Pub Date : 2021-06-30DOI: 10.11648/j.acm.20211003.14
E. S. Shoukralla
We establish a new straightforward interpolation method for solving linear Volterra integral equations with weakly singular kernels. The proposed method is fundamentally different from all other published methods for solving this type of equations. We have modified some vector-matrix barycentric Lagrange interpolation formulas to be convenient for interpolating the kernel twice concerning the two variables of the kernel and introducing new ideas for selecting interpolation nodes that ensure isolation of the singularity of the kernel. We create two rules for selecting the distribution nodes of the two kernel variables that do not allow the denominator of the kernel to contain an imaginary value. We interpolate the unknown and data functions into the corresponding interpolant polynomial; each of the same degree via three matrices, one of which is a monomial. By applying the presented method based on the two created rules, we transformed the kernel into a double interpolant polynomial with a degree equal to that of the unknown function via five matrices, two of which are monomials. We substitute the interpolate unknown function twice; on the left side and on the right side of the integral equation to get an algebraic linear system without applying the collocation method. The solution of this system yields the unknown coefficients matrix that is necessary to find the interpolant solution. We solve three different examples for different values of the upper integration variable. The obtained results as shown in tables and figures prove that the obtained interpolate solutions are extraordinarily faster to converge to the exact ones using interpolants of lowest degrees and give better results than those obtained by other methods. This confirms the originality and the potential of the presented method.
{"title":"Interpolation Method for Solving Weakly Singular Integral Equations of the Second Kind","authors":"E. S. Shoukralla","doi":"10.11648/j.acm.20211003.14","DOIUrl":"https://doi.org/10.11648/j.acm.20211003.14","url":null,"abstract":"We establish a new straightforward interpolation method for solving linear Volterra integral equations with weakly singular kernels. The proposed method is fundamentally different from all other published methods for solving this type of equations. We have modified some vector-matrix barycentric Lagrange interpolation formulas to be convenient for interpolating the kernel twice concerning the two variables of the kernel and introducing new ideas for selecting interpolation nodes that ensure isolation of the singularity of the kernel. We create two rules for selecting the distribution nodes of the two kernel variables that do not allow the denominator of the kernel to contain an imaginary value. We interpolate the unknown and data functions into the corresponding interpolant polynomial; each of the same degree via three matrices, one of which is a monomial. By applying the presented method based on the two created rules, we transformed the kernel into a double interpolant polynomial with a degree equal to that of the unknown function via five matrices, two of which are monomials. We substitute the interpolate unknown function twice; on the left side and on the right side of the integral equation to get an algebraic linear system without applying the collocation method. The solution of this system yields the unknown coefficients matrix that is necessary to find the interpolant solution. We solve three different examples for different values of the upper integration variable. The obtained results as shown in tables and figures prove that the obtained interpolate solutions are extraordinarily faster to converge to the exact ones using interpolants of lowest degrees and give better results than those obtained by other methods. This confirms the originality and the potential of the presented method.","PeriodicalId":55503,"journal":{"name":"Applied and Computational Mathematics","volume":"11 1","pages":""},"PeriodicalIF":10.0,"publicationDate":"2021-06-30","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"88489621","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":2,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2021-06-29DOI: 10.11648/j.acm.20211003.13
A. J. Ogunniran, Kayode S. Adekeye, J. Adewara, M. Adamu
When one or more observations fall outside the control limits, the chart signals the existence of a change in the process. Change point detection is helpful in modelling and prediction of time series and is found in broader areas of applications including process monitoring. Three approaches were proposed for estimating change point in process for the different types of changes in the literature. they are: Maximum Likelihood Estimator (MLE), the Cumulative Sum (CUSUM), and the Exponentially Weighted Moving Average (EWMA) approaches. This paper gives a synopsis of change point estimation, specifies, categorizes, and evaluates many of the methods that have been recommended for detecting change points in process monitoring. The change points articles in the literature were categorized broadly under five categories, namely: types of process, types of data, types of change, types of phase and methods of estimation. Aside the five broad categories, we also included the parameter involved. Furthermore, the use of control charts and other monitoring tools used to detect abrupt changes in processes were reviewed and the gaps for process monitoring/controlling were examined. A combination of different methods of estimation will be a valuable approach to finding the best estimates of change point models. Further research studies would include assessing the sensitivity of the various change point estimators to deviations in the underlying distributional assumptions.
