The profile error evaluation of complex curves and surfaces expressed inparametric form is considered. The linear error model is established on the base of two hypothesesfirstly. Then the profile error evaluation is c...The profile error evaluation of complex curves and surfaces expressed inparametric form is considered. The linear error model is established on the base of two hypothesesfirstly. Then the profile error evaluation is converted into one of these optimal formulations:MINIMAX, MAXMIN and MINIDEX problems, which are easier to be solved than the initial form. To eachone of them, geometric condition and algebraic condition are presented to arbitrate whether theideal element reaches to the optimal position. Exchange algorithm is proven highly effective insearching for solutions to these optimization problems. At last some key problems in tolerance offreeform surfaces and curves in B spline method are discussed.展开更多
This paper investigates the numerical solution of the uncertain inverse heat conduction problem. Uncertainties present in the system parameters are modelled through triangular convex normalized fuzzy sets. In the solu...This paper investigates the numerical solution of the uncertain inverse heat conduction problem. Uncertainties present in the system parameters are modelled through triangular convex normalized fuzzy sets. In the solution process, double parametric forms of fuzzy numbers are used with the variational iteration method （VIM）. This problem first computes the uncertain temperature distribution in the domain. Next, when the uncertain temperature measurements in the domain are known, the functions describing the uncertain temperature and heat flux on the boundary are reconstructed. Related example problems are solved using the present procedure. We have also compared the present results with those in [Inf. Sci. （2008） 178 1917] along with homotopy perturbation method （HPM） and [Int. Commun. Heat Mass Transfer （2012） 39 30] in the special cases to demonstrate the validity and applicability.展开更多
The fractional diffusion equation is one of the most important partial differential equations（PDEs） to model problems in mathematical physics. These PDEs are more practical when those are combined with uncertainties...The fractional diffusion equation is one of the most important partial differential equations（PDEs） to model problems in mathematical physics. These PDEs are more practical when those are combined with uncertainties. Accordingly, this paper investigates the numerical solution of a non-probabilistic viz. fuzzy fractional-order diffusion equation subjected to various external forces. A fuzzy diffusion equation having fractional order 0 〈 α≤ 1 with fuzzy initial condition is taken into consideration. Fuzziness appearing in the initial conditions is modelled through convex normalized triangular and Gaussian fuzzy numbers. A new computational technique is proposed based on double parametric form of fuzzy numbers to handle the fuzzy fractional diffusion equation. Using the single parametric form of fuzzy numbers, the original fuzzy diffusion equation is converted first into an interval-based fuzzy differential equation. Next, this equation is transformed into crisp form by using the proposed double parametric form of fuzzy numbers. Finally, the same is solved by Adomian decomposition method（ADM） symbolically to obtain the uncertain bounds of the solution. Computed results are depicted in terms of plots. Results obtained by the proposed method are compared with the existing results in special cases.展开更多
The search for an effective reduction method is one of the main topics in higher loop computation.Recently,an alternative reduction method was proposed by Chen in[1,2].In this paper,we test the power of Chen’s new me...The search for an effective reduction method is one of the main topics in higher loop computation.Recently,an alternative reduction method was proposed by Chen in[1,2].In this paper,we test the power of Chen’s new method using one-loop scalar integrals with propagators of higher power.More explicitly,with the improved version of the method,we can cancel the dimension shift and terms with unwanted power shifting.Thus,the obtained integrating-by-parts relations are significantly simpler and can be solved easily.Using this method,we present explicit examples of a bubble,triangle,box,and pentagon with one doubled propagator.With these results,we complete our previous computations in[3]with the missing tadpole coefficients and show the potential of Chen’s method for efficient reduction in higher loop integrals.展开更多
基金This project is supported by National Natural Science Foundation of China (N.59990470).
文摘The profile error evaluation of complex curves and surfaces expressed inparametric form is considered. The linear error model is established on the base of two hypothesesfirstly. Then the profile error evaluation is converted into one of these optimal formulations:MINIMAX, MAXMIN and MINIDEX problems, which are easier to be solved than the initial form. To eachone of them, geometric condition and algebraic condition are presented to arbitrate whether theideal element reaches to the optimal position. Exchange algorithm is proven highly effective insearching for solutions to these optimization problems. At last some key problems in tolerance offreeform surfaces and curves in B spline method are discussed.
基金the UGC, Government of India, for financial support under the Rajiv Gandhi National Fellowship (RGNF)
文摘This paper investigates the numerical solution of the uncertain inverse heat conduction problem. Uncertainties present in the system parameters are modelled through triangular convex normalized fuzzy sets. In the solution process, double parametric forms of fuzzy numbers are used with the variational iteration method （VIM）. This problem first computes the uncertain temperature distribution in the domain. Next, when the uncertain temperature measurements in the domain are known, the functions describing the uncertain temperature and heat flux on the boundary are reconstructed. Related example problems are solved using the present procedure. We have also compared the present results with those in [Inf. Sci. （2008） 178 1917] along with homotopy perturbation method （HPM） and [Int. Commun. Heat Mass Transfer （2012） 39 30] in the special cases to demonstrate the validity and applicability.
基金the UGC,Government of India,for financial support under Rajiv Gandhi National Fellowship(RGNF)
文摘The fractional diffusion equation is one of the most important partial differential equations（PDEs） to model problems in mathematical physics. These PDEs are more practical when those are combined with uncertainties. Accordingly, this paper investigates the numerical solution of a non-probabilistic viz. fuzzy fractional-order diffusion equation subjected to various external forces. A fuzzy diffusion equation having fractional order 0 〈 α≤ 1 with fuzzy initial condition is taken into consideration. Fuzziness appearing in the initial conditions is modelled through convex normalized triangular and Gaussian fuzzy numbers. A new computational technique is proposed based on double parametric form of fuzzy numbers to handle the fuzzy fractional diffusion equation. Using the single parametric form of fuzzy numbers, the original fuzzy diffusion equation is converted first into an interval-based fuzzy differential equation. Next, this equation is transformed into crisp form by using the proposed double parametric form of fuzzy numbers. Finally, the same is solved by Adomian decomposition method（ADM） symbolically to obtain the uncertain bounds of the solution. Computed results are depicted in terms of plots. Results obtained by the proposed method are compared with the existing results in special cases.
基金Supported by the National Natural Science Foundation of China(11935013)。
文摘The search for an effective reduction method is one of the main topics in higher loop computation.Recently,an alternative reduction method was proposed by Chen in[1,2].In this paper,we test the power of Chen’s new method using one-loop scalar integrals with propagators of higher power.More explicitly,with the improved version of the method,we can cancel the dimension shift and terms with unwanted power shifting.Thus,the obtained integrating-by-parts relations are significantly simpler and can be solved easily.Using this method,we present explicit examples of a bubble,triangle,box,and pentagon with one doubled propagator.With these results,we complete our previous computations in[3]with the missing tadpole coefficients and show the potential of Chen’s method for efficient reduction in higher loop integrals.
