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Applied Mathematics-A Journal of Chinese Universities Series B最新文献

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A Modified Right Helicoid Can Simulate the Inner Structure of the Cochlea in the Hearing Organ of Mammals 改良的右螺旋体可以模拟哺乳动物听觉器官中耳蜗的内部结构
IF 1 4区 数学
Applied Mathematics-A Journal of Chinese Universities Series B Pub Date : 2021-05-18 DOI: 10.4236/AM.2021.125028
M. Osaka
{"title":"A Modified Right Helicoid Can Simulate the Inner Structure of the Cochlea in the Hearing Organ of Mammals","authors":"M. Osaka","doi":"10.4236/AM.2021.125028","DOIUrl":"https://doi.org/10.4236/AM.2021.125028","url":null,"abstract":"The purpose of this study is to develop a mathematical model of the spiral basilar membrane in the center of the cochlea, which plays an important role in the mammalian auditory system. The basilar membrane transmits sound vibrations, which are converted into electrical potential changes by the inner hair cells. The basilar membrane is thought to lie on a locally undistorted curved surface because the inner hair cells, which are arranged in an orderly fashion on the basilar membrane, respond to their location-specific frequencies. In mammals, the number of rotations of this surface and the rate of change of its width with each rotation are different. It turns out that by modifying the right helicoid, we can obtain a mathematical model that satisfies these points. In conclusion, even though the three-dimensional structure of the basilar membrane varies among species, this model can reproduce this structure. This further suggests that there are common genetic determinants of cochlear development in mammals. From a practical standpoint, this may be useful for creating cochlear implants.","PeriodicalId":55568,"journal":{"name":"Applied Mathematics-A Journal of Chinese Universities Series B","volume":null,"pages":null},"PeriodicalIF":1.0,"publicationDate":"2021-05-18","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"88188460","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 2
Uniform Lipschitz Bound for a Competition Diffusion Advection System with Strong Competition 具有强竞争的竞争扩散平流系统的均匀Lipschitz界
IF 1 4区 数学
Applied Mathematics-A Journal of Chinese Universities Series B Pub Date : 2021-05-18 DOI: 10.4236/AM.2021.125027
Tingwei Huang, Shan Zhang
{"title":"Uniform Lipschitz Bound for a Competition Diffusion Advection System with Strong Competition","authors":"Tingwei Huang, Shan Zhang","doi":"10.4236/AM.2021.125027","DOIUrl":"https://doi.org/10.4236/AM.2021.125027","url":null,"abstract":"We prove the uniform Lipschitz bound of solutions for a nonlinear elliptic system modeling the steady state of populations that compete in a heterogeneous environment. This extends known quasi-optimal regularity results and covers the optimal case for this problem. The proof relies upon the blow-up technique and the almost monotonicity formula by Caffarelli, Jerison and Kenig.","PeriodicalId":55568,"journal":{"name":"Applied Mathematics-A Journal of Chinese Universities Series B","volume":null,"pages":null},"PeriodicalIF":1.0,"publicationDate":"2021-05-18","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"89298693","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 1
A Short Note on Converting a Series into a Form of Fraction 关于将级数转化为分数形式的简短说明
IF 1 4区 数学
Applied Mathematics-A Journal of Chinese Universities Series B Pub Date : 2021-04-28 DOI: 10.5923/J.AM.20211101.03
Ameha Tefera Tessema
{"title":"A Short Note on Converting a Series into a Form of Fraction","authors":"Ameha Tefera Tessema","doi":"10.5923/J.AM.20211101.03","DOIUrl":"https://doi.org/10.5923/J.AM.20211101.03","url":null,"abstract":"Let for all and If the sum of a series defined as and if where for n=i, , then the sum of a series can be converted into fraction as follows .","PeriodicalId":55568,"journal":{"name":"Applied Mathematics-A Journal of Chinese Universities Series B","volume":null,"pages":null},"PeriodicalIF":1.0,"publicationDate":"2021-04-28","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"79575499","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 0
Full Euclidean Algorithm by Means of a Steady Walk 基于稳定行走的全欧几里德算法
IF 1 4区 数学
Applied Mathematics-A Journal of Chinese Universities Series B Pub Date : 2021-04-14 DOI: 10.4236/AM.2021.124018
Carlos Rodriguez, M. A. Cruz, C. Falcon