{"title":"A Review of Change Point Estimation Methods for Process Monitoring","authors":"A. J. Ogunniran, Kayode S. Adekeye, J. Adewara, M. Adamu","doi":"10.11648/j.acm.20211003.13","DOIUrl":"https://doi.org/10.11648/j.acm.20211003.13","url":null,"abstract":"When one or more observations fall outside the control limits, the chart signals the existence of a change in the process. Change point detection is helpful in modelling and prediction of time series and is found in broader areas of applications including process monitoring. Three approaches were proposed for estimating change point in process for the different types of changes in the literature. they are: Maximum Likelihood Estimator (MLE), the Cumulative Sum (CUSUM), and the Exponentially Weighted Moving Average (EWMA) approaches. This paper gives a synopsis of change point estimation, specifies, categorizes, and evaluates many of the methods that have been recommended for detecting change points in process monitoring. The change points articles in the literature were categorized broadly under five categories, namely: types of process, types of data, types of change, types of phase and methods of estimation. Aside the five broad categories, we also included the parameter involved. Furthermore, the use of control charts and other monitoring tools used to detect abrupt changes in processes were reviewed and the gaps for process monitoring/controlling were examined. A combination of different methods of estimation will be a valuable approach to finding the best estimates of change point models. Further research studies would include assessing the sensitivity of the various change point estimators to deviations in the underlying distributional assumptions.","PeriodicalId":55503,"journal":{"name":"Applied and Computational Mathematics","volume":"120 1","pages":""},"PeriodicalIF":10.0,"publicationDate":"2021-06-29","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"77411836","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":2,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2021-06-26DOI: 10.11648/j.acm.20211003.12
Malick Fall, I. Faye, Alassane Sy, D. Seck
The fractional Laplacian is a nonlocal operator that appears in biology, in physic, in fluids dynamic, in financial mathematics and probability. This paper deals with shape optimization problem associated to the fractional laplacian ∆s, 0 under constraints volume. Finally, shape derivative of the functional is established by using Hadamard formula’s and an optimality condition is also given.
{"title":"On Shape Optimization Theory with Fractional Laplacian","authors":"Malick Fall, I. Faye, Alassane Sy, D. Seck","doi":"10.11648/j.acm.20211003.12","DOIUrl":"https://doi.org/10.11648/j.acm.20211003.12","url":null,"abstract":"The fractional Laplacian is a nonlocal operator that appears in biology, in physic, in fluids dynamic, in financial mathematics and probability. This paper deals with shape optimization problem associated to the fractional laplacian ∆s, 0 under constraints volume. Finally, shape derivative of the functional is established by using Hadamard formula’s and an optimality condition is also given.","PeriodicalId":55503,"journal":{"name":"Applied and Computational Mathematics","volume":"95 10","pages":""},"PeriodicalIF":10.0,"publicationDate":"2021-06-26","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"72538180","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":2,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2021-06-22DOI: 10.11648/j.acm.20211003.11
Nicolae Popoviciu
In a very small t-time interval, several runners could occupy the same place on the arrival line (hypothesis 1). Each runner has his own name and a competition number (on the shirt). The number of runners is a natural number n. For each given n, the hypothesis creates a combinatorial problem having a lot of posible states. All notations are choose so that to indicate easily by name their meaning. The states are separated into two classes: non-nominal states and nominal states. The states are related with the place I, II, III etc on arrival line. It is necessary to generate the total number of non-nominal states (on arrival line) and the total number of nominal states. In order to generate the states the work uses some formulas and some specialised algorithms. For example, the consrtuction of all non-nominal states recommends that the string for the position I to use a decreasing string. The same rule is validly for position II, but for sub-strings etc. A lot of numerical examples ilustrate the states generation. An independent method verifies the correctitude of states generation. In order to continue the study of combinatorial problem, the work introduces two new notions in section 5. The notions of partial frequency and final frequency are defined for a nominal known runner in final classification, together with computational formulas. The section 6 constructs the random variables attached to final classification and the probability of each place on arrival line. Each runner receives a score (a number of points) related with his final classification. May be the runner is interested to know the probability to ocuppy the first place (place I) and to estimate the number of possible points. All the results could be written in a centralisation table (section 7). Section 8 contains several numerical examples with statistical computations. At the end of the work we replace hypothesis 1 by hypothesis 2: only one runner could ocuppay each place. All the above notions have a new specific form. The numerical examples ilustrates the theory.
