Pub Date : 2017-04-01DOI: 10.13189/ujam.2017.050202
A. Zelenyy, A. Bunyakin
This article presents numerical simulation of planar potential flow around an airfoil with possibility of changing its shape. Two-dimensional unsteady flow model with scalar velocity potential, which allows us to calculate pressure distribution along an airfoil from Cauchy-Lagrange integral, is used. For this purpose, an airfoil contour is approximated by a complex cubic spline with possibility of displacement its vertices. This algorithm has been used in the context of fluid-structure interaction and has been applied successfully to determination of stability of an elastic airfoil segment interacting with a flow stream, so-called panel flutter problem. Calculation of external flow is carried out by vortex panel method with Kutta-Joukowski trailing edge condition, which makes mathematical solution unique. Using this method of approximation of an airfoil in combination with the method of discrete vortices provides a semi-analytical solution for complex potential for whole computational domain of air flow. This solution significantly accelerates process of numerical computation of time-averaged aerodynamic force as well as the dynamic stability problem for aeroelastic wing design and temporal evolution of its natural disturbances.
{"title":"Direct Numerical Simulation of the Airfoil Segment's Flutter and its Effect on the Aerodynamic Force","authors":"A. Zelenyy, A. Bunyakin","doi":"10.13189/ujam.2017.050202","DOIUrl":"https://doi.org/10.13189/ujam.2017.050202","url":null,"abstract":"This article presents numerical simulation of planar potential flow around an airfoil with possibility of changing its shape. Two-dimensional unsteady flow model with scalar velocity potential, which allows us to calculate pressure distribution along an airfoil from Cauchy-Lagrange integral, is used. For this purpose, an airfoil contour is approximated by a complex cubic spline with possibility of displacement its vertices. This algorithm has been used in the context of fluid-structure interaction and has been applied successfully to determination of stability of an elastic airfoil segment interacting with a flow stream, so-called panel flutter problem. Calculation of external flow is carried out by vortex panel method with Kutta-Joukowski trailing edge condition, which makes mathematical solution unique. Using this method of approximation of an airfoil in combination with the method of discrete vortices provides a semi-analytical solution for complex potential for whole computational domain of air flow. This solution significantly accelerates process of numerical computation of time-averaged aerodynamic force as well as the dynamic stability problem for aeroelastic wing design and temporal evolution of its natural disturbances.","PeriodicalId":372283,"journal":{"name":"Universal Journal of Applied Mathematics","volume":"33 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2017-04-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"122996395","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 : 2017-02-01DOI: 10.13189/ujam.2017.050102
S. Tomita, Oliver Couto
Historically equation ( pan+qbn+rcn=pun+qvn+rwn ) has been studied for degree 2, 3, 4 etc., and equation (pan+qbn=pcn+qdn ) herein called equation (1) has been published for n=4 ,p=1,q=4 (Ref.no. 1) by Ajai Choudhry. Also Tito Piezas & others has discussed about equation (1) (Ref. no. 3 & 2). While Ref. no. (1, 2 & 3) deals with equation no. (1) for degree n=4 this paper has provided parametric solutions for degree n=2, 3, 4, 5, 6, 7, 8 & 9. Also there are instances in this paper where parametric solutions have been arrived at using different methods.
{"title":"Parametric Solutions to Equation (pa n +qb n =pc n +qd n ) Where 'n' Stands for Degree 2, 3, 4, 5, 6, 7, 8 & 9","authors":"S. Tomita, Oliver Couto","doi":"10.13189/ujam.2017.050102","DOIUrl":"https://doi.org/10.13189/ujam.2017.050102","url":null,"abstract":"Historically equation ( pan+qbn+rcn=pun+qvn+rwn ) has been studied for degree 2, 3, 4 etc., and equation (pan+qbn=pcn+qdn ) herein called equation (1) has been published for n=4 ,p=1,q=4 (Ref.no. 1) by Ajai Choudhry. Also Tito Piezas & others has discussed about equation (1) (Ref. no. 3 & 2). While Ref. no. (1, 2 & 3) deals with equation no. (1) for degree n=4 this paper has provided parametric solutions for degree n=2, 3, 4, 5, 6, 7, 8 & 9. Also there are instances in this paper where parametric solutions have been arrived at using different methods.","PeriodicalId":372283,"journal":{"name":"Universal Journal of Applied Mathematics","volume":"47 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2017-02-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"129261836","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 : 2016-12-01DOI: 10.13189/UJAM.2016.040401
V. Chulaevsky
We present the adaptive feedback scaling method for the Anderson localization analysis of several large classes of random Hamiltonians in discrete and continuous disordered media. We also give a constructive scale-free criterion of localization with asymptotically exponential decay of eigenfunction correlators, which can be verified in applications with the help of numerical methods.
