The irreducible representations of the extended Galilean group are used to derive the symmetric and asymmetric wave equations. It is shown that among these equations only a new asymmetric wave equation is fundamental. By being fundamental the equation gives the most complete description of propagating waves as it accounts for the Doppler effect, forward and backward waves, and makes the wave speed to be the same in all inertial frames. To demonstrate these properties, the equation is applied to acoustic wave propagation in an isothermal atmosphere, and to determine Lamb’s cutoff frequency.
{"title":"A New Fundamental Asymmetric Wave Equation and Its Application to Acoustic Wave Propagation","authors":"Z. Musielak","doi":"10.1155/2023/5736419","DOIUrl":"https://doi.org/10.1155/2023/5736419","url":null,"abstract":"The irreducible representations of the extended Galilean group are used to derive the symmetric and asymmetric wave equations. It is shown that among these equations only a new asymmetric wave equation is fundamental. By being fundamental the equation gives the most complete description of propagating waves as it accounts for the Doppler effect, forward and backward waves, and makes the wave speed to be the same in all inertial frames. To demonstrate these properties, the equation is applied to acoustic wave propagation in an isothermal atmosphere, and to determine Lamb’s cutoff frequency.","PeriodicalId":49111,"journal":{"name":"Advances in Mathematical Physics","volume":" ","pages":""},"PeriodicalIF":1.2,"publicationDate":"2022-11-04","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"45860714","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"物理与天体物理","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
The effects of thermal conductivity which depend on temperature are conversely proportional with the linear function of temperature on free convective flow where the fluid is viscous and incompressible along a heated uniform and the vertical wavy surface has been examined in this study. The boundary layer equations with the associated boundary conditions that govern the flow are converted into a nondimensional form by using an appropriate transformation. In the domain of a vertical plate that is flat, the resulting method of nonlinear PDEs is mapped and then worked out numerically by applying the implicit central finite difference technique with Newton’s quasilinearization method, and the block Thomas algorithm is well known as the Keller-box method. The outputs are obtained in the terms of the heat transferring rate, the frictional coefficient of skin, the isotherms, and streamlines. The outcomes showed that the local heat transferring rate, the local skin friction coefficient, the temperature, and the velocity all are decreasing, and both the thermal layer of boundary and velocity become narrower with the rising values of reciprocal variation of temperature-dependent thermal conductivity. On the other hand, the friction coefficient of skin, the velocity, and the temperature decrease where the friction coefficient of skin and velocity decrease by 43% and 64%, respectively, but the heat transfer rate increases by 61% approximately, and both the boundary layer thermal and velocity become thinner when the Prandtl number increases.
{"title":"Analysis of Reciprocal Thermal Conductivity on Free Convection Flow along a Wavy Vertical Surface","authors":"T. Saha, N. Parveen, T. Islam","doi":"10.1155/2022/6389275","DOIUrl":"https://doi.org/10.1155/2022/6389275","url":null,"abstract":"The effects of thermal conductivity which depend on temperature are conversely proportional with the linear function of temperature on free convective flow where the fluid is viscous and incompressible along a heated uniform and the vertical wavy surface has been examined in this study. The boundary layer equations with the associated boundary conditions that govern the flow are converted into a nondimensional form by using an appropriate transformation. In the domain of a vertical plate that is flat, the resulting method of nonlinear PDEs is mapped and then worked out numerically by applying the implicit central finite difference technique with Newton’s quasilinearization method, and the block Thomas algorithm is well known as the Keller-box method. The outputs are obtained in the terms of the heat transferring rate, the frictional coefficient of skin, the isotherms, and streamlines. The outcomes showed that the local heat transferring rate, the local skin friction coefficient, the temperature, and the velocity all are decreasing, and both the thermal layer of boundary and velocity become narrower with the rising values of reciprocal variation of temperature-dependent thermal conductivity. On the other hand, the friction coefficient of skin, the velocity, and the temperature decrease where the friction coefficient of skin and velocity decrease by 43% and 64%, respectively, but the heat transfer rate increases by 61% approximately, and both the boundary layer thermal and velocity become thinner when the Prandtl number increases.","PeriodicalId":49111,"journal":{"name":"Advances in Mathematical Physics","volume":" ","pages":""},"PeriodicalIF":1.2,"publicationDate":"2022-11-02","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"42771492","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"物理与天体物理","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
In this paper, Lie symmetries of time-fractional KdV-Like equation with Riemann-Liouville derivative are performed. With the aid of infinitesimal symmetries, the vector fields and symmetry reductions of the equation are constructed, respectively; as a result, the invariant solutions are acquired in one case; we show that the KdV-like equation can be reduced to a fractional ordinary differential equation (FODE) which is connected with the Erdélyi-Kober functional derivative; for this kind of reduced form, we use the power series method for extracting the explicit solutions in the form of power series solution. Finally, Ibragimov’s theorem has been employed to construct the conservation laws.
