Analysis Of Mathematical Model Research Articles

Applicaton Of Mathematics In Big Data Analysis To Support Strategic Decision

This study aims to investigate the application of mathematical models in big data Analysis and their impact on strategic decision making in various industrial sectors. Using a quantitative approach to the survey, data was collected from 190 respondents from the technology, finance, manufacturing and healthcare sectors. The results showed that the application of mathematical models, such as predictive algorithms and machine learning, contributed significantly to improving the quality of strategic decisions. The study also identified that variables such as human resource competence and technological infrastructure moderate the relationship between big data Analysis and effective decision-making. The technology and finance sectors have proven to benefit the most from the application of math-based big data Analytics, with benefits seen in improved market prediction, risk management, and operational optimization. The findings underscore the importance of integrating mathematical models in data analysis to support data-driven decision-making in the digital age.

Development of Mathematical Support and Software for Ballistic Analysis and Optimization of Active-Missile Projectile Parameters

The paper presents the results of developing mathematical and software support for internal and external ballisticsmodelling, as well as optimizing the parameters of an active-reactive projectile. A complex mathematical model of active-reactive projectile ballistic analysis includes the problem of external ballistics, the problem of internal ballistics inside the gun barrel and the problem of internal ballistics of a solid-fuel jet engine. The problem of active-reactive projectile parameteroptimization is to increase the flight range with respecttomotion stabilitycondition along the entire trajectory. Based on the mathematical model of ballistic analysis, the algorithms for solving a multi-criteria problem of active-reactive projectileparameteroptimization have been developed. The developed software package includes a block of calculation modules implementing mathematical models and computational algorithms, a database of projectile parameters and simulation results, a block for visualization the computational experiment results in the form of diagrams and tables. The software package can be used in the design and optimization of the projectileparameters of artillery systems implementing the active-reactive throwingprinciple. The results of mathematical modeling and optimization of parameters are considered using the example of the designed active-reactive projectile for the 152 mm artillery system. To improve the projectilestability on the trajectory during jet engineoperation, it is proposed to install ribs at an angle to the projectile axis on the inner surface of the nozzle so as to create extra torque. Based on the developed model, the optimal characteristics of firing an active-reactive projectile of caliber 152 mm are determined. The results of internal and external ballisticsproblem solutionfor an active-reactive projectile obtained by means ofthe software package for ballistic process modeling are presented. The main problem of internal ballistics inside the gun barrel, the problem of internal ballistics of a solid-fuel jet engine, the direct problem of external ballistics of an active-reactive projectile and the study of the projectile motion stability along the trajectory are solved. Optimal parameters of internal and external ballistics, providing the maximum firing range of an active-reactive projectile with respect toitsmotionstability along the entire trajectory, are found.

OPTIMIZATION METHODS FOR PARAMETER IDENTIFICATION MODEL OF TEST ELECTRORETINOSIGNAL TO ASSESS NEUROTOXICITY RISKS

Introduction. The development of advanced optimization methods plays a crucial role in the enhancement of diagnostic tools in the biomedical field, particularly in the analysis of complex physiological signals. Electroretinography (ERG) is a widely used diagnostic technique that records electrical responses generated by the retina in response to light stimuli, providing valuable insights into the functional health of retinal cells. ERG is instrumental in diagnosing conditions such as retinitis pigmentosa, diabetic retinopathy, and neurotoxicity. However, the analysis of low-intensity electroretinograms (ERG) presents numerous challenges, particularly due to noise and signal distortion, which complicate accurate signal interpretation. Main purpose of this study.This paper is dedicated to developing an expert system for real-time analysis of electroretinographic signals (ERS), focusing on optimizing the parameters of a mathematical model for ERS analysis in conditions where noise and other distortions are present. The primary aim is to improve the accuracy and efficiency of ERG data processing, enabling early detection of neurotoxicity and other retinal conditions. To achieve this, we applied advanced optimization techniques, such as the Nelder-Mead method, known for its effectiveness in handling non-smooth, noisy functions. Conclusions. 1. The application of the Nelder-Mead algorithm for optimizing the complex and noisy ERS model significantly improved the performance of ERG data analysis. The algorithm's adaptability to varying optimization conditions allowed for more accurate model parameter determination, particularly in the context of real-time neurotoxicity detection. Reduction in Processing Time: The time complexity analysis revealed that the Nelder-Mead method reduced the time required to compute the model coefficients by approximately 15%. This improvement was achieved while maintaining the necessary precision for reproducing the test electroretinosignal, making it suitable for real-time applications. Computational Efficiency: One of the key findings of this study is that the use of the Nelder-Mead algorithm reduced the computational load by up to 30%. This makes the method feasible for use in expert systems designed for real-time ERS analysis, allowing for the monitoring of functional changes in the retina during the early stages of neurotoxicity detection.

