Mathematical Accuracy Research Articles

Control-Oriented Free-Boundary Equilibrium Solver for Tokamaks

A free-boundary equilibrium solver for an axisymmetric tokamak geometry was developed based on the finite difference method and Picard iteration in a rectangular computational area. The solver can run either in forward mode, where external coil currents are prescribed until the converged magnetic flux function ψ(R,Z) map is achieved, or in inverse mode, where the desired plasma boundary, with or without an X-point, is prescribed to determine the required coil currents. The equilibrium solutions are made consistent with prescribed plasma parameters, such as the total plasma current, poloidal beta, or safety factor at a specified flux surface. To verify the mathematical correctness and accuracy of the solver, the solution obtained using this numerical solver was compared with that from an analytic fixed-boundary equilibrium solver based on the EAST geometry. Additionally, the proposed solver was benchmarked against another numerical solver based on the finite-element and Newton-iteration methods in a triangular-based mesh. Finally, the proposed solver was compared with equilibrium reconstruction results in DIII-D experiments.

Exploring mathematical wellbeing across cultures: insights from diverse students

AbstractAcross many countries, including New Zealand, diverse groups including indigenous, migrant, and marginalised communities, are under-represented in mathematics, as evidenced by achievement disparities and disengagement from higher-level mathematics. Both research and policy have focused on developing equitable education outcomes for all students. A key aspect of this is wellbeing, including within mathematics classrooms, which includes identifying classroom environments that enable wellbeing. This study examines mathematical wellbeing (MWB) across different ethnicities and genders, with a case study focus on students from Pacific heritages. Analysing qualitative responses from over 12,000 diverse students revealed that positive relationships in the mathematics classroom were most commonly associated with students’ MWB. Accomplishment and cognitive factors, including mathematical accuracy, learning new things, and understanding, were also identified as important. Minor gender differences emerged, with female students emphasising mathematical understanding, accuracy, and relationships more than male students. The Pacific student case study highlighted the importance of both cognitive aspects (learning new things and understanding) and relationships (peer and teacher support), uncovering an alignment between cultural values and MWB. This study empirically confirms seven universal values supporting student MWB, previously identified in Australian and Chinese contexts, suggesting that teachers internationally may align pedagogical practices with these values to support most students’ MWB. However, the instrumental values serving these universal values appear culturally unique. This research contributes novel insights to the field by examining wellbeing with a subject-specific focus through student-generated responses, offering implications for developing more equitable and culturally inclusive mathematics classrooms.

TRANSLATING DIRECTIONAL ACCURACY INTO PROFITABILITY: MACHINE LEARNING BASED PREDICTIVE MODELS FOR GLOBAL STOCK INDICES

Understanding the linkage between directional accuracy and return remains a negligibly explored domain in the context of stock market prediction. Maximum studies in the given domain are based on mathematical accuracy measures and directional accuracy measures. Merely the efficiency of directional prediction may not suffice, as themagnitude of directional change also assumes importance in stock markets. Without any doubt, profitability measures reign supreme in the case of the stock market. The current study attempts to investigate the association between Accuracy rate and returns for data sets based on seven stock indices across the globe. The outcome of the study relies on machine learning: ANN (Artificial Neural Networks) and SVM (Support Vector Machine) based predictive models, built using 196 data sets of variable duration. The results of the current research reveal a strong positive correlation between accuracy rate and returns. Moreover, significant variations in the extent of therelationship are also observed. Quantile regression models indicate a relatively stronger relationship between accuracy rate and return at the lower range of returns. Findings of the study carry value for academicians, researchers, and practitioners in the field of machine learning and stock market predictions.

Frontoparietal Brain Network Plays a Crucial Role in Working Memory Capacity during Complex Cognitive Task.

Recent neurophysiological studies provide inconsistent results of frontoparietal network (FPN) stimulation for altering working memory (WM) capacity. This study aimed to boost WM capacity by manipulating the activity of the FPN via dual-site high-definition transcranial direct current stimulation. Forty-eight participants were randomly assigned to three stimulation groups, receiving either simultaneous anodal stimulation of the frontal and parietal areas (double stimulation), or stimulation of the frontal area only (single stimulation), or the placebo stimulation (sham) to frontal and parietal areas. After the stimulation, we used an operation span task to test memory accuracy, mathematical accuracy, time of calculation and memorizing, and recall response time across the three groups. The results revealed an enhancement of memory accuracy and a reduction of time of calculation in the double stimulation group compared with that in others. In addition, recall response time was significantly decreased in the double and single stimulation groups compared with that in sham. No differences in mathematical accuracy were observed. Our results confirm the pivotal role of the FPN in WM and suggest its functional dissociation, with the frontal component more implicated in the retrieval stage and the parietal component in the processing and retention stages.