{"title":"Renormalization Group Limit of Anderson Models","authors":"V. Chulaevsky","doi":"10.13189/UJAM.2016.040401","DOIUrl":"https://doi.org/10.13189/UJAM.2016.040401","url":null,"abstract":"We present the adaptive feedback scaling method for the Anderson localization analysis of several large classes of random Hamiltonians in discrete and continuous disordered media. We also give a constructive scale-free criterion of localization with asymptotically exponential decay of eigenfunction correlators, which can be verified in applications with the help of numerical methods.","PeriodicalId":372283,"journal":{"name":"Universal Journal of Applied Mathematics","volume":"24 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2016-12-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"126487796","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 : 2016-09-01DOI: 10.13189/ujam.2016.040303
S. Tomita, Oliver Couto
Consider the below mentioned equation: [aann + bbnn + ccnn + ddnn + eenn + ffnn] = [ppnn + qqnn + rrnn + ssnn + ttnn + uunn]----(A). Historically in math literature there are instances where solutions have been arrived at by different authors for equation (A) above. Ref.no. (1) by A. Bremner & J. Delorme and Ref. no. (10) by Tito Piezas. The difference is that this article has done systematic analysis of equation (A) for n=2,3,4,5,6,7,8 & 9. While numerical solutions for equation (A) is available on “Wolfram math” website, search for parametric solutions to equation (A) in various publications for all n=2,3,4,5,6,7,8 & 9 did not yield much success. The authors of this paper have selected six terms on each side of equation (A) since the difficulty of the problem increases every time a term is deleted on each side of equation (A). The authors have provided parametric solutions for equation (A) for n=2, 3, 4, 5 & 6 and for n=7, 8 & 9 solutions using elliptical curve theory has been provided. Also we would like to mention that solutions for n=7, 8 & 9 have infinite numerical solutions.
{"title":"Parametric Solutions to (six) n th Powers Equal to Another (six) n th Powers for Degree 'n' = 2,3,4,5,6,7,8,& 9","authors":"S. Tomita, Oliver Couto","doi":"10.13189/ujam.2016.040303","DOIUrl":"https://doi.org/10.13189/ujam.2016.040303","url":null,"abstract":"Consider the below mentioned equation: [aann + bbnn + ccnn + ddnn + eenn + ffnn] = [ppnn + qqnn + rrnn + ssnn + ttnn + uunn]----(A). Historically in math literature there are instances where solutions have been arrived at by different authors for equation (A) above. Ref.no. (1) by A. Bremner & J. Delorme and Ref. no. (10) by Tito Piezas. The difference is that this article has done systematic analysis of equation (A) for n=2,3,4,5,6,7,8 & 9. While numerical solutions for equation (A) is available on “Wolfram math” website, search for parametric solutions to equation (A) in various publications for all n=2,3,4,5,6,7,8 & 9 did not yield much success. The authors of this paper have selected six terms on each side of equation (A) since the difficulty of the problem increases every time a term is deleted on each side of equation (A). The authors have provided parametric solutions for equation (A) for n=2, 3, 4, 5 & 6 and for n=7, 8 & 9 solutions using elliptical curve theory has been provided. Also we would like to mention that solutions for n=7, 8 & 9 have infinite numerical solutions.","PeriodicalId":372283,"journal":{"name":"Universal Journal of Applied Mathematics","volume":"4 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2016-09-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"116043409","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 : 2016-09-01DOI: 10.13189/UJAM.2016.040302
Khaled K. Jaber, Shadi Al-Tarawneh
New exact solutions of the Fractional Riccati Differential equation y (a) = a ( x) y 2 + b ( x ) y + c ( x ) are presented. Exact solutions are obtained using several methods, firstly by reducing it to second order linear ordinary differential equation, secondly by transforming it to the Bernoulli equation, finally the solution is obtained by assuming an integral condition on c (x) involves an arbitrary function. Using the conditions imposed on Riccati equation's coefficients we choose the form of the coefficients of the Riccati equation. For this case the general solution of the Riccati equation is also presented.
