Pub Date : 2023-05-18DOI: 10.3389/fams.2023.1191661
Haihua Wang, Junhua Ku
The existence of fractional evolution equations has attracted a growing interest in recent years. The mild solution of fractional evolution equations constructed by a probability density function was first introduced by El-Borai. Inspired by El-Borai, Zhou and Jiao gave a definition of mild solution for fractional evolution equations with Caputo fractional derivative. Exact controllability is one of the fundamental issues in control theory: under some admissible control input, a system can be steered from an arbitrary given initial state to an arbitrary desired final state. In this article, using the (α, β) resolvent operator and three different fixed point theorems, we discuss the control problem for a class of Hilfer fractional Langevin evolution equations. The exact controllability of Hilfer fractional Langevin systems is established. An example is also discussed to illustrate the results.
{"title":"Controllability of Hilfer fractional Langevin evolution equations","authors":"Haihua Wang, Junhua Ku","doi":"10.3389/fams.2023.1191661","DOIUrl":"https://doi.org/10.3389/fams.2023.1191661","url":null,"abstract":"The existence of fractional evolution equations has attracted a growing interest in recent years. The mild solution of fractional evolution equations constructed by a probability density function was first introduced by El-Borai. Inspired by El-Borai, Zhou and Jiao gave a definition of mild solution for fractional evolution equations with Caputo fractional derivative. Exact controllability is one of the fundamental issues in control theory: under some admissible control input, a system can be steered from an arbitrary given initial state to an arbitrary desired final state. In this article, using the (α, β) resolvent operator and three different fixed point theorems, we discuss the control problem for a class of Hilfer fractional Langevin evolution equations. The exact controllability of Hilfer fractional Langevin systems is established. An example is also discussed to illustrate the results.","PeriodicalId":36662,"journal":{"name":"Frontiers in Applied Mathematics and Statistics","volume":" ","pages":""},"PeriodicalIF":1.4,"publicationDate":"2023-05-18","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"45316182","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2023-05-15DOI: 10.3389/fams.2023.1153666
O. Egbelowo, J. Munyakazi, P. Dlamini, F. Osaye, S. Simelane
The co-infection of visceral leishmaniasis (VL) and tuberculosis (TB) patients pose a major public health challenge. In this study, we develop a mathematical model to study the transmission dynamics of VL and TB co-infection by first analyzing the VL and TB sub-models separately. The dynamics of these sub-models and the full co-infection model are determined based on the reproduction number. When the associated reproduction number (R1) for the TB-only model and (R2) for the VL-only are less than unity, the model exhibits backward bifurcation. If max{R1,R2}=R1, then the TB-VL co-infection model exhibits backward bifurcation for values of R1. Furthermore, if max{R1,R2}=R2, and by choosing the transmission probability, βL as the bifurcation parameter, then the phenomenon of backward bifurcation occurs for values of R2. Consequently, the full model, whose associated reproduction number is R0, also exhibits backward bifurcation when R0=1. The equilibrium points and their stability for the models are determined and analyzed based on the magnitude of the respective reproduction numbers. Finally, some numerical simulations are presented to show the reliability of our theoretical results.