Methodology of Mosaicking and Georeferencing for Multi-Sheet Early Maps with Irregular Cuts Using the Example of the Topographic Chart of the Kingdom of Poland

The Topographic Chart of the Kingdom of Poland (pol. Topograficzna Karta Królestwa Polskiego, commonly referred to as ‘the Quartermaster’s Map’, hereinafter: TKKP) is the first Polish modern topographic map of Poland (1:126,000, 1843). Cartographic historians acclaim its conception by the General Quartermaster of the Polish Army, noting its editorial principles and technical execution as exemplars of the early 19th-century cartographic standards. Today, it stands as a national heritage relic, furnishing invaluable insights into the former Polish Kingdom’s topography. Although extensively utilised in geographical and historical inquiries, the TKKP has yet to undergo a comprehensive geomatic investigation and publication as spatial data services. Primarily, this delay stems from the challenges of mosaicking and georeferencing its 60 constituent sheets, owing to the uncertain mathematical framework and irregular sheet cuts. In 2023, the authors embarked on rectifying this by creating a unified TKKP mosaic and georeferencing the map to contemporary reference data benchmarks. This endeavour involved scrutinising the map’s mathematical accuracy and verifying prior findings. The resultant product is accessible via the ‘Maps with the Past’ platform, developed by the Institute of History of the Polish Academy of Sciences The dissemination of raster data services adhering to OGC standards such as WMTS (Web Map Tile Service), ECW (Enhanced Compression Wavelet), and COG (Cloud Optimized GeoTIFF) facilitates the swift and seamless integration of the generated data into web and GIS tools. The digital edition of the TKKP emerges as a pivotal resource for investigations spanning natural and anthropogenic environmental transformations, sustainable development, and cultural heritage studies.

"Sweet space" strategy for solvent system selection in countercurrent chromatography: A case study on separation of polyunsaturated fatty acids from borage oil.

This study presents a comprehensive strategy for the selection and optimization of solvent systems in countercurrent chromatography (CCC) for the effective separation of compounds. With a focus on traditional organic solvent systems, the research introduces a "sweet space" strategy that merges intuitive understanding with mathematical accuracy, addressing the significant challenges in solvent system selection, a critical bottleneck in the widespread application of CCC. By employing a combination of volume ratios and graphical representations, including both regular and trirectangular tetrahedron models, the proposed approach facilitates a more inclusive and user-friendly strategy for solvent system selection. This study demonstrates the potential of the proposed strategy through the successful separation of gamma-linolenic acid, oleic acid, and linoleic acid from borage oil, highlighting the strategy's effectiveness and practical applicability in CCC separations.

Primary school students’ awareness of their monitoring and regulation judgment accuracy

BackgroundImproving students' monitoring and regulation judgment accuracy is necessary for improving the effectiveness of self-regulated learning, but might not be sufficient: Students presumably also need to feel confident about the accuracy of their judgments to act upon them. However, little is known about students’ awareness of their monitoring judgment accuracy, and awareness of their regulation judgment accuracy has not yet been investigated. AimsWe investigated (1) primary school students’ awareness of their monitoring and regulation judgment accuracy in mathematics and (2) whether self-scoring, which is known to improve monitoring/regulation accuracy, would also improve awareness of their regulation judgment accuracy. Sample(s)Primary school students (9-10 year-olds) from 34 classes (N = 564). MethodsStudents completed problem-solving tasks twice (parallel versions) on two different days and made monitoring/regulation judgments, rated their confidence in the accuracy of those judgments, self-scored their work, and again made (confidence) judgments, on both occasions. If an increase/decrease in judgment accuracy from day 1 to day 2 would be accompanied by an increase/decrease in their confidence in the accuracy of their judgements, students show accuracy awareness. ResultsStudents' judgment accuracy did not predict their confidence in the accuracy of their judgments, indicating that students were not aware of their monitoring/regulation accuracy. Self-scoring improved students’ awareness of their regulation judgment accuracy for students whose regulation judgment accuracy increased or stayed maximally accurate after self-scoring, but not for students whose regulation judgment accuracy decreased or stayed equally inaccurate after self-scoring. ConclusionsPrimary school students were not aware of their monitoring/regulation judgment accuracy. Self-scoring improved the awareness of their regulation judgment accuracy for some students.

