Mathematical Calculations Research Articles

A shared tradition: transmitting maritime knowledge in print

As Europeans ventured more frequently on transoceanic voyages in the 16th century, it became essential for navigators to be able to carry out mathematical computations. Iberian educators rose to the occasion, developing textbooks and curricula to transmit these abstract concepts. At the same time that they strove to present new mathematical techniques, these maritime authors also captured the tacit skills that had been practiced for centuries. Thus, even though few working sailors put pen to paper, it is possible to recover aspects of their epistemology from these texts. Because books traveled so easily across borders, these academic sources also had far-reaching effects, inspiring similar educational programs across maritime Europe. This article recommends adopting a comparative perspective, since much can be learned by tracing the evolution of these shared practices as they traveled from Spain and Portugal to the Netherlands, France, and England, and back again.

ТЕХНОЛОГІЇ ЗАСТОСУВАННЯ СЕРЕДОВИЩ ДИНАМІЧНОЇ ГЕОМЕТРІЇ

The paper considers some problems and technologies of teaching geometry using dynamic geometry environments to students of advanced classes and specialized study of mathematics. Integrated application of knowledge of geometry, algebra and mathematical analysis and computer science provides implementation of intersubject relations and introduces to students the elements of the research approach. The author emphasizes the urgency of creating computer-oriented technologies in teaching mathematics, making appropriate amendments to the curriculum and textbooks, conducting systematic research of the effectiveness of their application considering educational risks.

Numerical Analysis of the Magnetic Moment in S/F/S-Josephson Junction

One particularly intriguing object in superconductivity is the Josephson junction, which is an integral part of quantum computer hardware. Analysing this object requires solving differential equations. Such problems often cannot be solved with analytical methods; therefore, numerical methods and computational mathematics must be utilized. This article explores a fundamental model of the Josephson junction. The model presents the spatial coordinates of the magnetic moment as unknown functions dependent on time in a system of three ordinary differential equations with initial conditions. Comparative analysis of various methods is conducted for different sets of parameters. Optimal numerical methods for these particular instances of the problem are found. Visual results are also presented.

Analysis of liquidity risk management using neural networks: An applied study on tesla company for the period 2016-2023

This research aims to study eagerness risk in Tesla Inc. by utilizing an artificial neural network to investigate financial data from 2016 until 2023. The current ratio, quick ratio, annual returns, stock price dispersion, profitability, debt-to-equity ratio, return on assets (ROA) and return on equity (ROE) were among the financial information collected. The financial information was analyzed by multilayer feed-forward neural network and recognized places where liquidity risk prevailed through mathematical computations as well. The results had shown that the model had achieved a prediction accuracy of 87.5%, thus indicating how neural networks can be used effectively when doing analysis on financial data and assessing liquidity risks. Numerical evidence has been provided by this study as regards the ability of Tesla’s financial liquidity changes prediction via the model making it a good tool for the purposes of financial planning including risk management as well.

An Approach to Near-Optimal Continuous-Thrust Solution for Plane Constellation Deployment

Paving the way in satellite constellation deployment, this article presents the Comprehensive Program (GCP) for planning constellation deployment missions by introducing a near-optimal solution for continuous-thrust maneuvers. The GCP establishes time constraints, enabling appropriate time scheduling and eliminating reconfiguration phases. It considers various cases of satellite departure and arrival sequences, collision avoidance constraints, and time limitations. A near-optimal solution for the continuous-thrust trajectory of each satellite is introduced, relying on the Fourier series approximation of the thrust pointing angle. The Fourier series with constant coefficients replaces the thrust angle in the satellite’s orbital motion equations in polar coordinates. The primary advantage of this near-optimal approach lies in its simplicity in accommodating space perturbations, posing no challenges in problem-solving. Additionally, the approach is beneficial due to its straightforward implementation and simple mathematical computations. This approach does not require pre-determining the revolution number of the transfer trajectory, unlike shape-based methods. The proposed method’s flexibility allows it to adapt and optimize the trajectory without prior assumptions about the number of revolutions required for the mission. Analyses demonstrate the proposed algorithm’s versatility and precision across various scenarios involving different orbital eccentricities, thrust forces, and thrust pointing angles. The constant coefficients of the Fourier series are determined by defining a set of objective functions and minimizing them using the Multi-Objective Particle Swarm Optimization algorithm (MOPSO). The first and second objective functions ensure that the transfer orbit reaches the desired deployment point, while the third and fourth ones guarantee the tangential conditions between the transfer orbit and the final orbit. An additional objective function minimizes the trajectory time. As a perturbation of interest, the effect of Earth’s oblateness is considered.