{"title":"Full Euclidean Algorithm by Means of a Steady Walk","authors":"Carlos Rodriguez, M. A. Cruz, C. Falcon","doi":"10.4236/AM.2021.124018","DOIUrl":"https://doi.org/10.4236/AM.2021.124018","url":null,"abstract":"Let x and y be two positive real numbers with x < y. Consider a traveler, on the interval [0, y/2], departing from 0 and taking steps of length equal to x. Every time a step reaches an endpoint of the interval, the traveler rebounds off the endpoint in order to complete the step length. We show that the footprints of the traveler are the output of a full Euclidean algorithm for x and y, whenever y/x is a rational number. In the case that y/x is irrational, the algorithm is, theoretically, not finite; however, it is a new tool for the study of its irrationality.","PeriodicalId":55568,"journal":{"name":"Applied Mathematics-A Journal of Chinese Universities Series B","volume":null,"pages":null},"PeriodicalIF":1.0,"publicationDate":"2021-04-14","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"76567811","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 0
Numerical Solutions of the Improved Boussinesq Equation with Stokes Damping 考虑Stokes阻尼的改进Boussinesq方程的数值解
IF 1 4区 数学
Applied Mathematics-A Journal of Chinese Universities Series B Pub Date : 2021-04-06 DOI: 10.4236/AM.2021.124015
Quanxiang Wang
{"title":"Numerical Solutions of the Improved Boussinesq Equation with Stokes Damping","authors":"Quanxiang Wang","doi":"10.4236/AM.2021.124015","DOIUrl":"https://doi.org/10.4236/AM.2021.124015","url":null,"abstract":"In this paper, we propose new finite volume element schemes to numerically solve the improved Boussinesq equation with Stokes damping. The new schemes can inherit characteristic properties of the conservation of mass and the decrease of total energy from the improved Boussinesq equation with Stokes damping. Numerical experiments illustrate that the proposed schemes are second-order accuracy in space and time.","PeriodicalId":55568,"journal":{"name":"Applied Mathematics-A Journal of Chinese Universities Series B","volume":null,"pages":null},"PeriodicalIF":1.0,"publicationDate":"2021-04-06","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"78697046","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 0
Existence for a Higher Order Coupled System of Korteweg-de Vries Equations 高阶Korteweg-de Vries方程组的存在性
IF 1 4区 数学
Applied Mathematics-A Journal of Chinese Universities Series B Pub Date : 2021-04-02 DOI: 10.4236/AM.2021.124021
Min Liu
{"title":"Existence for a Higher Order Coupled System of Korteweg-de Vries Equations","authors":"Min Liu","doi":"10.4236/AM.2021.124021","DOIUrl":"https://doi.org/10.4236/AM.2021.124021","url":null,"abstract":"Consider the following system of coupled Korteweg-de Vries equations, where u, v ⊆ W2,2, 2≤N≤7 and λi,β > 0, β denotes a real coupling parameter. Firstly, we prove the existence of the solutions of a coupled system of Korteweg-de Vries equations using variation approach and minimization techniques on Nehari manifold. Then, we show the multiplicity of the equations by a bifurcation theory which is rare for studying higher order equations.","PeriodicalId":55568,"journal":{"name":"Applied Mathematics-A Journal of Chinese Universities Series B","volume":null,"pages":null},"PeriodicalIF":1.0,"publicationDate":"2021-04-02","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"85464906","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 0
The Spectral Radii of Some Adhesive Graphs 一些黏着图的谱半径
IF 1 4区 数学
Applied Mathematics-A Journal of Chinese Universities Series B Pub Date : 2021-04-02 DOI: 10.4236/AM.2021.124017
Qingning Wang
{"title":"The Spectral Radii of Some Adhesive Graphs","authors":"Qingning Wang","doi":"10.4236/AM.2021.124017","DOIUrl":"https://doi.org/10.4236/AM.2021.124017","url":null,"abstract":"The spectral radius of a graph is the maximum eigenvalues of its adjacency matrix. In this paper, using the property of quotient graph, the sharp upper bounds for the spectral radii of some adhesive graphs are determined.","PeriodicalId":55568,"journal":{"name":"Applied Mathematics-A Journal of Chinese Universities Series B","volume":null,"pages":null},"PeriodicalIF":1.0,"publicationDate":"2021-04-02","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"74692793","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 0
A Stochastic SVIR Model for Measles 麻疹的随机SVIR模型
IF 1 4区 数学
Applied Mathematics-A Journal of Chinese Universities Series B Pub Date : 2021-03-30 DOI: 10.4236/AM.2021.123013
M. Seydou, Ousmane Moussa Tessa
