Pub Date : 2022-04-30DOI: 10.31349/revmexfise.19.020204
M. Ramantswana, A. Ikot, G. Rampho, C. Edet, U. Okorie
By employing the Nikiforov-Uvarov (NU) method, we solved the time-independent Schrödinger equation (SE) with Manning-Rosen plus a class of Yukawa potential (MRCYP) model. The eigensolutions expressions were obtained and thermodynamic function expressions were also obtained using Euler MacLaurin formula in closed forms. Numerical results of the energy were obtained with respect to different screening parameters and quantum numbers. In addition, the effects of temperature on the thermodynamic functions were discussed for various screening parameters and quantum states. Unique critical temperatures of entropy and specific heat capacity were seen to exist for the selected screening parameters and quantum numbers. Our results are also in sync with the results in literatures and they promise to be relevant in various areas of studies, including atomic, particle and nuclear physics.
{"title":"Thermodynamic functions of Manning-Rosen plus a class of Yukawa potential using Euler MacLaurin Formula","authors":"M. Ramantswana, A. Ikot, G. Rampho, C. Edet, U. Okorie","doi":"10.31349/revmexfise.19.020204","DOIUrl":"https://doi.org/10.31349/revmexfise.19.020204","url":null,"abstract":"By employing the Nikiforov-Uvarov (NU) method, we solved the time-independent Schrödinger equation (SE) with Manning-Rosen plus a class of Yukawa potential (MRCYP) model. The eigensolutions expressions were obtained and thermodynamic function expressions were also obtained using Euler MacLaurin formula in closed forms. Numerical results of the energy were obtained with respect to different screening parameters and quantum numbers. In addition, the effects of temperature on the thermodynamic functions were discussed for various screening parameters and quantum states. Unique critical temperatures of entropy and specific heat capacity were seen to exist for the selected screening parameters and quantum numbers. Our results are also in sync with the results in literatures and they promise to be relevant in various areas of studies, including atomic, particle and nuclear physics.","PeriodicalId":49600,"journal":{"name":"Revista Mexicana De Fisica E","volume":" ","pages":""},"PeriodicalIF":0.0,"publicationDate":"2022-04-30","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"47037078","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 : 2022-04-30DOI: 10.31349/revmexfise.19.020203
Sait San, R. Altunay
This study presents utilization of Jacobi elliptic function expansion method to obtain the di¤erent types solutions of 3+1dimensional Boussinesq equation with dual dispersion. By using this method hyperbolic solutions and trigonometric functionsolutions are also obtained. The resulting outcomes verify that the preferred method is valid and reliable for the analytical technique of an extensive application of nonlinear phenomena.
{"title":"Abundant travelling wave solutions of 3+1 dimensional Boussinesq equation with dual dispersion","authors":"Sait San, R. Altunay","doi":"10.31349/revmexfise.19.020203","DOIUrl":"https://doi.org/10.31349/revmexfise.19.020203","url":null,"abstract":"This study presents utilization of Jacobi elliptic function expansion method to obtain the di¤erent types solutions of 3+1dimensional Boussinesq equation with dual dispersion. By using this method hyperbolic solutions and trigonometric functionsolutions are also obtained. The resulting outcomes verify that the preferred method is valid and reliable for the analytical technique of an extensive application of nonlinear phenomena.","PeriodicalId":49600,"journal":{"name":"Revista Mexicana De Fisica E","volume":" ","pages":""},"PeriodicalIF":0.0,"publicationDate":"2022-04-30","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"43026766","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 : 2022-04-30DOI: 10.31349/revmexfise.19.020205
Aditya Yoga Purnama, H. Kuswanto, Syella Ayunisa Rani, H. Putranta
Constructing mathematical equations in physics often creates difficulties in students' learning process. Therefore, it is necessary to have technology-based simulations to understand physical phenomena. One technology that is easy to use for simulations in physics learning is the spreadsheet program. This study aims to use spreadsheet media to visualize the face-centered cubic (FCC) energy band using the tight-binding method and to compare the results with the JavaScript programming language. This paper succeeded in making visualization of face-centered cubic (FCC) energy band using a spreadsheet as an alternative to distance learning. The spreadsheet is easier to use because they do not use complicated programming languages like JavaScript. This paper shows the use of innovative learning media, spreadsheets, in materials courses.