Assessing the Environmental Kuznets Curve in Agricultural Transport: The Case of Brazilian Soy

Abstract This research investigates the Environmental Kuznets Curve (EKC) hypothesis within Brazil’s soy transportation sector. It aims to determine if CO2 emissions from soy transport show an “Inverted-U” or “N” shaped relationship with income from 2002 to 2017. Using a mathematical optimization model and System GMM for analysis, the study finds an “N” shaped EKC, indicating emissions initially increase, decrease, and then rise again with income. This suggests long-term environmental damage from sector growth, highlighting the need for targeted measures to mitigate emissions and enhance operational productivity, such as investments in intermodal transport and road efficiency improvements.

HARMONIC ANALYSIS OF MAGNETOMOTIVE FORCE IN THE AIR GAP OF SIX-PHASE ASYNCHRONOUS MACHINES

Asynchronous motors with six and more phases (usually n-three-phase) are increasingly accepted in electric drive systems of road transport, marine and even aeronautical transport. Multiphase machines are credited with multiple advantages such as: less torque ripple, better power distribution per phase, higher efficiency and fault tolerance capability compared to traditional three-phase machines. There are many publications, but few of them are dedicated to the in-depth study of the multiphase motor (m>3) and especially of the magnetic field in its air gap. The purpose of the present paper: the development of the mathematical model of the magnetomotive force in the air gap of the six-phase asynchronous machines, which determines the fundamental properties of the machine, the structure of the magnetic field and the torque developed, the efficiency, the error tolerance. The research is based on analytical studies and the results of suitable experimental measurements. The paper presents the mathematical model for the harmonic analysis of the magnetomotive force in the air gap of six-phase machines with possible variants of windings on the stator. Based on this study, it was demonstrated that only n-three-phase machines with asymmetrically arranged stator windings have the ability to attenuate higher harmonics with a major negative effect on the developed torque, the applicability and efficiency of traditional tools for reducing higher harmonics in the case of six-phase machines was confirmed. The results of measurements carried out on samples of six-phase machines confirm the findings and conclusions formulated in the paper.

A mathematical model for the dynamic analysis of multi-body floating platforms with complex mechanical constraints

The new methodology based on generalised coordinates for the analysis of floating multi-body systems with nonlinear geometric constraints is developed, and it is demonstrated through numerical application for a hybrid floating wind-wave platform consisting of a floating offshore wind turbine and an articulated wave energy converter that moves a hydraulic piston. The formulation is applied to achieve explicit formulae regarding the dynamic response in a low-dimensional scenario used to verify a post-processing code. The verification considers the nonlinear geometric constraints, hydrodynamic interaction, the dynamics of articulated arms, and the dynamics of hydraulic power take-off systems. An analytical expression for the system's natural frequencies is attained and verified likewise. The results presented in this paper indicate significant improvement in the simulation and analysis of multi-degrees-of-freedom nonlinear hydrodynamic systems, which will ultimately be necessary for designing efficient hybrid floating wind-wave platforms.

Development of an analytical model for assessing the risks of financial and economic activities of State (municipal) institutions based on the pairwise comparison method

Subject. The article considers developing an analytical model to assess the risks of financial and economic activities of State (municipal) institutions. Objectives. The aim is to devise a comprehensive analytical model for assessing the risks of financial and economic activities of State (municipal) institutions, taking into account their specific activities, and assess these risks. Methods. The study employs general and specific scientific methods of cognition (analysis and synthesis, induction and deduction, grouping, comparison, expert assessment, mathematical methods, like the method of analyzing hierarchies, etc.). Results. I designed an analytical (mathematical) model of integral indicator for risk assessment in State (municipal) institutions’ financial and economic activities, offered a scale used to assess such risks. The proposed mathematical model was tested in several State institutions, with the presentation of results. Conclusions. The development of software using intelligent technologies based on the analytical model of integral indicator will enable to more quickly and effectively assess the risks of financial and economic activities of a State (municipal) institution, and track the dynamics of risk changes.