{"title":"A Stochastic SVIR Model for Measles","authors":"M. Seydou, Ousmane Moussa Tessa","doi":"10.4236/AM.2021.123013","DOIUrl":"https://doi.org/10.4236/AM.2021.123013","url":null,"abstract":"In this article, we consider the construction of a SVIR (Susceptible, Vaccinated, Infected, Recovered) stochastic compartmental model of measles. We prove that the deterministic solution is asymptotically the average of the stochastic solution in the case of small population size. The choice of this model takes into account the random fluctuations inherent to the epidemiological characteristics of rural populations of Niger, notably a high prevalence of measles in children under 5, coupled with a very low immunization coverage.","PeriodicalId":55568,"journal":{"name":"Applied Mathematics-A Journal of Chinese Universities Series B","volume":null,"pages":null},"PeriodicalIF":1.0,"publicationDate":"2021-03-30","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"87374920","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 0
Uniqueness of Positive Radial Solutions for a Class of Semipositone Systems on the Exterior of a Ball 球表面一类半正子系统正径向解的唯一性
IF 1 4区 数学
Applied Mathematics-A Journal of Chinese Universities Series B Pub Date : 2021-03-11 DOI: 10.4236/AM.2021.123009
A. Mohamed, Khalid Ahmed Abbakar, Abuzar Awad, Omer Khalil, Bechir Mahamat Acyl, Abdoulaye Ali Youssouf, M. Mousa
{"title":"Uniqueness of Positive Radial Solutions for a Class of Semipositone Systems on the Exterior of a Ball","authors":"A. Mohamed, Khalid Ahmed Abbakar, Abuzar Awad, Omer Khalil, Bechir Mahamat Acyl, Abdoulaye Ali Youssouf, M. Mousa","doi":"10.4236/AM.2021.123009","DOIUrl":"https://doi.org/10.4236/AM.2021.123009","url":null,"abstract":"In this paper, we study the positive radial solutions for elliptic systems to the nonlinear BVP: \u0000 \u0000 , where Δu = div (∇u) and Δv = div (∇v) are the Laplacian of u, λ is a positive parameter, Ω = {x ∈ Rn : N > 2, |x| > r0, r0 > 0}, let i = [1,2] then Ki :[r0,∞] → (0,∞) is a continuous function such that limr→∞ ki(r) = 0 and  is The external natural derivative, and : [0, ∞) → (0, ∞) is a continuous function. We discuss existence and multiplicity results for classes of f with a) fi > 0, b) fi fi = 0. We base our presence and multiple outcomes via the Sub-solutions method. We also discuss some unique findings.","PeriodicalId":55568,"journal":{"name":"Applied Mathematics-A Journal of Chinese Universities Series B","volume":null,"pages":null},"PeriodicalIF":1.0,"publicationDate":"2021-03-11","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"86313980","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 0
Tuning of Prior Covariance in Generalized Least Squares 广义最小二乘中先验协方差的调整
IF 1 4区 数学
Applied Mathematics-A Journal of Chinese Universities Series B Pub Date : 2021-03-11 DOI: 10.4236/AM.2021.123011
W. Menke
{"title":"Tuning of Prior Covariance in Generalized Least Squares","authors":"W. Menke","doi":"10.4236/AM.2021.123011","DOIUrl":"https://doi.org/10.4236/AM.2021.123011","url":null,"abstract":"Generalized Least Squares (least squares with prior information) requires the correct assignment of two prior covariance matrices: one associated with the uncertainty of measurements; the other with the uncertainty of prior information. These assignments often are very subjective, especially when correlations among data or among prior information are believed to occur. However, in cases in which the general form of these matrices can be anticipated up to a set of poorly-known parameters, the data and prior information may be used to better-determine (or “tune”) the parameters in a manner that is faithful to the underlying Bayesian foundation of GLS. We identify an objective function, the minimization of which leads to the best-estimate of the parameters and provide explicit and computationally-efficient formula for calculating the derivatives needed to implement the minimization with a gradient descent method. Furthermore, the problem is organized so that the minimization need be performed only over the space of covariance parameters, and not over the combined space of model and covariance parameters. We show that the use of trade-off curves to select the relative weight given to observations and prior information is not a form of tuning, because it does not, in general maximize the posterior probability of the model parameters, and can lead to a different weighting than the procedure described here. We also provide several examples that demonstrate the viability, and discuss both the advantages and limitations of the method.","PeriodicalId":55568,"journal":{"name":"Applied Mathematics-A Journal of Chinese Universities Series B","volume":null,"pages":null},"PeriodicalIF":1.0,"publicationDate":"2021-03-11","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"89129145","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 3
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