Investigating preservice teachers’ feedback to students’ mathematical solutions

ABSTRACT Teachers require support in developing the pedagogical skill of interpreting students’ mathematical thinking and providing effective feedback that promotes learning. However, there is a lack of research assessing the quality of feedback based on teacher noticing in mathematics classes. This study analysed 20 preservice teachers’ (PSTs) feedback approaches through two perspectives: mathematical alignment and the responsiveness of feedback to students’ mathematical approaches. The findings indicated alignment of the focused mathematical concepts/processes in noticing and feedback. PSTs paid more attention to mathematical accuracy than the strength or potential of students’ strategies. Furthermore, there was a relationship between the complexity of student solutions and PSTs’ depth of noticing and the cognitive demands of feedback.

Design and Analysis of a Low Voltage Simulink Model (LVSM) of IEEE 57 Bus

The present power system is gaining momentum towards designing equivalent circuit models. The Ward and REI methods involve the admittance reduction method as well as being merged with the EMS model to derive boundary parameters, but these methods are limited and valid for a predefined condition. Therefore, it is required to design an equivalent circuit that adopts the real power system for analysis. In this paper, a new method is proposed to design a scaled-down power system model without changing the impedance of components. In this regard, a Low Voltage Simulink Model (LVSM) of the IEEE 57 bus network was designed in MATLAB/ Simulink so that it could be useful for laboratory model design purposes. The main objectives of this paper are to propose a mathematical procedure to scale down the network parameters and design a 3-phase LVSM of an IEEE 57 bus power system network within the Simulink platform. The performance of LVSM was analyzed with no-load, balanced load, and unbalanced load models. These simulation studies were validated and compared with the theoretical results to prove that the proposed LVSM modeling has good mathematical accuracy, robustness, and validity for practical model implementation.

Optimized carotenoid production and antioxidant capacity of Gordonia hongkongensis.

The current emphasis within the cosmetic market on sustainable ingredients has heightened the exploration of new sources for natural, active components. Actinomycetota, recognized for producing pigments with bioactive potential, offer promising functional cosmetic ingredients. This study aimed to optimize pigment and antioxidant metabolite production from the Gordonia hongkongensis strain EUFUS-Z928 by implementing the Plackett-Burman experimental design and response surface methodology. Extracts derived from this strain exhibited no cytotoxic activity against human primary dermal fibroblast (HDFa, ATCC® PCS-201-012™, Primary Dermal Fibroblast; Normal, Human, Adult). Eight variables, including inoculum concentration, carbon and nitrogen source concentration, NaCl concentration, pH, incubation time, temperature, and stirring speed, were analyzed using the Plackett-Burman experimental design. Subsequently, factors significantly influencing pigment and antioxidant metabolite production, such as temperature, inoculum concentration, and agitation speed, were further optimized using response surface methodology and Box-Behnken design. The results demonstrated a substantial increase in absorbance (from 0.091 to 0.32), DPPH radical scavenging capacity (from 27.60% to 84.61%), and ABTS radical scavenging capacity (from 17.39% to 79.77%) compared to responses obtained in the isolation medium. The validation of the mathematical model accuracy exceeded 90% for all cases. Furthermore, liquid chromatography coupled with mass spectrometry (LC-MS) facilitated the identification of compounds potentially responsible for enhanced pigment production and antioxidant capacity in extracts derived from G. hongkongensis. Specifically, six carotenoids, red-orange pigments with inherent antioxidant capacity, were identified as the main enhanced compounds. This comprehensive approach effectively optimized the culture conditions and medium of a G. hongkongensis strain, resulting in enhanced carotenoid production and antioxidant capacity. Beyond identifying bioactive compounds and their potential cosmetic applications, this study offers insights into the broader industrial applicability of these extracts. It underscores the potential of G. hongkongensis and hints at the future utilization of other untapped sources of rare actinomycetes within the industry.