{"title":"Symmetry Analysis, Invariant Solutions, and Conservation Laws of Fractional KdV-Like Equation","authors":"Maria Ihsane El Bahi, K. Hilal","doi":"10.1155/2022/5825938","DOIUrl":"https://doi.org/10.1155/2022/5825938","url":null,"abstract":"In this paper, Lie symmetries of time-fractional KdV-Like equation with Riemann-Liouville derivative are performed. With the aid of infinitesimal symmetries, the vector fields and symmetry reductions of the equation are constructed, respectively; as a result, the invariant solutions are acquired in one case; we show that the KdV-like equation can be reduced to a fractional ordinary differential equation (FODE) which is connected with the Erdélyi-Kober functional derivative; for this kind of reduced form, we use the power series method for extracting the explicit solutions in the form of power series solution. Finally, Ibragimov’s theorem has been employed to construct the conservation laws.","PeriodicalId":49111,"journal":{"name":"Advances in Mathematical Physics","volume":" ","pages":""},"PeriodicalIF":1.2,"publicationDate":"2022-10-28","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"41753718","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"物理与天体物理","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
In this paper, we study the stationary compressible nonisothermal nematic liquid crystal flows affected by the external force of general form in three-dimensional space. By using the contraction mapping principle, we prove the existence and uniqueness of strong solution around the constant state in some suitable function space.
{"title":"Stationary Solutions to the Three-Dimensional Compressible Nonisothermal Nematic Liquid Crystal Flows","authors":"Wanchen Cui, H. Cai","doi":"10.1155/2022/4695308","DOIUrl":"https://doi.org/10.1155/2022/4695308","url":null,"abstract":"In this paper, we study the stationary compressible nonisothermal nematic liquid crystal flows affected by the external force of general form in three-dimensional space. By using the contraction mapping principle, we prove the existence and uniqueness of strong solution around the constant state in some suitable function space.","PeriodicalId":49111,"journal":{"name":"Advances in Mathematical Physics","volume":" ","pages":""},"PeriodicalIF":1.2,"publicationDate":"2022-10-27","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"43584793","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"物理与天体物理","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
In this study, an efficient analytical method called the Sumudu Iterative Method (SIM) is introduced to obtain the solutions for the nonlinear delay differential equation (NDDE). This technique is a mixture of the Sumudu transform method and the new iterative method. The Sumudu transform method is used in this approach to solve the equation’s linear portion, and the new iterative method’s successive iterative producers are used to solve the equation’s nonlinear portion. Some basic properties and theorems which help us to solve the governing problem using the suggested approach are revised. The benefit of this approach is that it solves the equations directly and reliably, without the prerequisite for perturbations or linearization or extensive computer labor. Five sample instances from the DDEs are given to confirm the method’s reliability and effectiveness, and the outcomes are compared with the exact solution with the assistance of tables and graphs after taking the sum of the first eight iterations of the approximate solution. Furthermore, the findings indicate that the recommended strategy is encouraging for solving other types of nonlinear delay differential equations.
