Mathematical Methods Research Articles

INTERACTIVE ORIENTATION OF ADOLESCENTS IN THE PERSPECTIVE OF INCLUSIVE EDUCATIONAL SPACE

Relevanse. The paper presents the results of a research of interactive orientation in the context of its influence on the communication of adolescents in the inclusive educational space. Methodology. Methods: comparative analysis, quantitative and qualitative analysis of the obtained data using mathematical and statistical methods, generalization of conclusions. The sample of research consisted of 240 students (aged 11 - 14), 30 of whom had special needs (18 boys and 12 girls). The experimental base of our study was 14 inclusive classes of Ukrainian schools. Results. The obtained results provide grounds for statement that the orientation towards interaction is more characteristic of teenagers with typical development than their peers with special needs. A moderate negative correlation was found between interactive and marginal orientations. Therefore, adolescents who strive for interaction are less infantile and more capable of adequate perception and acceptance of the interlocutor. Conclusions. The importance and peculiarities of the interactive orientation of adolescents who are participants in the inclusive educational space have been revealed. This determines the importance of socio-psychological activities to reduce the level of concentration on personal interests or tendency to marginalization and, thus, increase the level of adaptability in communication, as teenagers with typical development and their classmates who have special needs. This will contribute not only to the optimization of the inclusive educational space, but also to the expansion of their opportunities for selfrealization in various spheres of society.

“Everyone Can Master the Correct Use of Mathematical Methods”: The Relevance of L.D. Kudryavtsev’s Ideas for Modern Mathematics Education

The article discusses the ideas, devoted to mathematics education, of Lev D. Kudryavtsev, corresponding member of the USSR Academy of Sciences, professor-mathematician. These ideas are based on more than half a century of practical experience of L. D. Kudryavtsev at the Moscow Institute of Physics and Technology – he presented his vision of the problems of educating students, the unity of mathematics, as well as methods of teaching it in the collection of articles. The thoughts and ideas of L. D. Kudryavtsev are still relevant today, in the age of digital transformation of the education system and of the entire life of society.

FEATURES OF COPING STRATEGIES IN CONDITIONS OF UNCERTAINTY OF WARTIME

Relevance. The purpose of this article is to empirically investigate the discrepancies in the selection of coping strategies among groups of people during war under various conditions of uncertainty. Methodology. The sample consists of 186 residents of Ukrainian cities who live under various conditions of uncertainty. Methods: author’s questionnaire, methods: «Test for psychological diagnostics of coping mechanisms (E. Heim)», «The Intolerance of Uncertainty Scale (IUS-12) (N. Carleton, adaptation by H. Gromova)»; mathematical methods for processing empirical data using the IBM SPSS Statistics 26 package. Results. Respondent groups, based on their location relative to the front line, show statistically significant discrepancies in cognitive and behavioral coping strategies. The empirical study’s analysis showed that individuals living in the front and near-front zones often compare their problems with others and downplay their difficulties more frequently (41,94%) than those living further from the front line (21.94%). Furthermore, individuals closer to the front line show a higher tendency to employ the adaptive coping strategy «altruism» (19.35%), that is, they offer help to others in overcoming difficulties more often than those living further from the front line (6.45%). Both groups predominantly employ relatively adaptive coping strategies. However, a divergence in problem-solving approaches exists: individuals in the front and near-front zones typically avoid problem-solving by engaging in a favorite activity, whereas the other group tends to evade problem-solving by resorting to alcohol, medicines, sedatives, or indulging in tasty food. The study did not identify statistically significant differences between groups regarding intolerance to uncertainty.