Road Management with Mathematical Accuracy

Paraskevov, A. V. Improving road traffic management based on the use of mathematical and instrumental methods of economics [Sovershenstvovanie upravleniya dorozhnym dvizheniem na osnove ispolzovaniya matematicheskikh i intrumentalnykh metodov ekonomiki]. Moscow, Vologda, Infra-Inzheneriya publ., 2023, 84 p. ISBN 978-5-9729-1283-4.The article is a review of the monograph «Improving traffic management based on the use of mathematical and instrumental methods of economics», written by A. V. Paraskevov, a senior lecturer at the Department of Computer Technologies and Systems of the Kuban State Agrarian University named after I. T. Trubilin and published by Infra-Inzheneriya [Infra-Engineering] publishing house. The work summarises and systematises extensive material on innovative methods for improving management of road traffic congestion levels. An also considered application for motorists is designed to build optimal routes taking into account the current situation on urban roads.

An Iterative Equal Area Criterion for Transient Stability Analysis of Grid-Tied Converter Systems With Varying Damping

With the increasing penetration of renewable energy generators, the stability issues of grid-tied converter systems become much more important. However, due to the high nonlinearity and varying damping of converter systems, conventional transient stability analysis methods are not applicable, which may bring to conservativeness or misjudgment on stability assessment. In this paper, the transient stability of grid-tied converter systems with varying damping is investigated to provide stability boundary estimation. Firstly, considering the frequency mutation of the phase-locked loop (PLL) caused by various perturbations, a modified swing equation model of grid-tied converter systems is built, which greatly improves the mathematical model accuracy under transient disturbances. To evaluate the impacts of varying damping and frequency mutation, an iterative equal area criterion (ITEAC) method is proposed with the iterative calculation of the accelerating and decelerating area, which renders stability boundaries with high accuracy. Moreover, the impacts of controller and system parameters on stability boundaries are quantitatively analyzed. Eventually, simulation and hardware-in-loop experiments are performed to verify the effectiveness and superiority of the proposed ITEAC.

ANALYZING STUDENTS' ABILITIES AS PROSPECTIVE TEACHERS OF MATHEMATICS IN CONSTRUCTING PROOFS: A STUDY OF GEOMETRY AND ALGEBRA

Mathematical proof demands accuracy and precision in formulating correct and logical arguments. Students need to develop their ability to produce accurate and precise proofs. This study aims to analyze the ability of prospective mathematics teachers in constructing geometry and algebraic proofs. The research subjects were 8 prospective mathematics teacher students, four male and four female. This descriptive qualitative research begins with giving tests to research subjects, then we conduct interviews. The results showed that male students were better at compiling geometry proofs than compiling algebraic proofs. While female students are better at compiling algebraic proofs than geometry. This is due to the spatial ability of men better than women. When compiling geometry proofs apply procedural proofs, syntactic proofs, and semantic proofs. When compiling algebraic proofs only apply procedural proofs. Female students when compiling geometry proofs only apply procedural proofs. When compiling algebraic proofs, they apply procedural proofs and syntactic proofs.

Pengaruh Pendekatan Permainan dalam Kartu Pinmat Math Hero terhadap Pemahaman Matematika di Tingkat Sekolah Dasar

This qualitative research investigates the use of the Math Hero Flashcards in elementary school children's mathematics education. Math Hero Flashcards are specially designed learning tools aimed at enhancing mathematical understanding, accuracy, and mastery of arithmetic operations for numbers 1-10 through interactive games. The study involves direct observation, interviews, and interactive play with children with the aim of understanding the effects of Math Hero Flashcards on children's mathematical understanding, learning motivation, and interest. The results of the research indicate that the use of Math Hero Flashcards enhances elementary school children's mathematical understanding, fosters motivation for learning, and creates a more enjoyable learning experience. However, some interview participants mentioned that they had found alternatives in the form of math game apps on their phones. Therefore, this research underscores the need for integration between physical learning tools like Math Hero Flashcards and learning technology to achieve holistic and engaging mathematics education for children.

