In this article, the authors study the growth of certain second order linear differential equation f″＋A（z）f′＋B（z）f=0 and give precise estimates for the hyperorder of solutions of infinite order. Under similar ...In this article, the authors study the growth of certain second order linear differential equation f″＋A（z）f′＋B（z）f=0 and give precise estimates for the hyperorder of solutions of infinite order. Under similar conditions, higher order differential equations will be considered.展开更多
This paper proposes a novel adaptive sliding mode control(SMC) method for synchronization of non-identical fractional-order(FO) chaotic and hyper-chaotic systems. Under the existence of system uncertainties and extern...This paper proposes a novel adaptive sliding mode control(SMC) method for synchronization of non-identical fractional-order(FO) chaotic and hyper-chaotic systems. Under the existence of system uncertainties and external disturbances,finite-time synchronization between two FO chaotic and hyperchaotic systems is achieved by introducing a novel adaptive sliding mode controller(ASMC). Here in this paper, a fractional sliding surface is proposed. A stability criterion for FO nonlinear dynamic systems is introduced. Sufficient conditions to guarantee stable synchronization are given in the sense of the Lyapunov stability theorem. To tackle the uncertainties and external disturbances, appropriate adaptation laws are introduced. Particle swarm optimization(PSO) is used for estimating the controller parameters. Finally, finite-time synchronization of the FO chaotic and hyper-chaotic systems is applied to secure communication.展开更多
In this paper, we investigate the hyper order of the solutions of high order linear differential equations with some dominated coefficient being lacunary series, and obtain some results which improve and extend previo...In this paper, we investigate the hyper order of the solutions of high order linear differential equations with some dominated coefficient being lacunary series, and obtain some results which improve and extend previous results.展开更多
In the Digital World scenario,the confidentiality of information in video transmission plays an important role.Chaotic systems have been shown to be effective for video signal encryption.To improve video transmission ...In the Digital World scenario,the confidentiality of information in video transmission plays an important role.Chaotic systems have been shown to be effective for video signal encryption.To improve video transmission secrecy,compressive encryption method is proposed to accomplish compression and encryption based on fractional order hyper chaotic system that incorporates Compressive Sensing(CS),pixel level,bit level scrambling and nucleotide Sequences operations.The measurement matrix generates by the fractional order hyper chaotic system strengthens the efficiency of the encryption process.To avoid plain text attack,the CS measurement is scrambled to its pixel level,bit level scrambling decreases the similarity between the adjacent measurements and the nucleotide sequence operations are done on the scrambled bits,increasing the encryption.Two stages are comprised in the reconstruction technique,the first stage uses the intra-frame similarity and offers robust preliminary retrieval for each frame,and the second stage iteratively improves the efficiency of reconstruction by integrating inter frame Multi Hypothesis(MH)estimation and weighted residual sparsity modeling.In each iteration,the residual coefficient weights are modified using a mathematical approach based on the MH predictions,and the Split Bregman iteration algorithm is defined to resolve weighted l1 regularization.Experimental findings show that the proposed algorithm provides good compression of video coupled with an efficient encryption method that is resistant to multiple attacks.展开更多
A series of CdS nanoparticles with different surfaces were prepared by colloidal chemical method and reverse micelle method. Their second-order nonlinear optical (NLO) properties were experimentally studied in solutio...A series of CdS nanoparticles with different surfaces were prepared by colloidal chemical method and reverse micelle method. Their second-order nonlinear optical (NLO) properties were experimentally studied in solution by newly developed hyper-Rayleigh scattering (HRS) technique. The results show that 'per particle' first-order hyperpolarizability beta values are sensitive To the synthetic method and the surface chemical modification.展开更多
The second-order optical nonlinearity of CdS nanoparticles with different diameters of 28.0, 30.0, 31.5, 50.0, and 91.0 A was studied by hyper-Rayleigh scattering technique. Results show that the first-order hyperpola...The second-order optical nonlinearity of CdS nanoparticles with different diameters of 28.0, 30.0, 31.5, 50.0, and 91.0 A was studied by hyper-Rayleigh scattering technique. Results show that the first-order hyperpolarizability P value per CdS partiele decreases as size is reduced to diameter of 31.5 A; however, as CdS size further decreases, this trend is reversed and (J value increases. Substantially, the normalized P value per CdS formula unit, β0, exhibits systematic enhancement with decreasing size. This phenomenon is interpreted in terms of a so-called surfaee contribution mechanism.展开更多