{"title":"Approximate Analytical Solution to Nonlinear Delay Differential Equations by Using Sumudu Iterative Method","authors":"Asfaw Tsegaye Moltot, Alemayehu Tamirie Deresse","doi":"10.1155/2022/2466367","DOIUrl":"https://doi.org/10.1155/2022/2466367","url":null,"abstract":"In this study, an efficient analytical method called the Sumudu Iterative Method (SIM) is introduced to obtain the solutions for the nonlinear delay differential equation (NDDE). This technique is a mixture of the Sumudu transform method and the new iterative method. The Sumudu transform method is used in this approach to solve the equation’s linear portion, and the new iterative method’s successive iterative producers are used to solve the equation’s nonlinear portion. Some basic properties and theorems which help us to solve the governing problem using the suggested approach are revised. The benefit of this approach is that it solves the equations directly and reliably, without the prerequisite for perturbations or linearization or extensive computer labor. Five sample instances from the DDEs are given to confirm the method’s reliability and effectiveness, and the outcomes are compared with the exact solution with the assistance of tables and graphs after taking the sum of the first eight iterations of the approximate solution. Furthermore, the findings indicate that the recommended strategy is encouraging for solving other types of nonlinear delay differential equations.","PeriodicalId":49111,"journal":{"name":"Advances in Mathematical Physics","volume":" ","pages":""},"PeriodicalIF":1.2,"publicationDate":"2022-10-19","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"41364000","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"物理与天体物理","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
City image reflects a city’s comprehensive competitiveness and is also an important indicator of a city’s spiritual civilization and urbanization process. A good city image is an intangible asset of a city, which can contribute to the political, economic, cultural, and social construction of a city and create more value for the city. This paper mainly discusses the research status and research methods of urban image at home and abroad. Based on the calculation method of wedge diffraction in geometrical optics, various heuristic uniform diffraction formulas of lossy wedge are compared and analyzed, and a better heuristic formula of uniform diffraction of lossy wedge is given. Finally, the selection of important channel parameters in the propagation channel is discussed, and a method for predicting the statistical parameters of the propagation channel of urban images based on the results of ray tracing is proposed. Then, the channel parameters are analyzed by using statistical parameters, and the channel parameters of the city image propagation model are analyzed.
{"title":"Analysis of the Relationship of Video Text and Urban Image Communication Based on the Calculation Method of Wedge Diffraction in Geometrical Optics","authors":"Qigan Sun","doi":"10.1155/2022/1528663","DOIUrl":"https://doi.org/10.1155/2022/1528663","url":null,"abstract":"City image reflects a city’s comprehensive competitiveness and is also an important indicator of a city’s spiritual civilization and urbanization process. A good city image is an intangible asset of a city, which can contribute to the political, economic, cultural, and social construction of a city and create more value for the city. This paper mainly discusses the research status and research methods of urban image at home and abroad. Based on the calculation method of wedge diffraction in geometrical optics, various heuristic uniform diffraction formulas of lossy wedge are compared and analyzed, and a better heuristic formula of uniform diffraction of lossy wedge is given. Finally, the selection of important channel parameters in the propagation channel is discussed, and a method for predicting the statistical parameters of the propagation channel of urban images based on the results of ray tracing is proposed. Then, the channel parameters are analyzed by using statistical parameters, and the channel parameters of the city image propagation model are analyzed.","PeriodicalId":49111,"journal":{"name":"Advances in Mathematical Physics","volume":" ","pages":""},"PeriodicalIF":1.2,"publicationDate":"2022-10-15","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"46927431","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"物理与天体物理","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Jayshree Patil, B. Hardan, Ahmed A. Hamoud, A. Bachhav, H. Emadifar, H. Günerhan
{"title":"Corrigendum to “Generalization Contractive Mappings on Rectangular b-Metric Space”","authors":"Jayshree Patil, B. Hardan, Ahmed A. Hamoud, A. Bachhav, H. Emadifar, H. Günerhan","doi":"10.1155/2022/9761017","DOIUrl":"https://doi.org/10.1155/2022/9761017","url":null,"abstract":"<jats:p />","PeriodicalId":49111,"journal":{"name":"Advances in Mathematical Physics","volume":" ","pages":""},"PeriodicalIF":1.2,"publicationDate":"2022-10-14","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"43848709","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"物理与天体物理","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Chickenpox or varicella is an infectious disease caused by the varicella-zoster virus V Z V . This virus is the cause of chickenpox (usually a primary infection in the nonimmune host) and herpes zoster. In this paper, a compartmental model for the dynamics of V Z transmission with the effect of vaccination is solved using the A B C fractional derivative. The possibility of using the fractal dimension as a biomarker to identify different diseases is being investigated. The problem is investigated in two different levels of research using two scale dimensions. To ascertain the existence and uniqueness of the solution, we qualitatively evaluate the model. We have used the Euler method to compute the numerical solution for the system. At the end, we provide the graphical results showing the effectiveness of two-scale dimension and fractional calculus in the current model.