{"title":"Modeling visceral leishmaniasis and tuberculosis co-infection dynamics","authors":"O. Egbelowo, J. Munyakazi, P. Dlamini, F. Osaye, S. Simelane","doi":"10.3389/fams.2023.1153666","DOIUrl":"https://doi.org/10.3389/fams.2023.1153666","url":null,"abstract":"The co-infection of visceral leishmaniasis (VL) and tuberculosis (TB) patients pose a major public health challenge. In this study, we develop a mathematical model to study the transmission dynamics of VL and TB co-infection by first analyzing the VL and TB sub-models separately. The dynamics of these sub-models and the full co-infection model are determined based on the reproduction number. When the associated reproduction number (R1) for the TB-only model and (R2) for the VL-only are less than unity, the model exhibits backward bifurcation. If max{R1,R2}=R1, then the TB-VL co-infection model exhibits backward bifurcation for values of R1. Furthermore, if max{R1,R2}=R2, and by choosing the transmission probability, βL as the bifurcation parameter, then the phenomenon of backward bifurcation occurs for values of R2. Consequently, the full model, whose associated reproduction number is R0, also exhibits backward bifurcation when R0=1. The equilibrium points and their stability for the models are determined and analyzed based on the magnitude of the respective reproduction numbers. Finally, some numerical simulations are presented to show the reliability of our theoretical results.","PeriodicalId":36662,"journal":{"name":"Frontiers in Applied Mathematics and Statistics","volume":" ","pages":""},"PeriodicalIF":1.4,"publicationDate":"2023-05-15","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"42517867","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2023-05-12DOI: 10.3389/fams.2023.1162760
Maizan Syamimi Meor Yahaya, J. Teo
The fields of medicine and neuroscience often face challenges in obtaining a sufficient amount of diverse data for training machine learning models. Data augmentation can alleviate this issue by artificially synthesizing new data from existing data. Generative adversarial networks (GANs) provide a promising approach for data augmentation in the context of images and biomarkers. GANs can synthesize high-quality, diverse, and realistic data that can supplement real data in the training process. This study provides an overview of the use of GANs for data augmentation in medicine and neuroscience. The strengths and weaknesses of various GAN models, including deep convolutional GANs (DCGANs) and Wasserstein GANs (WGANs), are discussed. This study also explores the challenges and ways to address them when using GANs for data augmentation in the field of medicine and neuroscience. Future works on this topic are also discussed.
{"title":"Data augmentation using generative adversarial networks for images and biomarkers in medicine and neuroscience","authors":"Maizan Syamimi Meor Yahaya, J. Teo","doi":"10.3389/fams.2023.1162760","DOIUrl":"https://doi.org/10.3389/fams.2023.1162760","url":null,"abstract":"The fields of medicine and neuroscience often face challenges in obtaining a sufficient amount of diverse data for training machine learning models. Data augmentation can alleviate this issue by artificially synthesizing new data from existing data. Generative adversarial networks (GANs) provide a promising approach for data augmentation in the context of images and biomarkers. GANs can synthesize high-quality, diverse, and realistic data that can supplement real data in the training process. This study provides an overview of the use of GANs for data augmentation in medicine and neuroscience. The strengths and weaknesses of various GAN models, including deep convolutional GANs (DCGANs) and Wasserstein GANs (WGANs), are discussed. This study also explores the challenges and ways to address them when using GANs for data augmentation in the field of medicine and neuroscience. Future works on this topic are also discussed.","PeriodicalId":36662,"journal":{"name":"Frontiers in Applied Mathematics and Statistics","volume":" ","pages":""},"PeriodicalIF":1.4,"publicationDate":"2023-05-12","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"48210856","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2023-04-28DOI: 10.3389/fams.2023.1124602
Charlotte Geier, M. Stender, N. Hoffmann
Data-driven reduced order modeling methods that aim at extracting physically meaningful governing equations directly from measurement data are facing a growing interest in recent years. The HAVOK-algorithm is a Koopman-based method that distills a forced, low-dimensional state-space model for a given dynamical system from a univariate measurement time series. This article studies the potential of HAVOK for application to mechanical oscillators by investigating which information of the underlying system can be extracted from the state-space model generated by HAVOK. Extensive parameter studies are performed to point out the strengths and pitfalls of the algorithm and ultimately yield recommendations for choosing tuning parameters. The application of the algorithm to real-world friction brake system measurements concludes this study.
