The construction of normalized biholomorphic convex mappings in the Reinhardt domain $D_p = \{ (z_1 ,z_2 , \cdots ,z_n ) \in \mathbb{C}^n :\left| {z_1 } \right|^{p_1 } + \left| {z_2 } \right|^{p_2 } + \cdots + \left| ...The construction of normalized biholomorphic convex mappings in the Reinhardt domain $D_p = \{ (z_1 ,z_2 , \cdots ,z_n ) \in \mathbb{C}^n :\left| {z_1 } \right|^{p_1 } + \left| {z_2 } \right|^{p_2 } + \cdots + \left| {z_n } \right|^{p_n } < 1\} $ , p j > 2, j = 1,2,?, n) of ? n is discussed. The authors set up a Decomposition Theorem for such mappings. As a special case, it is proved that, for each such mapping f, the first k-terms of the homogeneous expansion of its j-th component f j , j = 1, 2, ?, n, depends only on z j , where k is the number that satisfies k < min {p 1, p 2,?, p n ≤ k + 1. When p1,p2, ... ,pn → ∞ , this derives the Decomposition Theorem of normalized biholomorphic convex mappings in the polydisc which was gotten by T.J. Suffridge in 1970.展开更多
Multispectral image compression and encryption algorithms commonly suffer from issues such as low compression efficiency,lack of synchronization between the compression and encryption proces-ses,and degradation of int...Multispectral image compression and encryption algorithms commonly suffer from issues such as low compression efficiency,lack of synchronization between the compression and encryption proces-ses,and degradation of intrinsic image structure.A novel approach is proposed to address these is-sues.Firstly,a chaotic sequence is generated using the Lorenz three-dimensional chaotic mapping to initiate the encryption process,which is XORed with each spectral band of the multispectral image to complete the initial encryption of the image.Then,a two-dimensional lifting 9/7 wavelet transform is applied to the processed image.Next,a key-sensitive Arnold scrambling technique is employed on the resulting low-frequency image.It effectively eliminates spatial redundancy in the multispectral image while enhancing the encryption process.To optimize the compression and encryption processes further,fast Tucker decomposition is applied to the wavelet sub-band tensor.It effectively removes both spectral redundancy and residual spatial redundancy in the multispectral image.Finally,the core tensor and pattern matrix obtained from the decomposition are subjected to entropy encoding,and real-time chaotic encryption is implemented during the encoding process,effectively integrating compression and encryption.The results show that the proposed algorithm is suitable for occasions with high requirements for compression and encryption,and it provides valuable insights for the de-velopment of compression and encryption in multispectral field.展开更多
Research on the laser ablation behavior of SiC ceramics has great significance for the improvement of their anti-laser ability as high-performance mirrors in space and lasers, or the laser surface micro-machining tech...Research on the laser ablation behavior of SiC ceramics has great significance for the improvement of their anti-laser ability as high-performance mirrors in space and lasers, or the laser surface micro-machining technology as electronic components in micro-electron mechanical systems (MEMS). In this work, the laser ablation of SiC ceramics has been performed by using laser pulses of 12 ns duration at 1064 nm. The laser induced damage threshold (LIDT) below 0.1 J/cm(2) was obtained by 1-on-1 mode and its damage morphology appeared in the form of 'burning crater' with a clear boundary. Micro-Raman mapping technique was first introduced in our study on the laser ablation mechanisms of SiC surface by identifying physical and chemical changes between uninjured and laser-ablated areas. It has been concluded that during the ablation process, SiC surface mainly underwent decomposition to the elemental Si and C, accompanied by some transformation of crystal orientation. The oxidation of SiC also took place but only in small amount on the edges of target region, while there was no hint of SiO2 in the center with higher energy density, maybe because of deficiency of O-2 atmosphere in the ablated area, elimination of SiO2 by carbon at 1505 degrees C, or evaporating at 2230 degrees C.展开更多