Optimal design of an LCC-S WPT3 Z1 SAE J2954 compliant system, using NSGA-II with nested genetic algorithms for simultaneous local optimization

Wireless Power Transfer (WPT) for electric vehicles is one of the most promising methods that, given its advantages, will drive the deployment of electric vehicles. This paper presents a mathematical optimization method applied to the complete design of an LCC-S WPT3 Z1 11 kW system that complies with the SAE J2954 standard (Wireless Power Transfer for Light-Duty Plug-in/Electric Vehicles and Alignment Methodology, 2020). A design method based on three phases is proposed, allowing the complete inductor system, including ferrites shielding and compensation circuit components, to function in any relative primary and secondary position. In Phase 1, a multi-objective NSGA-II algorithm is designed, utilizing three nested genetic algorithms. The goal is simultaneously searching for the local optimum between the primary and secondary systems in three positions. This is achieved by modeling the circuit’s electrical and electromagnetic parameters with equations, enabling an iterative process with reduced computational time. The NSGA-II algorithm yields three scenarios: primary copper volume minimization, secondary copper volume minimization, and a compromise solution that optimizes the total volume. The result is then modeled in Phase 2 using a 3D finite element program that includes ferrite and optimal shielding, obtaining the values of inductances and mutual inductance in the three positions, as well as design data for manufacturing. This result is introduced in Phase 3 to optimize compensation circuit components using a second NSGA-II algorithm with three nested genetic algorithms. Again, three scenarios are obtained based on the desired system behavior and the optimal cost of the components. The result is validated through simulation with Matlab-Simulink and experimentally using a prototype constructed for this purpose.

Passive bionic motion of a flexible film in the wake of a circular cylinder: chaos and periodicity, flow–structure interactions and energy evolution

The self-sustained interactions between a flexible film and periodic vortices epitomize the spirit of fish swimming and flag flapping in nature, involving intricate patterns of flow–structure coupling. Here, we comprehensively investigate the multiple coupling states of a film in the cylinder wake mainly with experiments, complemented by theoretical solutions and nonlinear dynamical analyses. Four regimes of film motion states are identified in the parameter space spanned by the reduced velocity and the length ratio. These regimes are (i) keeping stationary, (ii) deflection flutter, (iii) hybrid flutter and (iv) periodic large-amplitude flapping, each governed by a distinct coupling mechanism, involving regular and irregular Kármán vortices, local instability of the elongated shear layers and 2P mode vortex shedding. The film futtering in regimes (ii) and (iii) is substantiated to be chaotic and bears a resemblance to the ‘entraining state’ of fish behind an obstacle in the river. The periodic flapping in regime (iv) manifests itself in an amalgam of standing and travelling waves, and has intrinsic relations to the ‘Kármán gaiting’ of fish in periodic vortices. With the spatiotemporal reconstruction for the periodic flapping, we procure the energy distributions on the film, revealing the energy transfer processes between the film and the large-scale vortices. The findings unequivocally indicate that the flow–structure interaction during the energy-release stage of the film is more intense than that during the energy-extraction stage. Given the similarities, the mathematical and physical methods presented in this work are also applicable to the research on biological undulatory locomotion.

New method for measuring and analyzing the deformability and eccentricity of the ferrule kilns.

Abstract In the industrial sector, particularly in the cement industry, the key aspect of the production process is the production of clinker through the use of a rotary kiln. Due to the large volume and high temperature involved, these complex structures are subjected to stress and deformation during operation. Therefore, it is crucial to conduct regular control measurements to verify the compliance of the basic geometric parameters. In this article, we examine the literature on various control techniques, with a particular focus on the misalignment of the rotating axis of the ferrule. To measure the rotating axis and ovality of the rotary kiln cylinder, a new data processing method was developed and subsequently implemented. This method was experimentally demonstrated by creating a prototype to validate it, and the results obtained by the prototype were then compared to those obtained by the coordinate measuring machine. 
The results indicate that the proposed method is effective for determining the real axis of the rotary kiln (eccentricity) and the ovality of the shell structure. With this purpose, the article proposes a new solution for processing spatial data using a mathematical method based on the geometric parameters of the shell structure. This study can be used to develop tools for controlling rotary kilns, particularly in the data collection process.