{"title":"Two Hypothesis on a Combinatorial Problem for Possible States on the Arrival Line for n Competitor Runners","authors":"Nicolae Popoviciu","doi":"10.11648/j.acm.20211003.11","DOIUrl":"https://doi.org/10.11648/j.acm.20211003.11","url":null,"abstract":"In a very small t-time interval, several runners could occupy the same place on the arrival line (hypothesis 1). Each runner has his own name and a competition number (on the shirt). The number of runners is a natural number n. For each given n, the hypothesis creates a combinatorial problem having a lot of posible states. All notations are choose so that to indicate easily by name their meaning. The states are separated into two classes: non-nominal states and nominal states. The states are related with the place I, II, III etc on arrival line. It is necessary to generate the total number of non-nominal states (on arrival line) and the total number of nominal states. In order to generate the states the work uses some formulas and some specialised algorithms. For example, the consrtuction of all non-nominal states recommends that the string for the position I to use a decreasing string. The same rule is validly for position II, but for sub-strings etc. A lot of numerical examples ilustrate the states generation. An independent method verifies the correctitude of states generation. In order to continue the study of combinatorial problem, the work introduces two new notions in section 5. The notions of partial frequency and final frequency are defined for a nominal known runner in final classification, together with computational formulas. The section 6 constructs the random variables attached to final classification and the probability of each place on arrival line. Each runner receives a score (a number of points) related with his final classification. May be the runner is interested to know the probability to ocuppy the first place (place I) and to estimate the number of possible points. All the results could be written in a centralisation table (section 7). Section 8 contains several numerical examples with statistical computations. At the end of the work we replace hypothesis 1 by hypothesis 2: only one runner could ocuppay each place. All the above notions have a new specific form. The numerical examples ilustrates the theory.","PeriodicalId":55503,"journal":{"name":"Applied and Computational Mathematics","volume":"32 1","pages":""},"PeriodicalIF":10.0,"publicationDate":"2021-06-22","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"74410475","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":2,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2021-06-16DOI: 10.11648/j.acm.20211002.12
Ernesto Borges Batista, Luis Alberto Escalona Fernández, Kirelis Napoles Dominguez, Y. Sarmiento, Claudia del Carmen Pupo Marrero
Aims: Fractal for comparison of radiological imagery between morphologic and pathological elements confirms the behavior of the experimental information through dimension itself. The irregularity of the human body is its own characteristic. However, it has traditionally been measured with Euclidean metrics, by approximating its shapes to regular lines, areas and volumes. In response to this impossibility of making reliable measurements of this class of objects, fractal geometry is developed, which allows to adequately characterize the irregular shape of the human body. Method: they use the theoretic methods: Analysis synthesis, induction deduction and abstraction concretion. Processes of understanding, explanation and interpretation. Methods, procedures and mathematical algorithms, as well as information-technology professional programs are applicable. Come true quest of information about the application of dimension fractal in the diagnostic one belonging to diseases, based in radiological imagery. The diagnostic method fractal consists in the calculation of dimension for three cellular objects defined as: the nucleus, the cytoplasm without a nucleus and the entire cell. Results: Methods and procedures to ratify diseases, where the different authors yield a mathematical model, propose which themselves fractal for the comparison of histological and pathological elements confirms the behavior of the experimental data represented in radiological imagery, by means of dimension. About fractal geometry, the fractal dimension is obtained, which is a numerical measure that represents the degree of irregularity of an object. However, it has traditionally been measured with Euclidean metrics, by approximating its shapes to regular lines, areas and volumes. In response to this impossibility of making reliable measurements of this class of objects, fractal geometry is developed, which allows to adequately characterize the irregular shape of the human body. Conclusions: A methodology of work based in radiological imagery by comparison of histological and pathological elements to determine different diseases in patients becomes established.
