Pub Date : 2022-01-01DOI: 10.4236/ajcm.2022.122012
Jonathan Martini, D. J. Fonseca
{"title":"Analysis of Soft Decision Trees for Passive-Expert Reinforcement Learning","authors":"Jonathan Martini, D. J. Fonseca","doi":"10.4236/ajcm.2022.122012","DOIUrl":"https://doi.org/10.4236/ajcm.2022.122012","url":null,"abstract":"","PeriodicalId":64456,"journal":{"name":"美国计算数学期刊(英文)","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":"70509855","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: 10.4236/ajcm.2022.121004
Arju Ara Runa, M. A. Alim, Md Shahidul Alam, K. H. Kabir
The phenomena of magneto-hydrodynamic natural convection in a two-dimensional semicircular top enclosure with triangular obstacle in the rectangular cavity were studied numerically. The governing differential equations are solved by using the most important method which is finite element method (weighted-residual method). The top wall is placed at cold Tc and bottom wall is heated Th. Here the sidewalls of the cavity assumed adiabatic. Also all the wall are occupied to be no-slip condition. A heated triangular obstacle is located at the center of the cavity. The study accomplished for Prandtl number Pr = 0.71; the Rayleigh number Ra = 103, 105, 5 × 105, 106 and for Hartmann number Ha = 0, 20, 50, 100. The results represent the streamlines, isotherms, velocity and temperature fields as well as local Nusselt number.
{"title":"Finite Element Analysis of Magnetohydrodynamic Natural Convection within Semi-Circular Top Enclosure with Triangular Obstacles","authors":"Arju Ara Runa, M. A. Alim, Md Shahidul Alam, K. H. Kabir","doi":"10.4236/ajcm.2022.121004","DOIUrl":"https://doi.org/10.4236/ajcm.2022.121004","url":null,"abstract":"The phenomena of magneto-hydrodynamic natural convection in a two-dimensional semicircular top enclosure with triangular obstacle in the rectangular cavity were studied numerically. The governing differential equations are solved by using the most important method which is finite element method (weighted-residual method). The top wall is placed at cold Tc and bottom wall is heated Th. Here the sidewalls of the cavity assumed adiabatic. Also all the wall are occupied to be no-slip condition. A heated triangular obstacle is located at the center of the cavity. The study accomplished for Prandtl number Pr = 0.71; the Rayleigh number Ra = 103, 105, 5 × 105, 106 and for Hartmann number Ha = 0, 20, 50, 100. The results represent the streamlines, isotherms, velocity and temperature fields as well as local Nusselt number.","PeriodicalId":64456,"journal":{"name":"美国计算数学期刊(英文)","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":"70509635","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: 10.4236/ajcm.2022.123019
H. Sarafian
Customarily in the physics of sound, static-acoustic-related topics are ad-dressed. For instance, the change in the sound level vs discrete change in the distance. In dynamic cases, e.g. the Doppler shit although the relative motion of the components, i.e. the source and the sensor are essential, the move-ments are limited to uniform motions. In this investigating report, scenarios departed from these limitations are considered. For the former case, time de-pendent sound level and for the latter case, nonuniform motions are analyzed. Aside from light long-hand mathematical formulations, the majority of the analysis is carried out utilizing a Computer Algebra System (CAS) specifically Mathematica. The analysis and format of the development are crafted flexibly conducive opportunities for furthering quests for the “what if” scenarios.
{"title":"Designing Physics Problems with Mathematica Example II","authors":"H. Sarafian","doi":"10.4236/ajcm.2022.123019","DOIUrl":"https://doi.org/10.4236/ajcm.2022.123019","url":null,"abstract":"Customarily in the physics of sound, static-acoustic-related topics are ad-dressed. For instance, the change in the sound level vs discrete change in the distance. In dynamic cases, e.g. the Doppler shit although the relative motion of the components, i.e. the source and the sensor are essential, the move-ments are limited to uniform motions. In this investigating report, scenarios departed from these limitations are considered. For the former case, time de-pendent sound level and for the latter case, nonuniform motions are analyzed. Aside from light long-hand mathematical formulations, the majority of the analysis is carried out utilizing a Computer Algebra System (CAS) specifically Mathematica. The analysis and format of the development are crafted flexibly conducive opportunities for furthering quests for the “what if” scenarios.","PeriodicalId":64456,"journal":{"name":"美国计算数学期刊(英文)","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":"70510034","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 : 2021-09-27DOI: 10.4236/ajcm.2021.113014
Ton-Lo Wang, Ziwen Jiang, Zhe Yin
In this paper, for the initial and boundary value problem of beams with structural damping, by introducing intermediate variables, the original fourth-order problem is transformed into second-order partial differential equations, and the mixed finite volume element scheme is constructed, and the existence, uniqueness and convergence of the scheme are analyzed. Numerical examples are provided to confirm the theoretical results. In the end, we test the value of δ to observe its influence on the model.
