THREE-DIMENSIONAL MATHEMATICAL MODEL AND ITS APPLICATION IN THE NEIGHBORHOOD OF THE THREE GORGES RESERVOIR DAM IN THE YANGTZE RIVER

The calculation of flow and sediment transport is one of the most important tasks in river engineering. The task is particularly difficult because a number of complex physical phenomena should be accounted for more realistically in a model with a predictive power. Three-dimensional calculations of river flow and suspended sediment transport are performed in this paper with application in the Three Gorges Reservoir in the Yangtze River. A period of 76 years after the dam is built is simulated and the results are compared with laboratory measurements obtained by Tsinghua University whereby the model is verified and calibrated. Generally speaking, the calculated results agree well with the experiments, demonstrating that the present model can be used for flow and sediment transport prediction in rivers.

THE STUDY ON THREE-DIMENSIONAL MATHEMATICAL MODEL OF RIVER BED EROSION FOR WATER-SEDIMENT TWO-PHASE FLOW

Based on the tensor analysis of water-sediment two-phase how, the basic model equations for clear water flow and sediment-laden flow are deduced in the general curve coordinates for natural water variable-density turbulent how. Furthermore, corresponding boundary conditions are also presented in connection with the composition and movement of non-uniform bed material. The theoretical results are applied to the calculation of the float open caisson in the construction period and good results are obtained.

Oxygen tension modulates cell function in an in vitro three-dimensional glioblastoma tumor model

Hypoxia is a typical feature of the tumor microenvironment,one of the most critical factors affecting cell behavior and tumor progression.However,the lack of tumor models able to precisely emulate natural brain tumor tissue has impeded the study of the effects of hypoxia on the progression and growth of tumor cells.This study reports a three-dimensional(3D)brain tumor model obtained by encapsulating U87MG(U87)cells in a hydrogel containing type I collagen.It also documents the effect of various oxygen concentrations(1%,7%,and 21%)in the culture environment on U87 cell morphology,proliferation,viability,cell cycle,apoptosis rate,and migration.Finally,it compares two-dimensional(2D)and 3D cultures.For comparison purposes,cells cultured in flat culture dishes were used as the control(2D model).Cells cultured in the 3D model proliferated more slowly but had a higher apoptosis rate and proportion of cells in the resting phase(G0 phase)/gap I phase(G1 phase)than those cultured in the 2D model.Besides,the two models yielded significantly different cell morphologies.Finally,hypoxia(e.g.,1%O2)affected cell morphology,slowed cell growth,reduced cell viability,and increased the apoptosis rate in the 3D model.These results indicate that the constructed 3D model is effective for investigating the effects of biological and chemical factors on cell morphology and function,and can be more representative of the tumor microenvironment than 2D culture systems.The developed 3D glioblastoma tumor model is equally applicable to other studies in pharmacology and pathology.

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.

Three-dimensional structural models,evolution and petroleum geological significances of transtensional faults in the Ziyang area,central Sichuan Basin,SW China

With drilling and seismic data of Transtensional(strike-slip)Fault System in the Ziyang area of the central Sichuan Basin,SW China plane-section integrated structural interpretation,3-D fault framework model building,fault throw analyzing,and balanced profile restoration,it is pointed out that the transtensional fault system in the Ziyang 3-D seismic survey consists of the northeast-trending F_(I)19 and F_(I)20 fault zones dominated by extensional deformation,as well as 3 sets of northwest-trending en echelon normal faults experienced dextral shear deformation.Among them,the F_(I)19 and F_(I)20 fault zones cut through the Neoproterozoic to Lower Triassic Jialingjiang Formation,presenting a 3-D structure of an“S”-shaped ribbon.And before Permian and during the Early Triassic,the F_(I)19 and F_(I)20 fault zones underwent at least two periods of structural superimposition.Besides,the 3 sets of northwest-trending en echelon normal faults are composed of small normal faults arranged in pairs,with opposite dip directions and partially left-stepped arrangement.And before Permian,they had formed almost,restricting the eastward growth and propagation of the F_(I)19 fault zone.The F_(I)19 and F_(I)20 fault zones communicate multiple sets of source rocks and reservoirs from deep to shallow,and the timing of fault activity matches well with oil and gas generation peaks.If there were favorable Cambrian-Triassic sedimentary facies and reservoirs developing on the local anticlinal belts of both sides of the F_(I)19 and F_(I)20 fault zones,the major reservoirs in this area are expected to achieve breakthroughs in oil and gas exploration.

