Pub Date : 2023-01-01DOI: 10.4236/jamp.2023.1110189
Peng Sun, Fuming Lin
Air pollution control has always been a global challenge, and significant progress has been made in recent years in controlling air pollutants. However, in some major cities, air pollutant concentrations still exceed the standards. Some scholars have used linear models or conditional autoregressive iterative models to apply the VaR method to predict pollutant concentrations. However, traditional methods based on quantile regression estimation can lead to inadequate risk estimates. Therefore, we propose a method based on the Conditional Autoregressive Value at Risk (CAViaR) model, which uses the kth power expectile regression to estimate VaR. This method does not specify the type of the distribution of data, is easier to calculate the asymptotic variance, more sensitive to extreme values. Applying our method to the data of PM10 in Beijing, we investigate the fitting effects in the case of k = 1, k = 2, and k = 1.9 through predictive tests. The results show that the kth power expectile regression estimates are better than quantile and expectile regression estimates to some extent.
{"title":"Air Quality Risk Measurement Based on CAViaR Model: A Case Study of PM10 in Beijing","authors":"Peng Sun, Fuming Lin","doi":"10.4236/jamp.2023.1110189","DOIUrl":"https://doi.org/10.4236/jamp.2023.1110189","url":null,"abstract":"Air pollution control has always been a global challenge, and significant progress has been made in recent years in controlling air pollutants. However, in some major cities, air pollutant concentrations still exceed the standards. Some scholars have used linear models or conditional autoregressive iterative models to apply the VaR method to predict pollutant concentrations. However, traditional methods based on quantile regression estimation can lead to inadequate risk estimates. Therefore, we propose a method based on the Conditional Autoregressive Value at Risk (CAViaR) model, which uses the kth power expectile regression to estimate VaR. This method does not specify the type of the distribution of data, is easier to calculate the asymptotic variance, more sensitive to extreme values. Applying our method to the data of PM10 in Beijing, we investigate the fitting effects in the case of k = 1, k = 2, and k = 1.9 through predictive tests. The results show that the kth power expectile regression estimates are better than quantile and expectile regression estimates to some extent.","PeriodicalId":15035,"journal":{"name":"Journal of Applied Mathematics and Physics","volume":"32 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2023-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"135053805","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 : 2023-01-01DOI: 10.4236/jamp.2023.1110196
Guoguang Lin, Keshun Peng
In this paper, we study the long time behavior of a class of generalized Beam-Kirchhoff equation , and prove the existence and uniqueness of the global solution of this class of equation by Galerkin method by making some assumptions about the nonlinear function term . The existence of the family of global attractor and its Hausdorff dimension and Fractal dimension estimation are proved.
{"title":"Long Time Behavior of a Class of Generalized Beam-Kirchhoff Equations","authors":"Guoguang Lin, Keshun Peng","doi":"10.4236/jamp.2023.1110196","DOIUrl":"https://doi.org/10.4236/jamp.2023.1110196","url":null,"abstract":"In this paper, we study the long time behavior of a class of generalized Beam-Kirchhoff equation , and prove the existence and uniqueness of the global solution of this class of equation by Galerkin method by making some assumptions about the nonlinear function term . The existence of the family of global attractor and its Hausdorff dimension and Fractal dimension estimation are proved.","PeriodicalId":15035,"journal":{"name":"Journal of Applied Mathematics and Physics","volume":"26 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2023-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"135157353","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 : 2023-01-01DOI: 10.4236/jamp.2023.1111213
Aman Chawla, Salvatore Domenic Morgera
{"title":"A Study of Compound Action Potentials in Current-Coupled Tracts: the General Case","authors":"Aman Chawla, Salvatore Domenic Morgera","doi":"10.4236/jamp.2023.1111213","DOIUrl":"https://doi.org/10.4236/jamp.2023.1111213","url":null,"abstract":"","PeriodicalId":15035,"journal":{"name":"Journal of Applied Mathematics and Physics","volume":"12 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2023-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"135448162","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 : 2023-01-01DOI: 10.4236/jamp.2023.119178
Frank Blume
We expand previously established results concerning the uniform representability of classical and relativistic gravitational field equations by means of velocity-field divergence equations by demonstrating that conservation equations for (probability) density functions give rise to velocity-field divergence equations the solutions of which generate—by way of superposition—the totality of solutions of various well-known classical and quantum-mechanical wave equations.
