interval are considered. A point definition of tangents for planar and spatial curves is presented, which consists in differentiating the equation of the original curve by the current parameter followed by a parallel transfer of the resulting segment to the tangent point. Directly conjugation is provided by means of arcs of the first order of smoothness. Several examples of the definition of the arcs of the outline in the point calculus and recommendations on their use for the conjugation of curves are presented. The point equations given in the article and the computational algorithms based on them are valid not only for conjugation of curves, but also for straight lines, proceeding from the fact that a straight line is a special case of a zero-curvature curve that does not require a tangent to be constructed. The prospect of further research is for the conjugation of surface bays, in which two tangents to the original surface bays will form surface bays with cross-sections in the form of arcs of the outline of the chosen shape.
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Lassong, Binandam Stephen, Mary Osei Fokuo, and Kwasi Frempong Sarfo. "Predictive factors affecting students’ performance in studying engineering mathematics in technical universities in Ghana." international journal of Education, Learning and Development 10, no. 7 (June 15, 2022): 16–27. http://dx.doi.org/10.37745/ijeld.2013/vol10n7pp1627.
Abstract:
The study's major purpose was to investigate the factors that influence engineering mathematics performance in Ghanaian technical universities. Three hundred and fifteen (315) participants were surveyed using questionnaires and six (6) expert interviews. Descriptive variables were examined using cross-tabulation, univariate, and bivariate statistical methods. The logistic regression model and Pearson's chi-square test were used to examine the relationship between the dependent variable (engineering student performance) and the predictive variables respectively. The study's findings revealed that several factors influence students’ performance in engineering mathematics, including age, terrible strain, and level of interest. It was revealed by an expert’s interview that students from senior high school like engineering mathematics whiles those from technical senior high school do not like engineering mathematics because of their poor background in mathematics. To reinvigorate students’ performance in this course area, pre-calculus classes for older students should be arranged to assist them to refresh their memory, according to the study, students should be encouraged to devote a significant amount of time to engineering mathematics coupled with tutorials.
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Wen, Jian-Ping. "Fractional Order Nonlinear Feedback Controller Design for PMSM Drives." Mathematical Problems in Engineering 2013 (2013): 1–5. http://dx.doi.org/10.1155/2013/290310.
Abstract:
Fractional order integral is introduced into active disturbance rejection controller (ADRC) to establish the structure of fractional order proportional integral controller (FPI). Fractional order ADRC (FADRC) is designed by replacing the nonlinear state error feedback control law using nonlinear function combination in ADRC with FPI, which can combine the high performance of ADRC estimating disturbances with the characteristics of fractional order calculus more really describing the physical object and spreading the stable region of the system parameters. The proposed FADRC is applied to permanent magnet synchronous motor (PMSM) speed servo system in order to improve robustness of system against the disturbances. Compared with ADRC, simulation results verify that the proposed control method has given very good robust results and fast speed tracking performance.
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Schnaudt, Christian, and Sebastian A. Popa. "How procedural and economic performance shape political trust: Affective and cognitive foundations of the performance-trust nexus." Zeitschrift für Vergleichende Politikwissenschaft 17, no. 1 (June 20, 2023): 31–57. http://dx.doi.org/10.1007/s12286-023-00570-y.
Abstract:
AbstractIn which ways and under what conditions do the procedural and economic performance of political systems matter for citizens’ political trust? While this question has been a recurring theme in research on political support, we still lack a clear understanding of the conditional nature of the performance-trust nexus. In this study, we focus on the affective and cognitive foundations of the performance-trust nexus, arguing that the impact of objective procedural and economic performance on political trust is conditioned by citizens’ political allegiances (i.e., status as electoral winner or loser) and political sophistication (i.e., political knowledge and political interest). Our empirical analysis using comparative survey data from two European high-quality surveys (European Election Study 2014 and European Social Survey 2002–2018) shows that procedural and economic performance feature particularly prominently in the trust calculus of politically more knowledgeable and interested citizens as well as electoral losers, while being less relevant for the political trust of less sophisticated citizens and electoral winners. Moreover, the analysis provides evidence that cognitive orientations are overall more important than affective ones in moderating the performance-trust nexus. These findings offer important implications concerning the nature and meaning of feelings of disenchantment and distrust in contemporary democracies.
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JAAFAR, ZURAIDA. "Logistic Regression in Analyzing the Determinants of University Students' Mathematics Performance." Mathematical Sciences and Informatics Journal 2, no. 2 (November 30, 2021): 67–75. http://dx.doi.org/10.24191/mij.v2i2.14977.
Abstract:
Mathematics provides an effective way of building mental discipline, encourages logical reasoning, and plays a crucial role in understanding the contents of other subjects. Mathematics performance is affected by several factors including grade, social economic status, background and many more. The aim of this study is to investigate the factors which are related to students’ mathematics performance and to identify the significant factors which affect the students’ mathematics performance of MAT133 course. This study was conducted in UiTM Negeri Sembilan, Kuala Pilah campus. 480 students were selected from various programs who had registered Pre-Calculus course (MAT133). This study employed Logistic regression analysis to test the relationship between predictor variables and the dichotomous outcome variable which is categorized as low or high achiever in MAT 133 course. About 55.7% of the students are high achiever who achieved higher than 70% marks in MAT133. The research findings reveal that students’ intake on July (OR = 2.941), male students (OR = 0.315), students who scored A+, A and A- in Modern Mathematics in SPM exam (OR = 0.340), students who had B+ and B- in Additional Mathematics in SPM (OR = 0.512) and assessment marks for MAT133 were found to have a significantly higher possibility to be high-achiever in MAT133. Acquiring strong mathematical background is a priority as a fundamental preparation for students to learn mathematics in higher institution.