{"title":"Mixed Finite Volume Element Method for Vibration Equations of Beam with Structural Damping","authors":"Ton-Lo Wang, Ziwen Jiang, Zhe Yin","doi":"10.4236/ajcm.2021.113014","DOIUrl":"https://doi.org/10.4236/ajcm.2021.113014","url":null,"abstract":"In this \u0000paper, for the initial and boundary value problem of beams with structural damping, by introducing intermediate \u0000variables, the original fourth-order problem is transformed into \u0000second-order partial differential equations, and the mixed finite volume \u0000element scheme is constructed, and the existence, uniqueness and convergence of \u0000the scheme are analyzed. Numerical examples are provided to confirm the theoretical results. In \u0000the end, we test the value of δ to observe its influence on the \u0000model.","PeriodicalId":64456,"journal":{"name":"美国计算数学期刊(英文)","volume":" ","pages":""},"PeriodicalIF":0.0,"publicationDate":"2021-09-27","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"46567983","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 : 2021-09-27DOI: 10.4236/ajcm.2021.113015
D. C. Kay
The unsolved number theory problem known as the 3x + 1 problem involves sequences of positive integers generated more or less at random that seem to always converge to 1. Here the connection between the first integer (n) and the last (m) of a 3x + 1 sequence is analyzed by means of characteristic zero-one strings. This method is used to achieve some progress on the 3x + 1 problem. In particular, the long-standing conjecture that nontrivial cycles do not exist is virtually proved using probability theory.
{"title":"Collatz Sequences and Characteristic Zero-One Strings: Progress on the 3x + 1 Problem","authors":"D. C. Kay","doi":"10.4236/ajcm.2021.113015","DOIUrl":"https://doi.org/10.4236/ajcm.2021.113015","url":null,"abstract":"The unsolved number theory problem known as the 3x + 1 problem involves \u0000sequences of positive integers generated more or less at random that seem to \u0000always converge to 1. Here the connection between the first integer (n) and the last (m) of a 3x + 1 sequence is analyzed by \u0000means of characteristic zero-one strings. This method is used to achieve some \u0000progress on the 3x + 1 problem. In particular, the long-standing conjecture that nontrivial cycles do not exist is virtually \u0000proved using probability theory.","PeriodicalId":64456,"journal":{"name":"美国计算数学期刊(英文)","volume":"1 1","pages":""},"PeriodicalIF":0.0,"publicationDate":"2021-09-27","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"43621974","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 : 2021-05-10DOI: 10.4236/AJCM.2021.112011
Md. Abdul Mannan, Md Rashidur Rahman, Halima Akter, N. Nahar, S. Mondal
This paper aims at treating a study of Banach fixed point theorem for mapping results that introduced in the setting of normed space. The classical Banach fixed point theorem is a generalization of this work. A fixed point theory is a beautiful mixture of Mathematical analysis to explain some conditions in which maps give excellent solutions. Here later many mathematicians used this fixed point theory to establish their results, see for instance, Picard-Lindel of Theorem, The Picard theorem, Implicit function theorem etc. Also, we developed ideas that many of known fixed point theorems can easily be derived from the Banach theorem. It extends some recent works on the extension of Banach contraction principle to metric space with norm spaces.
{"title":"A Study of Banach Fixed Point Theorem and It’s Applications","authors":"Md. Abdul Mannan, Md Rashidur Rahman, Halima Akter, N. Nahar, S. Mondal","doi":"10.4236/AJCM.2021.112011","DOIUrl":"https://doi.org/10.4236/AJCM.2021.112011","url":null,"abstract":"This paper aims at treating a study of Banach fixed point theorem for mapping results that introduced in the setting of normed space. The classical Banach fixed point theorem is a generalization of this work. A fixed point theory is a beautiful mixture of Mathematical analysis to explain some conditions in which maps give excellent solutions. Here later many mathematicians used this fixed point theory to establish their results, see for instance, Picard-Lindel of Theorem, The Picard theorem, Implicit function theorem etc. Also, we developed ideas that many of known fixed point theorems can easily be derived from the Banach theorem. It extends some recent works on the extension of Banach contraction principle to metric space with norm spaces.","PeriodicalId":64456,"journal":{"name":"美国计算数学期刊(英文)","volume":"11 1","pages":"157-174"},"PeriodicalIF":0.0,"publicationDate":"2021-05-10","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"46131431","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 : 2021-05-10DOI: 10.4236/AJCM.2021.112007
H. Sarafian
We consider the motion of a massive point-like projectile thrown with initial velocity with respect to horizontal in a two-dimensional vertical plane under the influence of gravity in a viscose media. Two different velocity-dependent resistive media models are considered—linear and quadratic. With an objective to utilizing a Computer Algebra System (CAS), specifically Mathematica [1] numerically we solve the corresponding equations of motions. For a set of compatible parameters characterizing viscose forces graphically we display comparing the trajectories explicitly showing the impact of the models. Utilizing the model-dependent trajectory equations numerically we evaluate their associated arc-lengths. What distinguishes our approach vs. the existing body of work is the notion of the “reverse engineering”. Meaning, utilizing our numeric data we establish their corresponding analytic counter parts. Ultimately, utilizing both outputs numerically and analytically we determine the matching initial projectile angles maximizing their respective arc-lengths.