Investigating frontoparietal networks and activation in children with mathematics learning difficulties: Cases with different deficit profiles.

Approximately 15%-20% of school-aged children suffer from mathematics learning difficulties (MLD). Most children with developmental dyscalculia (DD) or MLD also have comorbid cognitive deficits. Recent literature suggests that research should focus on uncovering the neural underpinnings of MLD across more inclusive samples, rather than limiting studies to pure cases of DD or MLD with highly stringent inclusion criteria. Therefore, this study aims to identify neural aberrancies that may be common across multiple MLD cases with different deficit profiles. Nine MLD cases and 45 typically developing (TD) children, all around 7 years old (27 boys), were recruited. Using functional near-infrared spectroscopy (fNIRS), brain data were collected during an approximate resting state and a mathematical computation task (addition). Graph theory was then applied to assess global and nodal network indicators of brain function. When comparing the network indicators and brain activation of the MLD cases to those of TD children, no unified neural aberrancy was found across all cases. However, three MLD cases did show distinct neural aberrancies compared to TD children. The study discusses the implications of these findings, considering both the neural aberrancies in the three MLD cases and the neural similarities found in the other six cases, which were comparable to those of the TD children. This raises important questions about the presence and nature of aberrant neural indicators in MLD across large cohorts and highlights the need for further research in this area.

The role of self-awareness and reflection in academic achievement: A psychological and Bayesian analysis

The ability to properly evaluate one’s own academic progress has long been considered a predictor of academic success. However, its distinctive role in the context of computational mathematics remains underexplored. Grounded in social cognitive theory, this study investigates the critical role of self-regulated learning (SRL) strategies in enhancing mathematics learning, particularly in programming-based contexts. Focusing on two components of SRL, self-awareness and reflection, the study provides empirical evidence on the psychological effectiveness of SRL in academic outcomes through the implementation of an e-portfolio-based intervention. Using Bayesian inference, the study models individual learning processes, offering personalized insights for effective educational interventions. The analysis reveals that the use of e-portfolios significantly fosters self-awareness and enhances learning among students. Nevertheless, the study also addresses psychological challenges in programming-based mathematical education, such as complex problem-solving and abstract thinking. The findings highlight the need for interactive, technology-enhanced teaching approaches to keep university-level students engaged and motivated. Key psychological implications are discussed for relevant measures in mathematics education.

Enhancing Learning Methodologies in the Clinical Pharmacokinetic Course Through Student-Driven Insights and Suggestions

The clinical pharmacokinetics (CPK) course can be quite challenging and difficult for students to understand its applications, as it involves a combination of abstract yet complex concepts and mathematical calculations. Studies have reported that the conventional lecture-based learning process in CPK often results in a poor understanding, especially when it comes to apply the knowledge to real cases. This study aimed to identify strategies to improve the current learning methodology by using self-developed, validated online questionnaires among 37 fourth-year undergraduate pharmacy students who failed their CPK course in mid-semester test at UiTM Puncak Alam, Selangor. We analysed and interpreted the data through descriptive analysis. The majority of students (91.9%) found online quizzes to be the most engaging tool for learning CPK, with 89.2% choosing to include feedback and marks for their answers. Most of them preferred new learning materials that covered both basic concepts and applications-based (86.5%), featuring colourful pictures and diagram interfaces (70.3%) and being accessible anytime and anywhere (83.8%). These preferences have proven to be more effective in enhancing knowledge. The students understood the topics better, which helped improve their engagement and grades. While developing and incorporating educational games into the current CPK course can be time-consuming, the results can be tremendous, transforming the current pharmacy curriculum into something more innovative and fun. Further research related to the development and implementation of alternative learning materials based on these preferences can be conducted to assess its effectiveness in improving students’ performance. Therefore, it is crucial to incorporate the insights of students when enhancing the current learning methodology in the future.