Enantiomorphs no more: Indigenous agroecology and the future of food sovereignty: Reflections on the U.S. United States Agroecology Summit 2023

I was part of a plenary panel on “Bridge Build­ers” at the 2023 Colorado Food Summit in Denver in December 2023. Echoing a statement I first made at the U.S. Agroecology Summit 2023, I explained how the first “bridge” we are building at The Acequia Institute (TAI) is between Indigenous Knowledge (IK) and so-called Western Science (WS). TAI does this work not to verify and legiti­mize IK by invoking the presumably more rigorous and mathematical methods and materials of WS. TAI enunciates and practices IK through autono­mous place-based food sovereignty initiatives. In this work we have determined how best to inte­grate the methods and materials of selected domains of Western knowledge systems in forms useful for us and the locality. These issues were discussed at the U.S. Agroecology Summit, but in the end they were left largely unresolved. The entire Summit was, as Carmen Cortez and others have rightly observed, plagued by being “Devoid of this spirit of place and people…” (Agroecology Summit ‘Outside Empire’ Subgroup, 2024, p. 2). In my view, it was a gathering fractured by pre-existing and possibly inadvertent and unconscious acts of epistemic violence reminding me of the difference Michael Redclift (1987) observed between top-down environmental managerialism and bottom-up collaborative environmental management. . . .

Livelihood Alternatives in Restored Peatland Areas in South Sumatra Province, Indonesia

Livelihood loss and lower income because of peatland mismanagement are crucial issues that must be resolved in peatland areas. Although many studies have assessed farmers’ livelihoods and income enhancement, progress in addressing these problems remains inadequate. To address this issue, this study aimed to analyze various existing alternative livelihoods in the peatland community in Ogan Komering Ilir District, South Sumatra Province, Indonesia, and analyze scenarios for creating livelihoods and increasing people’s incomes through changes in peat ecosystem management and peatland restoration programs. This study used a survey method conducted in South Sumatra Province’s OKI District, one of the four priority peat-restoration districts in the province. We used three sampling stages, while descriptive, tabulated, and mathematical methods were used for analysis. We analyzed the feasibility of livelihoods that used benefit-cost analysis. The results showed that Sonor cultivation of paddies and catching fish in Rawang (swamp) were the livelihoods of farmers in peatlands. The community has also been processing peatland commodities into other products, such as Purun woven, and Gula Puan (buffalo milk processing). Several alternative livelihood scenarios that are financially profitable and can be developed include salted and smoked fish, Purun woven handicrafts, paludiculture, and agrosilvofishery, which can provide farmers with short-, medium-, and long-term income opportunities. This study can contribute to policymaking by fully considering the role of peat resources in rural livelihoods.

Utilization of absorbance subtraction and ratio difference green spectrophotometric methods for the quantification of alfuzosin hydrochloride and tadalafil in their binary mixture

Alfuzosin hydrochloride and tadalafil fixed-dose combination tablets were recently formulated for the treatment of individuals with lower urinary tract symptoms caused by benign prostatic hyperplasia. Herein, the first spectrophotometric methods for quantitative analysis of alfuzosin hydrochloride and tadalafil in their binary mixture were established. The spectral overlapping of alfuzosin hydrochloride and tadalafil made direct simultaneous analysis unfeasible. Therefore, two mathematical methods were used to solve these overlapping spectra: absorbance subtraction and ratio difference. The absorbance subtraction method manipulates the zero absorption spectra of the studied drugs at the isoabsorptive point (272 nm) and uses the absorbance factor of pure ALF to calculate the absorbance of the studied drugs in the mixture at the isoabsorptive point. The ratio spectra method, on the other hand, manipulates the ratio spectra of the studied drugs, which are obtained by dividing each drug’s zero absorption spectra by a divisor spectrum from the second drug. The ratio amplitude difference between 251 nm and 211 nm was directly proportional to alfuzosin hydrochloride, whereas between 292 nm and 222 nm it was directly proportional to tadalafil. The methods used were verified in accordance with the recommendations of the ICH and demonstrated adequate linear regression in working ranges of 1–15 µg/mL for alfuzosin hydrochloride and 3–40 µg/mL for tadalafil. The methods were accurate, precise, and selectively employed to quantify alfuzosin hydrochloride and tadalafil in their combined tablets.