{"title":"Visualization of face-centered cubic energy band using spreadsheet and javascript as innovative learning","authors":"Aditya Yoga Purnama, H. Kuswanto, Syella Ayunisa Rani, H. Putranta","doi":"10.31349/revmexfise.19.020205","DOIUrl":"https://doi.org/10.31349/revmexfise.19.020205","url":null,"abstract":"Constructing mathematical equations in physics often creates difficulties in students' learning process. Therefore, it is necessary to have technology-based simulations to understand physical phenomena. One technology that is easy to use for simulations in physics learning is the spreadsheet program. This study aims to use spreadsheet media to visualize the face-centered cubic (FCC) energy band using the tight-binding method and to compare the results with the JavaScript programming language. This paper succeeded in making visualization of face-centered cubic (FCC) energy band using a spreadsheet as an alternative to distance learning. The spreadsheet is easier to use because they do not use complicated programming languages like JavaScript. This paper shows the use of innovative learning media, spreadsheets, in materials courses.","PeriodicalId":49600,"journal":{"name":"Revista Mexicana De Fisica E","volume":" ","pages":""},"PeriodicalIF":0.0,"publicationDate":"2022-04-30","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"43755410","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 : 2022-04-30DOI: 10.31349/revmexfise.19.020201
Julio C. Aguiar, H. D. Di Rocco
The expressions for the energy matrix elements and for the radiative transitions in the jj coupling can be obtained from the respective LS expressions by making a few simple changes. The results shown as examples are compared with other treatments, where the two formulations are deduced in parallel, without making use of these simple rules. We emphasize that the rules were found by heuristic reasoning. In all cases the application of the rules are in accordance with published results. This work completes two previous papers published in this journal (References 19 and 20).
{"title":"A heuristic procedure to go from LS to jj expressions in atomic and nuclear spectroscopy","authors":"Julio C. Aguiar, H. D. Di Rocco","doi":"10.31349/revmexfise.19.020201","DOIUrl":"https://doi.org/10.31349/revmexfise.19.020201","url":null,"abstract":"The expressions for the energy matrix elements and for the radiative transitions in the jj coupling can be obtained from the respective LS expressions by making a few simple changes. The results shown as examples are compared with other treatments, where the two formulations are deduced in parallel, without making use of these simple rules. We emphasize that the rules were found by heuristic reasoning. In all cases the application of the rules are in accordance with published results. This work completes two previous papers published in this journal (References 19 and 20).","PeriodicalId":49600,"journal":{"name":"Revista Mexicana De Fisica E","volume":" ","pages":""},"PeriodicalIF":0.0,"publicationDate":"2022-04-30","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"44815038","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 : 2022-04-30DOI: 10.31349/revmexfise.19.020206
M. Arroyo-Ureña, R. Gaitan, T. A. Valencia-Pérez
We present a pedagogical Mathematica package, so-called SpaceMath, for Beyond the Standard Model parameter space searches. This software is directed mainly for the training of human resources related to elementary particle physics phenomenology, however, it is sophisticated enough to be used in researches. In this first version, SpaceMath v1.0 works with Higgs Boson Data whose results are the most up-to-date experimental measurements made at the Large Hadron Collider. In addition, we also include the expected results at future colliders, namely, High Luminosity LHC and High Energy LHC. SpaceMath v1.0 is able to find allowed regions for free parameters of extension models using the Higgs Boson Data within a friendly interface and an intuitive environment in which the user enters the couplings symbolically, sets parameters and execute Mathematica in the traditional way. As result, both tables as plots with values and areas agree with experimental data are generated. We present examples using SpaceMath v1.0 to analyze the free Two-Higgs Doublet Model and the Simplest Little Higgs Model parameter spaces, step by step, in order to start new users in a fast and efficient way. Finally, to validate SpaceMath v1.0, widely known results are reproduced.