{"title":"Data-driven reduced order modeling for mechanical oscillators using Koopman approaches","authors":"Charlotte Geier, M. Stender, N. Hoffmann","doi":"10.3389/fams.2023.1124602","DOIUrl":"https://doi.org/10.3389/fams.2023.1124602","url":null,"abstract":"Data-driven reduced order modeling methods that aim at extracting physically meaningful governing equations directly from measurement data are facing a growing interest in recent years. The HAVOK-algorithm is a Koopman-based method that distills a forced, low-dimensional state-space model for a given dynamical system from a univariate measurement time series. This article studies the potential of HAVOK for application to mechanical oscillators by investigating which information of the underlying system can be extracted from the state-space model generated by HAVOK. Extensive parameter studies are performed to point out the strengths and pitfalls of the algorithm and ultimately yield recommendations for choosing tuning parameters. The application of the algorithm to real-world friction brake system measurements concludes this study.","PeriodicalId":36662,"journal":{"name":"Frontiers in Applied Mathematics and Statistics","volume":"085 1","pages":""},"PeriodicalIF":1.4,"publicationDate":"2023-04-28","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"91158496","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2023-04-27DOI: 10.3389/fams.2023.1156785
J. Hay, L. Schories, E. Bayerschen, P. Wimmer, Oliver Zehbe, S. Kirschbichler, J. Fehr
Surrogate models are a must-have in a scenario-based safety simulation framework to design optimally integrated safety systems for new mobility solutions. The objective of this study is the development of surrogate models for active human model responses under consideration of multiple sampling strategies. A Gaussian process regression is chosen for predicting injury values based on the collision scenario, the occupant's seating position after a pre-crash movement and selected restraint system parameters. The trained models are validated and assessed for each sampling method and the best-performing surrogate model is selected for restraint system parameter optimization.
{"title":"Application of data-driven surrogate models for active human model response prediction and restraint system optimization","authors":"J. Hay, L. Schories, E. Bayerschen, P. Wimmer, Oliver Zehbe, S. Kirschbichler, J. Fehr","doi":"10.3389/fams.2023.1156785","DOIUrl":"https://doi.org/10.3389/fams.2023.1156785","url":null,"abstract":"Surrogate models are a must-have in a scenario-based safety simulation framework to design optimally integrated safety systems for new mobility solutions. The objective of this study is the development of surrogate models for active human model responses under consideration of multiple sampling strategies. A Gaussian process regression is chosen for predicting injury values based on the collision scenario, the occupant's seating position after a pre-crash movement and selected restraint system parameters. The trained models are validated and assessed for each sampling method and the best-performing surrogate model is selected for restraint system parameter optimization.","PeriodicalId":36662,"journal":{"name":"Frontiers in Applied Mathematics and Statistics","volume":" ","pages":""},"PeriodicalIF":1.4,"publicationDate":"2023-04-27","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"48238662","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2023-04-26DOI: 10.3389/fams.2023.1094971
D. Aldila, Chita Aulia Puspadani, Rahmi Rusin
This study proposes a dengue spread model that considers the nonlinear transmission rate to address the level of human ignorance of dengue in their environment. The SIR − UV model has been proposed, where SIR denotes the classification of the human population and UV denotes the classification of the mosquito population. Assuming that the total human population is constant, and the mosquito population is already in its steady-state condition, using the Quasi-Steady State Approximation (QSSA) method, we reduce our SIR − UV model into a more simple IR-model. Our analytical result shows that a stable disease-free equilibrium exists when the basic reproduction number is <1. Furthermore, our model also shows the possibility of a backward bifurcation. The more ignorant the society is about dengue, the higher the possibility that backward bifurcation phenomena may appear. As a result, the condition of the basic reproduction number being <1 is insufficient to guarantee the extinction of dengue in a population. Furthermore, we found that increasing the recovery rate, reducing the waning immunity rate, and mosquito life expectancy can reduce the possibility of backward bifurcation phenomena. We use dengue incidence data from Jakarta to calibrate the parameters in our model. Through the fast Fourier transform analysis, it was found that dengue incidence in Jakarta has a periodicity of 52.4, 73.4, and 146.8 weeks. This result indicates that dengue will periodically appear at least every year in Jakarta. Parameter estimation for our model parameters was carried out by assuming the infection rate of humans as a sinusoidal function by determining the three most dominant frequencies. Numerical and sensitivity analyses were conducted to observe the impact of community ignorance on dengue endemicity. From the sensitivity analysis, we found that, although a larger community ignorance can trigger a backward bifurcation, this threshold can be minimized by increasing the recovery rate, prolonging the temporal immunity, or reducing the mosquito population. Therefore, to control dengue transmission more effectively, media campaigns undertaken by the government to reduce community ignorance should be accompanied by other interventions, such as a good treatment in the hospital or vector control programs. With this combination of interventions, it will be easier to achieve a condition of dengue-free population when the basic reproduction number is less than one.