A technical evaluation on the mathematical attitudes and fitting accuracy of soil moisture retention curve models

Numerous mathematical equations have been formulated in the literature of different researchers for describing soil moisture retention curve (SMRC), which can be applied to simulate and solve soil hydraulic modeling problems. The primary concern lies in selecting an efficient model to simulate accurately the S-shaped curve or sigmoid-type of the SMRC for soils with different textures. Therefore, the objective of this study was a comprehensive and technical evaluation of 50 developed models of the SMRC based on the influence of parameters on the behavior of the curve and the ability of their fitting accuracy on 728 soil samples of the UNSODA dataset, that has not been investigated so far. Statistical criteria including corrected Akaike’s information criterion (AICc), root mean square error (RMSE) and coefficient of determination (R2) together with Duncan's multiple range test and cluster analysis were employed to assess the fitting accuracy of SMRC models to measured data. Results from fitting accuracy on the UNSODA dataset indicated that Brutsaert model provided the best fit to the measured data compared to other models in 14.6% of the soil samples with RMSE = 0.0125 and AICc = -94.18. This model was classified in the same cluster with Groenevelt and Grant (GG1, GG2 and GG3), Dexter, Mualem, and Fredlund and Xing models and did not have a significant difference in terms of RMSE. Also, Brutsaert model had the highest fitting accuracy in 67% of different soil textural classes compared to other models. Finally, the technical evaluation in terms of accuracy, flexibility and simplicity of the fitting process showed that the Brutsaert, Mualem, Dexter and GG3 models can be selected for better simulation of the SMRC in water and soil research.

Characterization, rheological behaviour, and dynamic viscosity of ZrO2-SiC (50–50)/DW hybrid nanofluid under different temperatures and solid volume fractions: An experimental study and proposing a new correlation

Researchers, engineers, scientists, and other professionals have been focusing on the exploitation of nanotechnology with specific attention to nanofluids and their property of dynamic viscosity that can do wonders in the field of engineering. This study was aimed at determining the dynamic viscosity of the given hybrid nanofluid (distilled water based ZrO2/SiC) by studying the nanofluid's rheology. In this regard, a two-step method was employed for the dispersal of nanoparticles in the base fluid. The nano-powder was composed of ZrO2 and SiC in a ratio of 1:1 (50% - 50%). The dynamic viscosity of solid volume fractions 0.025% - 0.1% was measured in temperatures 20–60 °C by using DV2TRVTBG Brookfield digital viscometer. The research indicated the association between the nanofluid's viscosity and the factors of temperature and solid volume fraction. At first, in order to assessment the characteristics and stability of nanoparticles into the base fluid, XRD, TEM, FESEM, EDX, UV–vis spectrometer, DLS, and zeta potential test were used on ZrO2 and SiC nanoparticles. The results indicated an increase in dynamic viscosity at higher solid concentrations and falling temperatures. The dynamic viscosity increase of the nanofluid was recorded at 20 and 60 °C, which showed a 29.6% and 64.2% rise in the viscosity respectively in the presence of 0.025% of nanoparticles in the nanofluid. This implies that the viscosity of nanoparticles becomes more sensitive at high temperatures. The experiment showed a maximum viscosity rise of 169.4%. The experiments also discovered that ZrO2-SiC /DW hybrid nanofluid can be successfully used in different devices as a Newtonian fluid since it depicts Newtonian properties at various temperatures. In addition, the study put forward a new correlation for determining the dynamic viscosity of hybrid nanofluid using the experimental data (temperature and solid volume fraction). The value of mathematical correlation accuracy was 98.92%. During the experiment, the sensitivity of viscosity in response to a rise in solid volume fraction was evaluated. Lastly, an acceptable level of accuracy of the correlation outputs was seen when the theoretical and practical values were contrasted.

Diatomic molecular energy spectra and thermodynamic properties of exponential inversely quadratic plus improved deformed exponential-type potential

By employing the Pekeris-type approximation to deal with the centrifugal term, we study the thermodynamic properties and approximate analytical solutions of the Schrödinger equation with the exponential inversely quadratic plus improved deformed exponential-type potential using parametric Nikiforov–Uvarov method and hypergeometric functional analysis method. The complex eigen energy equation was presented in a closed and compact form and extended to study partition function and other thermodynamic properties. The total normalized wave functions were also obtained and expressed in terms of hypergeometric Jacobi polynomial. The mathematical accuracy of analytical calculation can be verified consistently by comparing numerical data and results of different arbitrarily l state. The potential also reduces to improved deformed exponential-type potential as a special case. We calculated energy spectra for some selected diatomic molecules namely: Silicon Flouride (SiF+ (X1∑+), Oxygen molecule O2+ (X2∏g), Nitrogen molecule, N2+ (X1∑g+), Sulphur chloride SCl and Rubidium hydride RbH using standard molecular spectroscopic constants as applied to the two methods. The results show that the energy eigenvalues for these selected diatomic molecules are in excellent agreement using the two methods and also increases with an increase in quantum state.