{"title":"Dimension Fractal in Radiological Imagery for Comparison of Data Between Morphologic and Pathological Elements","authors":"Ernesto Borges Batista, Luis Alberto Escalona Fernández, Kirelis Napoles Dominguez, Y. Sarmiento, Claudia del Carmen Pupo Marrero","doi":"10.11648/j.acm.20211002.12","DOIUrl":"https://doi.org/10.11648/j.acm.20211002.12","url":null,"abstract":"Aims: Fractal for comparison of radiological imagery between morphologic and pathological elements confirms the behavior of the experimental information through dimension itself. The irregularity of the human body is its own characteristic. However, it has traditionally been measured with Euclidean metrics, by approximating its shapes to regular lines, areas and volumes. In response to this impossibility of making reliable measurements of this class of objects, fractal geometry is developed, which allows to adequately characterize the irregular shape of the human body. Method: they use the theoretic methods: Analysis synthesis, induction deduction and abstraction concretion. Processes of understanding, explanation and interpretation. Methods, procedures and mathematical algorithms, as well as information-technology professional programs are applicable. Come true quest of information about the application of dimension fractal in the diagnostic one belonging to diseases, based in radiological imagery. The diagnostic method fractal consists in the calculation of dimension for three cellular objects defined as: the nucleus, the cytoplasm without a nucleus and the entire cell. Results: Methods and procedures to ratify diseases, where the different authors yield a mathematical model, propose which themselves fractal for the comparison of histological and pathological elements confirms the behavior of the experimental data represented in radiological imagery, by means of dimension. About fractal geometry, the fractal dimension is obtained, which is a numerical measure that represents the degree of irregularity of an object. However, it has traditionally been measured with Euclidean metrics, by approximating its shapes to regular lines, areas and volumes. In response to this impossibility of making reliable measurements of this class of objects, fractal geometry is developed, which allows to adequately characterize the irregular shape of the human body. Conclusions: A methodology of work based in radiological imagery by comparison of histological and pathological elements to determine different diseases in patients becomes established.","PeriodicalId":55503,"journal":{"name":"Applied and Computational Mathematics","volume":"44 1","pages":""},"PeriodicalIF":10.0,"publicationDate":"2021-06-16","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"74014481","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":2,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2021-04-16DOI: 10.11648/J.ACM.20211002.11
Bazuaye Frank Etin-Osa, Ezeora Jeremiah
The use of Mathematical models to describe the transmission of infectious diseases has attracted a lot of interest over the years and serious worldwide effort is accelerating the developments in the establishment of a global efforts for combating pandemics of infectious diseases. Scientists from different fields have teamed up for rapid assessment of potentially immediate situations. Toward this aim, mathematical modeling plays an important role in efforts that focus on predicting, assessing, and controlling potential outbreaks. The recent outbreak of covid 19 pandemic had increased the curiosity for the formulation of Mathematical models to describe and analyze the propagation of the disease. This paper focuses on the modeling and analysis of an infectious diseases model using the extended Laplace Adomian Decomposition (LAD) method. The method is used to obtain solutions in the form of infinite series. The result of the research with the aid of MAPLE indicates that physical contact with an infected person is the major cause of the propagation of any infectious disease in the absence of pharmaceutical and non pharmaceutical safety protocols such as the proper use of face mask, physical and social distancing. It becomes vital to subject the infected persons in isolation and adhere to the necessary protocols by relevance agencies and this will significantly flattened the curve of the spread of the infectious disease.