给出了分数阶Riccati微分方程y (a) = a (x) y 2 + b (x) y + c (x)的新的精确解。首先将其化为二阶线性常微分方程，然后将其转化为伯努利方程，最后通过假设c (x)涉及任意函数的积分条件得到解。利用对里卡第方程系数所施加的条件，选择了里卡第方程系数的形式。对于这种情况，也给出了Riccati方程的通解。
{"title":"Exact Solution of Riccati Fractional Differential Equation","authors":"Khaled K. Jaber, Shadi Al-Tarawneh","doi":"10.13189/UJAM.2016.040302","DOIUrl":"https://doi.org/10.13189/UJAM.2016.040302","url":null,"abstract":"New exact solutions of the Fractional Riccati Differential equation y (a) = a ( x) y 2 + b ( x ) y + c ( x ) are presented. Exact solutions are obtained using several methods, firstly by reducing it to second order linear ordinary differential equation, secondly by transforming it to the Bernoulli equation, finally the solution is obtained by assuming an integral condition on c (x) involves an arbitrary function. Using the conditions imposed on Riccati equation's coefficients we choose the form of the coefficients of the Riccati equation. For this case the general solution of the Riccati equation is also presented.","PeriodicalId":372283,"journal":{"name":"Universal Journal of Applied Mathematics","volume":"29 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2016-09-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"114798310","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 : 2016-06-01DOI: 10.13189/UJAM.2016.040201
S. Tomita, Oliver Couto
Different authors have done analysis regarding sums of powers (Ref. no. 1,2 & 3), but systematic approach for solving Diophantine equations having sums of many bi-quadratics equal to a quartic has not been done before. In this paper we give methods for finding numerical solutions to equation (A) given above in section one. Next in section two, we give methods for finding numerical solutions for equation (B) given above. It is known that finding parametric solutions to biquadratic equations is not easy by conventional method. So the authors have found numerical solutions to equation (A) & (B) using elliptic curve theory.
{"title":"Methods for Arriving at Numerical Solutions for Equations of the Type (k+3) & (k+5) Bi-quadratic's Equal to a Bi-quadratic (For Different Values of k)","authors":"S. Tomita, Oliver Couto","doi":"10.13189/UJAM.2016.040201","DOIUrl":"https://doi.org/10.13189/UJAM.2016.040201","url":null,"abstract":"Different authors have done analysis regarding sums of powers (Ref. no. 1,2 & 3), but systematic approach for solving Diophantine equations having sums of many bi-quadratics equal to a quartic has not been done before. In this paper we give methods for finding numerical solutions to equation (A) given above in section one. Next in section two, we give methods for finding numerical solutions for equation (B) given above. It is known that finding parametric solutions to biquadratic equations is not easy by conventional method. So the authors have found numerical solutions to equation (A) & (B) using elliptic curve theory.","PeriodicalId":372283,"journal":{"name":"Universal Journal of Applied Mathematics","volume":"16 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2016-06-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"127653277","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 : 2016-03-01DOI: 10.13189/ujam.2016.040103
S. Tomita, Oliver Couto
Consider the below mentioned equation: x4+y4+z4=w∗tn----(A). Historically Leonard Euler has given parametric solution for equation (A) when w=1 (Ref. no. 9) and degree ‘n'=2. Also S. Realis has given parametric solution for equation (A) when ‘w' equals 1 and degree ‘n' =3. More examples can be found in math literature (Ref. no.6). As is known that solving Diophantine equations for degree greater than four is difficult and the novelty of this paper is that we have done a systematic approach and has provided parametric solutions for degree's ‘n' = (2,3,4,5,6,7,8 & 9 ) for different values of 'w'. The paper is divided into sections (A to H) for degrees (2 to 9) respectively. x4+y4+z4=w∗tn--- (A)
{"title":"Sum of Three Biquadatics a Multiple of a n th Power, n = (2,3,4,5,6,7,8 & 9)","authors":"S. Tomita, Oliver Couto","doi":"10.13189/ujam.2016.040103","DOIUrl":"https://doi.org/10.13189/ujam.2016.040103","url":null,"abstract":"Consider the below mentioned equation: x4+y4+z4=w∗tn----(A). Historically Leonard Euler has given parametric solution for equation (A) when w=1 (Ref. no. 9) and degree ‘n'=2. Also S. Realis has given parametric solution for equation (A) when ‘w' equals 1 and degree ‘n' =3. More examples can be found in math literature (Ref. no.6). As is known that solving Diophantine equations for degree greater than four is difficult and the novelty of this paper is that we have done a systematic approach and has provided parametric solutions for degree's ‘n' = (2,3,4,5,6,7,8 & 9 ) for different values of 'w'. The paper is divided into sections (A to H) for degrees (2 to 9) respectively. x4+y4+z4=w∗tn--- (A)","PeriodicalId":372283,"journal":{"name":"Universal Journal of Applied Mathematics","volume":"198 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2016-03-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"114617813","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 : 2014-10-01DOI: 10.13189/UJAM.2014.020801
Z. Khan, R. Razali, Sarfaraz Ahmed
The Reliability Prediction is an important tool for designing, decision making and estimating future system success. Design engineers are often required to develop and estimate Reliability before the product is produced. Inaccurate predictions can lead to over design and/or excessive spare parts procurement. This work is based on the study of Reliability Analysis carried out on Electronic Communication Systems used in the aircraft avionics. This system was applied in the beginning for the Secure Speech Equipment designed specifically to encrypt voices as well as for fax and computer data. The Part Stress Analysis modeling is used in this study which is a worldwide standard for performing reliability predictions. The Reliability Block diagram is also developed as a tool for reliability prediction.