水痘是由水痘-带状疱疹病毒V Z V引起的一种传染病。这种病毒是水痘（通常是非免疫宿主的原发性感染）和带状疱疹的病因。在本文中，使用a B C分数导数求解了具有疫苗接种效应的V Z传播动力学的房室模型。目前正在研究使用分形维数作为生物标志物来识别不同疾病的可能性。该问题在两个不同层次的研究中使用两个尺度维度进行了调查。为了确定解的存在性和唯一性，我们对模型进行了定性评估。我们已经使用欧拉方法来计算该系统的数值解。最后，我们提供了图形结果，显示了在当前模型中二维和分数演算的有效性。
{"title":"<math xmlns=\"http://www.w3.org/1998/Math/MathML\" id=\"M1\">\u0000 <mi mathvariant=\"script\">A</mi>\u0000 <mi mathvariant=\"script\">B</mi>\u0000 <mi mathvariant=\"script\">C</mi>\u0000 </math> Fractional Derivative for Varicella-Zoster Virus Using Tw","authors":"Jirong Yang, F. Afzal, Perpetual Appiah","doi":"10.1155/2022/1725110","DOIUrl":"https://doi.org/10.1155/2022/1725110","url":null,"abstract":"Chickenpox or varicella is an infectious disease caused by the varicella-zoster virus \u0000 \u0000 \u0000 \u0000 V\u0000 Z\u0000 V\u0000 \u0000 \u0000 \u0000 . This virus is the cause of chickenpox (usually a primary infection in the nonimmune host) and herpes zoster. In this paper, a compartmental model for the dynamics of \u0000 \u0000 V\u0000 Z\u0000 \u0000 transmission with the effect of vaccination is solved using the \u0000 \u0000 A\u0000 B\u0000 C\u0000 \u0000 fractional derivative. The possibility of using the fractal dimension as a biomarker to identify different diseases is being investigated. The problem is investigated in two different levels of research using two scale dimensions. To ascertain the existence and uniqueness of the solution, we qualitatively evaluate the model. We have used the Euler method to compute the numerical solution for the system. At the end, we provide the graphical results showing the effectiveness of two-scale dimension and fractional calculus in the current model.","PeriodicalId":49111,"journal":{"name":"Advances in Mathematical Physics","volume":" ","pages":""},"PeriodicalIF":1.2,"publicationDate":"2022-10-14","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"45830090","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"物理与天体物理","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
3D modeling is the most basic technology to realize VR (virtual reality). VOS (video object segmentation) is a pixel-level task, which aims to segment the moving objects in each frame of the video. Combining theory with practice, this paper studies the process of 3D virtual scene construction, and on this basis, researches the optimization methods of 3D modeling. In this paper, an unsupervised VOS algorithm is proposed, which initializes the target by combining the moving edge of the target image and the appearance edge of the target and assists the modeling of the VR 3D model, which has reference significance for the future construction of large-scale VR scenes. The results show that the segmentation accuracy of this algorithm can reach more than 94%, which is about 9% higher than that of the FASTSEG method. 3D modeling technology is the foundation of 3D virtual scene; so, it is of practical significance to study the application of 3D modeling technology. At the same time, it is of positive significance to use the unsupervised VOS algorithm to assist the VR 3D model modeling.
