Department of Applied Mathematics (1991 - Present)
Math
, Wales, England
Math
, Montreal, Canada
Math
, Razi University of Kermanshah,
Research field:
Expert:
Phone:
Address:
Please see my resume
In this paper, a novel scheme based on strongly continuous semigroup is proposed to find a pointwise optimal control function in a biological tissue. Here, mathematical model for hyperthermia therapy involves solution to the thermal wave equation as state while the control is given by the pointwise time dependent heat source. The target is the temperature at a given point within the tumor. Pointwise optimal control problem on and inside a tissue is solved subject to thermal wave model with Dirichlet and Rubin boundary conditions. The pointwise heating source induced by heating probe inserted at the tumor site as control at specific depth inside the biological body. Solutions for both thermal wave problem and its associated adjoint problem a
In this paper, the boundary element method is combined with Chebyshev operational matrix technique to solve two‐dimensional multiorder time‐fractional partial differential equations: nonlinear and linear in respect to spatial and temporal variables, respectively. Fractional derivatives are estimated by Caputo sense. Boundary element method is used to convert the main problem into a system of a multiorder fractional ordinary differential equation. Then, the produced system is approximated by Chebyshev operational matrix technique, and its condition number is analyzed. Accuracy and efficiency of the proposed hybrid scheme are demonstrated by solving three different types of two‐dimensional time‐fractional convection–diffusion equati
In this paper, the problem of social distancing in the spread of infectious diseases in the human network is extended by optimal control and differential game approaches. Hear, SEAIR model on simulation network is used. Total costs for both approaches are formulated as objective functions. SEAIR dynamics for group k that contacts with k individuals including susceptible, exposed, asymptomatically infected, symptomatically infected and improved or safe individuals is modeled. A novel random model including the concept of social distancing and relative risk of infection using Markov process is proposed. For each group, an aggregate investment is derived and computed using adjoint equations and maximum principle. Results show that for each gr
In this paper, we focus on two basic issues:(a) the classification of sound by neural networks based on frequency and sound intensity parameters (b) evaluating the health of different human ears as compared to of those a healthy person. Sound classification by a specific feed forward neural network with two inputs as frequency and sound intensity and two hidden layers is proposed. This process results in categorization of audible and non-audible (dangerous) sounds for a healthy person. In the diagnosis of healthy ear, having the relevant parameters, using the method of machine learning by feed forward neural networks, and simpson and trapezoidal numerical integration rules, the hearing and pain thresholds of the patientchr ('39') s ear are
In order to simulate the hyperthermia cancer therapy in multilayer skin, a solution for Pennes’ bioheat transfer equation based on the strongly continuous semigroups, domain decomposition technique, Laplace transform and numerical inversion of Laplace transform is proposed. In the existence of a tumor, solution at the presence of internal heat source and surface cooling temperature is considered. This solution considers both Dirichlet (body core condition) and Neumann (surface cooling condition) type boundary conditions. The interface conditions for a multilayer problem are derived from the corresponded eigenvalue–eigenfunction formulation of infinitesimal generators. It is proved that an infinitesimal generator is Riesz spectral operat
The home network has become a norm in today's life. Previous studies have shown that home network management is a problem for users who are not in the field of network technology. The existing network management tools are far too difficult to understand by ordinary home network users. Its interface is complex, and does not address the home user's needs in their daily use. This paper presents an interactive network management tool, which emphasizes support features for home network users. The tool combine interactive visual appearance with persuasive approach that support sustainability. It is not only understandable to all categories of home network users, but also acts as a feature for the user to achieve usability.
This paper presents a numerical approach to solve the Hamilton-Jacobi-Bellman (HJB) problem which appears in feedback solution of the optimal control problems. In this method, first, by using Chebyshev pseudospectral spatial discretization, the HJB problem is converted to a system of ordinary differential equations with terminal conditions. Second, the time-marching Runge-Kutta method is used to solve the corresponding system of differential equations. Then, an approximate solution for the HJB problem is computed. In addition, to get more efficient and accurate method, the domain decomposition strategy is proposed with the pseudospectral spatial discretization. Five numerical examples are presented to demonstrate the efficiency and accuracy
In this paper, a neural network model for solving a class of multiextremal smooth nonconvex constrained optimization problems is proposed. Neural network is designed in such a way that its equilibrium points coincide with the local and global optimal solutions of the corresponding optimization problem. Based on the suitable underestimators for the Lagrangian of the problem, one give geometric criteria for an equilibrium point to be a global minimizer of multiextremal constrained optimization problem with or without bounds on the variables. Both necessary and sufficient global optimality conditions for a class of multiextremal constrained optimization problems are presented to determine a global optimal solution. By study of the resulting dy
In this paper, simulation of heat transfer in a heat sink with macroscopic and microscopic scales when one pin-fin is added to the system is investigated by the proposed spectral method. In the microscopic problems, heat transfer model uses dual-phase lag formulas in contrast with macroscopic problems when Fourier law is used to formulate the governing equation. In macroscopic problem, the results are compared with COMSOL multiphysics software results and a good agreement between the results are shown. In microscopic problems, 3D Gaussian heat source is used and boundary conditions obey the Newton law. Comparisons show the efficiency of the current method, while the results are compared with existed literature. It is shown that
In this paper, a compact alternating direction implicit (ADI) method has been developed for solving two-dimensional Riesz space fractional diffusion equation. The precision of the discretization method used in spatial directions is twice the order of the corresponding fractional derivatives. It is proved that the proposed method is unconditionally stable via the matrix analysis method and the maximum error in achieving convergence is discussed. Several numerical examples are considered aiming to demonstrate the validity and applicability of the proposed technique.
