New better estimates, which are given in terms of elementary functions, for the function r →（2/π）（1 -r2）κ（r）κ′（r） ＋ logr appearing in Hubner＇s sharp upper bound for the Hersch-Pfluger distortion functio...New better estimates, which are given in terms of elementary functions, for the function r →（2/π）（1 -r2）κ（r）κ′（r） ＋ logr appearing in Hubner＇s sharp upper bound for the Hersch-Pfluger distortion function are obtained. With these estimates, some known bounds for the Hersch-Pfluger distortion function in quasiconformal theory are improved, thus. improving the explicit quasiconformal Schwarz lemma and some known estimates for the solutions to the Ramanujan modular equations.展开更多
In this paper, we establish several inequalities for the the generalized linear distortion function λ（a, K） by using the monotonicity and convexity of certain combinations λ（a, K）.
Nowadays,emoji image is widely used in social networks.To achieve covert communication in emoji images,this paper proposes a distortion function for emoji images steganography.The profile of image content,the intra-an...Nowadays,emoji image is widely used in social networks.To achieve covert communication in emoji images,this paper proposes a distortion function for emoji images steganography.The profile of image content,the intra-and inter-frame correlation are taken into account in the proposed distortion function to fit the unique properties of emoji image.The three parts are combined together to measure the risks of detection due to the modification on the cover data.With the popular syndrome trellis coding(STC),the distortion of stego emoji image is minimized using the proposed distortion function.As a result,less detectable artifacts could be found in the stego images.Experimental results show that the proposed distortion function performs much higher undetectability than current state-of-the-art distortion function HILL which is designed for natural image.展开更多
This paper introduces and represents conditional coherent risk measures as essential suprema of conditional expectations over a convex set of probability measures and as distorted expectations given a concave distorti...This paper introduces and represents conditional coherent risk measures as essential suprema of conditional expectations over a convex set of probability measures and as distorted expectations given a concave distortion function.A model is then developed for the bid and ask prices of a European-type asset by a conic formulation.The price process is governed by a modified geometric Brownian motion whose drift and diffusion coefficients depend on a Markov chain.The bid and ask prices of a European-type asset are then characterized using conic quantization.展开更多
基金Supported by National 973 Project of China(2006CB708304)National Natural Science Foundation of China(10771195)
文摘New better estimates, which are given in terms of elementary functions, for the function r →（2/π）（1 -r2）κ（r）κ′（r） ＋ logr appearing in Hubner＇s sharp upper bound for the Hersch-Pfluger distortion function are obtained. With these estimates, some known bounds for the Hersch-Pfluger distortion function in quasiconformal theory are improved, thus. improving the explicit quasiconformal Schwarz lemma and some known estimates for the solutions to the Ramanujan modular equations.
基金Supported by the National Natural Science Foundation of China(11071069, 11171307)the Natural Science Foundation of Hunan Province(09JJ6003)
文摘In this paper, we establish several inequalities for the the generalized linear distortion function λ（a, K） by using the monotonicity and convexity of certain combinations λ（a, K）.
基金This work was supported by the Natural Science Foundation of China(U1736213,61572308)the Natural Science Foundation of Shanghai(18ZR1427500),the Shanghai Dawn Scholar Plan(14SG36)and the Shanghai Excellent Academic Leader Plan(16XD1401200).
文摘Nowadays,emoji image is widely used in social networks.To achieve covert communication in emoji images,this paper proposes a distortion function for emoji images steganography.The profile of image content,the intra-and inter-frame correlation are taken into account in the proposed distortion function to fit the unique properties of emoji image.The three parts are combined together to measure the risks of detection due to the modification on the cover data.With the popular syndrome trellis coding(STC),the distortion of stego emoji image is minimized using the proposed distortion function.As a result,less detectable artifacts could be found in the stego images.Experimental results show that the proposed distortion function performs much higher undetectability than current state-of-the-art distortion function HILL which is designed for natural image.
文摘This paper introduces and represents conditional coherent risk measures as essential suprema of conditional expectations over a convex set of probability measures and as distorted expectations given a concave distortion function.A model is then developed for the bid and ask prices of a European-type asset by a conic formulation.The price process is governed by a modified geometric Brownian motion whose drift and diffusion coefficients depend on a Markov chain.The bid and ask prices of a European-type asset are then characterized using conic quantization.