{"title":"Mathematical analysis of the impact of community ignorance on the population dynamics of dengue","authors":"D. Aldila, Chita Aulia Puspadani, Rahmi Rusin","doi":"10.3389/fams.2023.1094971","DOIUrl":"https://doi.org/10.3389/fams.2023.1094971","url":null,"abstract":"This study proposes a dengue spread model that considers the nonlinear transmission rate to address the level of human ignorance of dengue in their environment. The SIR − UV model has been proposed, where SIR denotes the classification of the human population and UV denotes the classification of the mosquito population. Assuming that the total human population is constant, and the mosquito population is already in its steady-state condition, using the Quasi-Steady State Approximation (QSSA) method, we reduce our SIR − UV model into a more simple IR-model. Our analytical result shows that a stable disease-free equilibrium exists when the basic reproduction number is <1. Furthermore, our model also shows the possibility of a backward bifurcation. The more ignorant the society is about dengue, the higher the possibility that backward bifurcation phenomena may appear. As a result, the condition of the basic reproduction number being <1 is insufficient to guarantee the extinction of dengue in a population. Furthermore, we found that increasing the recovery rate, reducing the waning immunity rate, and mosquito life expectancy can reduce the possibility of backward bifurcation phenomena. We use dengue incidence data from Jakarta to calibrate the parameters in our model. Through the fast Fourier transform analysis, it was found that dengue incidence in Jakarta has a periodicity of 52.4, 73.4, and 146.8 weeks. This result indicates that dengue will periodically appear at least every year in Jakarta. Parameter estimation for our model parameters was carried out by assuming the infection rate of humans as a sinusoidal function by determining the three most dominant frequencies. Numerical and sensitivity analyses were conducted to observe the impact of community ignorance on dengue endemicity. From the sensitivity analysis, we found that, although a larger community ignorance can trigger a backward bifurcation, this threshold can be minimized by increasing the recovery rate, prolonging the temporal immunity, or reducing the mosquito population. Therefore, to control dengue transmission more effectively, media campaigns undertaken by the government to reduce community ignorance should be accompanied by other interventions, such as a good treatment in the hospital or vector control programs. With this combination of interventions, it will be easier to achieve a condition of dengue-free population when the basic reproduction number is less than one.","PeriodicalId":36662,"journal":{"name":"Frontiers in Applied Mathematics and Statistics","volume":" ","pages":""},"PeriodicalIF":1.4,"publicationDate":"2023-04-26","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"42448151","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2023-04-21DOI: 10.3389/fams.2023.1138663
Mauricio Contreras G., Roberto Ortiz H.
The authors proved three theorems about the exact solutions of a generalized or interacting Black–Scholes equation that explicitly includes arbitrage bubbles. These arbitrage bubbles can be characterized by an arbitrage number AN. The first theorem states that if AN = 0, then the solution at maturity of the interacting equation is identical to the solution of the free Black–Scholes equation with the same initial interest rate of r. The second theorem states that if AN ≠ 0, then the interacting solution can be expressed in terms of all higher derivatives of the solutions to the free Black–Scholes equation with an initial interest rate of r. The third theorem states that for a given arbitrage number, the interacting solution is a solution to the free Black–Scholes equation but with a variable interest rate of r(τ) = r + (1/τ)AN(τ), where τ = T − t.