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.

Effects of three-dimensional quality assessment nursing intervention on efficacy and disease management of patients undergoing esophageal cancer surgery

BACKGROUND Esophageal cancer is one of the most common malignant tumors.The three-dimensional quality structure model is a quality assessment theory that includes three dimensions:Structure,process,and results.AIM To investigate the effects of nursing interventions with three-dimensional quality assessment on the efficacy and disease management ability of patients undergoing esophageal cancer surgery.METHODS In this prospective study,the control group received routine nursing,and the intervention group additionally received a three-dimensional quality assessment intervention based on the above routine care.Self-efficacy and patient disease management abilities were evaluated using the General Self-Efficacy Scale(GSES)and Exercise of Self-Care Agency scale,respectively.IBM SPSS Statistics for Windows,version 17.0,was used for the data processing.RESULTS This study recruited 112 patients who were assigned to the control and experi-mental groups(n=56 per group).Before the intervention,there was no significant difference in GSES scores between the two groups(P>0.05).After the inter-vention,the GSES scores of both groups increased,with the experimental group showing higher values(P<0.05).At the time of discharge and three months after discharge,the scores for positive attitudes,self-stress reduction,and total score of health promotion in the experimental group were higher than those in the control group(P<0.05).CONCLUSION The implementation of a three-dimensional quality structure model for postoperative patients with esophageal cancer can effectively improve their self-management ability and self-efficacy of postoperative patients.

Critical Analysis of Increasingly Mathematical Economics in the Modern Society

This paper critically examines the escalating trend of mathematization in economics,highlighting its implications and controversies in contemporary economic research.While the application of sophisticated mathematical models and statistical techniques has enhanced the precision,rigor,and status of economics within academia and practical application,concerns arise regarding the potential oversimplification and detachment from real-world complexities.The adoption of mathematical tools has arguably led to a focus on theoretically tractable problems at the expense of those more relevant to practical economic and social issues.This paper explores both the benefits and limitations of this trend,discussing how the reliance on quantitative methods affects the innovation,comprehensibility,and application of economic theories.We argue for a balanced approach that fosters innovation by integrating qualitative insights and embracing interdisciplinary methods to ensure economics remains both rigorous and relevant to societal needs.

Research on Three-Dimensional Simulation of the Internal Arc Gear Skiving

Aiming at the problems that the simulation accuracy which is reduced due to the simplification of the model,a three-dimensional simulation method based on solid modeling is being proposed.By analyzing the motion relationship and positional relationship between the caries knife and the workpiece,the coordinate system of the caries machining was established.With the MATLAB software,the cutting edge model and the blade sweeping surface model of the boring cutter are sequentially established.Boolean operation is performed on the blade swept surface formed by the tooth cutter teeth with time t and the workpiece tooth geometry as well as the undeformed three-dimensional chip geometry model and the instantaneous cogging geometry model are obtained at different times.Through the compare between gear end face simulation tooth profile and the theoretical inner arc tooth profile,we verified the accuracy and rationality of the proposed method.