In this paper, we first give the definition of weakly (K1,K2-quasiregular mappings, and then by using the Hodge decomposition and the weakly reverse H?lder inequality, we obtain their regularity property: For anyq 1 t...In this paper, we first give the definition of weakly (K1,K2-quasiregular mappings, and then by using the Hodge decomposition and the weakly reverse H?lder inequality, we obtain their regularity property: For anyq 1 that satisfies $0< K_1 n^{(n + 4)/2} 2^{n + 1} \times 100^{n^2 } [2^{3n/2} (2^{5n} + 1)](n - q_1 )< 1$ , there existsp 1=p 1(n,q 1,K 1,K 2)>n, such that any (K1, K2)-quasiregular mapping $f \in W_{loc}^{1,q_1 } (\Omega ,R^n )$ is in fact in $W_{loc}^{1,p_1 } (\Omega , R^n )$ . That is, f is (K1,K2)-quasiregular in the usual sense.展开更多
Watermarking is a widely used solution to the problems of authentication and copyright protection of digital media especially for images,videos,and audio data.Chaos is one of the emerging techniques adopted in image w...Watermarking is a widely used solution to the problems of authentication and copyright protection of digital media especially for images,videos,and audio data.Chaos is one of the emerging techniques adopted in image watermarking schemes due to its intrinsic cryptographic properties.This paper proposes a new chaotic hybrid watermarking method combining Discrete Wavelet Transform(DWT),Z-transform(ZT)and Bidiagonal Singular Value Decomposition(BSVD).The original image is decomposed into 3-level DWT,and then,ZT is applied on the HH3 and HL3 sub-bands.The watermark image is encrypted using Arnold Cat Map.BSVD for the watermark and transformed original image were computed,and the watermark was embedded by modifying singular values of the host image with the singular values of the watermark image.Robustness of the proposed scheme was examined using standard test images and assessed against common signal processing and geometric attacks.Experiments indicated that the proposed method is transparent and highly robust.展开更多
This paper develops a powerful technique called threshold decomposition which is introduced for the analysis and implementation of median filter. This technique called generalized decomposition(GTD) is better than the...This paper develops a powerful technique called threshold decomposition which is introduced for the analysis and implementation of median filter. This technique called generalized decomposition(GTD) is better than the original method in the theoretical analysis and VLSI realization.展开更多
A characteristic parameter α_D of a domain D in R^n is introduced. D is unifonm if and only if α_D<∞. And α_D=1 if D is a ball or a half space. It is proved that the decomposability and the uniformity of a doma...A characteristic parameter α_D of a domain D in R^n is introduced. D is unifonm if and only if α_D<∞. And α_D=1 if D is a ball or a half space. It is proved that the decomposability and the uniformity of a domain in R^n are still equivalent. Some problems on uniform domains and decomposition domains are discussed.展开更多
基金This work was supported by 973 Project, the National Natural Science Foundation of China (Grant No. 19871081) the Natural Science Foundation of Guangdong Province and Anhui Province.
文摘The construction of normalized biholomorphic convex mappings in the Reinhardt domain $D_p = \{ (z_1 ,z_2 , \cdots ,z_n ) \in \mathbb{C}^n :\left| {z_1 } \right|^{p_1 } + \left| {z_2 } \right|^{p_2 } + \cdots + \left| {z_n } \right|^{p_n } < 1\} $ , p j > 2, j = 1,2,?, n) of ? n is discussed. The authors set up a Decomposition Theorem for such mappings. As a special case, it is proved that, for each such mapping f, the first k-terms of the homogeneous expansion of its j-th component f j , j = 1, 2, ?, n, depends only on z j , where k is the number that satisfies k < min {p 1, p 2,?, p n ≤ k + 1. When p1,p2, ... ,pn → ∞ , this derives the Decomposition Theorem of normalized biholomorphic convex mappings in the polydisc which was gotten by T.J. Suffridge in 1970.
基金the National Natural Science Foundation of China(No.11803036)Climbing Program of Changchun University(No.ZKP202114).
