Multi-Objective Mathematical Model for the Optimal Time to Harvest Sugarcane

In this paper, the sugarcane and sugar industry in Thailand is studied. The government determines the sugarcane prices which is based on the two main factors: 1) weight and 2) commercial cane sugar (standard value equal 10 C.C.S.). Usually, the C.C.S. will increase with time and the weight will decrease. The main purpose of this research is to find the optimal harvest time to maximize revenue and minimize gathering cost. The mathematical model is first formulated under the regulations of the Office of the Cane and Sugar Board (OCSB). The -constraints method is then applied to solve the multi-objective mathematical model. The optimal harvest times in the four regions of Thailand (Northern, Central, Eastern, North-Eastern) for crop years 2012/ 13, 2013/14 and 2014/15 are obtained for comparison.

DeepSurNet-NSGA II:Deep Surrogate Model-Assisted Multi-Objective Evolutionary Algorithm for Enhancing Leg Linkage in Walking Robots

This research paper presents a comprehensive investigation into the effectiveness of the DeepSurNet-NSGA II(Deep Surrogate Model-Assisted Non-dominated Sorting Genetic Algorithm II)for solving complex multiobjective optimization problems,with a particular focus on robotic leg-linkage design.The study introduces an innovative approach that integrates deep learning-based surrogate models with the robust Non-dominated Sorting Genetic Algorithm II,aiming to enhance the efficiency and precision of the optimization process.Through a series of empirical experiments and algorithmic analyses,the paper demonstrates a high degree of correlation between solutions generated by the DeepSurNet-NSGA II and those obtained from direct experimental methods,underscoring the algorithm’s capability to accurately approximate the Pareto-optimal frontier while significantly reducing computational demands.The methodology encompasses a detailed exploration of the algorithm’s configuration,the experimental setup,and the criteria for performance evaluation,ensuring the reproducibility of results and facilitating future advancements in the field.The findings of this study not only confirm the practical applicability and theoretical soundness of the DeepSurNet-NSGA II in navigating the intricacies of multi-objective optimization but also highlight its potential as a transformative tool in engineering and design optimization.By bridging the gap between complex optimization challenges and achievable solutions,this research contributes valuable insights into the optimization domain,offering a promising direction for future inquiries and technological innovations.

Prediction Model-based Multi-objective Optimization for Mix-ratio Design of Recycled Aggregate Concrete

The prediction model for mechanical properties of RAC was established through the Bayesian optimization-based Gaussian process regression(BO-GPR)method,where the input variables in BO-GPR model depend on the mix ratio of concrete.Then the compressive strength prediction model,the material cost,and environmental factors were simultaneously considered as objectives,while a multi-objective gray wolf optimization algorithm was developed for finding the optimal mix ratio.A total of 730 RAC datasets were used for training and testing the predication model,while the optimal design method for mix ratio was verified through RAC experiments.The experimental results show that the predicted,testing,and expected compressive strengths are nearly consistent,illustrating the effectiveness of the proposed method.

MATHEMATICAL MODELING AND BIFURCATION ANALYSIS FOR A BIOLOGICAL MECHANISM OF CANCER DRUG RESISTANCE

Drug resistance is one of the most intractable issues in targeted therapy for cancer diseases.It has also been demonstrated to be related to cancer heterogeneity,which promotes the emergence of treatment-refractory cancer cell populations.Focusing on how cancer cells develop resistance during the encounter with targeted drugs and the immune system,we propose a mathematical model for studying the dynamics of drug resistance in a conjoint heterogeneous tumor-immune setting.We analyze the local geometric properties of the equilibria of the model.Numerical simulations show that the selectively targeted removal of sensitive cancer cells may cause the initially heterogeneous population to become a more resistant population.Moreover,the decline of immune recruitment is a stronger determinant of cancer escape from immune surveillance or targeted therapy than the decay in immune predation strength.Sensitivity analysis of model parameters provides insight into the roles of the immune system combined with targeted therapy in determining treatment outcomes.

Aggravation of Cancer,Heart Diseases and Diabetes Subsequent to COVID-19 Lockdown via Mathematical Modeling