Proposal and Validation of a New Index to Assess the Difficulty of Lower Third Molar Extraction

There is no current consensus on the parameters that determine the difficulty of mandibular third molar extraction in terms of the time required, which is essential to prevent complications and optimize the time of the intervention. This study aims to obtain, using the mathematical method of multiple linear regression, an equation that allows estimating the extraction time of a lower third molar according to its complexity, as well as to validate this equation in a sample of external wisdom teeth. Methods: A prospective cohort study on a sample of patients of the Master of Oral Surgery of the University of Seville in which multiple linear regression coefficients were calculated with a subsequent validation study of the results in the sample of patients operated in the Hospital Palmaplanas of Mallorca. Results: The regression line obtained after applying the statistical methodology to the cohort of patients from the University of Seville obtained significant dependent variables such as depth, roots, and odontosection. Once applied to the cohort of patients from the Palmaplanas Hospital in Mallorca, a regression coefficient was obtained between the data received and the estimated 0.770. Conclusions: The formula proposed in this article presents significant validity in the prediction of the surgical time of extraction of the lower third molars included.

Methodological Considerations Regarding the Quantification of DNA Impurities in the COVID-19 mRNA Vaccine Comirnaty®

DNA impurities can impact the safety of genetically engineered pharmaceuticals; thus, a specific limit value must be set for them during marketing authorisation. This particularly applies to mRNA vaccines, as large quantities of DNA templates are used for their production. Furthermore, when quantifying the total DNA content in the final product, we must observe that, in addition to the mRNA active ingredient, DNA impurities are also encased in lipid nanoparticles and are therefore difficult to quantify. In fact, the manufacturer of the mRNA vaccine Comirnaty (BioNTech/Pfizer) only measures DNA impurities in the active substance by means of a quantitative polymerase chain reaction (qPCR), whose DNA target sequence is less than just 1% of the originally added DNA template. This means that no direct DNA quantification takes place, and compliance with the limit value for DNA contamination is only estimated from the qPCR data using mathematical extrapolation methods. However, it is also possible to dissolve the lipid nanoparticles with a detergent to directly measure DNA contamination in the final product by using fluorescence spectroscopic methods. Experimental testing of this approach confirms that reliable values can be obtained in this way.

Research on the analysis and management measures of land subsidence caused by groundwater exploitation in Tianjin, China

Since the 20th century, there has been an increasing reliance on groundwater due to the rapid development of agriculture and industry. This has resulted in the exploitation of groundwater in large quantities, leading to global land subsidence problems. Tianjin is one of the cities where this problem first emerged, but few studies and surveys have been conducted. As a result, the lack of management of groundwater extraction has caused the issue of land subsidence to become more prominent in recent years. By investigating and collating global research on land subsidence problems caused by groundwater extraction, it is concluded that mathematical and numerical methods, global information systems, remote sensing, and other technologies can be utilized to monitor and predict groundwater levels. Regional management measures can then be developed based on simulation results. However, the application of such technology in Tianjin is insufficient, and there is a need to strengthen the connection between management measures and research data analysis results.

Application of deep reinforcement learning in electricity demand response market: Demand response decision-making of load aggregator

With the large-scale integration of renewable energy generation, developing the potential of demand response is becoming more and more significant. However, the number of consumers is huge, the electricity consumption behaviors are various and the information of consumers is incomplete, thus there are great difficulties in modeling and processing demand response by the conventional mathematical methods. Therefore, how to accurately predict the response behaviors of consumers and select the appropriate consumers for demand response is worthy of in-depth discussion. In this paper, the decision-making method of the load aggregators who participant in demand response market on behalf of the small and medium-sized consumers based on Deep Q-network algorithm is proposed, supporting the aggregators to properly guide the potential demand response consumers. At the same time, a dynamic consumer classification method based on self-organizing maps algorithm is also proposed, supporting the aggregators to accurately predict the response behaviors of the consumers. Simulation results show that the proposed method can effectively realize the classification of the consumers and result in a more beneficial demand response.•The proposed method does not require complete information, such as demand response behavior parameters of the consumers.•Self-organizing maps can realize a dynamic classification of demand response consumers as the case may be.•DQN algorithm can effectively realize the demand response decision-making of aggregators under the condition of incomplete information.