Study of the geomagnetic field's regional gradients in Chinese continent using three-dimensional surface Spline model

We combined domestic ground-based and satellite magnetic measurements to create a regional three-dimensional surface Spline(3DSS)gradient model of the main geomagnetic field over the Chinese continent.To improve the precision of the model,we considered the data gap between the ground and satellite data.We compared and analyzed the results of the Taylor polynomial,surface Spline,and CHAOS-6(the CHAMP,?rsted and SAC-C model of Earth’s magnetic field)gradient models.Results showed that the gradients in the south-north and east-west directions of the four models were consistent.The 3DSS model was able to express not only gradients at different altitudes,but also average gradients inside the research area.The two Spline models were able to capture more information on gradient anomalies than were the fitted models.Strong local anomalies were observed in northern Xinjiang,Beijing,and the junction area between Jiangsu and Zhejiang,and the total intensity F decreased whereas the altitude increased.The gradient decreased by 21.69%in the south-north direction and increased by 11.78%in the east-west direction.In addition,the altitude gradient turned from negative to positive while the altitude increased.The Spline model and the two fitted models differed mainly in the field sources they expressed and the modeling theory.

Can preoperative planning using IRIS™three-dimensional anatomical virtual models predict operative findings during robot-assisted partial nephrectomy?

Objective To evaluate the predictive validity of IRIS™(Intuitive Surgical®,Sunnyvale,CA,USA)as a planning tool for robot-assisted partial nephrectomy(RAPN)by assessing the degree of overlap with intraoperative execution.Methods Thirty-one patients scheduled for RAPN by four experienced urologists were enrolled in a prospective study.Prior to surgery,urologists reviewed the IRIS™three-dimensional model on an iphone Operating System(iOS)app and completed a questionnaire outlining their surgical plan including surgical approach,and ischemia technique as well as confidence in executing this plan.Postoperatively,questionnaires assessing the procedural approach,clinical utility,efficiency,and effectiveness of IRIS™were completed.The degree of overlap between the preoperative and intraoperative questionnaires and between the planned approach and actual execution of the procedure was analyzed.Questionnaires were answered on a 5-point Likert scale and scores of 4 or greater were considered positive.Results Mean age was 65.1 years with a mean tumor size of 27.7 mm(interquartile range 17.5-44.0 mm).Hilar tumors consisted of 32.3%;48.4%of patients had R.E.N.A.L.nephrometry scores of 7-9.On preoperative questionnaires,the surgeons reported that in 67.7%cases they were confident that they can perform the procedure successfully,and on intraoperative questionnaires,the surgeons reported that in 96.8%cases IRIS™helped achieve good spatial sensation of the anatomy.There was a high degree of overlap between preoperative and intraoperative questionnaires for the surgical approach,interpreting anatomical details and clinical utility.When comparing plans for selective or off-clamp,the preoperative plan was executed in 90.0%of cases intraoperatively.Conclusion A high degree of overlap between the preoperative surgical approach and intraoperative RAPN execution was found using IRIS™.This is the first study to evaluate the predictive accuracy of IRIS™during RAPN by comparing preoperative plan and intraoperative execution.

Refined mathematical model for the breaching of concrete-face sand-gravel dams due to overtopping failure

Overtopping is one of the main reasons for the breaching of concrete-face sand-gravel dams(CFSGDs).In this study,a refined mathematical model was established based on the characteristics of the overtopping breaching of CFSGDs.The model characteristics were as follows:(1)Based on the Renormailzation Group(RNG)k-εturbulence theory and volume of fluid(VOF)method,the turbulent characteristics of the dam-break flow were simulated,and the erosion surface of the water and soil was tracked;(2)In consideration of the influence of the change in the sediment content on the dam-break flow,the dam material transport equation,which could reflect the characteristics of particle settlement and entrainment motion,was used to simulate the erosion process of the sand gravels;(3)Based on the bending moment balance method,a failure equation of the concrete face slab under dead weight and water load was established.The proposed model was verified through a case study on the failure of the Gouhou CFSGD.The results showed that the proposed model could well simulate the erosion mode of the special vortex flow of the CFSGD scouring the support body of the concrete face slab inward and reflect the mutual coupling relationship between the dam-break flow,sand gravels,and concrete face slabs.Compared with the measured values,the relative errors of the peak discharge,final breach average width,dam breaching duration,and maximum failure length of the face slab calculated using the proposed model were all less than 12%,thus verifying the rationality of the model.The proposed model was demonstrated to perform better and provide more detailed results than three selected parametric models and three simplified mathematical models.The study results can aid in establishing the risk level and devising early warning strategies for CFSGDs.