{"title":"Modelling and Solution of Infectious Diseases Using the Extended Laplace Adomian Decomposition Techniques","authors":"Bazuaye Frank Etin-Osa, Ezeora Jeremiah","doi":"10.11648/J.ACM.20211002.11","DOIUrl":"https://doi.org/10.11648/J.ACM.20211002.11","url":null,"abstract":"The use of Mathematical models to describe the transmission of infectious diseases has attracted a lot of interest over the years and serious worldwide effort is accelerating the developments in the establishment of a global efforts for combating pandemics of infectious diseases. Scientists from different fields have teamed up for rapid assessment of potentially immediate situations. Toward this aim, mathematical modeling plays an important role in efforts that focus on predicting, assessing, and controlling potential outbreaks. The recent outbreak of covid 19 pandemic had increased the curiosity for the formulation of Mathematical models to describe and analyze the propagation of the disease. This paper focuses on the modeling and analysis of an infectious diseases model using the extended Laplace Adomian Decomposition (LAD) method. The method is used to obtain solutions in the form of infinite series. The result of the research with the aid of MAPLE indicates that physical contact with an infected person is the major cause of the propagation of any infectious disease in the absence of pharmaceutical and non pharmaceutical safety protocols such as the proper use of face mask, physical and social distancing. It becomes vital to subject the infected persons in isolation and adhere to the necessary protocols by relevance agencies and this will significantly flattened the curve of the spread of the infectious disease.","PeriodicalId":55503,"journal":{"name":"Applied and Computational Mathematics","volume":"368 1","pages":""},"PeriodicalIF":10.0,"publicationDate":"2021-04-16","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"76758156","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":2,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2021-03-30DOI: 10.11648/J.ACM.20211001.13
Francis Bassono, Rasmané Yaro, J. B. Yindoula, Gires Dimitri Nkaya, Gabriel Bissanga
Data on solving of nonlinear integro-differential equations using Laplace-SBA method are scarce. The objective of this paper is to determine exact solution of nonlinear 2 dimensionnal Voltera-Fredholm differential equation by this method. First, SBA method and Laplace SBA method are described. Second, three nonlinear Voolterra-Fredholm integro-differential equations are solved using each method. Application of each method give an exact solution. However, application of Laplace-SBA method permits for solve integro-differential equation compared with SBA method. This proves that this last method can be fruitfully applied in the resolution of integro-differential equations.
{"title":"About Exact Solution of Some Non Linear Partial Integro-differential Equations","authors":"Francis Bassono, Rasmané Yaro, J. B. Yindoula, Gires Dimitri Nkaya, Gabriel Bissanga","doi":"10.11648/J.ACM.20211001.13","DOIUrl":"https://doi.org/10.11648/J.ACM.20211001.13","url":null,"abstract":"Data on solving of nonlinear integro-differential equations using Laplace-SBA method are scarce. The objective of this paper is to determine exact solution of nonlinear 2 dimensionnal Voltera-Fredholm differential equation by this method. First, SBA method and Laplace SBA method are described. Second, three nonlinear Voolterra-Fredholm integro-differential equations are solved using each method. Application of each method give an exact solution. However, application of Laplace-SBA method permits for solve integro-differential equation compared with SBA method. This proves that this last method can be fruitfully applied in the resolution of integro-differential equations.","PeriodicalId":55503,"journal":{"name":"Applied and Computational Mathematics","volume":"1 1","pages":""},"PeriodicalIF":10.0,"publicationDate":"2021-03-30","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"75425084","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":2,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2021-03-12DOI: 10.11648/J.ACM.20211001.12
S. Charles, R. John, Adicka Daniel
The Navier-Stokes (N-S) equations for incompressible fluid flow comprise of a system of four nonlinear equations with five flow fields such as pressure P, density ρ and three velocity components u, v, and w. The system of equations is generally complex due to the fact that it is nonlinear and a mixture of the three classes of partial differential equations (PDEs) each with distinct solution methods. The N-S equations fully describe the unsteady fluid flow behaviour of laminar and turbulent types. Previous studies have shown existence of general solutions of fluid flow models but little has been done on numerical solution for velocity of flow in N-S equation of incompressible fluid flow by Crank-Nicolson implicit scheme. In practice, real fluid flows are compressible due to the inevitable variations in density caused by temperature changes and other physical factors. Numerical approximations of the general system of Navier-Stokes equations were made to develop numerical solution model for incompressible fluid flow. Adequate solutions of the latter produce numerical solutions applicable in numerical simulation of fluid flows useful in engineering and science. Non-dimensionalization of variables involved was done. Crank-Nicolson (C.N) implicit scheme was implemented to discretize partial derivatives and appropriate approximation made at the boundaries yielded a linear system of N-S equations model. The linear numerical system was then expressed in matrix form for computation of velocity field by Computational fluid dynamics (CFD) approach using MATLAB software. Numerical results for velocity field in two dimensional space, u(x,y,t)and v(x,y,t) generated in uniform 32×32 grids points of the square flow domains, 0≤x≤1.0 and 0≤y≤1.0 were presented in three dimensional figures. Results showed that the velocity in two dimensional space does not change suddenly for any change in spatial levels, x and y. Therefore, C-N implicit Scheme applied to solve the N-S equations for fluid flow is consistent.