In this paper, the boundary element method is combined with Chebyshev operational matrix technique to solve two-dimensional multi-order linear/nonlinear time fractional partial differential equations. Fractional derivatives are estimated by Caputo sense. Boundary element method is used to convert the main problem into a system of multi-order fractional ordinary differential equation. Then, the produced system is approximated by Chebyshev operational matrix technique. Accuracy and efficiency of the proposed hybrid scheme are demonstrated by solving three different types of two-dimensional time fractional convection-diffusion equations numerically. The convergent rates are calculated for different meshing within the boundary element technique
This paper presents a class of semi-implicit finite difference weighted essentially non-oscillatory (WENO) schemes for solving the nonlinear heat equation. For the discretization of second-order spatial derivatives, a sixth-order modified WENO scheme is directly implemented. This scheme preserves the positivity principle and rejects spurious oscillations close to non-smooth points. In order to admit large time steps, a class of implicit Runge–Kutta methods is used for the temporal discretization. The implicit parts of these methods are linearized in time by using the local Taylor expansion of the flux. The stability analysis of the semi-implicit WENO scheme with 3-stages form is provided. Finally, some comparative results for one-, two-an
This paper is about QR code-based automated gate system. The aim of the research is to develop and implement a type of medium-level security gate system especially for small companies that cannot afford to install high-tech auto gate system. IAGS is a system that uses valid staffs' QR code pass card to activate the gate without triggering the alarm. It is developed to connect to the internet and provide a real-time email notification if any unauthorized activities detected. Besides that, it is also designed to record all the incoming and outgoing activities for all staff. All QR code pass cards that are generated to staff will be encrypted to provide integrity to the data. The system is based on items such as PIR motion sensor, servo motor
This paper is about QR code-based automated gate system. The aim of the research is to develop and implement a type of medium-level security gate system especially for small companies that cannot afford to install high-tech auto gate system. IAGS is a system that uses valid staffs’ QR code pass card to activate the gate without triggering the alarm. It is developed to connect to the internet and provide a real-time email notification if any unauthorized activities detected. Besides that, it is also designed to record all the incoming and outgoing activities for all staff. All QR code pass cards that are generated to staff will be encrypted to provide integrity to the data. The system is based on items such as PIR motion sensor, servo moto
In this paper, the boundary element method is combined with Chebyshev operational matrix technique to solve two-dimensional multi-order linear/nonlinear time-fractional partial differential equations. Fractional derivatives are estimated by Caputo sense. Boundary element method is used to convert the main problem into a system of a multi-order fractional ordinary differential equation. Then, the produced system is approximated by Chebyshev operational matrix technique. Accuracy and efficiency of the proposed hybrid scheme are demonstrated by solving three different types of two-dimensional time fractional convection-diffusion equations numerically. The convergent rates are calculated for different meshing within the boundary element techniq
This paper presents a class of semi-implicit finite difference weighted essentially non-oscillatory (WENO) schemes for solving the nonlinear heat equation. For the discretization of second-order spatial derivatives, a sixth-order modified WENO scheme is directly implemented. This scheme preserves the positivity principle and rejects spurious oscillations close to non-smooth points. In order to admit large time steps, a class of implicit Runge-Kutta methods is used for the temporal discretization. The implicit parts of these methods are linearized in time by using the local Taylor expansion of the flux. The stability analysis of the semi-implicit WENO scheme with 3-stages form is provided. Finally, some comparative results for one-, two-and
In this paper, a compact alternating direction implicit (ADI) method has been developed for solving two-dimensional Riesz space fractional diffusion equation. The precision of the discretization method used in spatial directions is twice the order of the corresponding fractional derivatives. It is proved that the proposed method is unconditionally stable via the matrix analysis method and the maximum error in achieving convergence is discussed. Numerical example is considered aiming to demonstrate the validity and applicability of the proposed technique.
This paper presents some novel problems associated with the steady natural convection flow in an inclined square cavity filled with a saturated porous medium. The proposed method is a high-accurate spectral method based on the Fourier–Galerkin technique. The numerical results have demonstrated the advantage for the following reasons. (a) The high-accurate method deals with inclined geometries successfully. (b) The streamlines, isotherms, and the average Nusselt numbers are affected significantly by the inclination of the cavity for high values of Rayleigh number. (c) In contrast with the finite element method a highly accurate and efficient solution with less computational effort is obtained.
In this paper, synchronized control is used for five story structure of Kajima Shizuoka under the EL - Centro earthquake load ?( 1940) seismic record. According to coupled values of displacement, drift and position error the related partial differential equation for motion and state is solved successfully. The Riccati equation is solved based on the close loop transfer function with respect to uncertainty parameters and random dynamic processes. Numerical simulations along with comparisons are made to evaluate the efficiency of this hybrid technique.
no record found