The global populationhas beenandwill continue to be severely impacted by theCOVID-19 epidemic.The primary objective of this research is to demonstrate the future impact of COVID-19 on those who suffer from other fatal conditions such as cancer,heart disease,and diabetes.Here,using ordinary differential equations(ODEs),two mathematical models are developed to explain the association between COVID-19 and cancer and between COVID-19 and diabetes and heart disease.After that,we highlight the stability assessments that can be applied to these models.Sensitivity analysis is used to examine how changes in certain factors impact different aspects of disease.The sensitivity analysis showed that many people are still nervous about seeing a doctor due to COVID-19,which could result in a dramatic increase in the diagnosis of various ailments in the years to come.The correlation between diabetes and cardiovascular illness is also illustrated graphically.The effects of smoking and obesity are also found to be significant in disease compartments.Model fitting is also provided for interpreting the relationship between real data and the results of thiswork.Diabetic people,in particular,need tomonitor their health conditions closely and practice heart health maintenance.People with heart diseases should undergo regular checks so that they can protect themselves from diabetes and take some precautions including suitable diets.The main purpose of this study is to emphasize the importance of regular checks,to warn people about the effects of COVID-19(including avoiding healthcare centers and doctors because of the spread of infectious diseases)and to indicate the importance of family history of cancer,heart diseases and diabetes.The provision of the recommendations requires an increase in public consciousness.

Mathematical Modeling of Cell Polarity Establishment of Budding Yeast

The budding yeast Saccharomyces cerevisiae is a powerful model system for studying the cell polarity establishment.The cell polarization process is regulated by signaling molecules,which are initially distributed in the cytoplasm and then recruited to a proper location on the cell membrane in response to spatial cues or spontaneously.Polarization of these signaling molecules involves complex regulation,so the mathematical models become a useful tool to investigate the mechanism behind the process.In this review,we discuss how mathematical modeling has shed light on different regulations in the cell polarization.We also propose future applications for the mathematical modeling of cell polarization and morphogenesis.

A Mathematical Modeling of 3D Cubical Geometry Hypothetical Reservoir under the Effect of Nanoparticles Flow Rate,Porosity,and Relative Permeability

This study aims to formulate a steady-state mathematical model for a three-dimensional permeable enclosure(cavity)to determine the oil extraction rate using three distinct nanoparticles,SiO_(2),Al_(2)O_(3),and Fe_(2)O_(3),in unconventional oil reservoirs.The simulation is conducted for different parameters of volume fractions,porosities,and mass flow rates to determine the optimal oil recovery.The impact of nanoparticles on relative permeability(kr)and water is also investigated.The simulation process utilizes the finite volume ANSYS Fluent.The study results showed that when the mass flow rate at the inlet is low,oil recovery goes up.In addition,they indicated that silicon nanoparticles are better at getting oil out of the ground(i.e.,oil reservoir)than Al_(2)O_(3)and Fe_(2)O_(3).Most oil can be extracted from SiO_(2),Al_(2)O_(3),and Fe_(2)O_(3)at a rate of 97.8%,96.5%,and 88%,respectively.

Practical Use of the Subjective Mathematical Model of Bayes and Its External Validation in Dental Medicine & Dentistry

Objective: Our study aims to validate the subjective Bayes mathematical model using the mathematical model of logistic regression. Expert systems are being utilized increasingly in medical fields for the purposes of assisting diagnosis and treatment planning in Dentistry. Existing systems used few symptoms for dental diagnosis. In Dentistry, few symptoms are not enough for diagnosis. In this research, a conditional probability model (Bayes rule) was developed with increased number of symptoms associated with a disease for diagnosis. A test set of recurrent cases was then used to test the diagnostic capacity of the system. The generated diagnosis matched that of the human experts. The system was also tested for its capacity to handle uncommon dental diseases and the system portrayed useful potential. Method: The study used the Subjective Mathematical Bayes Model (SBM) approach and employed Logistic Regression Mathematical Model (LMR) techniques. The external validation of the subjective mathematical Bayes model (MSB) concerns the real cases of 625 patients who developed alveolar osteitis (OA). We propose strategies for reproducibility and reporting standards, outlining an updated WAMBS (when to Worry and how to Avoid the Misuse of Bayesian Statistics) checklist. Finally, we outline the impact of Bayesian analysis Logistic Regression Mathematical Model (LMR) techniques and on artificial intelligence, a major goal in the next decade. Results: The internal validation had identified seven (7) etiological factors of OA, which will be compared to the cases of MRL, for the external validation which retained six (6) etiological factors of OA. The experts in the internal validation of the MSB had generated 40 cases of OA and a COP of (0.5), which will be compared to the MRL that collected 625 real cases of OA to produce a Cop of (0.6) in the external validation, which discriminates between healthy patients (Se) and sick patients (Sp). Compared to real cases and the logistic regression model, the Bayesian model is efficient and its validity is established.