Study on the performance of flat-plate collectors with a bottom-mounted non-tracking broken line type reflector

The current flat-plate collectors commonly utilize non-tracking reflectors, primarily in a flat configuration, which is not optimal because it has a large reflection loss at varying solar altitude angles. Broken line type structures have been proven to exhibit better light concentration effects. However, existing research has focused solely on broken line type reflector installed at the top of the collector, leaving a gap in the study of broken line type reflector installed at the bottom. This paper investigates this aspect. Mathematical models for the performance analysis of collectors with/without bottom-mounted reflectors are established. The accuracy of the models is verified using the light tracing software, TracePro. The study includes the simulation analyses of the collector's performance and reflection losses under different conditions. The results indicate that the plate type reflector and broken line type reflector increase the heat collection by 27.92 % and 34.4 %, respectively. So the reflector can make the collector effectively operate in a wider range of ambient temperatures and radiation intensity. Increasing the horizontal length of the collector or adopting a series arrangement can effectively reduce reflection losses. This study provides theoretical guidance for the optimization design of flat-plate collectors with bottom-mounted broken line type reflectors.

Numerical modeling and the ultimate bending experiment of the directional drill pipes bending at the dog-leg of the multi-branch well

Directional drill pipes are prone to failure in the fish-bone branch wells. The primary cause of the directional drill pipes failure is excessive bending. This paper established a mathematical analysis model for the bending stress of the directional drill pipes at any point along its trajectory. Tested the mechanical properties of the directional drill pipe. An ultimate bending experiment was conducted on the directional drill pipes based on the pure bending moment theory. Additionally, a non-linear finite element model(FEM) of the directional drill pipes was established to analyze the influence of different bending loads on the stress distribution of the directional drill pipes connection. The FEM results were consistent with the results of the ultimate bending experiment. The FEM results indicate that the Box bending under transverse force is the primary cause of the failure for the Tooth top. The research results enable engineers and operators to easily obtain the stress distribution of the directional drill pipes under borehole curvature.

Theoretical study on nonlinear seepage mechanism in fractal dendritic fracture network of low permeability coal with water injection

Coal seam water injection technology is adopted by many mines as an effective means of dust reduction in coal mines. There is a threshold pressure gradient phenomenon in the process of water injection in low permeability coal seam, which makes the flow of pressure water in the fracture structure of coal body present nonlinear seepage characteristics. To reveal the theoretical relationship between the structural parameters of coal and the nonlinear seepage characteristics, firstly, the Bingham fluid constitutive equation is used to describe the non-Newtonian behavior in low-permeability coal. Combined with the fractal tree-like bifurcation fracture network model, a mathematical analytical model of threshold pressure gradient is established. Secondly, the model was verified by high-pressure water invasion and radial seepage experiments, and the sensitivity of the model was analyzed. The results show that the error between the theoretical calculation value and the experimental measurement value is between 8.65 % and 42.4 %, which verifies the validity of the model. The above research results can provide a theoretical basis for improving the water injection effect of low permeability coal seam.

A Modified SIVR Mathematical Model of Covid-19 Post-vaccination Stability Analysis in Kenya

In this paper, the study focused on carrying out a stability analysis on a modified SIR model for the COVID-19 pandemic for the period after vaccination in Kenya. The purpose of the work was to show that whereas the rate and the extent of disease spread amongst the Kenyan people was not as wide spread as happened in other parts of the world, it was necessary for government and policy makers to roll out a robust civic education to convince the majority of the Kenyan population to embrace vaccination as a major containment measure in curbing the spread of COVID-19 and other infectious diseases since the study revealed that the infections drastically reduced to near zero after vaccination except for a few isolated cases that were and still continue to exhibit mild symptoms to none at all. This was attributed to the development of the vaccine which upon a massive campaign by the Kenyan government, led into a significant portion of the population being vaccinated. It is believed this vaccination drive enhanced herd immunity amongst the population. This development has had a significant effect in the control of more recent COVID-19 variants like JN-1 that have remained largely mild and undetected in the country. Both local and global post vaccination stabilities were analyzed for the system using the Lyapunov function. The main objective of the study was therefore to carry out a post vaccination stability analysis by estimating key parameters such as the basic reproduction number, ( R0) and herd immunity threshold (HIT) for infectious diseases by fitting data into the model to enable predictions of future dynamics of the disease. The study used the Next Generation matrix and the least square method besides the Python software to solve generated differential equations of the model for and HIT parameters. Results obtained showed that, there was a significant reduction in infections due to enhanced herd immunity attributed largely to the roll out of vaccination.