{"title":"SpaceMath version 1.0 A Mathematica package for beyond the standard model parameter space searches","authors":"M. Arroyo-Ureña, R. Gaitan, T. A. Valencia-Pérez","doi":"10.31349/revmexfise.19.020206","DOIUrl":"https://doi.org/10.31349/revmexfise.19.020206","url":null,"abstract":"We present a pedagogical Mathematica package, so-called SpaceMath, for Beyond the Standard Model parameter space searches. This software is directed mainly for the training of human resources related to elementary particle physics phenomenology, however, it is sophisticated enough to be used in researches. In this first version, SpaceMath v1.0 works with Higgs Boson Data whose results are the most up-to-date experimental measurements made at the Large Hadron Collider. In addition, we also include the expected results at future colliders, namely, High Luminosity LHC and High Energy LHC. SpaceMath v1.0 is able to find allowed regions for free parameters of extension models using the Higgs Boson Data within a friendly interface and an intuitive environment in which the user enters the couplings symbolically, sets parameters and execute Mathematica in the traditional way. As result, both tables as plots with values and areas agree with experimental data are generated. We present examples using SpaceMath v1.0 to analyze the free Two-Higgs Doublet Model and the Simplest Little Higgs Model parameter spaces, step by step, in order to start new users in a fast and efficient way. Finally, to validate SpaceMath v1.0, widely known results are reproduced.","PeriodicalId":49600,"journal":{"name":"Revista Mexicana De Fisica E","volume":" ","pages":""},"PeriodicalIF":0.0,"publicationDate":"2022-04-30","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"45495364","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 : 2022-04-30DOI: 10.31349/revmexfise.19.020202
Tomas Rada Crespo, Oscar Hernández Bustos, Diana Rueda Delgado, Heydy Robles Noriega, Juan Miranda Crespo
Este trabajo se dise˜n´o para caracterizar y estudiar las creencias que manejan los estudiantes de diferentes programas de ingenier´ıa con respecto al aprendizaje de la F´ısica empleando la encuesta CLASS. Las creencias y actitudes que muestran los estudiantes hacia el aprendizaje de esta asignatura representan un buen predictor del desempe˜no de los estudiantes que toman los primeros cursos de ciencias y cuyos contenidos son v´alidos en un mundo cada vez m´as globalizado. Adem´as, el conocimiento de estas creencias por parte del profesor le permitir´a tener una idea m´as clara de lo que piensan los estudiantes sobre como aprenden esta asignatura. Por tanto, aqu´ı se plantean ambientes de aprendizaje que potencialicen las creencias favorables y modifiquen las desfavorables, lo que representar´a para el profesor una alta posibilidad de mejorar los resultados en el aprendizaje de la F´ısica. En este estudio encontramos diferencias significativas acerca de c´omo el estudiante percibe laimportancia de aprender F´ısica en su formaci´on como ingeniero dependiendo del programa de ingenier´ıa que cursan. Es necesario entonces, que el docente establezca una l´ınea de acci´on pedag´ogica que acerque m´as al estudiante a un aprendizaje efectivo y donde se orienten las competencias desarrolladas en el aprendizaje de la F´ısica al desarrollo de su formaci´on profesional.