Mathematical Modeling of HIV Investigating the Effect of Inconsistent Treatment

HIV is a retrovirus that infects and impairs the cells and functions of the immune system. It has caused a great challenge to global public health systems and leads to Acquired Immunodeficiency Syndrome (AIDS), if not attended to in good time. Antiretroviral therapy is used for managing the virus in a patient’s lifetime. Some of the symptoms of the disease include lean body mass and many opportunistic infections. This study has developed a SIAT mathematical model to investigate the impact of inconsistency in treatment of the disease. The arising non-linear differential equations have been obtained and analyzed. The DFE and its stability have been obtained and the study found that it is locally asymptotically stable when the basic reproduction number is less than unity. The endemic equilibrium has been obtained and found to be globally asymptotically stable when the basic reproduction number is greater than unity. Numerical solutions have been obtained and analyzed to give the trends in the spread dynamics. The inconsistency in treatment uptake has been analyzed through the numerical solutions. The study found that when the treatment rate of those infected increases, it leads to an increase in treatment population, which slows down the spread of HIV and vice versa. An increase in the rate of treatment of those with AIDS leads to a decrease in the AIDS population, the reverse happens when this rate decreases. The study recommends that the community involvement in advocating for consistent treatment of HIV to curb the spread of the disease.

Mathematical Modeling of the Co-Infection Dynamics of HIV and Tuberculosis Incorporating Inconsistency in HIV Treatment

A non-linear HIV-TB co-infection has been formulated and analyzed. The positivity and invariant region has been established. The disease free equilibrium and its stability has been determined. The local stability was determined and found to be stable under given conditions. The basic reproduction number was obtained and according to findings, co-infection diminishes when this number is less than unity, and persists when the number is greater than unity. The global stability of the endemic equilibrium was calculated. The impact of HIV on TB was established as well as the impact of TB on HIV. Numerical solution was also done and the findings indicate that when the rate of HIV treatment increases the latent TB increases while the co-infected population decreases. When the rate of HIV treatment decreases the latent TB population decreases and the co-infected population increases. Encouraging communities to prioritize the consistent treatment of HIV infected individuals must be emphasized in order to reduce the scourge of HIV-TB co-infection.

Analysis and Evaluation of Housing Price Factors Using Mathematical Modeling

In recent years,the real estate industry has achieved significant progress,driving the development of related sectors and playing a crucial role in economic growth.However,rapid real estate market expansion has led to challenges,particularly concerning housing prices,which have drawn widespread societal attention.This article explores the theories of housing prices,analyzes factors influencing them,and conducts an empirical investigation of the impact of representative factors on ordinary residential prices.Using regression analysis and the entropy weight method,a mathematical model was developed to examine how various factors affect housing prices.

MATHEMATICAL MODEL OF ~4He QUANTUM INTERFEROMETER GYROSCOPE

The mathematical model of 4He quantum interferometer gyroscope is presented. The model includes the driven equation, the current equation and the position equation. Therefore, it can sufficiently describe the gyro- scope system. The driven equation shows the thermally driven gyroscope can work for a long time but the pres- sure driven one cannot. From the current equation, the superfluid currents passing through the weak link contain the AC currents which show the rotation flux, and other currents caused by drive. As shown in the position equa- tion, the displacement of diaphragm is the only detectable parameter in the gyroscope system. The model is tested by the simulations based on experimental parameters, and can be used to research performance of the gyroscope and analyse the gyroscope error.

Application of the Sediment Mathematical Modelling on Planned Project of Lingdingyang Bay

Based on the combined hydraulic calculation for the eastern network region at the Pearl River estuary and several outlets to the Lingdingyang Bay, the sediment calculation modelling was introduced in the establishment of the sediment mathematical model for Lingdingyang Bay and the eastern region with one and two dimensional flow calculation. Model adjustment and verification were performed in conjunction with field data. The simulated results coincide well with measured data.In addition the model is applied to predict the shore-line planning scheme of Lingdingyang Bay.The theoretical criterion is provided for the shore line plan in the model.And a new mathematical simulated method is put out to research the planning engineering concerned with one-dimensional net rivers and two-dimensional estuary.

MATHEMATICAL MODEL OF SELF-REPAIRING FLIGHT CONTROL

The most prospective method for certain structural failures and damages that cannot employ redundancy is self-repairing techniques, to ensure especially the maximum flight safety. Based on the characters of self-repairing aircraft, this paper states some basic assumptions of the self-repairing aircraft, and puts forward some special new conceptions concerning the self-repairing aircraft: control input, operating input, command input, repair input and operating and control factor as well as their relationships. Thus it provides a simple and reliable mathematical model structure for the research on the self-repairing control of the aircraft.

Mathematical Models of Tire-Longitudinal Road Adhesion and Their Use in the Study of Road Vehicle Dynamics

Mathematical models of tire-longitudinal road adhesion for use in the study of road vehicle dynamics are set up so as to express the relations of longitudinal adhesion coefficients with the slip ratio. They perfect the Pacejka's models in practical use by taking into account the influences of all essential parameters such as road surface condition. vehicle velocity. slip angle. vertical load and slip ratio on the longitudinal adhesion coefficients. The new models are more comprehensive more concise. simpler and more convenient in application in all kinds of simulations of car dynamics in various sorts of braking modes.