Development of a Device for Primary Purification of Mung Bean Grain from Pods and Optimization of Its Main Design Dimensions and Operating Modes

It is important to create a technically and technologically improved device that reduces the damage to the mung during the process of removing the pods from the currently cultivated mung grain. Therefore, it is necessary to develop the design of the device, to justify its parameters and operating modes, for the complete separation and preliminary cleaning of mung beans without damaging them. The article presents the results of optimization of the main design dimensions and operating modes of the device for separating mung bean from the pods. The results of experimental studies showed that the proposed device has a high degree of completeness in separating mung bean from its pods and a low level of damage, low grain damage and high grain purity, which can be ensured with a sag length of 170 mm, a shaft oscillation number of 300 min-1, the amplitude of the shaft is 11.5 mm, its angle of inclination is 12 degrees. The design of the device for preliminary cleaning of mung grain by separating it from pods has been developed. The scientific significance of the research results is based on the structural dimensions and operating modes, as well as the resulting analytical connections and mathematical models, to ensure the quality of initial cleaning, to separate mung beans from pods completely and without damage, using less energy and resources. can be used to justify the parameters of similar devices. The developed device reduces the consumption of energy and labor during the initial cleaning of mung grain from pods, as well as the loss of grain.

Structural evolution in desalting Merluccius hubbsi fillets: comparative analysis of varied salting techniques

SummaryThis study investigates the reversible and irreversible structural changes in proteins induced by different salting methods (brining, mixed salting, and dry salting) during the desalting process of Merluccius hubbsi fillets. We focused on mass changes, water content, and NaCl content, employing mathematical models for kinetic analysis and sorption isotherms. Image analysis was utilised to examine tissue microstructure and texture profile analysis assessed the mechanical properties. Our results indicate that salting methods significantly influence mass changes and yield during desalting. Specifically, brining led to the highest weight gain due to controlled salt absorption and enhanced water retention. The Peleg model accurately described NaCl and water content dynamics during desalting. Microscopic analysis revealed substantial structural alterations, while mechanical properties showed significant differences; dry and mixed salting methods caused notable tissue damage and protein denaturation. These findings provide valuable insights for enhancing salting processes and improving the quality of desalted seafood products.

A Systematic Review of Modeling and Simulation for Precision Diamond Wire Sawing of Monocrystalline Silicon.

Precision processing of monocrystalline silicon presents significant challenges due to its unique crystal structure and chemical properties. Effective modeling and simulation are essential for advancing the understanding of the manufacturing process, optimizing design, and refining production parameters to enhance product quality and performance. This review provides a comprehensive analysis of the modeling and simulation techniques applied in the precision machining of monocrystalline silicon using diamond wire sawing. Firstly, the principles of mathematical analytical model, molecular dynamics, and finite element methods as they relate to monocrystalline silicon processing are outlined. Subsequently, the review explores how mathematical analytical models address force-related issues in this context. Molecular dynamics simulations provide valuable insights into atomic-scale processes, including subsurface damage and stress distribution. The finite element method is utilized to investigate temperature variations and abrasive wear during wire cutting. Furthermore, similarities, differences, and complementarities among these three modeling approaches are examined. Finally, future directions for applying these models to precision machining of monocrystalline silicon are discussed.