文摘Multispectral image compression and encryption algorithms commonly suffer from issues such as low compression efficiency,lack of synchronization between the compression and encryption proces-ses,and degradation of intrinsic image structure.A novel approach is proposed to address these is-sues.Firstly,a chaotic sequence is generated using the Lorenz three-dimensional chaotic mapping to initiate the encryption process,which is XORed with each spectral band of the multispectral image to complete the initial encryption of the image.Then,a two-dimensional lifting 9/7 wavelet transform is applied to the processed image.Next,a key-sensitive Arnold scrambling technique is employed on the resulting low-frequency image.It effectively eliminates spatial redundancy in the multispectral image while enhancing the encryption process.To optimize the compression and encryption processes further,fast Tucker decomposition is applied to the wavelet sub-band tensor.It effectively removes both spectral redundancy and residual spatial redundancy in the multispectral image.Finally,the core tensor and pattern matrix obtained from the decomposition are subjected to entropy encoding,and real-time chaotic encryption is implemented during the encoding process,effectively integrating compression and encryption.The results show that the proposed algorithm is suitable for occasions with high requirements for compression and encryption,and it provides valuable insights for the de-velopment of compression and encryption in multispectral field.
基金funds from the National Natural Science Foundation of China
文摘Research on the laser ablation behavior of SiC ceramics has great significance for the improvement of their anti-laser ability as high-performance mirrors in space and lasers, or the laser surface micro-machining technology as electronic components in micro-electron mechanical systems (MEMS). In this work, the laser ablation of SiC ceramics has been performed by using laser pulses of 12 ns duration at 1064 nm. The laser induced damage threshold (LIDT) below 0.1 J/cm(2) was obtained by 1-on-1 mode and its damage morphology appeared in the form of 'burning crater' with a clear boundary. Micro-Raman mapping technique was first introduced in our study on the laser ablation mechanisms of SiC surface by identifying physical and chemical changes between uninjured and laser-ablated areas. It has been concluded that during the ablation process, SiC surface mainly underwent decomposition to the elemental Si and C, accompanied by some transformation of crystal orientation. The oxidation of SiC also took place but only in small amount on the edges of target region, while there was no hint of SiO2 in the center with higher energy density, maybe because of deficiency of O-2 atmosphere in the ablated area, elimination of SiO2 by carbon at 1505 degrees C, or evaporating at 2230 degrees C.
基金supported by the Doctor's Foundation of Hebei University
文摘In this paper, we first give the definition of weakly (K1,K2-quasiregular mappings, and then by using the Hodge decomposition and the weakly reverse H?lder inequality, we obtain their regularity property: For anyq 1 that satisfies $0< K_1 n^{(n + 4)/2} 2^{n + 1} \times 100^{n^2 } [2^{3n/2} (2^{5n} + 1)](n - q_1 )< 1$ , there existsp 1=p 1(n,q 1,K 1,K 2)>n, such that any (K1, K2)-quasiregular mapping $f \in W_{loc}^{1,q_1 } (\Omega ,R^n )$ is in fact in $W_{loc}^{1,p_1 } (\Omega , R^n )$ . That is, f is (K1,K2)-quasiregular in the usual sense.
文摘Watermarking is a widely used solution to the problems of authentication and copyright protection of digital media especially for images,videos,and audio data.Chaos is one of the emerging techniques adopted in image watermarking schemes due to its intrinsic cryptographic properties.This paper proposes a new chaotic hybrid watermarking method combining Discrete Wavelet Transform(DWT),Z-transform(ZT)and Bidiagonal Singular Value Decomposition(BSVD).The original image is decomposed into 3-level DWT,and then,ZT is applied on the HH3 and HL3 sub-bands.The watermark image is encrypted using Arnold Cat Map.BSVD for the watermark and transformed original image were computed,and the watermark was embedded by modifying singular values of the host image with the singular values of the watermark image.Robustness of the proposed scheme was examined using standard test images and assessed against common signal processing and geometric attacks.Experiments indicated that the proposed method is transparent and highly robust.
基金Supported by the National Natural Science Foundation of China
文摘This paper develops a powerful technique called threshold decomposition which is introduced for the analysis and implementation of median filter. This technique called generalized decomposition(GTD) is better than the original method in the theoretical analysis and VLSI realization.
文摘A characteristic parameter α_D of a domain D in R^n is introduced. D is unifonm if and only if α_D<∞. And α_D=1 if D is a ball or a half space. It is proved that the decomposability and the uniformity of a domain in R^n are still equivalent. Some problems on uniform domains and decomposition domains are discussed.