{"title":"The Reliability Predictions for the Avionics Equipment","authors":"Z. Khan, R. Razali, Sarfaraz Ahmed","doi":"10.13189/UJAM.2014.020801","DOIUrl":"https://doi.org/10.13189/UJAM.2014.020801","url":null,"abstract":"The Reliability Prediction is an important tool for designing, decision making and estimating future system success. Design engineers are often required to develop and estimate Reliability before the product is produced. Inaccurate predictions can lead to over design and/or excessive spare parts procurement. This work is based on the study of Reliability Analysis carried out on Electronic Communication Systems used in the aircraft avionics. This system was applied in the beginning for the Secure Speech Equipment designed specifically to encrypt voices as well as for fax and computer data. The Part Stress Analysis modeling is used in this study which is a worldwide standard for performing reliability predictions. The Reliability Block diagram is also developed as a tool for reliability prediction.","PeriodicalId":372283,"journal":{"name":"Universal Journal of Applied Mathematics","volume":"45 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2014-10-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"129945627","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 : 2014-08-01DOI: 10.13189/UJAM.2014.020702
P. Sharma, Mukesh Dutt
This communication investigates the effect of magnetic field on unsteady free convection oscillatory flow through vertical parallel porous flat plates, when free stream velocity, temperature and concentration oscillates in time about a non zero constant mean. The governing equations are solved by adopting complex variable notations. The analytical expression for velocity, temperature and concentration fields have been obtained using perturbation technique. The effect of various parameters on mean flow velocity, transient velocity, transient temperature, transient concentration, mean skin frication, amplitude and phase of skin-friction and heat transfer have been discussed and shown graphically.
{"title":"MHD Oscillatory Free Convection Flow Past Parallel Plates with Periodic Temperature and Concentration","authors":"P. Sharma, Mukesh Dutt","doi":"10.13189/UJAM.2014.020702","DOIUrl":"https://doi.org/10.13189/UJAM.2014.020702","url":null,"abstract":"This communication investigates the effect of magnetic field on unsteady free convection oscillatory flow through vertical parallel porous flat plates, when free stream velocity, temperature and concentration oscillates in time about a non zero constant mean. The governing equations are solved by adopting complex variable notations. The analytical expression for velocity, temperature and concentration fields have been obtained using perturbation technique. The effect of various parameters on mean flow velocity, transient velocity, transient temperature, transient concentration, mean skin frication, amplitude and phase of skin-friction and heat transfer have been discussed and shown graphically.","PeriodicalId":372283,"journal":{"name":"Universal Journal of Applied Mathematics","volume":"13 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2014-08-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"116695263","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 : 2014-08-01DOI: 10.13189/UJAM.2014.020701
A. Denk, S. Topal
In this paper, we consider the existence of triple positive solutions for the second order semipositone m-point boundary value problem on time scales. We emphasize that the nonlinear term f may take a negative value.
本文考虑了时间尺度上二阶半正数m点边值问题三正解的存在性。我们强调非线性项f可以取负值。
{"title":"Existence of Three Positive Solutions of Semipositone Boundary Value Problems on Time Scales","authors":"A. Denk, S. Topal","doi":"10.13189/UJAM.2014.020701","DOIUrl":"https://doi.org/10.13189/UJAM.2014.020701","url":null,"abstract":"In this paper, we consider the existence of triple positive solutions for the second order semipositone m-point boundary value problem on time scales. We emphasize that the nonlinear term f may take a negative value.","PeriodicalId":372283,"journal":{"name":"Universal Journal of Applied Mathematics","volume":"46 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2014-08-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"128048470","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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