{"title":"Three little arbitrage theorems","authors":"Mauricio Contreras G., Roberto Ortiz H.","doi":"10.3389/fams.2023.1138663","DOIUrl":"https://doi.org/10.3389/fams.2023.1138663","url":null,"abstract":"The authors proved three theorems about the exact solutions of a generalized or interacting Black–Scholes equation that explicitly includes arbitrage bubbles. These arbitrage bubbles can be characterized by an arbitrage number AN. The first theorem states that if AN = 0, then the solution at maturity of the interacting equation is identical to the solution of the free Black–Scholes equation with the same initial interest rate of r. The second theorem states that if AN ≠ 0, then the interacting solution can be expressed in terms of all higher derivatives of the solutions to the free Black–Scholes equation with an initial interest rate of r. The third theorem states that for a given arbitrage number, the interacting solution is a solution to the free Black–Scholes equation but with a variable interest rate of r(τ) = r + (1/τ)AN(τ), where τ = T − t.","PeriodicalId":36662,"journal":{"name":"Frontiers in Applied Mathematics and Statistics","volume":" ","pages":""},"PeriodicalIF":1.4,"publicationDate":"2023-04-21","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"46917930","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2023-04-17DOI: 10.3389/fams.2023.1045218
D. Devianto, Mutia Yollanda, M. Maiyastri, F. Yanuar
Introduction Time series models on financial data often have problems with the stationary assumption of variance on the residuals. It is well known as the heteroscedasticity effect. The heteroscedasticity is represented by a nonconstant value that varies over time. Methods The heteroscedasticity effect contained in the basic classical time series model of Autoregressive Integrated Moving Average (ARIMA) can adjust its residuals as the variance model by using Generalized Autoregressive Conditional Heteroscedasticity (GARCH). In improving the model accuracy and overcoming the heteroscedasticity problems, it is proposed a combination model of ARIMA and Feed-Forward Neural Network (FFNN), namely ARIMA-FFNN. The model is built by applying the soft computing method of FFNN to replace the variance model. This soft computing approach is one of the numerical methods that can not be only applied in the theoretical subject but also in the data processing. Results In this research, the accuracy of the time series model using the case study of the exchange rate United States dollar-Indonesia rupiah with a monthly period from January 2001 to May 2021 shows that the best accuracy of the possible models is the model of ARIMA-FFNN, which applies soft computing to obtain the optimal fitted parameters precisely. Discussion This result indicates that the ARIMA-FFNN model is better used to approach this exchange rate than the rest model of ARIMA-GARCH and ARIMA-GARCH-FFNN.
{"title":"The soft computing FFNN method for adjusting heteroscedasticity on the time series model of currency exchange rate","authors":"D. Devianto, Mutia Yollanda, M. Maiyastri, F. Yanuar","doi":"10.3389/fams.2023.1045218","DOIUrl":"https://doi.org/10.3389/fams.2023.1045218","url":null,"abstract":"Introduction Time series models on financial data often have problems with the stationary assumption of variance on the residuals. It is well known as the heteroscedasticity effect. The heteroscedasticity is represented by a nonconstant value that varies over time. Methods The heteroscedasticity effect contained in the basic classical time series model of Autoregressive Integrated Moving Average (ARIMA) can adjust its residuals as the variance model by using Generalized Autoregressive Conditional Heteroscedasticity (GARCH). In improving the model accuracy and overcoming the heteroscedasticity problems, it is proposed a combination model of ARIMA and Feed-Forward Neural Network (FFNN), namely ARIMA-FFNN. The model is built by applying the soft computing method of FFNN to replace the variance model. This soft computing approach is one of the numerical methods that can not be only applied in the theoretical subject but also in the data processing. Results In this research, the accuracy of the time series model using the case study of the exchange rate United States dollar-Indonesia rupiah with a monthly period from January 2001 to May 2021 shows that the best accuracy of the possible models is the model of ARIMA-FFNN, which applies soft computing to obtain the optimal fitted parameters precisely. Discussion This result indicates that the ARIMA-FFNN model is better used to approach this exchange rate than the rest model of ARIMA-GARCH and ARIMA-GARCH-FFNN.","PeriodicalId":36662,"journal":{"name":"Frontiers in Applied Mathematics and Statistics","volume":" ","pages":""},"PeriodicalIF":1.4,"publicationDate":"2023-04-17","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"45379488","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2023-04-17DOI: 10.3389/fams.2023.961158
Abdou Khadre Dit Jadir Fall
This article aimed to study the choice that people have to make between two health insurance systems in a monopolistic scheme. The first health insurance system proposes a uniform contribution level and the second one proposes a contribution level that is proportional to the probability of getting sick. The individuals differ (or are distinguished) by their number in a group, the net income, the contribution level, the probability of getting sick, and health cost. Two kinds of voting models using the welfare function are used; a direct vote that involves a size effect and a probabilistic vote that involves a bias in favor of one system. The results, according to theoretical models, indicate that a uniform contribution level is adopted by high-risk individuals and also if wealth and illness are strongly negatively correlated. However, when wealth and illness are not correlated or are poorly correlated, a contribution proportional to the probability of getting sick is adopted. These results were explained by the fact that the loss of wellbeing for low-income and sick people is more important.
