The delay-dependent absolute stability for a class of Lurie systems with interval time-varying delay is studied. By employing an augmented Lyapunov functional and combining a free-weighting matrix approach and the rec...The delay-dependent absolute stability for a class of Lurie systems with interval time-varying delay is studied. By employing an augmented Lyapunov functional and combining a free-weighting matrix approach and the reciprocal convex technique, an improved stability condition is derived in terms of linear matrix inequalities （LMIs）. By retaining some useful terms that are usually ignored in the derivative of the Lyapunov function, the proposed sufficient condition depends not only on the lower and upper bounds of both the delay and its derivative, but it also depends on their differences, which has wider application fields than those of present results. Moreover, a new type of equality expression is developed to handle the sector bounds of the nonlinear function, which achieves fewer LMIs in the derived condition, compared with those based on the convex representation. Therefore, the proposed method is less conservative than the existing ones. Simulation examples are given to demonstrate the validity of the approach.展开更多
High density of phenyl rings makes PAF-1 have robust structure and highly lipophilic pore, which make it very suitable for organocatalysis. However, there is no report about using PAF-1 as platform for enantioselectiv...High density of phenyl rings makes PAF-1 have robust structure and highly lipophilic pore, which make it very suitable for organocatalysis. However, there is no report about using PAF-1 as platform for enantioselective organocatalysis.In this paper, using PAF-1 as the platform, a chiral prolinamide catalytic site was introduced onto the framework of PAF-1 via a series of stepwise post-synthetic modifications,obtaining a novel PAF-supported chiral catalyst named PAF-1-NHPro. Then its enantioselective catalytic performance was studied by subjecting it to catalyze the model Aldol reaction between p-nitrobenzaldehyde and cyclohexanone.PAF-1-NHPro showed good diastereoselectivity and enantioselectivity with excellent and easy recyclability.展开更多
In this work we study the Lagrangian and the conservation laws for a wave equation with a dissipative source. Using semi-inverse method, we show that the equation possesses a nonlocal Lagrangian with an auxiliary func...In this work we study the Lagrangian and the conservation laws for a wave equation with a dissipative source. Using semi-inverse method, we show that the equation possesses a nonlocal Lagrangian with an auxiliary function.As a result, from a modified Noether's theorem and the nonclassical Noether symmetry generators, we construct some conservation laws for this equation, which are different from the ones obtained by Ibragimov's theorem in [Y. Wang and L. Wei, Abstr. App. Anal. 2013(2013) 407908]. The results show that our method work for arbitrary functions f(u)and g(u) rather than special ones.展开更多
基金The National Natural Science Foundation of China(No.60835001,60875035,60905009,61004032,61004064,11071001)China Postdoctoral Science Foundation(No.201003546)+2 种基金the Ph.D.Programs Foundation of Ministry of Education of China(No.20093401110001)the Major Program of Higher Education of Anhui Province(No.KJ2010ZD02)the Natural Science Research Project of Higher Education of Anhui Province(No.KJ2011A020)
文摘The delay-dependent absolute stability for a class of Lurie systems with interval time-varying delay is studied. By employing an augmented Lyapunov functional and combining a free-weighting matrix approach and the reciprocal convex technique, an improved stability condition is derived in terms of linear matrix inequalities （LMIs）. By retaining some useful terms that are usually ignored in the derivative of the Lyapunov function, the proposed sufficient condition depends not only on the lower and upper bounds of both the delay and its derivative, but it also depends on their differences, which has wider application fields than those of present results. Moreover, a new type of equality expression is developed to handle the sector bounds of the nonlinear function, which achieves fewer LMIs in the derived condition, compared with those based on the convex representation. Therefore, the proposed method is less conservative than the existing ones. Simulation examples are given to demonstrate the validity of the approach.
基金supported by National Basic Research Program of China (2014CB931804)the National Natural Science Foundation of China (21302061 and 21531003)
文摘High density of phenyl rings makes PAF-1 have robust structure and highly lipophilic pore, which make it very suitable for organocatalysis. However, there is no report about using PAF-1 as platform for enantioselective organocatalysis.In this paper, using PAF-1 as the platform, a chiral prolinamide catalytic site was introduced onto the framework of PAF-1 via a series of stepwise post-synthetic modifications,obtaining a novel PAF-supported chiral catalyst named PAF-1-NHPro. Then its enantioselective catalytic performance was studied by subjecting it to catalyze the model Aldol reaction between p-nitrobenzaldehyde and cyclohexanone.PAF-1-NHPro showed good diastereoselectivity and enantioselectivity with excellent and easy recyclability.
基金Supported by National Natural Science Foundation of China under Grant No.11101111Zhejiang Provincial Natural Science Foundation of China under Grant Nos.LY14A010029 and LY12A01003
文摘In this work we study the Lagrangian and the conservation laws for a wave equation with a dissipative source. Using semi-inverse method, we show that the equation possesses a nonlocal Lagrangian with an auxiliary function.As a result, from a modified Noether's theorem and the nonclassical Noether symmetry generators, we construct some conservation laws for this equation, which are different from the ones obtained by Ibragimov's theorem in [Y. Wang and L. Wei, Abstr. App. Anal. 2013(2013) 407908]. The results show that our method work for arbitrary functions f(u)and g(u) rather than special ones.