Enhancing Learning Methodologies in the Clinical Pharmacokinetic Course Through Student-Driven Insights and Suggestions

The clinical pharmacokinetics (CPK) course can be quite challenging and difficult for students to understand its applications, as it involves a combination of abstract yet complex concepts and mathematical calculations. Studies have reported that the conventional lecture-based learning process in CPK often results in a poor understanding, especially when it comes to apply the knowledge to real cases. This study aimed to identify strategies to improve the current learning methodology by using self-developed, validated online questionnaires among 37 fourth-year undergraduate pharmacy students who failed their CPK course in mid-semester test at UiTM Puncak Alam, Selangor. We analysed and interpreted the data through descriptive analysis. The majority of students (91.9%) found online quizzes to be the most engaging tool for learning CPK, with 89.2% choosing to include feedback and marks for their answers. Most of them preferred new learning materials that covered both basic concepts and applications-based (86.5%), featuring colourful pictures and diagram interfaces (70.3%) and being accessible anytime and anywhere (83.8%). These preferences have proven to be more effective in enhancing knowledge. The students understood the topics better, which helped improve their engagement and grades. While developing and incorporating educational games into the current CPK course can be time-consuming, the results can be tremendous, transforming the current pharmacy curriculum into something more innovative and fun. Further research related to the development and implementation of alternative learning materials based on these preferences can be conducted to assess its effectiveness in improving students’ performance. Therefore, it is crucial to incorporate the insights of students when enhancing the current learning methodology in the future.

A stable combination of non-stable genes outperforms standard reference genes for RT-qPCR data normalization

Gene expression profiling is of key importance in all domains of life sciences, as medicine, environment, and plants, for both basic and applied research. Despite the emergence of microarrays and high-throughput sequencing, qPCR remains a standard method for gene expression analyses, with its data normalization step being crucial for ensuring accuracy. Currently, the most widely used normalization method is based on the use of reference genes, assumed to be stably expressed across all experimental conditions. In the present study, we show that finding a stable combination of genes, regardless of their individual stability, outperforms standard reference genes for RT-qPCR data normalization. A stable combination of genes consists of a fixed number of genes whose individual expression balance each other all along experimental conditions of interest. Moreover, the present study shows that such an optimal combination of genes can be found using a comprehensive database of RNA-Seq data. Indeed, assuming that such a comprehensive database contains accurate gene expression profiles, we can extract in silico, by the way of the mathematical variance calculation, a stable combination of genes that reflects in vivo stability. As a case study, this new method was developed using the tomato model plant, with corresponding RNA-Seq data from the TomExpress database. However, the method is potentially applicable to other organisms with available RNA-seq data. Our results demonstrate the superiority of the reported method over commonly used housekeeping genes or other stably expressed genes. We therefore recommend the use of our new method together with classic ones in order to always obtain the best reference genes for a given experimental design.

EXPLORATION OF THE USE OF PHET SIMULATION ON NEWTON'S LAW MATERIALS TO IMPROVE STUDENT PHYSICS LEARNING OUTCOMES

AbstractThe background to this research is that physics lessons are often considered difficult and less interesting by students, especially because of their abstract nature, the complexity of mathematical calculations, and the difficulty in connecting theory with practice. One of the challenging topics is Newton's Law of motion, which includes the relationship between force, mass and acceleration. This research was carried out at MA Muallimin UNIVA Medan, by applying the Problem Based Learning (PBL) learning model, an innovative learning media that is relevant to development. technology. This research utilizes PHET (Physics Education Technology), an interactive simulation platform developed by the University of Colorado Boulder, to support learning Newton's Laws. PHET allows students to carry out virtual experiments independently with various variables, such as mass, force and surface type, so that student learning outcomes increase. The research method used is quantitative in class X-G. The instrument used is a written test (essay) with a total of 10 questions. It is known that the pretest and posttest data are normally distributed with a significance value of Pretest (0), Posttest (0,), and are declared homogeneous with a significance value Based on Mean (0.245) where the normality and homogeneity test values exceed (>) the real level used in the measurement namely α = 0.05 or 5%. With the help of SPSS, it is known that the average posttest student learning outcomes (85.93) are higher than the pretest (58.80), so it can be concluded that the hypothesis is accepted.