{"title":"How Classical, Quantum-Mechanical, and Relativistic Wave and Field Equations Are Uniformly Generated by Velocity-Field Divergence Equations","authors":"Frank Blume","doi":"10.4236/jamp.2023.119178","DOIUrl":"https://doi.org/10.4236/jamp.2023.119178","url":null,"abstract":"We expand previously established results concerning the uniform representability of classical and relativistic gravitational field equations by means of velocity-field divergence equations by demonstrating that conservation equations for (probability) density functions give rise to velocity-field divergence equations the solutions of which generate—by way of superposition—the totality of solutions of various well-known classical and quantum-mechanical wave equations.","PeriodicalId":15035,"journal":{"name":"Journal of Applied Mathematics and Physics","volume":"39 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2023-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"135798366","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 : 2023-01-01DOI: 10.4236/jamp.2023.119177
Steven D. P. Moore
The theory of relativity links space and time to account for observed events in four-dimensional space. In this article we describe an alternative static state causal discrete time modeling system using an omniscient viewpoint of dynamical systems that can express object relations in the moment(s) they are observed. To do this, three key components are required, including the introduction of independent object-relative dimensional metrics, a zero-dimensional frame of reference, and application of Euclidean geometry for modeling. Procedures separate planes of matter, extensions of space (relational distance) and time (duration) using object-oriented dimensional quantities. Quantities are converted into base units using symmetry for space (Dihedral360), time (Dihedral12), rotation (Dihedral24), and scale (Dihedral10). Geometric elements construct static state outputs in discrete time models rather than continuous time using calculus, thereby using dimensional and positional natural number numerals that can visually encode complex data instead of using abstraction and irrationals. Static state Euclidean geometric models of object relations are both measured and expressed in the state they are observed in zero-time as defined by a signal. The frame can include multiple observer frames of reference where each origin, point, is the location of a distinct privileged point of reference. Two broad and diverse applications are presented: a one-dimensional spatiotemporal orbital model, and a thought experiment related to a physical theory beyond Planck limits. We suggest that expanding methodologies and continued formalization, novel tools for physics can be considered along with applications for computational discrete geometric modeling.
{"title":"Separating Space and Time for Dimensional Analysis and Euclidean Relational Modeling","authors":"Steven D. P. Moore","doi":"10.4236/jamp.2023.119177","DOIUrl":"https://doi.org/10.4236/jamp.2023.119177","url":null,"abstract":"The theory of relativity links space and time to account for observed events in four-dimensional space. In this article we describe an alternative static state causal discrete time modeling system using an omniscient viewpoint of dynamical systems that can express object relations in the moment(s) they are observed. To do this, three key components are required, including the introduction of independent object-relative dimensional metrics, a zero-dimensional frame of reference, and application of Euclidean geometry for modeling. Procedures separate planes of matter, extensions of space (relational distance) and time (duration) using object-oriented dimensional quantities. Quantities are converted into base units using symmetry for space (Dihedral360), time (Dihedral12), rotation (Dihedral24), and scale (Dihedral10). Geometric elements construct static state outputs in discrete time models rather than continuous time using calculus, thereby using dimensional and positional natural number numerals that can visually encode complex data instead of using abstraction and irrationals. Static state Euclidean geometric models of object relations are both measured and expressed in the state they are observed in zero-time as defined by a signal. The frame can include multiple observer frames of reference where each origin, point, is the location of a distinct privileged point of reference. Two broad and diverse applications are presented: a one-dimensional spatiotemporal orbital model, and a thought experiment related to a physical theory beyond Planck limits. We suggest that expanding methodologies and continued formalization, novel tools for physics can be considered along with applications for computational discrete geometric modeling.","PeriodicalId":15035,"journal":{"name":"Journal of Applied Mathematics and Physics","volume":"65 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2023-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"135800061","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 : 2023-01-01DOI: 10.4236/jamp.2023.118144