Mathematical Models of Tire-Lateral Road Adhesion for Use in Road Vehicle Dynamics Studies

Mathematical models of tire-lateral mad adhesion for use in mad vehicle dynamics studies are set up to express the relations of adhesion coefficients with slip ratio in lateral direction.The models of tire-lateral mad adhesion revolutionize the Pacejka's model in concept and therefore make it possible for applications in vehicle dynamics studies by the expression of lateral adhesion coefficient as a function of wheel slip ratio,instead of the wheel slip angle,taking into account in the mean time the influences of mad surface condition, vehicle velocity,vertical load,tire slip angle,and wheel camber angle.

Mathematical model for precursor gas residence time in isothermal CVD process of C/C composites

In the chemical vapor deposition（CVD） process of C/C composites,the dynamics and mechanism of precursor gas flowing behavior were analyzed mathematically,in which the precursor gas was infiltrated by the pressure difference of the gas flowing through felt.Differential equations were educed which characterized the relations among the pressure inside the felt,the pressure outside the felt of the precursor gas and the porosity of the felt as a function of CVD duration.The gas residence time during the infiltration process through the felt was obtained from the differential equations.The numerical verification is in good agreement with the practical process,indicating the good reliability of the current mathematical model.

STREAMLINE-BASED MATHEMATICAL MODEL FOR CO_2 MISCIBLE FLOODING

According to the research theory of improved black oil simulator, a practical mathematical model for CO2 miscible flooding was presented. In the model, the miscible process simulation was realized by adjusting oil/gas relative permeability and effective viscosity under the condition of miscible flow. In order to predict the production performance（fast,） streamline method is employed to solve this model as an alternative to traditional finite（difference） （methods.） Based on streamline distribution of steady-state flow through porous media with complex boundary confirmed with the boundary element method （BEM）, an explicit total variation diminishing （TVD） method is used to solve the one-dimensional flow problem. At the same time, influences of development scheme, solvent slug size, and injection periods on CO2 drive recovery are discussed. The model has the advantages of less（information） need, fast calculation, and adaptation to calculate CO2 drive performance of all kinds of patterns in a random shaped porous media with assembly boundary. It can be an（effective） tool for early stage screening and reservoir dynamic management of the CO2（miscible） oil field.

Experimental Research and Mathematical Model of Drag Torque in Single-plate Wet Clutch

Reduction of drag torque is one of important potentials to improve transmission efficiency.Existing mathematical model of drag torque was not accurate to predict the decrease after oil film shrinking because of the difficulty in modeling the flow pattern between two plates.Flow pattern was considered as laminar flow and full oil film in the gap between two plates in traditional model.Subsequent equivalent circumferential degree model presented an improvement in oil film shrinking due to centrifugal force,but was also based on full oil film in the gap,which resulted difference between model prediction and experimental data.The objective of this paper is to develop an accurate mathematical model for the above problem by using experimental verification.An experimental apparatus was set up to test drag torque of disengaged wet clutch consisting of single friction and separate plate.A high speed camera was used to record the flow pattern through transparent quartz disk plate.The visualization of flow pattern in the clearance was investigated to evaluate the characteristics of oil film shrinking.Visual test results reveal that the oil film begins to shrink from outer radius to inner radius at the stationary plate and only flows along the rotating plate after shrinking.Meanwhile,drag torque decreases sharply due to little contact area between the stationary plate and the oil.A three-dimensional Navier-Stokes （N-S） equation based on laminar flow is presented to model the drag torque.Pressure distributions in radial and circumferential directions as well as speed distributions are deduced.The model analysis reveals that the acceleration of flow in radial direction caused by centrifugal force is the key reason for the shrinking at the constant feeding flow rate.An approach to descript flow pattern was presented on the basis of visual observation.The drag torque predicted by the model agrees well with test data for non-grooved wet clutch.The proposed model enhances the precision for predicting drag torque,and lays down a framework on which some subsequent models are developed.

Mathematical Model for Electroslag Remelting Process

A mathematical model, including electromagnetic field equation, fluid flow equation, and temperature field equation, was established for the simulation of the electroslag remelting process. The distribution of temperature field was obtained by solving this model. The relationship between the local solidification time and the interdendritic spacing during the ingot solidification process was established, which has been regarded as a criterion for the evaluation of the quality of crystallization. For a crucible of 950 mm in diameter, the local solidification time is more than 1 h at the center of the ingot with the longest interdendritic spacing, whereas it is the shortest at the edge of the ingot according to the calculated results. The model can be used to understand the ESR process and to predict the ingot quality.