{"title":"Percepci´on del aprendizaje de la f´ısica en diferentes programas de ingenier´ıa","authors":"Tomas Rada Crespo, Oscar Hernández Bustos, Diana Rueda Delgado, Heydy Robles Noriega, Juan Miranda Crespo","doi":"10.31349/revmexfise.19.020202","DOIUrl":"https://doi.org/10.31349/revmexfise.19.020202","url":null,"abstract":"Este trabajo se dise˜n´o para caracterizar y estudiar las creencias que manejan los estudiantes de diferentes programas de ingenier´ıa con respecto al aprendizaje de la F´ısica empleando la encuesta CLASS. Las creencias y actitudes que muestran los estudiantes hacia el aprendizaje de esta asignatura representan un buen predictor del desempe˜no de los estudiantes que toman los primeros cursos de ciencias y cuyos contenidos son v´alidos en un mundo cada vez m´as globalizado. Adem´as, el conocimiento de estas creencias por parte del profesor le permitir´a tener una idea m´as clara de lo que piensan los estudiantes sobre como aprenden esta asignatura. Por tanto, aqu´ı se plantean ambientes de aprendizaje que potencialicen las creencias favorables y modifiquen las desfavorables, lo que representar´a para el profesor una alta posibilidad de mejorar los resultados en el aprendizaje de la F´ısica. En este estudio encontramos diferencias significativas acerca de c´omo el estudiante percibe laimportancia de aprender F´ısica en su formaci´on como ingeniero dependiendo del programa de ingenier´ıa que cursan. Es necesario entonces, que el docente establezca una l´ınea de acci´on pedag´ogica que acerque m´as al estudiante a un aprendizaje efectivo y donde se orienten las competencias desarrolladas en el aprendizaje de la F´ısica al desarrollo de su formaci´on profesional.","PeriodicalId":49600,"journal":{"name":"Revista Mexicana De Fisica E","volume":" ","pages":""},"PeriodicalIF":0.0,"publicationDate":"2022-04-30","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"46642140","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 : 2022-02-23DOI: 10.31349/revmexfise.19.020207
Álvaro Suárez, D. Baccino, M. Monteiro, A. Martí
For this study, we compared the attitudes and beliefs about science of physical science (physics and mathematics) and life science (biochemistry and biology) students at the beginning of their university degrees using the CLASS (Colorado Learning Attitudes about Science Survey) tool. It is worth noting that both groups of students received similar physics courses during their high-school education. Through a detailed analysis of the different categories of the test, we examined the differences in performance in each of the areas that make up the questionnaire. Among other aspects, we found that a considerable percentage of life science students (higher than that of physical science students) adopted a novice type of behavior in problem solving. Finally, we discussed the possible causes of the differences found and their implications for teaching.
{"title":"Differences in the attitudes and beliefs about science of students in the physics-mathematics and life sciences areas and their impact on teaching","authors":"Álvaro Suárez, D. Baccino, M. Monteiro, A. Martí","doi":"10.31349/revmexfise.19.020207","DOIUrl":"https://doi.org/10.31349/revmexfise.19.020207","url":null,"abstract":"For this study, we compared the attitudes and beliefs about science of physical science (physics and mathematics) and life science (biochemistry and biology) students at the beginning of their university degrees using the CLASS (Colorado Learning Attitudes about Science Survey) tool. It is worth noting that both groups of students received similar physics courses during their high-school education. Through a detailed analysis of the different categories of the test, we examined the differences in performance in each of the areas that make up the questionnaire. Among other aspects, we found that a considerable percentage of life science students (higher than that of physical science students) adopted a novice type of behavior in problem solving. Finally, we discussed the possible causes of the differences found and their implications for teaching.","PeriodicalId":49600,"journal":{"name":"Revista Mexicana De Fisica E","volume":" ","pages":""},"PeriodicalIF":0.0,"publicationDate":"2022-02-23","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"45029217","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 : 2022-01-01DOI: 10.31349/revmexfise.19.010212
José Nieto Villar, J. Rieumont, R. Mansilla
It is shown how through the entropy production rate a natural unification between the formalism of classical thermodynamics and chemical kinetics is achieved. It is also shown how the entropy production rate represents an alternative way to the sensitivity analysis method in order to determine the fundamental steps in a reaction mechanism.
