Detailed mathematical deduction is presented to improve the graphics quality of aircraft dashboards. Generation of rhumb lines with such kind of algorithm shows that the new approach is effective.
Abstract There exists rare integration formulas over quaternions due to the noncommutativity of quarternions multplication. Based on the class operator＇s formula of rotation group we derive a Gaussian integral formul...Abstract There exists rare integration formulas over quaternions due to the noncommutativity of quarternions multplication. Based on the class operator＇s formula of rotation group we derive a Gaussian integral formula for quaternions, which is similar in form to the integration for coherent state＇s completeness relation.展开更多
The traditional calculation method of frequency-domain Green function mainly utilizes series or asymptotic expansion to carry out numerical approximation, however, this method requires very careful zoning, thus the co...The traditional calculation method of frequency-domain Green function mainly utilizes series or asymptotic expansion to carry out numerical approximation, however, this method requires very careful zoning, thus the computing process is complex with many cycles, which has greatly affected the computing efficiency. To improve the computing efficiency, this paper introduces Gaussian integral to the numerical calculation of the frequency-domain Green function and its partial derivatives. It then compares the calculation result with that in existing references. The comparison results demonstrate that, on the basis of its sufficient accuracy, the method has greatly simplified the computing process, reduced the zoning and improved the computing efficiency.展开更多
In this paper,a new computation scheme based on parallelization is proposed for Isogeometric analysis.The parallel computing is introduced to the whole progress of Isogeometric analysis.Firstly,with the help of the“t...In this paper,a new computation scheme based on parallelization is proposed for Isogeometric analysis.The parallel computing is introduced to the whole progress of Isogeometric analysis.Firstly,with the help of the“tensorproduct”and“iso-parametric”feature,all the Gaussian integral points in particular element can be mapped to a global matrix using a transformation matrix that varies from element.Then the derivatives of Gauss integral points are computed in parallel,the results of which can be stored in a global matrix.And a middle layer is constructed to assemble the final stiffness matrices in parallel.The numerical example results show that:the method presented in the paper can reduce calculation time and improve the use rate of computing resources.展开更多
Nowadays,it is common for suppliers to be separated from their buyers by great distances.This means that,if some items in the lot turn out to be defective,the distance makes it uneconomical to order replacements from ...Nowadays,it is common for suppliers to be separated from their buyers by great distances.This means that,if some items in the lot turn out to be defective,the distance makes it uneconomical to order replacements from the original supplier.Moreover,both Type I and Type II errors may occur in the screening process for eliminating defective items and the combination of defective items and inspection errors may lead to shortages.Working with these assumptions,this paper develops two distinct models.Under the first model,defective items are repaired by a local repair shop subject to a repair charge and a mark-up margin.Under the second model,a local supplier replaces the defective with good ones,but at a higher cost.The expected total profit per cycle is developed,together with the expected cycle time,and,employing the renewal reward theorem,the objective function is derived,from which the optimum values are obtained for the order and shortage quantities.The paper presents numerical results and a discussion for both models.The study finds that repairing defective items generally leads to greater total profit than purchasing local replacements.展开更多
基金Supported by the condition guarantee of 995 engineering (sx004)
文摘Detailed mathematical deduction is presented to improve the graphics quality of aircraft dashboards. Generation of rhumb lines with such kind of algorithm shows that the new approach is effective.
基金National Natural Science Foundation of China under Grant No.10475056
文摘Abstract There exists rare integration formulas over quaternions due to the noncommutativity of quarternions multplication. Based on the class operator＇s formula of rotation group we derive a Gaussian integral formula for quaternions, which is similar in form to the integration for coherent state＇s completeness relation.
基金Supported by the National Natural Science Foundation of China under Grant No.50779007the National Science Foundation for Young Scientists of China under Grant No.50809018+2 种基金the Specialized Research Fund for the Doctoral Program of Higher Education of China under Grant No.20070217074the Defence Advance Research Program of Science and Technology of Ship Industry under Grant No.07J1.1.6Harbin Engineering University Foundation under Grant No.HEUFT07069
文摘The traditional calculation method of frequency-domain Green function mainly utilizes series or asymptotic expansion to carry out numerical approximation, however, this method requires very careful zoning, thus the computing process is complex with many cycles, which has greatly affected the computing efficiency. To improve the computing efficiency, this paper introduces Gaussian integral to the numerical calculation of the frequency-domain Green function and its partial derivatives. It then compares the calculation result with that in existing references. The comparison results demonstrate that, on the basis of its sufficient accuracy, the method has greatly simplified the computing process, reduced the zoning and improved the computing efficiency.
基金supported by the Natural Science Foundation of Hubei Province(CN)(Grant No.2019CFB693)the Research Foundation of the Education Department of Hubei Province(CN)(Grant No.B2019003)the open Foundation of the Key Laboratory of Metallurgical Equipment and Control of Education Ministry(CN)(Grant No.2015B14).
文摘In this paper,a new computation scheme based on parallelization is proposed for Isogeometric analysis.The parallel computing is introduced to the whole progress of Isogeometric analysis.Firstly,with the help of the“tensorproduct”and“iso-parametric”feature,all the Gaussian integral points in particular element can be mapped to a global matrix using a transformation matrix that varies from element.Then the derivatives of Gauss integral points are computed in parallel,the results of which can be stored in a global matrix.And a middle layer is constructed to assemble the final stiffness matrices in parallel.The numerical example results show that:the method presented in the paper can reduce calculation time and improve the use rate of computing resources.
文摘Nowadays,it is common for suppliers to be separated from their buyers by great distances.This means that,if some items in the lot turn out to be defective,the distance makes it uneconomical to order replacements from the original supplier.Moreover,both Type I and Type II errors may occur in the screening process for eliminating defective items and the combination of defective items and inspection errors may lead to shortages.Working with these assumptions,this paper develops two distinct models.Under the first model,defective items are repaired by a local repair shop subject to a repair charge and a mark-up margin.Under the second model,a local supplier replaces the defective with good ones,but at a higher cost.The expected total profit per cycle is developed,together with the expected cycle time,and,employing the renewal reward theorem,the objective function is derived,from which the optimum values are obtained for the order and shortage quantities.The paper presents numerical results and a discussion for both models.The study finds that repairing defective items generally leads to greater total profit than purchasing local replacements.