Solving the problem of technological object identification

Abstract. Problem. The identification task is formulated as follows: based on the results of observations of the input and output variables of a system, a model, i.e. a formalized representation of this system, should be built that is optimal in some sense. This shows the connection between the identification task and the above general scheme of establishing regularities based on the results of observations. The identification task is based on modern control theory. To solve it, modern computers are used. The latter, with their high speed and virtually unlimited memory capacity, create the prerequisites for receiving, transmitting and processing large arrays of observations that are necessary for building adequate models of real objects. Goal. Studying the possibilities of solving the problem of identifying technological objects using MATLAB+Simulink. Job tasks: to consider the tasks of identifying technological objects of management; to choose an identification method; identify the electric motor model. Methodology. The research problems should be solved by methods of analysis and synthesis of automatic control systems by the method of least squares. Results. In the work, experimental data on the dependence of the engine idling speed on the excitation current were obtained and solved the identification problem using the MATLAB+SIMULINK package. Originality. Based on the analysis of existing solutions, it was found that the works did not consider the calculation of absolute and relative errors of the results of identifying the object and the model developed using the least squares method. Thus, there is a need to develop a system for identifying a model of a technological object made by the least squares method. To solve the identification problem, an electric motor is chosen as the object of study. Practical value. The paper examines the methods used to identify complex objects. The comparative analysis showed that the most acceptable method is the least squares method, due to simple mathematical calculations in comparison with the other methods. To illustrate the application of this method, two tasks were solved: identification of the model of an electric motor; identification of the model of an alarm system. The studies have shown that model identification can be performed using the MATLAB+Simulink package. The research results obtained on the model differ from the experimental data by no more than 4 %

Urban heat island relation with land use land cover change in Hetauda sub-metropolitan city of Nepal

Urban areas are expanding globally at the expense of natural productive land which affects the quality of life of urban residents. Hetauda sub-metropolitan city of Nepal has been undergoing rapid urban growth for the last few decades causing local climatic effects such as land surface temperature (LST) variation. Thus, exploring spatio-temporal changes in land use, land cover (LULC), and urban heat island (UHI) analysis could be an effective means of exposing local environmental issues caused by anthropogenic activities. Development in thermal Remote Sensing and Geographic Information System (GIS) has enabled the monitoring of spatial LST, UHI, and its correlation to LULC. We used Landsat 8 OLI/TIRS satellite data and a supervised classification algorithm for land use land classification for the years 1995, 2008, and 2018 in Arc map software. The spatial pattern of LST was obtained through mathematical calculation of the thermal band of Landsat images. Correlation analysis was applied to explore the relationship between LST, LULC types, and LUCL indices. The LST was higher for urban/built-up and cultivated land use types. There was approximately 4°C mean LST variation for all three years of study. The regression analysis showed a positive correlation of urban/built-up with the Normal Difference Built-Up Index (NDBI) however a negative correlation with the Normal Difference Vegetation Index (NDVI) which implies that green structure weakens the UHI effects while urban/built-up areas strengthen the UHI. Overall, the study can be useful for urban planners in sustainable urban planning and management as well as to raise public awareness of climate change and the warming effect.

METHOD FOR IMPROVING SECURITY OF IOT DEVICES PAIRING

Background. The usage of IoT technologies leads to the social, technological and financial development of society. While complex systems play an important role in the IoT, the design, integration and use of simple devices really drive the technology's widespread adoption. At the same time, ensuring a high level of security for simple IoT devices is a difficult task. The reasons for this are device limited computing resources and low power consumption requirements. It prevents the implementation of most modern cryptographic protocols for simple IoT devices. From a security point of view, the most critical communication stage is device pairing, when shared encryption keys are formed to establish a secure communication channel. Objective. The purpose of the paper is to analyse the main vulnerabilities of a simple IoT device pairing process and develop a method for improving security of this process. The method should provide proximity-based device authentication and pairing process protection against known attacks, such as man-in-the-middle attack. Methods. The method of pairing process security improvement includes proximity-based device authentication using analysis of the wireless signal strength. The security of the authentication method is proven analytically and by results of practical experiments with measurement of wireless signal strength change with distance and obstacles between devices. Results. Performed research demonstrated that the proposed method guarantees secure user authentication at a close distance between devices and protection against attacker located at least 10 meters from the paired device. Provided theoretical calculations and experimental results show that the level of attacker's wireless signal power increase required for a successful attack exceeds technical capabilities of existing communication devices. Conclusions. The article solves an important issue of improving the security of simple device pairing. The proposed method of proximity-based IoT device authentication provides pairing process protection against man-in-the-middle attacks. Mathematical calculations were confirmed by conducting a number of experiments to research wireless signal power change depending on the distance and types of obstacles between devices. The proposed authentication method can be integrated into the existing JustWorks protocol for connecting simple IoT devices using the BLE communication channel.