In this paper, authors investigate the order of growth and the hyper order of solutions of a class of the higher order linear differential equation, and improve results of M. Ozawa, G. Gundersen and J.K. Langley, Li C...In this paper, authors investigate the order of growth and the hyper order of solutions of a class of the higher order linear differential equation, and improve results of M. Ozawa, G. Gundersen and J.K. Langley, Li Chun-hong.展开更多
In this paper,the precise estimation of the order and hyper-order of solutions of a class of three order homogeneous and non-homogeneous linear differential equations are obtained.The results of M.Ozawa(1980),G.Gunder...In this paper,the precise estimation of the order and hyper-order of solutions of a class of three order homogeneous and non-homogeneous linear differential equations are obtained.The results of M.Ozawa(1980),G.Gundersen(1988) and J.K.Langley(1986) are improved.展开更多
In this paper, we consider the growth of solutions of some homogeneous and non- homogeneous higher order differential equations. It is proved that under some conditions for entire functions F, Aji and polynomials Pj（...In this paper, we consider the growth of solutions of some homogeneous and non- homogeneous higher order differential equations. It is proved that under some conditions for entire functions F, Aji and polynomials Pj（z）, Oj（z） （j = 0, 1,..., k - 1; i = 1, 2） with degree n ≥ 1, the equation f（k） ＋ （Ak-l,1 （z）e pk-l（z） ＋Ak-1,2 （z）eQk-l（z））f（x-1） ＋...＋ （A0,1 （z）eP0（z） ＋ A0,2（z）eQ0（z））f = F, where k ≥ 2, satisfies the properties： When F ≡ 0, all the non-zero solu- tions are of infinite order; when F ≠ 0, there exists at most one exceptional solution f0 with finite order, and all other solutions satisfy -λ（f） = A（f） = σ（f） = ∞.展开更多
In this paper, during the masking process the encrypted message is convolved and embedded into a Qi hyper-chaotic system characterizing a high disorder degree. The masking scheme was tested using both Qi hyper-chaos a...In this paper, during the masking process the encrypted message is convolved and embedded into a Qi hyper-chaotic system characterizing a high disorder degree. The masking scheme was tested using both Qi hyper-chaos and Lorenz chaos and indicated that Qi hyper-chaos based masking can resist attacks of the filtering and power spectrum analysis, while the Lorenz based scheme fails for high amplitude data. To unmask the message at the receiving end, two methods are proposed. In the first method, a model-free synchronizer, i.e. a multivariable higher-order differential feedback controller between the transmitter and receiver is employed to de-convolve the message embedded in the receiving signal. In the second method, no synchronization is required since the message is de-convolved using the information of the estimated derivative.展开更多
基金the National Natural Science Foundation of China(10161006,10571044)the Natural Science Foundation of Guangdong Prov(06025059)
文摘In this article, the authors study the growth of certain second order linear differential equation f″＋A（z）f′＋B（z）f=0 and give precise estimates for the hyperorder of solutions of infinite order. Under similar conditions, higher order differential equations will be considered.
文摘This paper proposes a novel adaptive sliding mode control(SMC) method for synchronization of non-identical fractional-order(FO) chaotic and hyper-chaotic systems. Under the existence of system uncertainties and external disturbances,finite-time synchronization between two FO chaotic and hyperchaotic systems is achieved by introducing a novel adaptive sliding mode controller(ASMC). Here in this paper, a fractional sliding surface is proposed. A stability criterion for FO nonlinear dynamic systems is introduced. Sufficient conditions to guarantee stable synchronization are given in the sense of the Lyapunov stability theorem. To tackle the uncertainties and external disturbances, appropriate adaptation laws are introduced. Particle swarm optimization(PSO) is used for estimating the controller parameters. Finally, finite-time synchronization of the FO chaotic and hyper-chaotic systems is applied to secure communication.
基金Supported by the National Natural Science Foundation of China (Grant Nos. 11171119 11126145)+1 种基金the Natural Science Foundation of Jiangxi Province (Grant No. 2010GQS0103)the Foundation of Education Bureau of Jiangxi Province (Grant No. 2012GJJ12206)
文摘In this paper, we investigate the hyper order of the solutions of high order linear differential equations with some dominated coefficient being lacunary series, and obtain some results which improve and extend previous results.