Decision-Making Support in Vehicle Routing Problems: A Review of Recent Literature

The Vehicle Routing Problem (VRP) involves a set of customers with known locations, each having a certain demand for goods or services. There is also a fleet of vehicles available, each with limited capacity and often a fixed starting point. With the aid of mathematical programming tools, this paper offers an overview of the most recent VRP research. This study also examines the algorithms for solving VRP models and categorizes them in terms of their application areas. For these reasons, related publications that appeared in the international journal have been compiled and studied. According to the literature review, multi-criteria decision-making (MCDM) techniques have yet to constitute the most mathematical programming methods used to solve the VRP problem.

Ultra‐fast finite element analysis of coreless axial flux permanent magnet synchronous machines

AbstractLarge‐scale design optimisation techniques enable the design of high‐performance electric machines. Electromagnetic 3D finite element analysis (FEA) is typically employed in optimisation studies for accurate analysis of axial flux permanent magnet (AFPM) machines, which require extensive computational resources. To reduce the computational burden, a FEA‐based mathematical method relying on the geometric and magnetic symmetry of coreless AFPM machines is proposed to estimate the machine performance indicators using the least number of FEA solutions, thereby significantly lowering the running time. This method is generally applicable to AFPM machines with low saturation effects and cogging torque as exemplified for a printed circuit board (PCB) stator coreless AFPM machine. To further reduce the computation time, a systematically simplified equivalent 3D FEA model for planar PCB coils integrated with this machine is also proposed. The practical implementation of the introduced method is elaborated based on an example optimisation study, and an analytical method for fast design scaling is also discussed. The results of the proposed approach are compared with detailed transient FEA results, and a prototype 26‐pole PCB stator coreless AFPM machine was also used to validate the results experimentally.

A novel mathematical optimization method to obtain the maximum-power electrical configuration of thermoelectric generators for energy harvesting

Waste thermal energy recovery with thermoelectric generators has been widely studied as a method to make systems that produce hot exhaust gases, such as aircrafts, ground vehicles and factories, more sustainable. In this type of applications, the mismatch in hot and cold side temperatures of thermoelectric modules (TEMs) creates a mismatch in the electrical output. For each situation, there is a certain electrical interconnection between the modules that gives the maximum global power output. Three optimization models to find what is the best way of connecting the TEMs without a trial-and-error process, as usually done in previous literature, based on mathematical programming are proposed: single branch of series-connected TEMs, multiple parallel-connected branches of series-connected TEMs, and multiple groups of independent series-connected TEMs. The main novel contributions of this paper are: (i) a mathematical optimization approach that provides how to connect the thermoelectric modules one by one, (ii) the application of the above-mentioned method in a common case study: an automotive thermoelectric generator, (iii) information about how the optimal connection between modules changes if the heat source changes its operation (iv) a method for selecting a fixed optimal connection even when the heat source operation changes, e.g. different operation modes in a thermal engine, based on introducing weighting parameters in the optimization mathematical model. The optimization approach followed here is novel and has not been applied before to thermoelectric generators.

ASSESSMENT OF THE IMPLEMENTATION OF CROSS-INDUSTRY PERFORMANCE INDICATORS OF ENERGY SAVING PROGRAMS IN THE LIFE CYCLE OF BUILDINGS

This article is devoted to the study of the possibility of energy saving of buildings. The relevance of the article lies in the fact that the role of efficiency of energy saving programs is currently growing. The novelty of the research lies in the development of methodology and new approaches for the analysis of energy saving. The author suggests cross-industry indicators of strategic management of energy saving programs. They can provide analysis of a wide range of useful information to confirm the costs of investment, operation and efficiency of a project. Information modeling of buildings is used as the basis of the research in the article. Based on the analysis of scientific literature, the author has developed cross-sectoral indicators of strategic management of energy saving programs. The author proposes a calculation of energy saving taking into account such new indicators as indicators in terms of replacement cost, indicators of power losses, environmental impact, reliability indicators. A methodology for assessing the impact of energy management solutions and the use of key performance indicators is proposed. The methodology consists of a preparatory stage and a two-stage assessment. It can be used to quantify specific aspects or objectives of a project, such as economic feasibility, environmental impact, reliability and quality of electricity. In the study, the author used general scientific methods of systematization and classification of data, methods of statistical processing and generalization, logical, comparative and system analysis, as well as mathematical methods.

