Objective: Our study aims to validate the subjective Bayes mathematical model using the mathematical model of logistic regression. Expert systems are being utilized increasingly in medical fields for the purposes of a...Objective: Our study aims to validate the subjective Bayes mathematical model using the mathematical model of logistic regression. Expert systems are being utilized increasingly in medical fields for the purposes of assisting diagnosis and treatment planning in Dentistry. Existing systems used few symptoms for dental diagnosis. In Dentistry, few symptoms are not enough for diagnosis. In this research, a conditional probability model (Bayes rule) was developed with increased number of symptoms associated with a disease for diagnosis. A test set of recurrent cases was then used to test the diagnostic capacity of the system. The generated diagnosis matched that of the human experts. The system was also tested for its capacity to handle uncommon dental diseases and the system portrayed useful potential. Method: The study used the Subjective Mathematical Bayes Model (SBM) approach and employed Logistic Regression Mathematical Model (LMR) techniques. The external validation of the subjective mathematical Bayes model (MSB) concerns the real cases of 625 patients who developed alveolar osteitis (OA). We propose strategies for reproducibility and reporting standards, outlining an updated WAMBS (when to Worry and how to Avoid the Misuse of Bayesian Statistics) checklist. Finally, we outline the impact of Bayesian analysis Logistic Regression Mathematical Model (LMR) techniques and on artificial intelligence, a major goal in the next decade. Results: The internal validation had identified seven (7) etiological factors of OA, which will be compared to the cases of MRL, for the external validation which retained six (6) etiological factors of OA. The experts in the internal validation of the MSB had generated 40 cases of OA and a COP of (0.5), which will be compared to the MRL that collected 625 real cases of OA to produce a Cop of (0.6) in the external validation, which discriminates between healthy patients (Se) and sick patients (Sp). Compared to real cases and the logistic regression model, the Bayesian model is efficient and its validity is established.展开更多
In this paper, we use the fractional complex transform and the （G＇/G）-expansion method to study the nonlinear fractional differential equations and find the exact solutions. The fractional complex transform is prop...In this paper, we use the fractional complex transform and the （G＇/G）-expansion method to study the nonlinear fractional differential equations and find the exact solutions. The fractional complex transform is proposed to convert a partial fractional differential equation with Jumarie＇s modified Riemann-Liouville derivative into its ordinary differential equation. It is shown that the considered transform and method are very efficient and powerful in solving wide classes of nonlinear fractional order equations.展开更多
In this work, we propose a new approach, namely ansatz method, for solving fractional differential equations based on a fractional complex transform and apply it to the nonlinear partial space-time fractional modified...In this work, we propose a new approach, namely ansatz method, for solving fractional differential equations based on a fractional complex transform and apply it to the nonlinear partial space-time fractional modified Benjamin-Bona- Mahoney （mBBM） equation, the time fractional mKdV equation and the nonlinear fractional Zoomeron equation which gives rise to some new exact solutions. The physical parameters in the soliton solutions： amplitude, inverse width, free parameters and velocity are obtained as functions of the dependent model coefficients. This method is suitable and more powerful for solving other kinds of nonlinear fractional PDEs arising in mathematical physics. Since the fractional deriva- tives are described in the modified Riemann-Liouville sense.展开更多
In this article,we establish new and more general traveling wave solutions of space-time fractional Klein–Gordon equation with quadratic nonlinearity and the space-time fractional breaking soliton equations using the...In this article,we establish new and more general traveling wave solutions of space-time fractional Klein–Gordon equation with quadratic nonlinearity and the space-time fractional breaking soliton equations using the modified simple equation method.The proposed method is so powerful and effective to solve nonlinear space-time fractional differential equations by with modified Riemann–Liouville derivative.展开更多
The present paper deals with the Sharma-Tasso-Olver-Burgers equation(STOBE)and its conservation laws and kink solitons.More precisely,the formal Lagrangian,Lie symmetries,and adjoint equations of the STOBE are firstly...The present paper deals with the Sharma-Tasso-Olver-Burgers equation(STOBE)and its conservation laws and kink solitons.More precisely,the formal Lagrangian,Lie symmetries,and adjoint equations of the STOBE are firstly constructed to retrieve its conservation laws.Kink solitons of the STOBE are then extracted through adopting a series of newly well-designed approaches such as Kudryashov and exponential methods.Diverse graphs in 2 and 3D postures are formally portrayed to reveal the dynamical features of kink solitons.According to the authors’knowledge,the outcomes of the current investigation are new and have been listed for the first time.展开更多
In this article, the fractional derivatives in the sense of modified Riemann-Liouville derivative and the Exp-function method are employed for constructing the exact solutions of nonlinear time fractional partial diff...In this article, the fractional derivatives in the sense of modified Riemann-Liouville derivative and the Exp-function method are employed for constructing the exact solutions of nonlinear time fractional partial differential equations in mathematical physics. As a result, some new exact solutions for them are successfully established. It is indicated that the solutions obtained by the Exp-function method are reliable, straightforward and effective method for strongly nonlinear fractional partial equations with modified Riemann-Liouville derivative by Jumarie's. This approach can also be applied to other nonlinear time and space fractional differential equations.展开更多