{"title":"The entropy production rate a bridge between thermodynamics and chemical kinetics","authors":"José Nieto Villar, J. Rieumont, R. Mansilla","doi":"10.31349/revmexfise.19.010212","DOIUrl":"https://doi.org/10.31349/revmexfise.19.010212","url":null,"abstract":"It is shown how through the entropy production rate a natural unification between the formalism of classical thermodynamics and chemical kinetics is achieved. It is also shown how the entropy production rate represents an alternative way to the sensitivity analysis method in order to determine the fundamental steps in a reaction mechanism.","PeriodicalId":49600,"journal":{"name":"Revista Mexicana De Fisica E","volume":" ","pages":""},"PeriodicalIF":0.0,"publicationDate":"2022-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"41830540","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 : 2022-01-01DOI: 10.31349/revmexfise.19.010210
Alexander Nahmad, D. San-Roman-Alerigi, Edna Magdalena Hernández González, E. Barrios, Gustavo Armendariz Peña, V. V. Velazquez Aguilar
In this article we explain in a new light two fundamental concepts ofquantum optics, the quantum beam splitter and the quantum interferometer, in termsof two state quantum wave functions. This method is consistent with the concept ofentanglement, and hence the algebra needed to describe them is reduced to additionsand products of the components of the quantum states. Furthermore, under thepremises of this method it is possible to study quantum states of greater complexity,like those arising from the addition and products of single photon states.
{"title":"The quantum beam splitter revisited without a vacuum state","authors":"Alexander Nahmad, D. San-Roman-Alerigi, Edna Magdalena Hernández González, E. Barrios, Gustavo Armendariz Peña, V. V. Velazquez Aguilar","doi":"10.31349/revmexfise.19.010210","DOIUrl":"https://doi.org/10.31349/revmexfise.19.010210","url":null,"abstract":"In this article we explain in a new light two fundamental concepts ofquantum optics, the quantum beam splitter and the quantum interferometer, in termsof two state quantum wave functions. This method is consistent with the concept ofentanglement, and hence the algebra needed to describe them is reduced to additionsand products of the components of the quantum states. Furthermore, under thepremises of this method it is possible to study quantum states of greater complexity,like those arising from the addition and products of single photon states.","PeriodicalId":49600,"journal":{"name":"Revista Mexicana De Fisica E","volume":"1 1","pages":""},"PeriodicalIF":0.0,"publicationDate":"2022-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"41576987","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}
This study aims to find equations and simulations that satisfy the characteristics of graphene’s energy dispersion and identify misconceptions that may occur. Here we give students nine articles about graphene’s dispersion energy. They were asked to identify the equations, parameters, and software used in each of the articles. The assignment was then to make the distribution of the data in a spreadsheet. The parameters used were the lattice constant of 2.46 Å, the range of the k wave function for the x and y axes of -2πa to 2πa, and the interval for each range of 0.1. Each equation is divided into two parts, E(+) and E(-). The analysis was carried out by making a slice in the middle of the x and y axes, as well as the main and off-diagonals. Graphene has Dirac points where the band gap is zero. This means that there is no distance or very small distance between the valence and conduction bands. From this activity, it can be concluded that Rozhkov (2016) has the equations and simulations that best satisfy graphene’s dispersion energy. Misconceptions occur in almost all existing equations and simulations.
{"title":"The misconception in graphene’s dispersion energy simulations","authors":"Syella Ayunisa Rani, Heru Kuswanto, Himawan Putranta, Aditya Yoga Purnama, Wipsar Sunu Brams Dwandaru","doi":"10.31349/revmexfise.19.010208","DOIUrl":"https://doi.org/10.31349/revmexfise.19.010208","url":null,"abstract":"This study aims to find equations and simulations that satisfy the characteristics of graphene’s energy dispersion and identify misconceptions that may occur. Here we give students nine articles about graphene’s dispersion energy. They were asked to identify the equations, parameters, and software used in each of the articles. The assignment was then to make the distribution of the data in a spreadsheet. The parameters used were the lattice constant of 2.46 Å, the range of the k wave function for the x and y axes of -2πa to 2πa, and the interval for each range of 0.1. Each equation is divided into two parts, E(+) and E(-). The analysis was carried out by making a slice in the middle of the x and y axes, as well as the main and off-diagonals. Graphene has Dirac points where the band gap is zero. This means that there is no distance or very small distance between the valence and conduction bands. From this activity, it can be concluded that Rozhkov (2016) has the equations and simulations that best satisfy graphene’s dispersion energy. Misconceptions occur in almost all existing equations and simulations.","PeriodicalId":49600,"journal":{"name":"Revista Mexicana De Fisica E","volume":" ","pages":""},"PeriodicalIF":0.0,"publicationDate":"2022-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"41590862","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：