This paper presents a class of hybrid one-step methods that are obtained by using Cramer's rule and rational approximations to function exp(q). The algorithms fall into the catalogue of implicit formula, which inv...This paper presents a class of hybrid one-step methods that are obtained by using Cramer's rule and rational approximations to function exp(q). The algorithms fall into the catalogue of implicit formula, which involves sth order derivative and s+1 free parameters. The order of the algorithms satisfies s+1≤p≤2s+2. The stability of the methods is also studied, necessary and sufficient conditions for A-stability and L-stability are given. In addition, some examples are also given to demonstrate the method presented.展开更多
Degradation and delamination resulting from environmental humidity have been technically challenging for poly(3,4-ethylenedioxythiophene):poly(styrene sulfonate)(PEDOT:PSS)thin-film processing.To overcome this problem...Degradation and delamination resulting from environmental humidity have been technically challenging for poly(3,4-ethylenedioxythiophene):poly(styrene sulfonate)(PEDOT:PSS)thin-film processing.To overcome this problem,we introduced a one-step photolithographic method to both pattern and link a PEDOT:PSS film onto a poly(ethylene glycol)(PEG)layer as a hybrid thin film structure on a flexible substrate.This film exhibited excellent long-term moisture stability(more than 10 days)and lithographic resolution(as low as 2μm).Mechanical characterizations were performed,including both stretching and bending tests,which illustrated the strong adhesion present between the PEDOT:PSS and PEG layers as well as between the hybrid thin film and substrate.Moreover,the hybrid moisture-absorbable film showed a quick response of its permittivity to environmental humidity variations,in which the patterned PEDOT:PSS layer served as an electrode and the PEG layer as a moisture-sensing element.Perspiration tracking over various parts of the body surface as well as breath rate measurement under the nose were successfully carried out as demonstrations,which illustrated the potential utility of this stable hybrid thin film for emerging flexible and wearable electronic applications.展开更多
基金the National Natural Science Foundation of China (No.69574034)by the Management,Decision and Information System Lab.,Chinese Academy of Sciences.
文摘This paper presents a class of hybrid one-step methods that are obtained by using Cramer's rule and rational approximations to function exp(q). The algorithms fall into the catalogue of implicit formula, which involves sth order derivative and s+1 free parameters. The order of the algorithms satisfies s+1≤p≤2s+2. The stability of the methods is also studied, necessary and sufficient conditions for A-stability and L-stability are given. In addition, some examples are also given to demonstrate the method presented.
基金This work was supported in part by the NSF Award(ECCS-1307831)NIH Award(1R21CA173243-01A1)to TP.RL acknowledges the fellowship support from the China Scholarship Council(CSC).
文摘Degradation and delamination resulting from environmental humidity have been technically challenging for poly(3,4-ethylenedioxythiophene):poly(styrene sulfonate)(PEDOT:PSS)thin-film processing.To overcome this problem,we introduced a one-step photolithographic method to both pattern and link a PEDOT:PSS film onto a poly(ethylene glycol)(PEG)layer as a hybrid thin film structure on a flexible substrate.This film exhibited excellent long-term moisture stability(more than 10 days)and lithographic resolution(as low as 2μm).Mechanical characterizations were performed,including both stretching and bending tests,which illustrated the strong adhesion present between the PEDOT:PSS and PEG layers as well as between the hybrid thin film and substrate.Moreover,the hybrid moisture-absorbable film showed a quick response of its permittivity to environmental humidity variations,in which the patterned PEDOT:PSS layer served as an electrode and the PEG layer as a moisture-sensing element.Perspiration tracking over various parts of the body surface as well as breath rate measurement under the nose were successfully carried out as demonstrations,which illustrated the potential utility of this stable hybrid thin film for emerging flexible and wearable electronic applications.