Advanced exergoeconomic analysis and mathematical modelling of the natural gas fired gas turbine unit used for industrial cogeneration system

In this study, mathematical model of advanced exergoeconomic analysis (ADEXEC) basing on advanced specific exergy cost (ADSPECO) and advanced exergy-cost-energy-mass (EXCEM) (ADEXCEM) methods are applied to the industrial cogeneration system (COGEN) which consists of natural gas fired gas turbine unit (with combustion chamber (CC), turbine (GT) and air compressor (AC)), pipe line (PL), wall (WD) and ground (GD) tile dryers under the dead state conditions of 10 °C, 15 °C, 20 °C, 25 °C and 30 °C. According to ADSPECO analysis; although CC ($6.97/GJ) has the lowest unit fuel exergy cost among the components, it has the highest exergy destruction cost rate ($252,391/hour at 30 °C) due to its high exergy destruction value. Although more than 40 % of the exergy destruction cost rate in the COGEN system is detected in CC, WD (105.541 $/h at 30 °C) and GD (107.499 $/h at 30 °C) which together account for more than 67 % of COGEN's avoidable exergy destruction are understood to be the first components to focus on. The fact that the exergy destruction cost rates of all components except PL is higher than the exogenous part of the endogenous part at all dead state temperatures reveals the weakness of the relationship between the components.

Numerical Calculation and Application for Crushing Rate and Fracture Conductivity of Combined Proppants

Proppant is one of the key materials for hydraulic fracturing. For special situations, such as middle-deep reservoirs and closure pressures ranging from 40 MPa to 60 MPa, using a single proppant cannot solve the contradiction between performance, which means crushing rate and fracture conductivity, and cost. However, using combined proppants is an economically effective method for hydraulic fracturing of such special reservoirs. Firstly, for different types, particle sizes, and proportions of combined proppants, various contact relationships between proppant particles are considered. The random phenomenon of proppant particle arrangement is described using the Monte Carlo method, and the deterministic phenomenon of proppant particles is processed using an optimization model, achieving computer simulation of the microscopic arrangement of proppant particles. Secondly, a mathematical model for the force analysis of combined proppant particles is established, and an improved singular value decomposition method is used for numerical solution. A computational model for the crushing rate and fracture conductivity of combined proppants is proposed. Thirdly, the numerical calculation results are compared and discussed with the test values, verifying the accuracy of the computational model. Finally, the application of combined proppants is discussed, and a model for optimizing the proportion of combined proppants is proposed. The onsite construction technology is introduced, and the cost and economic benefits of combined proppants are compared with those of all ceramic particles and excessive all-quartz sand. It is proved that combined proppants can balance performance and price, and are an economically effective method for hydraulic fracturing of special reservoirs. The research results can select the optimal proppant material and optimize the combination of different proppant types, which can help achieve cost reduction and efficiency increase in oil and gas development.

Using terahertz spectroscopy to quantify bioactive flavonoids in Moxa Wool as predictor of rheumatoid arthritis treatment outcomes

BackgroundMoxibustion, a traditional Chinese medicine practice, employs Moxa Wool, derived from Artemisia argyi. Flavonoids, the key pharmacological constituents in Moxa Wool, are known for their anti-inflammatory and analgesic properties. The purity of Moxa Wool, particularly its flavonoid content, directly influences the efficacy of moxibustion treatments. However, quantifying these bioactive flavonoids accurately and non-destructively has been a challenge. PurposeThis study introduces terahertz spectroscopy as a non-destructive optical detection method for qualitative detection and quantitative analysis of flavonoids in Moxa Wool. By establishing a mathematical model between spectral signals and clinical efficacy, a reliable correlation between flavonoid concentration and the therapeutic effect of moxibustion can be established, providing a potential predictive model for the treatment outcomes of rheumatoid arthritis. Study DesignWe adopted terahertz spectroscopy technology and combined it with terahertz metamaterial biosensors to achieve rapid, efficient, and non-destructive testing of the quality of Moxa Wool. This method reduces the detection time from hours to minutes while lowering the sample detection limit, overcoming the limitations of traditional detection methods in pharmacological research. MethodsThrough terahertz metamaterial biosensors, rapid detection of the purity of Moxa Wool has been achieved. A combination of molecular simulation and terahertz spectroscopy was used to quantitatively analyze the flavonoid content in different purities of Moxa Wool. To ensure accuracy, the quantitative results of flavonoids obtained by terahertz spectroscopy were validated using high-performance liquid chromatography (HPLC). In addition, moxibustion treatment was performed on rats with rheumatoid arthritis using Moxa Wool, and medical indicator information was recorded. A mathematical analysis model was established to evaluate the correlation between flavonoid content and analgesic and anti-inflammatory effects. ResultsTerahertz spectroscopy analysis shows that there is a direct correlation between the flavonoid content in moxibustion and the absorption peak intensity. The maximum R2 in the model analysis is 0.98, indicating a high accuracy in predicting the purity of Moxa Wool. These results were also validated by HPLC. In a rat model, the purity of 30:1 Moxa Wool samples showed a 50 % decrease in TNF-α, IL-1β, and IL-6 levels during treatment compared to low-purity samples, significantly reducing inflammation markers and pain symptoms. Meanwhile, The PLS prediction model established a correlation between terahertz-detected flavonoid levels and treatment outcomes (PWL and IL-1β). The maximum R2 in the model is 0.91, indicating a high correlation between flavonoid levels and the anti-inflammatory and analgesic effects of moxibustion treatment. ConclusionThis study not only demonstrates the effectiveness of terahertz spectroscopy in the pharmacological quantification of bioactive compounds but also establishes a novel predictive model for the efficacy of moxibustion in rheumatoid arthritis treatment. It underscores the potential of integrating traditional medicine insights with advanced technology to enhance therapeutic strategies in pharmacology.