{"title":"Application of Virtual Reality Technology and Unsupervised Video Object Segmentation Algorithm in 3D Model Modeling","authors":"Hui-Lin Yang, Qiuming Liu","doi":"10.1155/2022/4743456","DOIUrl":"https://doi.org/10.1155/2022/4743456","url":null,"abstract":"3D modeling is the most basic technology to realize VR (virtual reality). VOS (video object segmentation) is a pixel-level task, which aims to segment the moving objects in each frame of the video. Combining theory with practice, this paper studies the process of 3D virtual scene construction, and on this basis, researches the optimization methods of 3D modeling. In this paper, an unsupervised VOS algorithm is proposed, which initializes the target by combining the moving edge of the target image and the appearance edge of the target and assists the modeling of the VR 3D model, which has reference significance for the future construction of large-scale VR scenes. The results show that the segmentation accuracy of this algorithm can reach more than 94%, which is about 9% higher than that of the FASTSEG method. 3D modeling technology is the foundation of 3D virtual scene; so, it is of practical significance to study the application of 3D modeling technology. At the same time, it is of positive significance to use the unsupervised VOS algorithm to assist the VR 3D model modeling.","PeriodicalId":49111,"journal":{"name":"Advances in Mathematical Physics","volume":" ","pages":""},"PeriodicalIF":1.2,"publicationDate":"2022-10-13","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"47955128","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"物理与天体物理","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
In view of the present situation of “learning difficulty” in health statistics, this paper proposes a video visualization technology based on the convolutional neural network, which updates parameters by calculating the gradient of loss function to obtain accurate or nearly accurate loss function. Taking the students from 2014 to 2017 in a university in Henan as the research object, this paper analyzes the video visualization technology and its application effect on the teaching of college students’ health statistics from the aspects of students’ course awareness, learning behavior, communication between teachers and students, knowledge mastery, and course satisfaction. The results show that the external model load difference between each explicit variable and latent variable is statistically significant. Learning behavior and communication between teachers and students have a direct impact on the mastery of knowledge, and the degree of influence from high to low is as follows: learning behavior and communication between teachers and students. The teaching effect model of health statistics based on video visualization technology of the convolutional neural network has certain practicability.
{"title":"Video Visualization Technology and Its Application in Health Statistics Teaching for College Students","authors":"Chengfei Li, Yuan-long Xie, Shuanbao Li","doi":"10.1155/2022/3212014","DOIUrl":"https://doi.org/10.1155/2022/3212014","url":null,"abstract":"In view of the present situation of “learning difficulty” in health statistics, this paper proposes a video visualization technology based on the convolutional neural network, which updates parameters by calculating the gradient of loss function to obtain accurate or nearly accurate loss function. Taking the students from 2014 to 2017 in a university in Henan as the research object, this paper analyzes the video visualization technology and its application effect on the teaching of college students’ health statistics from the aspects of students’ course awareness, learning behavior, communication between teachers and students, knowledge mastery, and course satisfaction. The results show that the external model load difference between each explicit variable and latent variable is statistically significant. Learning behavior and communication between teachers and students have a direct impact on the mastery of knowledge, and the degree of influence from high to low is as follows: learning behavior and communication between teachers and students. The teaching effect model of health statistics based on video visualization technology of the convolutional neural network has certain practicability.","PeriodicalId":49111,"journal":{"name":"Advances in Mathematical Physics","volume":" ","pages":""},"PeriodicalIF":1.2,"publicationDate":"2022-10-13","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"44644041","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"物理与天体物理","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
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