文摘In the Digital World scenario,the confidentiality of information in video transmission plays an important role.Chaotic systems have been shown to be effective for video signal encryption.To improve video transmission secrecy,compressive encryption method is proposed to accomplish compression and encryption based on fractional order hyper chaotic system that incorporates Compressive Sensing(CS),pixel level,bit level scrambling and nucleotide Sequences operations.The measurement matrix generates by the fractional order hyper chaotic system strengthens the efficiency of the encryption process.To avoid plain text attack,the CS measurement is scrambled to its pixel level,bit level scrambling decreases the similarity between the adjacent measurements and the nucleotide sequence operations are done on the scrambled bits,increasing the encryption.Two stages are comprised in the reconstruction technique,the first stage uses the intra-frame similarity and offers robust preliminary retrieval for each frame,and the second stage iteratively improves the efficiency of reconstruction by integrating inter frame Multi Hypothesis(MH)estimation and weighted residual sparsity modeling.In each iteration,the residual coefficient weights are modified using a mathematical approach based on the MH predictions,and the Split Bregman iteration algorithm is defined to resolve weighted l1 regularization.Experimental findings show that the proposed algorithm provides good compression of video coupled with an efficient encryption method that is resistant to multiple attacks.
基金National Natural Science Foundation of China! (No.59582005)
文摘A series of CdS nanoparticles with different surfaces were prepared by colloidal chemical method and reverse micelle method. Their second-order nonlinear optical (NLO) properties were experimentally studied in solution by newly developed hyper-Rayleigh scattering (HRS) technique. The results show that 'per particle' first-order hyperpolarizability beta values are sensitive To the synthetic method and the surface chemical modification.
基金supposed by the National Natural Science Foundation of China(Nos.50202009,10074023)the National Postdoctoral Foundation(No.2002031222).
文摘The second-order optical nonlinearity of CdS nanoparticles with different diameters of 28.0, 30.0, 31.5, 50.0, and 91.0 A was studied by hyper-Rayleigh scattering technique. Results show that the first-order hyperpolarizability P value per CdS partiele decreases as size is reduced to diameter of 31.5 A; however, as CdS size further decreases, this trend is reversed and (J value increases. Substantially, the normalized P value per CdS formula unit, β0, exhibits systematic enhancement with decreasing size. This phenomenon is interpreted in terms of a so-called surfaee contribution mechanism.
基金This work is supported by the National Natural Science Foundation of China(10161006)the Natural Science Foundation of Jiangxi Prov(001109)Korea Research Foundation Grant(KRF-2001-015-DP0015)
文摘In this paper, authors investigate the order of growth and the hyper order of solutions of a class of the higher order linear differential equation, and improve results of M. Ozawa, G. Gundersen and J.K. Langley, Li Chun-hong.
文摘In this paper,the precise estimation of the order and hyper-order of solutions of a class of three order homogeneous and non-homogeneous linear differential equations are obtained.The results of M.Ozawa(1980),G.Gundersen(1988) and J.K.Langley(1986) are improved.
基金Supported by the National Natural Science Foundation of China(Grant Nos.1130123211171119)the Natural Science Foundation of Jiangxi Province(Grant No.20132BAB211009)
文摘In this paper, we consider the growth of solutions of some homogeneous and non- homogeneous higher order differential equations. It is proved that under some conditions for entire functions F, Aji and polynomials Pj（z）, Oj（z） （j = 0, 1,..., k - 1; i = 1, 2） with degree n ≥ 1, the equation f（k） ＋ （Ak-l,1 （z）e pk-l（z） ＋Ak-1,2 （z）eQk-l（z））f（x-1） ＋...＋ （A0,1 （z）eP0（z） ＋ A0,2（z）eQ0（z））f = F, where k ≥ 2, satisfies the properties： When F ≡ 0, all the non-zero solu- tions are of infinite order; when F ≠ 0, there exists at most one exceptional solution f0 with finite order, and all other solutions satisfy -λ（f） = A（f） = σ（f） = ∞.
基金Project supported by the Incentive Funding National Research Foundation of South Africa(Grant No.70722)the Eskom Tertiary Education Support Programme of South Africa
文摘In this paper, during the masking process the encrypted message is convolved and embedded into a Qi hyper-chaotic system characterizing a high disorder degree. The masking scheme was tested using both Qi hyper-chaos and Lorenz chaos and indicated that Qi hyper-chaos based masking can resist attacks of the filtering and power spectrum analysis, while the Lorenz based scheme fails for high amplitude data. To unmask the message at the receiving end, two methods are proposed. In the first method, a model-free synchronizer, i.e. a multivariable higher-order differential feedback controller between the transmitter and receiver is employed to de-convolve the message embedded in the receiving signal. In the second method, no synchronization is required since the message is de-convolved using the information of the estimated derivative.