Приближенное решение гиперсингулярного интегрального уравнения с применением рядов Чебышева на классе функций, ограниченных на одном конце и неограниченных на другом конце интервала интегрирования

Approximate methods for solving hypersingular integral equations are an actively developing field of computational mathematics. This is due to the numerous applications of hypersingular integral equations in various fields of mathematics and the fact that analytical solutions of such equations are possible only in exceptional cases. A method for finding a solution, limited at one end and unlimited at the other end of the integration interval [-1,1], of hypersingular integral equations of the first kind using Chebyshev series is proposed and justified. The core and the right side of the equation are also decomposed into Chebyshev series, the decomposition coefficients of which are calculated approximately using quadrature Gauss formulas with the highest degree of accuracy. The coefficients of decomposition of an unknown function into a Chebyshev series are found by solving systems of linear algebraic equations. Methods of functional analysis and the theory of orthogonal polynomials are used to substantiate the computational scheme. The Helder space of functions with corresponding norms is introduced. Given hypersingular and corresponding approximate operators are considered in this space. When the condition for the existence of derivatives up to a certain order belonging to the Helder class for given functions is fulfilled, the calculation error is estimated and the order of its tendency to zero is given.

Modernization of Existing Level Crossings in the Areas of Construction of the European Standard Railway Track in Ukraine

Purpose. The article aims to analyze modern technological solutions to improve the level of safety at railway crossings, prevent emergencies and ensure uninterrupted traffic. Methodology. The study is based on the use of mathematical modeling and numerical methods to analyze the impact of modernization and new projects on the level of safety at railway crossings. Using computer modeling, mathematical models were built that reflect different scenarios of crossings. Based on the data obtained, the effectiveness of the proposed measures was assessed and recommendations for further optimization of the security system were developed. To evaluate the effectiveness of the proposed measures, a system of indicators has been developed to quantify the level of safety of railway crossings before and after modernization. These indicators take into account the daily intensity of train traffic through the crossing, the daily intensity of traffic on the road, the equipment of the crossing, the radius of the curve in the plan and the longitudinal slope of the road on the approaches to the crossing. Findings. An improvement of the method of the final accident rate, which is one of the most common tools for assessing traffic safety at railroad crossings, is proposed. The application of this method made it possible to quantify the level of risk of accidents and analyze the effectiveness of measures aimed at improving safety. The method is relatively easy to use and does not require complex mathematical calculations, and allows taking into account a wide range of factors affecting traffic safety at a level crossing, such as traffic volume, design features of the level crossing, availability of signaling, etc. The final coefficient was used to compare the safety level of different crossings and track the dynamics of changes in their equipment over time. This made it possible to identify crossings that require priority modernization, as well as to predict changes in the initial and calculated data and plan measures to introduce innovative technologies that improve traffic safety at crossings. Originality. An integrated model for assessing the safety of railroad crossings has been developed that takes into account not only traditional indicators (frequency of accidents, traffic intensity) but also new factors such as equipment reliability, human factor, and the impact of external conditions. The proposed model makes it possible to determine a more accurate risk forecast and choose optimal solutions for the modernization of level crossings, taking into account specific operating conditions. Practical value. The formulated recommendations can be used to develop effective programs for the modernization of railway crossings in Ukraine. The implementation of the proposed technologies will increase the level of traffic safety by 20% and reduce the average waiting time at a crossing by 15%. In addition, it will help to increase railroad capacity and reduce infrastructure maintenance costs.