In this paper, an approximate function for the Galerkin method is composed using the combination of the exponential B-spline functions. Regularized long wave equation （RLW） is integrated fully by using an exponentia...In this paper, an approximate function for the Galerkin method is composed using the combination of the exponential B-spline functions. Regularized long wave equation （RLW） is integrated fully by using an exponential B-spline Galerkin method in space together with Crank-Nicolson method in time. Three numerical examples related to propagation of sin- gle solitary wave, interaction of two solitary waves and wave generation are employed to illustrate the accuracy and the efficiency of the method. Obtained results are compared with some early studies.展开更多
The Thin Plate Regression Spline (TPRS) was introduced as a means of smoothing off the differences between the satellite and in-situ observations during the two dimensional (2D) blending process in an attempt to calib...The Thin Plate Regression Spline (TPRS) was introduced as a means of smoothing off the differences between the satellite and in-situ observations during the two dimensional (2D) blending process in an attempt to calibrate ocean chlorophyll. The result was a remarkable improvement on the predictive capabilities of the penalized model making use of the satellite observation. In addition, the blending process has been extended to three dimensions (3D) since it is believed that most physical systems exist in the three dimensions (3D). In this article, an attempt to obtain more reliable and accurate predictions of ocean chlorophyll by extending the penalization process to three dimensional (3D) blending is presented. Penalty matrices were computed using the integrated least squares (ILS) and integrated squared derivative (ISD). Results obtained using the integrated least squares were not encouraging, but those obtained using the integrated squared derivative showed a reasonable improvement in predicting ocean chlorophyll especially where the validation datum was surrounded by available data from the satellite data set, however, the process appeared computationally expensive and the results matched the other methods on a general scale. In both case, the procedure for implementing the penalization process in three dimensional blending when penalty matrices were calculated using the two techniques has been well established and can be used in any similar three dimensional problem when it becomes necessary.展开更多
In this study, we investigate the form of the solutions of the following rational difference equation systems? , , such that their solutions are associated with Padovan numbers.
The current study deals with the Kaup-Kupershmidt(KK)equation to construct formal Lagrangian,con-servation laws,and exact solutions.KK is basically a special case of the 5th-order KdV equation.The conservation laws ob...The current study deals with the Kaup-Kupershmidt(KK)equation to construct formal Lagrangian,con-servation laws,and exact solutions.KK is basically a special case of the 5th-order KdV equation.The conservation laws obtained by using the conservation theorem are trivial conservation laws.In addition,exact solutions are found via the modified simple equation(MSE)method.For a suitable value of solu-tions,the 3D surfaces have been plotted using MAPLE.These plots giving novel exact solutions are made to reveal important wave characteristics.Our obtained results in this work concerning our investigated equation are essential to explain many physical and oceanographic applications involving ocean gravity waves and many other related phenomena.展开更多
文摘Objective: Our study aims to validate the subjective Bayes mathematical model using the mathematical model of logistic regression. Expert systems are being utilized increasingly in medical fields for the purposes of assisting diagnosis and treatment planning in Dentistry. Existing systems used few symptoms for dental diagnosis. In Dentistry, few symptoms are not enough for diagnosis. In this research, a conditional probability model (Bayes rule) was developed with increased number of symptoms associated with a disease for diagnosis. A test set of recurrent cases was then used to test the diagnostic capacity of the system. The generated diagnosis matched that of the human experts. The system was also tested for its capacity to handle uncommon dental diseases and the system portrayed useful potential. Method: The study used the Subjective Mathematical Bayes Model (SBM) approach and employed Logistic Regression Mathematical Model (LMR) techniques. The external validation of the subjective mathematical Bayes model (MSB) concerns the real cases of 625 patients who developed alveolar osteitis (OA). We propose strategies for reproducibility and reporting standards, outlining an updated WAMBS (when to Worry and how to Avoid the Misuse of Bayesian Statistics) checklist. Finally, we outline the impact of Bayesian analysis Logistic Regression Mathematical Model (LMR) techniques and on artificial intelligence, a major goal in the next decade. Results: The internal validation had identified seven (7) etiological factors of OA, which will be compared to the cases of MRL, for the external validation which retained six (6) etiological factors of OA. The experts in the internal validation of the MSB had generated 40 cases of OA and a COP of (0.5), which will be compared to the MRL that collected 625 real cases of OA to produce a Cop of (0.6) in the external validation, which discriminates between healthy patients (Se) and sick patients (Sp). Compared to real cases and the logistic regression model, the Bayesian model is efficient and its validity is established.