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Wood, K. L., and E. K. Antonsson. "Computations with Imprecise Parameters in Engineering Design: Background and Theory." Journal of Mechanisms, Transmissions, and Automation in Design 111, no. 4 (December 1, 1989): 616–25. http://dx.doi.org/10.1115/1.3259045.
Abstract:
A technique to perform design calculations on imprecise representations of parameters has been developed and is presented. The level of imprecision in the description of design elements is typically high in the preliminary phase of engineering design. This imprecision is represented using the fuzzy calculus. Calculations can be performed using this method, to produce (imprecise) performance parameters from imprecise (input) design parameters. The Fuzzy Weighted Average technique is used to perform these calculations. A new metric, called the γ-level measure, is introduced to determine the relative coupling between imprecise inputs and outputs. The background and theory supporting this approach are presented, along with one example.
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Hace, Aleš. "The Improved Division-Less MT-Type Velocity Estimation Algorithm for Low-Cost FPGAs." Electronics 8, no. 3 (March 25, 2019): 361. http://dx.doi.org/10.3390/electronics8030361.
Abstract:
Advanced motion control applications require smooth and highly accurate high-bandwidth velocity feedback, which is usually provided by an incremental encoder. Furthermore, high sampling rates are also demanded in order to achieve cutting-edge system performance. Such control system performance with high accuracy can be achieved easily by FPGA-based controllers. On the other hand, the well-known MT method for velocity estimation has been well proven in practice. However, its complexity, which is related to the inherent arithmetic division involved in the calculus part of the method, prevents its holistic implementation as a single-chip solution on small-size low-cost FPGAs that are suitable for practical optimized control systems. In order to overcome this obstacle, we proposed a division-less MT-type algorithm that consumes only minimal FPGA resources, which makes it proper for modern cost-optimized FPGAs. In this paper, we present new results. The recursive discrete algorithm has been further optimized, in order to improve the accuracy of the velocity estimation. The novel algorithm has also been implemented on the experimental FPGA board, and validated by practical experiments. The enhanced algorithm design resulted in improved practical performance.
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Jihe, Chen, Jerito Pereira, Xinxin Li, Ying Zhou, Maximus Tamur, and Syaharuddin Syaharuddin. "Correlation between Mathematics and Physics Achievement of Senior High School Students." Tarbawi : Jurnal Ilmu Pendidikan 17, no. 1 (June 13, 2021): 14–26. http://dx.doi.org/10.32939/tarbawi.v17i1.768.
Abstract:
Physics and mathematics are the two most closely related natural rudimentary subjects. In the study of physics, often need to rely on mathematical rigorous reasoning and argumentation and need to use a variety of mathematical methods for investigation, reasoning, calculus, test, discussion, but students often appear in these difficulties. To explain the influence of mathematics achievement on physics achievement from the high school mathematics achievement and physics achievement. The results of math and physics in the first semester of 6 classes of senior high school student's grade 12 were selected, and the data were analyzed with SPSS.22 software, and three students of different learning abilities were interviewed in detail. The innovation of this paper lies in the use of hierarchical research methods to compare classes of mathematics achievement and physics achievement. The conclusions are (1) in objective level, there is a positive linear relationship between math achievement and physics achievement; (2) on the subjective level, students accept the view that the performance of mathematics can promote the performance of physics; students' subjective cognition will affect their cognitive structure and learning behavior, to actively seek for the relationship between mathematical knowledge and physical knowledge, and then slowly affect the objective level of students, and then in mathematics and physics performance, and (3) applying mathematical thinking to physics learning can improve the efficiency of learning physics. Use mathematical knowledge of trigonometry to solve the force analysis problem of physical movement. This shows that math scores play a very important role in physics scores. Remind us that in the process of teaching, we should pay attention to the integration of mathematical ideas into physics learning, and help students to learn physics knowledge better with mathematical ideas.
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Ma, Qun, Yonggang Liu, Peng Tan, Shanshan Liu, Hang Shi, and Xin Feng. "A new method for identification of natural, artificial and in vitro cultured Calculus bovis using high-performance liquid chromatography-mass spectrometry." Pharmacognosy Magazine 11, no. 42 (2015): 304. http://dx.doi.org/10.4103/0973-1296.153083.
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Latha, S., and Dhanalakshmi Samiappan. "Despeckling of Carotid Artery Ultrasound Images with a Calculus Approach." Current Medical Imaging Formerly Current Medical Imaging Reviews 15, no. 4 (April 11, 2019): 414–26. http://dx.doi.org/10.2174/1573405614666180402124438.
Abstract:
<P>Background: Carotid artery images indicate any presence of plaque content, which may lead to atherosclerosis and stroke. Early identification of the disease is possible by taking B-mode ultrasound images in the carotid artery. Speckle is the inherent noise content in the ultrasound images, which essentially needs to be minimized. </P><P> Objective: The objective of the proposed method is to convert the multiplicative speckle noise into additive, after which the frequency transformations can be applied. </P><P> Method: The method uses simple differentiation and integral calculus and is named variable gradient summation. It differs from the conventional homomorphic filter, by preserving the edge features to a great extent and better denoising. The additive image is subjected to wavelet decomposition and further speckle filtering with three different filters Non Local Means (NLM), Vectorial Total Variation (VTV) and Block Matching and 3D filtering (BM3D) algorithms. By this approach, the components dependent on the image are identified and the unwanted noise content existing in the high frequency portion of the image is removed. </P><P> Results & Conclusion: Experiments conducted on a set of 300 B-mode ultrasound carotid artery images and the simulation results prove that the proposed method of denoising gives enhanced results as compared to the conventional process in terms of the performance evaluation methods like peak signal to noise ratio, mean square error, mean absolute error, root mean square error, structural similarity, quality factor, correlation and image enhancement factor.</P>