Quantum simulation of time-dependent Hamiltonians via commutator-free quasi-Magnus operators

Hamiltonian simulation is arguably the most fundamental application of quantum computers. The Magnus operator is a popular method for time-dependent Hamiltonian simulation in computational mathematics, yet its usage requires the implementation of exponentials of commutators, which has previously made it unappealing for quantum computing. The development of commutator-free quasi-Magnus operators (CFQMs) circumvents this obstacle, at the expense of a lack of provable global numeric error bounds. In this work, we establish one such error bound for CFQM-based time-dependent quantum Hamiltonian simulation by carefully estimating the error of each step involved in their definition. This allows us to compare its cost with the alternatives, and show that CFQMs are often the most efficient product-formula technique available by more than an order of magnitude. As a result, we find that CFQMs may be particularly useful to simulate time-dependent Hamiltonians on early fault-tolerant quantum computers.

Conscious and Correct Use of Biostatistical Methods in Medical Researches: From Planning to Reporting the Results - Part II

In this part of the review, statistical tests utilized to examine hypotheses regarding population parameters on a representative sample, which forms the fundamentals of inferential statistics are discussed. The selection of an appropriate statistical test by verifying its assumptions and interpreting the results objectively is crucial for obtaining accurate conclusions. Understanding the terms related to type I and type II errors, p-value, power of the study, effect size, and confidence interval will contribute to the correct interpretation of both the results obtained from statistical tests in scientific research and the findings of articles read from the literature. In addition to univariate tests, the three most commonly employed multiple regression models are also addressed to control for the effect of potential confounding factors and other independent variables utilized in the study. Statistical computing has become much more accessible in recent times, with researchers having access to freeware packages or web applications to perform basic and advanced statistical analyses. Researchers frequently focus on the calculation of statistical tests used in data analysis, whereas, understanding the rationale behind statistical methods should be the primary goal. Therefore, this review emphasizes the logic of selecting appropriate statistical methods and interpreting the results rather than mathematical calculations. It is essential to recognize that biostatistical principles should be considered not only in the data analysis phase but also in all phases of research, from planning to report writing. It should be note that, no statistical analysis method can correct erroneous data obtained from a poorly designed study.

Tasks with parameters: a digitized approach

Technological and methodological aspects of using freeware software, such as GeoGebra, Wolfram|Alpha, Maxima, SageMath and GRAN1, for solving tasks with parameters, are presented in the article. Criteria were defined for selection of computer mathematics system (CMS) to solve tasks with parameters, including plotting a graph of a function given in explicit and implicit forms, using a parameter in a function’s analytical definition, and automatically changing the graph of a function depending on the parameter value; ability to changing the parameter step change; plotting of a tangent and a normal to a curve at a point; ability to change the scale; determination of the coordinates of the intersection of graphs of functions; obtaining an analytical solution. In the article, some examples were presented for graphic and analytical tasks that used CMS parameters. GRAN1 and GeoGebra are recommended to use for plotting and analyzing of the graphs

Stereotactic Frame-based Targeting of the Posterior Fossa: A systematic workflow for the Leksell G Frame.

Introduction Cerebellar deep brain stimulation (DBS) is gaining traction as a potential treatment for movement disorders and stroke and there is renewed interest in the cerebellum as a target for neuromodulation. Despite the safety and accuracy of frame-based approaches to the posterior fossa, unconventional stereotactic frame placement may be necessary to allow for low posterior fossa trajectories. Current literature lacks a comprehensive protocol detailing inverted frame placement and targeting. Methods Preoperative imaging was acquired prone. An inverted Leksell G frame was applied along with an open-topped CT fiducial box, followed by a prone CT with the scanner set to the "legs first, nose up" configuration. Target coordinates were extracted from navigation software after image fusion. Intraoperatively, the patient was positioned prone and the stereotactic arc was mounted in the lateral-right orientation, with inverted arc supports. Confirmatory stereotaxy to a scalp staple was performed and the DBS leads were then inserted. Conclusion Our standardized protocol provides a flexible platform for posterior fossa DBS, allowing for low trajectories and multiple electrodes. Unlike conventional upright frame placement, an inverted frame permits an unobstructed view of suboccipital entry sites and incision placement. A conventional frame and regular planning software are sufficient, with no additional mathematical calculations required.