{"title":"Numerical Solution of the Navier-Stokes Equations for Incompressible Fluid Flow by Crank-Nicolson Implicit Scheme","authors":"S. Charles, R. John, Adicka Daniel","doi":"10.11648/J.ACM.20211001.12","DOIUrl":"https://doi.org/10.11648/J.ACM.20211001.12","url":null,"abstract":"The Navier-Stokes (N-S) equations for incompressible fluid flow comprise of a system of four nonlinear equations with five flow fields such as pressure P, density ρ and three velocity components u, v, and w. The system of equations is generally complex due to the fact that it is nonlinear and a mixture of the three classes of partial differential equations (PDEs) each with distinct solution methods. The N-S equations fully describe the unsteady fluid flow behaviour of laminar and turbulent types. Previous studies have shown existence of general solutions of fluid flow models but little has been done on numerical solution for velocity of flow in N-S equation of incompressible fluid flow by Crank-Nicolson implicit scheme. In practice, real fluid flows are compressible due to the inevitable variations in density caused by temperature changes and other physical factors. Numerical approximations of the general system of Navier-Stokes equations were made to develop numerical solution model for incompressible fluid flow. Adequate solutions of the latter produce numerical solutions applicable in numerical simulation of fluid flows useful in engineering and science. Non-dimensionalization of variables involved was done. Crank-Nicolson (C.N) implicit scheme was implemented to discretize partial derivatives and appropriate approximation made at the boundaries yielded a linear system of N-S equations model. The linear numerical system was then expressed in matrix form for computation of velocity field by Computational fluid dynamics (CFD) approach using MATLAB software. Numerical results for velocity field in two dimensional space, u(x,y,t)and v(x,y,t) generated in uniform 32×32 grids points of the square flow domains, 0≤x≤1.0 and 0≤y≤1.0 were presented in three dimensional figures. Results showed that the velocity in two dimensional space does not change suddenly for any change in spatial levels, x and y. Therefore, C-N implicit Scheme applied to solve the N-S equations for fluid flow is consistent.","PeriodicalId":55503,"journal":{"name":"Applied and Computational Mathematics","volume":"17 1","pages":"10"},"PeriodicalIF":10.0,"publicationDate":"2021-03-12","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"88978570","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":2,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2021-02-10DOI: 10.11648/J.ACM.20211001.11
J. Pahade, M. Jha
Dealing with problems on portfolio selection models fuzzy set theory is effectively interpolating investor’s attitude. The credibility theory (Branch of fuzzy set theory) is broadly utilized to describe uncertainty of the financial markets. We regard the return rate of each risky stock as a trapezoidal fuzzy number. Variance and semi-variance of fuzzy return on stocks are widely accepted as risk measures in portfolio selection models. This paper obtains credibilistic semi-variance of trapezoidal fuzzy variable and applied this concept to quantify the risk in stock fuzzy portfolio selection. A multi-criteria credibilistic mean-semivariance-skewness model is proposed with numerical illustration taking historical data set from the premier market for financial assets. Three objectives are taken into account namely, expected portfolio return, risk on expected portfolio return and portfolio skewness to construct multi-objective programming problem, along with cardinality constraint, complete capital utilization, floor and ceiling constraint, no short selling constraints. To solve the proposed multi-objective optimization problem, optimal goal programming approach is suggested. Finally, a case study is conducted to highlight the effectiveness of the proposed models through the real-world data from the Bombay Stock Exchange (BSE), an Indian premier market for financial stocks. Furthermore, results comparison of semi-variance as risk measure with other existing risk measures is performed.
