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L^p CONTINUITY OF HRMANDER SYMBOL OPERATORS OpS_(0,0) ~m AND NUMERICAL ALGORITHM
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作者 杨奇祥 《Acta Mathematica Scientia》 SCIE CSCD 2011年第4期1517-1534,共18页
If we use Littlewood-Paley decomposition, there is no pseudo-orthogonality for Ho¨rmander symbol operators OpS m 0 , 0 , which is different to the case S m ρ,δ (0 ≤δ 〈 ρ≤ 1). In this paper, we use a spec... If we use Littlewood-Paley decomposition, there is no pseudo-orthogonality for Ho¨rmander symbol operators OpS m 0 , 0 , which is different to the case S m ρ,δ (0 ≤δ 〈 ρ≤ 1). In this paper, we use a special numerical algorithm based on wavelets to study the L p continuity of non infinite smooth operators OpS m 0 , 0 ; in fact, we apply first special wavelets to symbol to get special basic operators, then we regroup all the special basic operators at given scale and prove that such scale operator’s continuity decreases very fast, we sum such scale operators and a symbol operator can be approached by very good compact operators. By correlation of basic operators, we get very exact pseudo-orthogonality and also L 2 → L 2 continuity for scale operators. By considering the influence region of scale operator, we get H 1 (= F 0 , 2 1 ) → L 1 continuity and L ∞→ BMO continuity. By interpolation theorem, we get also L p (= F 0 , 2 p ) → L p continuity for 1 〈 p 〈 ∞ . Our results are sharp for F 0 , 2 p → L p continuity when 1 ≤ p ≤ 2, that is to say, we find out the exact order of derivations for which the symbols can ensure the resulting operators to be bounded on these spaces. 展开更多
关键词 Ho¨rmander symbol class wavelet and numerical algorithm basic operators and scale operators approximation by compact operator and operator’s continuity
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STUDY OF FLOW AND TEMPERATURE IN RESIN TRANSFER MOLDING PROCESS BY NUMERICAL MODEL
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作者 陈仁良 李明成 《Transactions of Nanjing University of Aeronautics and Astronautics》 EI 2003年第2期165-171,共7页
A mathematical model of resin flow and temperature variation in the filling stage of the resin transfer molding (RTM) is developed based on the control volume/finite element method (CV/FEM). The effects of the heat tr... A mathematical model of resin flow and temperature variation in the filling stage of the resin transfer molding (RTM) is developed based on the control volume/finite element method (CV/FEM). The effects of the heat transfer and chemical reaction of the resin on the flow and temperature are considered. The numerical algorithm of the resin flow and temperature variation in the process of RTM are studied. Its accuracy and convergence are analyzed. The comparison of temperature variations between experimental results and model predictions is carried out for two RTM cases. Result shows that the model is efficient for evaluating the flow and temperature variation in the filling stage of RTM and there is a good coincidence between theory and experiment. 展开更多
关键词 resin transfer molding mathematical modeling numerical algorithm heat transfer
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Proximal point algorithm for a new class of fuzzy set-valued variational inclusions with (H,η)-monotone mappings
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作者 李红刚 《Journal of Chongqing University》 CAS 2008年第1期79-84,共6页
We introduced a new class of fuzzy set-valued variational inclusions with (H,η)-monotone mappings. Using the resolvent operator method in Hilbert spaces, we suggested a new proximal point algorithm for finding approx... We introduced a new class of fuzzy set-valued variational inclusions with (H,η)-monotone mappings. Using the resolvent operator method in Hilbert spaces, we suggested a new proximal point algorithm for finding approximate solutions, which strongly converge to the exact solution of a fuzzy set-valued variational inclusion with (H,η)-monotone. The results improved and generalized the general quasi-variational inclusions with fuzzy set-valued mappings proposed by Jin and Tian Jin MM, Perturbed proximal point algorithm for general quasi-variational inclusions with fuzzy set-valued mappings, OR Transactions, 2005, 9(3): 31-38, (In Chinese); Tian YX, Generalized nonlinear implicit quasi-variational inclusions with fuzzy mappings, Computers & Mathematics with Applications, 2001, 42: 101-108. 展开更多
关键词 variational inclusion (H η)-monotone mapping resolvent operator technique fuzzy set-valued mapping proximal point algorithm convergence of numerical methods
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A NOVEL METHOD FOR NONLINEAR IMPULSIVE DIFFERENTIAL EQUATIONS IN BROKEN REPRODUCING KERNEL SPACE
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作者 Liangcai MEI 《Acta Mathematica Scientia》 SCIE CSCD 2020年第3期723-733,共11页
In this article,a new algorithm is presented to solve the nonlinear impulsive differential equations.In the first time,this article combines the reproducing kernel method with the least squares method to solve the sec... In this article,a new algorithm is presented to solve the nonlinear impulsive differential equations.In the first time,this article combines the reproducing kernel method with the least squares method to solve the second-order nonlinear impulsive differential equations.Then,the uniform convergence of the numerical solution is proved,and the time consuming Schmidt orthogonalization process is avoided.The algorithm is employed successfully on some numerical examples. 展开更多
关键词 Nonlinear impulsive differential equations Broken reproducing kernel space numerical algorithm
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Dynamic thermo-mechanical coupled response of random particulate composites:A statistical two-scale method
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作者 杨自豪 陈云 +1 位作者 杨志强 马强 《Chinese Physics B》 SCIE EI CAS CSCD 2014年第7期605-616,共12页
This paper focuses on the dynamic thermo-mechanical coupled response of random particulate composite materials. Both the inertia term and coupling term are considered in the dynamic coupled problem. The formulation of... This paper focuses on the dynamic thermo-mechanical coupled response of random particulate composite materials. Both the inertia term and coupling term are considered in the dynamic coupled problem. The formulation of the problem by a statistical second-order two-scale (SSOTS) analysis method and the algorithm procedure based on the finite-element difference method are presented. Numerical results of coupled cases are compared with those of uncoupled cases. It shows that the coupling effects on temperature, thermal flux, displacement, and stresses are very distinct, and the micro- characteristics of particles affect the coupling effect of the random composites. Furthermore, the coupling effect causes a lag in the variations of temperature, thermal flux, displacement, and stresses. 展开更多
关键词 random particulate composites statistical second-order two-scale (SSOTS) analysis method thermo-mechanical coupling effect numerical algorithm
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