Well-Posedness and a Finite Difference Approximation for a Mathematical Model of HPV-Induced Cervical Cancer

We present a first-order finite difference scheme for approximating solutions of a mathematical model of cervical cancer induced by the human papillomavirus (HPV), which consists of four nonlinear partial differential equations and a nonlinear first-order ordinary differential equation. The scheme is analyzed and used to provide an existence-uniqueness result. Numerical simulations are performed in order to demonstrate the first-order rate of convergence. A sensitivity analysis was done in order to compare the effects of two drug types, those that increase the death rate of HPV-infected cells, and those that increase the death rate of the precancerous cell population. The model predicts that treatments that affect the precancerous cell population by directly increasing the corresponding death rate are far more effective than those that increase the death rate of HPV-infected cells.

Three-Dimensional Analytical Modeling of Axial-Flux Permanent Magnet Drivers

In this paper, the axial-flux permanent magnet driver is modeledand analyzed in a simple and novel way under three-dimensional cylindricalcoordinates. The inherent three-dimensional characteristics of the deviceare comprehensively considered, and the governing equations are solved bysimplifying the boundary conditions. The axial magnetization of the sectorshapedpermanent magnets is accurately described in an algebraic form bythe parameters, which makes the physical meaning more explicit than thepurely mathematical expression in general series forms. The parameters of theBessel function are determined simply and the magnetic field distribution ofpermanent magnets and the air-gap is solved. Furthermore, the field solutionsare completely analytical, which provides convenience and satisfactoryaccuracy for modeling a series of electromagnetic performance parameters,such as the axial electromagnetic force density, axial electromagnetic force,and electromagnetic torque. The correctness and accuracy of the analyticalmodels are fully verified by three-dimensional finite element simulations and a15 kW prototype and the results of calculations, simulations, and experimentsunder three methods are highly consistent. The influence of several designparameters on magnetic field distribution and performance is studied and discussed.The results indicate that the modeling method proposed in this papercan calculate the magnetic field distribution and performance accurately andrapidly, which affords an important reference for the design and optimizationof axial-flux permanent magnet drivers.

Quantification of Ride Comfort Using Musculoskeletal Mathematical Model Considering Vehicle Behavior

This research aims to quantify driver ride comfort due to changes in damper characteristics between comfort mode and sport mode,considering the vehicle’s inertial behavior.The comfort of riding in an automobile has been evaluated in recent years on the basis of a subjective sensory evaluation given by the driver.However,reflecting driving sensations in design work to improve ride comfort is abstract in nature and difficult to express theoretically.Therefore,we evaluated the human body’s effects while driving scientifically by quantifying the driver’s behavior while operating the steering wheel and the behavior of the automobile while in motion using physical quantities.To this end,we collected driver and vehicle data using amotion capture system and vehicle CAN and IMU sensors.We also constructed a three-dimensional musculoskeletal mathematical model to simulate driver movements and calculate the power and amount of energy per unit of time used for driving the joints and muscles of the human body.Here,we used comfort mode and sport mode to compare damper characteristics in terms of hardness.In comfort mode,damper characteristics are soft and steering stability is mild,but vibration from the road is not easily transmitted to the driver making for a lighter load on the driver.In sport mode,on the other hand,damper characteristics are hard and steering stability is comparatively better.Still,vibration from the road is easily transmitted to the driver,whichmakes it easy for a load to be placed on the driver.As a result of this comparison,it was found that a load was most likely to be applied to the driver’s neck.This result in relation to the neck joint can therefore be treated as an objective measure for quantifying ride comfort.