{"title":"Multi-criteria Credibilistic Portfolio Selection Model with Various Risk Comparisons Using Trapezoidal Fuzzy Variable","authors":"J. Pahade, M. Jha","doi":"10.11648/J.ACM.20211001.11","DOIUrl":"https://doi.org/10.11648/J.ACM.20211001.11","url":null,"abstract":"Dealing with problems on portfolio selection models fuzzy set theory is effectively interpolating investor’s attitude. The credibility theory (Branch of fuzzy set theory) is broadly utilized to describe uncertainty of the financial markets. We regard the return rate of each risky stock as a trapezoidal fuzzy number. Variance and semi-variance of fuzzy return on stocks are widely accepted as risk measures in portfolio selection models. This paper obtains credibilistic semi-variance of trapezoidal fuzzy variable and applied this concept to quantify the risk in stock fuzzy portfolio selection. A multi-criteria credibilistic mean-semivariance-skewness model is proposed with numerical illustration taking historical data set from the premier market for financial assets. Three objectives are taken into account namely, expected portfolio return, risk on expected portfolio return and portfolio skewness to construct multi-objective programming problem, along with cardinality constraint, complete capital utilization, floor and ceiling constraint, no short selling constraints. To solve the proposed multi-objective optimization problem, optimal goal programming approach is suggested. Finally, a case study is conducted to highlight the effectiveness of the proposed models through the real-world data from the Bombay Stock Exchange (BSE), an Indian premier market for financial stocks. Furthermore, results comparison of semi-variance as risk measure with other existing risk measures is performed.","PeriodicalId":55503,"journal":{"name":"Applied and Computational Mathematics","volume":"1 1","pages":""},"PeriodicalIF":10.0,"publicationDate":"2021-02-10","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"78234358","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":2,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
: With the increasingly serious air pollution problem, PM2.5 concentration, as an effective indicator to evaluate air quality, has attracted extensive attention from all sectors of society. Accurate prediction of PM2.5 concentrations is of great significance in providing the public with early air pollution warning information to protect public health. With a decade of development, artificial intelligence technology has given birth to various prediction models with high-performance, in particular, brought new impetus to the prediction of PM2.5 concentrations. In this study, a stacking-based ensemble model with self-adaptive hyper-parameter optimization is proposed to solve the PM2.5 concentrations prediction problem. First, the raw data are preprocessed with the normalization method to reduce the influence of the different orders of magnitude of input variables on model performance. Second, the Bayesian optimization method is used to optimize the hyper-parameters of the base predictors to improve their performance. Finally, a stacking ensemble method is applied to integrate the optimized base predictors into an ensemble model for final prediction. In the experiments, two datasets from the air quality stations in different areas are tested with four metrics to evaluate the performance of the proposed model in PM2.5 concentration prediction. The experimental results show that the proposed model outperforms other baseline models in solving the PM2.5 concentrations prediction problem.
{"title":"Predicting PM2.5 Concentrations Using Stacking-based Ensemble Model","authors":"Haoyuan Zhang, Yilun Jin, Jiaxuan Shi, Shuai Zhang","doi":"10.11648/j.acm.20211006.14","DOIUrl":"https://doi.org/10.11648/j.acm.20211006.14","url":null,"abstract":": With the increasingly serious air pollution problem, PM2.5 concentration, as an effective indicator to evaluate air quality, has attracted extensive attention from all sectors of society. Accurate prediction of PM2.5 concentrations is of great significance in providing the public with early air pollution warning information to protect public health. With a decade of development, artificial intelligence technology has given birth to various prediction models with high-performance, in particular, brought new impetus to the prediction of PM2.5 concentrations. In this study, a stacking-based ensemble model with self-adaptive hyper-parameter optimization is proposed to solve the PM2.5 concentrations prediction problem. First, the raw data are preprocessed with the normalization method to reduce the influence of the different orders of magnitude of input variables on model performance. Second, the Bayesian optimization method is used to optimize the hyper-parameters of the base predictors to improve their performance. Finally, a stacking ensemble method is applied to integrate the optimized base predictors into an ensemble model for final prediction. In the experiments, two datasets from the air quality stations in different areas are tested with four metrics to evaluate the performance of the proposed model in PM2.5 concentration prediction. The experimental results show that the proposed model outperforms other baseline models in solving the PM2.5 concentrations prediction problem.","PeriodicalId":55503,"journal":{"name":"Applied and Computational Mathematics","volume":"231 1","pages":""},"PeriodicalIF":10.0,"publicationDate":"2021-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"80260317","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":2,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
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