Haoyu Zhao
In this paper, we study the long-time behavior of solutions of the single-layer quasi-geostrophic model arising from geophysical fluid dynamics. We obtain the lower bound of the decay estimate of the solution. Utilizing the Fourier splitting method, under suitable assumptions on the initial data, for any multi-index α, we show that the solution Ψ satisfies
{"title":"Lower Bounds of Decay Rates for Solution to the Single-Layer Quasi-Geostrophic Model","authors":"Haoyu Zhao","doi":"10.4236/jamp.2023.118144","DOIUrl":"https://doi.org/10.4236/jamp.2023.118144","url":null,"abstract":"In this paper, we study the long-time behavior of solutions of the single-layer quasi-geostrophic model arising from geophysical fluid dynamics. We obtain the lower bound of the decay estimate of the solution. Utilizing the Fourier splitting method, under suitable assumptions on the initial data, for any multi-index α, we show that the solution Ψ satisfies","PeriodicalId":15035,"journal":{"name":"Journal of Applied Mathematics and Physics","volume":"139 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2023-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"136078756","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 : 2023-01-01DOI: 10.4236/jamp.2023.118145
Fagueye Ndiaye, Mouhamadou Ngom, Diaraf Seck
In this paper, we provide an explicit expression for the full Dirichlet-to-Neumann map corresponding to a radial potential for a hyperbolic differential equation in 3-dimensional. We show that the Dirichlet-Neumann operators corresponding to a potential radial have the same properties for hyperbolic differential equations as for elliptic differential equations. We numerically implement the coefficients of the explicit formulas. Moreover, a Lipschitz type stability is established near the edge of the domain by an estimation constant. That is necessary for the reconstruction of the potential from Dirichlet-to-Neumann map in the inverse problem for a hyperbolic differential equation.
{"title":"Dirichlet-to-Neumann Map for a Hyperbolic Equation","authors":"Fagueye Ndiaye, Mouhamadou Ngom, Diaraf Seck","doi":"10.4236/jamp.2023.118145","DOIUrl":"https://doi.org/10.4236/jamp.2023.118145","url":null,"abstract":"In this paper, we provide an explicit expression for the full Dirichlet-to-Neumann map corresponding to a radial potential for a hyperbolic differential equation in 3-dimensional. We show that the Dirichlet-Neumann operators corresponding to a potential radial have the same properties for hyperbolic differential equations as for elliptic differential equations. We numerically implement the coefficients of the explicit formulas. Moreover, a Lipschitz type stability is established near the edge of the domain by an estimation constant. That is necessary for the reconstruction of the potential from Dirichlet-to-Neumann map in the inverse problem for a hyperbolic differential equation.","PeriodicalId":15035,"journal":{"name":"Journal of Applied Mathematics and Physics","volume":"113 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2023-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"136078761","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 : 2023-01-01DOI: 10.4236/jamp.2023.1110200
Jinqing Zhang, Xintong Zhang
The aim of this paper is to study the 3x + 1 problem based on the Collatz iterative formula. It can be seen from the iterative formula that the necessary condition for the Collatz iteration convergence is that its slope being less than 1. An odd number N that satisfies the condition of a slope less than 1 after nth Collatz iterations is defined as an n-step odd number. Through statistical analysis, it is found that after nth Collatz iterations, the iterative value of any n-step odd number N that is greater than 1 is less than N, which proves that the slope less than 1 is a sufficient and necessary condition for Collatz iteration convergence.