Harmonic Sequence Component Model-Based Small-Signal Stability Analysis in Synchronous Machines during Asymmetrical Faults

Power systems are complex and often subject to faults, requiring accurate mathematical models for a thorough analysis. Traditional time-domain models are employed to evaluate the dynamic response of power system elements during transmission system faults. However, only the positive sequence components are considered for unbalanced faults, so the small-signal stability analysis is no longer accurate when assuming balanced conditions for asymmetrical faults. The dynamic phasor approach extends traditional models by representing synchronous machines with harmonic sequence components, making it suitable for an unbalanced condition analysis and revealing dynamic couplings not evident in conventional methods. By modeling electrical and mechanical equations with harmonic sequence components, the study implements an eigenvalue sensitivity analysis and participation factor analysis to identify the variable with significant participation in the critical modes and consequently in the dynamic response of synchronous machines during asymmetric faults, thereby control strategies can be proposed to improve system stability. The article validates the dynamic phasor model through simulations of a single-phase short circuit, demonstrating its accuracy and effectiveness in representing the transient and dynamic behavior of synchronous machines, and correctly identifies the harmonic sequence component with significant participation in the critical modes identified by the eigenvalue sensitivity to the rotor angular velocity and rotor angle.

A method for assessing guide layout and error on implant accuracy

Functional and esthetic results require accurate implant placement. We aimed to develop a predictive method for assessing guide layout and error on implant accuracy. A mathematical model for position error analysis was constructed based on triangular mesh data. This model examines the relationship between the spatial shifts of multiple surfaces and the spatial shifts of specific points. It involves encasing these surfaces in a cuboid bounding box and expressing them in a local coordinate system. The influence of positioning surface error and layout of surgical guide were researched with a simulation test. The result shows that error in the implant site position is directly related to the error in the guide locating surface under the same layout. When the guide locating surface layout varies, as the length, width, and height of the minimum cuboid envelope increase, the maximum deviation in the implant site position decreases.

Mathematical optimization modeling for scenario analysis of integrated steelworks transitioning towards hydrogen-based reduction

To reduce carbon dioxide emissions from the steel industry, efforts are made to introduce a steelmaking route based on hydrogen reduction of iron ore instead of the commonly used coke-based reduction in a blast furnace. Changing fundamental pieces of steelworks affects the functions of most every system unit involved, and thus warrants the question of how such a transition could optimally take place over time, and no rigorous attempts have until now been made to tackle this problem mathematically. This article presents a steel plant optimization model, written as a mixed-integer non-linear programming problem, where aging blast furnaces and basic oxygen furnaces could potentially be replaced with shaft furnaces and electric arc furnaces, minimizing costs or emissions over a long-term time horizon to identify possible transition pathways. Example cases show how various parameters affect optimal investment pathways, stressing the necessity of appropriate planning tools for analyzing diverse cases.