{"title":"Modeling the political choice of public health insurance","authors":"Abdou Khadre Dit Jadir Fall","doi":"10.3389/fams.2023.961158","DOIUrl":"https://doi.org/10.3389/fams.2023.961158","url":null,"abstract":"This article aimed to study the choice that people have to make between two health insurance systems in a monopolistic scheme. The first health insurance system proposes a uniform contribution level and the second one proposes a contribution level that is proportional to the probability of getting sick. The individuals differ (or are distinguished) by their number in a group, the net income, the contribution level, the probability of getting sick, and health cost. Two kinds of voting models using the welfare function are used; a direct vote that involves a size effect and a probabilistic vote that involves a bias in favor of one system. The results, according to theoretical models, indicate that a uniform contribution level is adopted by high-risk individuals and also if wealth and illness are strongly negatively correlated. However, when wealth and illness are not correlated or are poorly correlated, a contribution proportional to the probability of getting sick is adopted. These results were explained by the fact that the loss of wellbeing for low-income and sick people is more important.","PeriodicalId":36662,"journal":{"name":"Frontiers in Applied Mathematics and Statistics","volume":" ","pages":""},"PeriodicalIF":1.4,"publicationDate":"2023-04-17","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"43415342","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2023-04-11DOI: 10.3389/fams.2023.1206017
Alex Van'o-Vinuales
Gravitational radiation and some global properties of spacetimes can only be unambiguously measured at future null infinity (ℐ+). This motivates the interest in reaching it within simulations of coalescing compact objects, whose waveforms are extracted for gravitational wave modeling purposes. One promising method to include future null infinity in the numerical domain is the evolution on hyperboloidal slices: smooth spacelike slices that reach future null infinity. The main challenge in this approach is the treatment of the compactified asymptotic region at ℐ+. Evolution on a hyperboloidal slice of a spacetime including a black hole entails an extra layer of difficulty in part due to the finite coordinate distance between the black hole and future null infinity. Spherical symmetry is considered here as the simplest setup still encompassing the full complication of the treatment along the radial coordinate. First, the construction of constant-mean-curvature hyperboloidal trumpet slices for Schwarzschild and Reissner-Nordström black hole spacetimes is reviewed from the point of view of the puncture approach. Then, the framework is set for solving hyperboloidal-adapted hyperbolic gauge conditions for stationary trumpet initial data, providing solutions for two specific sets of parameters. Finally, results of testing these initial data in evolution are presented.
{"title":"Spherically symmetric black hole spacetimes on hyperboloidal slices","authors":"Alex Van'o-Vinuales","doi":"10.3389/fams.2023.1206017","DOIUrl":"https://doi.org/10.3389/fams.2023.1206017","url":null,"abstract":"Gravitational radiation and some global properties of spacetimes can only be unambiguously measured at future null infinity (ℐ+). This motivates the interest in reaching it within simulations of coalescing compact objects, whose waveforms are extracted for gravitational wave modeling purposes. One promising method to include future null infinity in the numerical domain is the evolution on hyperboloidal slices: smooth spacelike slices that reach future null infinity. The main challenge in this approach is the treatment of the compactified asymptotic region at ℐ+. Evolution on a hyperboloidal slice of a spacetime including a black hole entails an extra layer of difficulty in part due to the finite coordinate distance between the black hole and future null infinity. Spherical symmetry is considered here as the simplest setup still encompassing the full complication of the treatment along the radial coordinate. First, the construction of constant-mean-curvature hyperboloidal trumpet slices for Schwarzschild and Reissner-Nordström black hole spacetimes is reviewed from the point of view of the puncture approach. Then, the framework is set for solving hyperboloidal-adapted hyperbolic gauge conditions for stationary trumpet initial data, providing solutions for two specific sets of parameters. Finally, results of testing these initial data in evolution are presented.","PeriodicalId":36662,"journal":{"name":"Frontiers in Applied Mathematics and Statistics","volume":" ","pages":""},"PeriodicalIF":1.4,"publicationDate":"2023-04-11","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"42905789","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
京公网安备 11010802042870号
京ICP备2023020795号-1
扫码关注我们
求助内容：
应助结果提醒方式：