CT methods for measuring glenoid bone loss are inaccurate, and not reproducible or interchangeable.

Glenoid bone loss is a significant problem in the management of shoulder instability. The threshold at which the bone loss is considered "critical" requiring bony reconstruction has steadily dropped and is now approximately 15%. This necessitates accurate measurement in order that the correct operation is performed. CT scanning is the most commonly used modality and there are a number of techniques described to measure the bone loss however few have been validated. The aim of this study was to assess the accuracy of the most commonly used techniques for measuring glenoid bone loss on CT. Anatomically accurate models with known glenoid diameter and degree of bone loss were used to determine the mathematical and statistical accuracy of six of the most commonly described techniques (relative diameter, linear ipsilateral circle of best fit (COBF), linear contralateral COBF, Pico, Sugaya, and circle line methods). The models were prepared at 13.8%, 17.6%, and 22.9% bone loss. Sequential CT scans were taken and randomized. Blinded reviewers made repeated measurements using the different techniques with a threshold for theoretical bone grafting set at 15%. At 13.8%, only the Pico technique measured under the threshold. At 17.6% and 22.9% bone loss all techniques measured above the threshold. The Pico technique was 97.1% accurate, but had a high false-negative rate and poor sensitivity underestimating the need for grafting. The Sugaya technique had 100% specificity but 25% of the measurements were incorrectly above the threshold. A contralateral COBF underestimates the area by 16% and the diameter by 5 to 7%. No one method stands out as being truly accurate and clinicians need to be aware of the limitations of their chosen technique. They are not interchangeable, and caution must be used when reading the literature as comparisons are not reliable.

ChatGPT is a Breakthrough in Science and Education but Fails a Test in Sports and Exercise Psychology

Released less than fve months ago, ChatGPT became the center of attention of scholars worldwide. This artifcial intelligence (AI) language model has over 100 million subscribers worldwide, generating many discussions concerning its accuracy, advantages, and threats to science and education. Its accuracy in law, linguistics, mathematics, and medicine has already been evaluated. Most results suggest that ChatGPT could generate a passing grade in these domains. However, its performance in sports science and psychology has yet to be tested. The large amount of information in this general area may yield more accurate performance. Still, specifc subjects in the feld, with controversial research fndings, can lead to signifcant errors, which teachers and researchers could quickly spot. In this study, ChatGPT was tested on its accuracy on exercise addiction, a sports science and psychology subject associated with more than 1,000 publications. ChatGPT gave several correct answers to 20 questions but failed the test with 45%. Its performance was like in other already tested subjects. However, when prompted to write a general introductory editorial on AI’s role in sports, ChatGPT performed well. Plagiarism detectors could not identify the AI-originated text, but AI detectors did. Therefore, it can be concluded that the system does a relatively good job on general issues but needs further development in more specifc areas. Students and scholars cannot rely on ChatGPT to do their job. Still, future versions could yield dilemmas of originality since the system does not provide information for its source(s) of information. Keywords: artifcial intelligence; computers, information; language model; plagiarism.

General Approach to the Evolving Plasma Equilibria with a Resistive Wall in Tokamaks

The dynamic problem of plasma equilibrium in a tokamak is considered taking into account the electromagnetic reaction of the vacuum vessel resistive wall. The currents induced in the wall during transient events contribute to the external magnetic field that determines the plasma shape and position. Accordingly, the plasma geometry must evolve so that the inductive excitation of the wall current would properly compensate for the resistive losses. Simultaneous consideration of these factors presents the main difficulty of the description. It is performed in a general form using the Green’s function method that guarantees the mathematical accuracy of expressions for the magnetic fields from each source. At the same time, it is desirable to minimize the related complications, which is one of the goals here. The starting point is the standard solution of the external equilibrium problem given by integral relating the poloidal magnetic flux to the magnetic field at the plasma boundary. In the evolutionary problem, the additional equations for the plasma-wall electromagnetic coupling are transformed to an equation with a similar integral over the wall, but with either the time derivative of the poloidal magnetic flux or the wall current density in the integrand. The mentioned similarity allows to use the already developed techniques, which makes this formulation compact and convenient. It provides the basis for extension of the existing analytical theory of equilibrium to the case with non-circular plasma and wall.