In this paper, we shall establish that each weak solution of p-harmonic type systems with the gradients below the controllable growth belongs to, Holder continuity spaces with any HSlder exponent α∈ [0, 1）. Further...In this paper, we shall establish that each weak solution of p-harmonic type systems with the gradients below the controllable growth belongs to, Holder continuity spaces with any HSlder exponent α∈ [0, 1）. Furthermore, we can obtain that the gradients of the corresponding weak solutions also belong to locally Hoelder continuity spaces with some Hoelder exponent. Keywords controllable growth, p-harmonic systems, full regularity MR（2000） Subject Classification 35J60, 35B65展开更多
In this paper,we exploited a unique procedure for obtaining thorny gold nanoparticles(Au NPs)with controllable length of thorns without using seeds and surfacta nts.A larger number of Ag+ions was added into the reacti...In this paper,we exploited a unique procedure for obtaining thorny gold nanoparticles(Au NPs)with controllable length of thorns without using seeds and surfacta nts.A larger number of Ag+ions was added into the reaction system containing with HAuCI4 and NH2 OH·HCl,so as to forming colloidal AgCl.AgCl could induce the growth of thorny Au NPs.The morphology of Au NPs changed from short-thorns,longthorns to no-thorns,as the amount of AgNO3 increased.The obtained Au NPs exhibited shapedetermined surface-enhanced Raman spectroscopy(SERS)activity toward rhodamine 6 G(R6 G);indicating their potential for use in SERS-based detections and analysis.展开更多
基金Supported by Beijing Jiaotong University Science Research Foundation(2004SM056)
文摘In this paper, we shall establish that each weak solution of p-harmonic type systems with the gradients below the controllable growth belongs to, Holder continuity spaces with any HSlder exponent α∈ [0, 1）. Furthermore, we can obtain that the gradients of the corresponding weak solutions also belong to locally Hoelder continuity spaces with some Hoelder exponent. Keywords controllable growth, p-harmonic systems, full regularity MR（2000） Subject Classification 35J60, 35B65
基金financially supported by the National Natural Science Foundation of China(No. 21277055)the 111 Project (No. B17019)
文摘In this paper,we exploited a unique procedure for obtaining thorny gold nanoparticles(Au NPs)with controllable length of thorns without using seeds and surfacta nts.A larger number of Ag+ions was added into the reaction system containing with HAuCI4 and NH2 OH·HCl,so as to forming colloidal AgCl.AgCl could induce the growth of thorny Au NPs.The morphology of Au NPs changed from short-thorns,longthorns to no-thorns,as the amount of AgNO3 increased.The obtained Au NPs exhibited shapedetermined surface-enhanced Raman spectroscopy(SERS)activity toward rhodamine 6 G(R6 G);indicating their potential for use in SERS-based detections and analysis.