Vortex waves in fluid–structure interaction with high Froude number and a damped structure

In this paper, we study the non-linear dynamic response generated as a result of a fluid–structure interaction between a flexible structure and a flowing fluid, when the structure is subjected to non-linear excitations. In first place, the use of semi-discrete approximations allowed us to show that the motion of a flexible structure coupled with a surrounding fluid flowing could be modelled and analysed via a coupled Complex Cubic Ginzburg–Landau equations (CCGLEs). Through the obtained CCGLEs, we were able to show that modulational instability (MI) is the main mechanism responsible for the generation of vortex shedding. Moreover, we showed that the stability of continuous wave depends on the coupling parameters between the fluid and the structure. Secondly, using a mathematical method, namely the G’/G expansion method, we found that vortex wave trains could be generated as cylindrical waves. These results are highly significant from a theoretical point of view and could be a plus to explain the process of generation of Kármán Vortex as a consequence of unstable coupling between two continuous wave in the fluid–structure system. Moreover, considering the industrial interest, such as floating wind turbines, this work aims to provide an additional understanding of the interactions between a flexible body and a surrounding flow.

Current and future trends in vertical transportation

In the middle of the 19th century, the invention of a safety device that prevented elevators from falling enabled the construction of tall buildings and skyscrapers. In the middle of the 20th century, control systems started to serve the given calls automatically by relay technology, and later by electro-mechanical systems. In the 1970s-80s, software-based control systems invaded elevator technology. Passenger service levels improved with the application of mathematical methods such as artificial intelligence. When the old relay boards of the skyscrapers in New York were modernized by software-based group controls, passenger waiting times dropped to less than half. In this millennium, the need to reduce elevator core space has further increased, since a significant number of buildings already exceed 300 meters. The challenge in constructing tall buildings is that elevator groups can occupy the rentable area of a building. At the elevator planning stage, elevator core space can be decreased by zoning the building. The latest trends include systems with several elevator cars running in the same shaft. With modern control systems, passenger journey times can be decreased and handling capacity increased. This article deals with mathematical methods used in elevator dispatching problems. Building traffic simulation is utilized to search for an elevator arrangement that saves the most space in an example building. The design criteria of the ISO 8100-32 standard are used in selecting the elevator arrangements.

Compound dry and hot events over major river basins of the world from 1921 to 2020

Compound dry and hot events (CDHEs) are among the most destructive compound extremes. Under global warming, changes in precipitation, temperature and their dependence make profound contributions to CDHEs. In this paper, the contributions of these three factors are explicitly quantified based on a novel mathematical method. Specifically, time series of precipitation and temperature are employed to identify CDHEs and then changes of CDHEs are attributed by using the partial derivatives-based sensitivity analysis. Based on the Climatic Research Unit Time-Series (CRU TS), a case study of CDHEs is devised for the major river basins (MRBs) of the world. The results highlight that from the period 1921-1970 to the period 1971-2020, CDHEs did occur more frequently across most MRBs. The temperature tended to make the largest contribution, followed by precipitation and the dependence between precipitation and temperature. In Africa, South America and Western Europe, the rising temperature is generally the dominant factor for increases of heatwaves that contribute to CDHEs. In Asia, increases of droughts along with increases of heatwaves raise the risk of CDHEs. For MRBs with moderate increases in temperature, increasing precipitation is shown to mitigate or even offset the risks of CDHEs. In the meantime, the increasing dependence is observed to reduce the frequency of CDHEs in the Huai He and the Mississippi even though therein temperature is increasing. Overall, the attributing results of CDHEs from 1921 to 2020 can serve as a reference for the preparation and mitigation of CDHEs for MRBs across the world.