{"title":"What Projective Angle Makes the Arc-Length of the Trajectory in a Resistive Media Maximum? A Reverse Engineering Approach","authors":"H. Sarafian","doi":"10.4236/AJCM.2021.112007","DOIUrl":"https://doi.org/10.4236/AJCM.2021.112007","url":null,"abstract":"We consider the motion of a massive point-like projectile thrown with initial velocity with respect to horizontal in a two-dimensional vertical plane under the influence of gravity in a viscose media. Two different velocity-dependent resistive media models are considered—linear and quadratic. With an objective to utilizing a Computer Algebra System (CAS), specifically Mathematica [1] numerically we solve the corresponding equations of motions. For a set of compatible parameters characterizing viscose forces graphically we display comparing the trajectories explicitly showing the impact of the models. Utilizing the model-dependent trajectory equations numerically we evaluate their associated arc-lengths. What distinguishes our approach vs. the existing body of work is the notion of the “reverse engineering”. Meaning, utilizing our numeric data we establish their corresponding analytic counter parts. Ultimately, utilizing both outputs numerically and analytically we determine the matching initial projectile angles maximizing their respective arc-lengths.","PeriodicalId":64456,"journal":{"name":"美国计算数学期刊(英文)","volume":"11 1","pages":"71-82"},"PeriodicalIF":0.0,"publicationDate":"2021-05-10","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"48973209","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 : 2021-05-10DOI: 10.4236/AJCM.2021.112008
Xiaojie Zheng
In theorem LP [1], Liu proves the theorem when N = 2, but it can’t be ex-tended to the general case in his proof. So we consider the condition that the families of holomorphic curves share eleven hyperplanes, and we get the theorem 1.1.
{"title":"Shared Hyperplanes and Normal Families of Holomorphic Curves","authors":"Xiaojie Zheng","doi":"10.4236/AJCM.2021.112008","DOIUrl":"https://doi.org/10.4236/AJCM.2021.112008","url":null,"abstract":"In theorem LP [1], Liu proves the theorem when N = 2, but it can’t be ex-tended to the general case in his proof. So we consider the condition that the families of holomorphic curves share eleven hyperplanes, and we get the theorem 1.1.","PeriodicalId":64456,"journal":{"name":"美国计算数学期刊(英文)","volume":" ","pages":""},"PeriodicalIF":0.0,"publicationDate":"2021-05-10","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"44388628","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 : 2021-05-10DOI: 10.4236/ajcm.2021.112012
Bin Li
The main purpose of verifiable secret sharing scheme is to solve the honesty problem of participants. In this paper, the concept of nonzero k-submatrix and theresidual vector of system of hyperplane intersecting line equations is proposed. Based on certain projective transformations in projective space, a verifiable (t, n)-threshold secret sharing scheme is designed by using the structure of solutions of linear equations and the difficulty of solving discrete logarithm problems. The results show that this scheme can verify the correctness of the subkey provided by each participant before the reconstruction of the master key, and can effectively identify the fraudster. The fraudster can only cheat by guessing and the probability of success is only 1/p. The design of the scheme is exquisite and the calculation complexity is small. Each participant only needs to hold a subkey, which is convenient for management and use. The analysis shows that the scheme in this paper meets the security requirements and rules of secret sharing, and it is a computationally secure and effective scheme with good practical value.
{"title":"Verifiable Secret Sharing Scheme Based on Certain Projective Transformation","authors":"Bin Li","doi":"10.4236/ajcm.2021.112012","DOIUrl":"https://doi.org/10.4236/ajcm.2021.112012","url":null,"abstract":"The main purpose of verifiable secret sharing scheme is to solve the honesty problem of participants. In this paper, the concept of nonzero k-submatrix and theresidual vector of system of hyperplane intersecting line equations is proposed. Based on certain projective transformations in projective space, a verifiable (t, n)-threshold secret sharing scheme is designed by using the structure of solutions of linear equations and the difficulty of solving discrete logarithm problems. The results show that this scheme can verify the correctness of the subkey provided by each participant before the reconstruction of the master key, and can effectively identify the fraudster. The fraudster can only cheat by guessing and the probability of success is only 1/p. The design of the scheme is exquisite and the calculation complexity is small. Each participant only needs to hold a subkey, which is convenient for management and use. The analysis shows that the scheme in this paper meets the security requirements and rules of secret sharing, and it is a computationally secure and effective scheme with good practical value.","PeriodicalId":64456,"journal":{"name":"美国计算数学期刊(英文)","volume":" ","pages":""},"PeriodicalIF":0.0,"publicationDate":"2021-05-10","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"49161891","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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