文摘In this paper, we use the fractional complex transform and the （G＇/G）-expansion method to study the nonlinear fractional differential equations and find the exact solutions. The fractional complex transform is proposed to convert a partial fractional differential equation with Jumarie＇s modified Riemann-Liouville derivative into its ordinary differential equation. It is shown that the considered transform and method are very efficient and powerful in solving wide classes of nonlinear fractional order equations.
文摘In this work, we propose a new approach, namely ansatz method, for solving fractional differential equations based on a fractional complex transform and apply it to the nonlinear partial space-time fractional modified Benjamin-Bona- Mahoney （mBBM） equation, the time fractional mKdV equation and the nonlinear fractional Zoomeron equation which gives rise to some new exact solutions. The physical parameters in the soliton solutions： amplitude, inverse width, free parameters and velocity are obtained as functions of the dependent model coefficients. This method is suitable and more powerful for solving other kinds of nonlinear fractional PDEs arising in mathematical physics. Since the fractional deriva- tives are described in the modified Riemann-Liouville sense.
文摘In this article,we establish new and more general traveling wave solutions of space-time fractional Klein–Gordon equation with quadratic nonlinearity and the space-time fractional breaking soliton equations using the modified simple equation method.The proposed method is so powerful and effective to solve nonlinear space-time fractional differential equations by with modified Riemann–Liouville derivative.
文摘The present paper deals with the Sharma-Tasso-Olver-Burgers equation(STOBE)and its conservation laws and kink solitons.More precisely,the formal Lagrangian,Lie symmetries,and adjoint equations of the STOBE are firstly constructed to retrieve its conservation laws.Kink solitons of the STOBE are then extracted through adopting a series of newly well-designed approaches such as Kudryashov and exponential methods.Diverse graphs in 2 and 3D postures are formally portrayed to reveal the dynamical features of kink solitons.According to the authors’knowledge,the outcomes of the current investigation are new and have been listed for the first time.
文摘In this article, the fractional derivatives in the sense of modified Riemann-Liouville derivative and the Exp-function method are employed for constructing the exact solutions of nonlinear time fractional partial differential equations in mathematical physics. As a result, some new exact solutions for them are successfully established. It is indicated that the solutions obtained by the Exp-function method are reliable, straightforward and effective method for strongly nonlinear fractional partial equations with modified Riemann-Liouville derivative by Jumarie's. This approach can also be applied to other nonlinear time and space fractional differential equations.
基金supported by the Scientific and Technological Research Council of Turkey(Grant No.113F394)
文摘In this paper, an approximate function for the Galerkin method is composed using the combination of the exponential B-spline functions. Regularized long wave equation （RLW） is integrated fully by using an exponential B-spline Galerkin method in space together with Crank-Nicolson method in time. Three numerical examples related to propagation of sin- gle solitary wave, interaction of two solitary waves and wave generation are employed to illustrate the accuracy and the efficiency of the method. Obtained results are compared with some early studies.
文摘The Thin Plate Regression Spline (TPRS) was introduced as a means of smoothing off the differences between the satellite and in-situ observations during the two dimensional (2D) blending process in an attempt to calibrate ocean chlorophyll. The result was a remarkable improvement on the predictive capabilities of the penalized model making use of the satellite observation. In addition, the blending process has been extended to three dimensions (3D) since it is believed that most physical systems exist in the three dimensions (3D). In this article, an attempt to obtain more reliable and accurate predictions of ocean chlorophyll by extending the penalization process to three dimensional (3D) blending is presented. Penalty matrices were computed using the integrated least squares (ILS) and integrated squared derivative (ISD). Results obtained using the integrated least squares were not encouraging, but those obtained using the integrated squared derivative showed a reasonable improvement in predicting ocean chlorophyll especially where the validation datum was surrounded by available data from the satellite data set, however, the process appeared computationally expensive and the results matched the other methods on a general scale. In both case, the procedure for implementing the penalization process in three dimensional blending when penalty matrices were calculated using the two techniques has been well established and can be used in any similar three dimensional problem when it becomes necessary.
文摘In this study, we investigate the form of the solutions of the following rational difference equation systems? , , such that their solutions are associated with Padovan numbers.
文摘The current study deals with the Kaup-Kupershmidt(KK)equation to construct formal Lagrangian,con-servation laws,and exact solutions.KK is basically a special case of the 5th-order KdV equation.The conservation laws obtained by using the conservation theorem are trivial conservation laws.In addition,exact solutions are found via the modified simple equation(MSE)method.For a suitable value of solu-tions,the 3D surfaces have been plotted using MAPLE.These plots giving novel exact solutions are made to reveal important wave characteristics.Our obtained results in this work concerning our investigated equation are essential to explain many physical and oceanographic applications involving ocean gravity waves and many other related phenomena.