{"title":"Collatz Iterative Trajectories of All Odd Numbers Attain Bounded Values","authors":"Jinqing Zhang, Xintong Zhang","doi":"10.4236/jamp.2023.1110200","DOIUrl":"https://doi.org/10.4236/jamp.2023.1110200","url":null,"abstract":"The aim of this paper is to study the 3x + 1 problem based on the Collatz iterative formula. It can be seen from the iterative formula that the necessary condition for the Collatz iteration convergence is that its slope being less than 1. An odd number N that satisfies the condition of a slope less than 1 after nth Collatz iterations is defined as an n-step odd number. Through statistical analysis, it is found that after nth Collatz iterations, the iterative value of any n-step odd number N that is greater than 1 is less than N, which proves that the slope less than 1 is a sufficient and necessary condition for Collatz iteration convergence.","PeriodicalId":15035,"journal":{"name":"Journal of Applied Mathematics and Physics","volume":"6 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2023-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"135210965","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 : 2023-01-01DOI: 10.4236/jamp.2023.118153
Bo Peng
European compound option pricing model is established by using the mixed bifractional Brownian motion. Firstly, using the principle of risk-neutral pricing, the European option pricing formulas and the parity formulas are obtained. Secondly, with the Delta hedging strategy, the corresponding compound option pricing formulas and the parity formulas are got. Finally, using the daily closing price data of “Lingang B shares” and “Yitai B shares” respectively, the results show that the mixed model is closer to the true value than the previous model.
{"title":"Asset Pricing and Simulation Analysis Based on the New Mixture Gaussian Processes","authors":"Bo Peng","doi":"10.4236/jamp.2023.118153","DOIUrl":"https://doi.org/10.4236/jamp.2023.118153","url":null,"abstract":"European compound option pricing model is established by using the mixed bifractional Brownian motion. Firstly, using the principle of risk-neutral pricing, the European option pricing formulas and the parity formulas are obtained. Secondly, with the Delta hedging strategy, the corresponding compound option pricing formulas and the parity formulas are got. Finally, using the daily closing price data of “Lingang B shares” and “Yitai B shares” respectively, the results show that the mixed model is closer to the true value than the previous model.","PeriodicalId":15035,"journal":{"name":"Journal of Applied Mathematics and Physics","volume":"11 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2023-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"136256649","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 : 2023-01-01DOI: 10.4236/jamp.2023.119180
Ziye Zhang
Chiral nanostructures have attracted much attention due to the valuable applications in biochemistry, medicine industries, and photonic devices. In this study, we propose an ease-of-fabrication planar nanostructure that consists of rectangular nanohole arrays in which the Z-shaped nanorod is arranged. Theoretically, such chiral nanostructure supports significant absorption circular dichroism (CD) compared with the Z-shaped nanorod because charge distributions are tuned after the introduction of the rectangular frame. Meanwhile, the Z-shaped nanorod directs the flow of current on the rectangular frame, thereby generating the effective quadruple electron oscillation in the Z-shaped nanorod. A novel mode also emerges when an identical Z-shaped nanorod is added into the rectangular hole. The studies will provide a novel approach to enhance the CD effect of planar structures.
{"title":"Enhanced Circular Dichroism of Z-Shaped Nanorod in Rectangular Nanohole Arrays","authors":"Ziye Zhang","doi":"10.4236/jamp.2023.119180","DOIUrl":"https://doi.org/10.4236/jamp.2023.119180","url":null,"abstract":"Chiral nanostructures have attracted much attention due to the valuable applications in biochemistry, medicine industries, and photonic devices. In this study, we propose an ease-of-fabrication planar nanostructure that consists of rectangular nanohole arrays in which the Z-shaped nanorod is arranged. Theoretically, such chiral nanostructure supports significant absorption circular dichroism (CD) compared with the Z-shaped nanorod because charge distributions are tuned after the introduction of the rectangular frame. Meanwhile, the Z-shaped nanorod directs the flow of current on the rectangular frame, thereby generating the effective quadruple electron oscillation in the Z-shaped nanorod. A novel mode also emerges when an identical Z-shaped nanorod is added into the rectangular hole. The studies will provide a novel approach to enhance the CD effect of planar structures.","PeriodicalId":15035,"journal":{"name":"Journal of Applied Mathematics and Physics","volume":"115 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2023-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"135838154","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}
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