Ensuring digital media security through robust image watermarking is essential to prevent unauthorized distribution,tampering,and copyright infringement.This study introduces a novel hybrid watermarking framework that...Ensuring digital media security through robust image watermarking is essential to prevent unauthorized distribution,tampering,and copyright infringement.This study introduces a novel hybrid watermarking framework that integrates Discrete Wavelet Transform(DWT),Redundant Discrete Wavelet Transform(RDWT),and Möbius Transformations(MT),with optimization of transformation parameters achieved via a Genetic Algorithm(GA).By combining frequency and spatial domain techniques,the proposed method significantly enhances both the imper-ceptibility and robustness of watermark embedding.The approach leverages DWT and RDWT for multi-resolution decomposition,enabling watermark insertion in frequency subbands that balance visibility and resistance to attacks.RDWT,in particular,offers shift-invariance,which improves performance under geometric transformations.Möbius transformations are employed for spatial manipulation,providing conformal mapping and spatial dispersion that fortify watermark resilience against rotation,scaling,and translation.The GA dynamically optimizes the Möbius parameters,selecting configurations that maximize robustness metrics such as Peak Signal-to-Noise Ratio(PSNR),Structural Similarity Index Measure(SSIM),Bit Error Rate(BER),and Normalized Cross-Correlation(NCC).Extensive experiments conducted on medical and standard benchmark images demonstrate the efficacy of the proposed RDWT-MT scheme.Results show that PSNR exceeds 68 dB,SSIM approaches 1.0,and BER remains at 0.0000,indicating excellent imperceptibility and perfect watermark recovery.Moreover,the method exhibits exceptional resilience to a wide range of image processing attacks,including Gaussian noise,JPEG compression,histogram equalization,and cropping,achieving NCC values close to or equal to 1.0.Comparative evaluations with state-of-the-art watermarking techniques highlight the superiority of the proposed method in terms of robustness,fidelity,and computational efficiency.The hybrid framework ensures secure,adaptive watermark embedding,making it highly suitable for applications in digital rights management,content authentication,and medical image protection.The integration of spatial and frequency domain features with evolutionary optimization presents a promising direction for future watermarking technologies.展开更多
With respect to oceanic fluid dynamics,certain models have appeared,e.g.,an extended time-dependent(3+1)-dimensional shallow water wave equation in an ocean or a river,which we investigate in this paper.Using symbolic...With respect to oceanic fluid dynamics,certain models have appeared,e.g.,an extended time-dependent(3+1)-dimensional shallow water wave equation in an ocean or a river,which we investigate in this paper.Using symbolic computation,we find out,on one hand,a set of bilinear auto-Backlund transformations,which could connect certain solutions of that equation with other solutions of that equation itself,and on the other hand,a set of similarity reductions,which could go from that equation to a known ordinary differential equation.The results in this paper depend on all the oceanic variable coefficients in that equation.展开更多
Let T:T^(d)→T^(d),defined by Tx=AX(mod 1),where A is a d×d integer matrix with eigenvalues 1<|λ_(1)|≤|λ_(2)|≤…≤|λ_(d)|,We investigate the Hausdorff dimension of the recurrence set R(ψ)={x∈T^(d):T^(n)...Let T:T^(d)→T^(d),defined by Tx=AX(mod 1),where A is a d×d integer matrix with eigenvalues 1<|λ_(1)|≤|λ_(2)|≤…≤|λ_(d)|,We investigate the Hausdorff dimension of the recurrence set R(ψ)={x∈T^(d):T^(n)x∈B(x,ψ(n))for infinitely many n}forα≥log|λ_(d)/λ_(1)|,whereψis a positive decreasing function defined onℕand its lower order at infinity isα=lim inf_(n→∞)-logψ(n)/n.In the case that A is diagonalizable overℚwith integral eigenvalues,we obtain the dimension formula.展开更多
The synthesized molecular clusters featuring the cubic[4Fe–4S]core have been studied for several decades,as they serve as true analogs of the active components in ferritin within biological systems.Such a model clust...The synthesized molecular clusters featuring the cubic[4Fe–4S]core have been studied for several decades,as they serve as true analogs of the active components in ferritin within biological systems.Such a model cluster has been extensively investigated in various fields,including structural modulation,catalysis,and self-assembly under laboratory conditions,with the aim of gaining an in-depth understanding of their roles in biological functions.Herein,we revisited three well-known[Fe_(4)S_(4)(SR)_(4)]^(2–)molecules,namely[Me_(4)N]_(2)[Fe_(4)S_(4)(SR)_(4)](R=o-MBT,m-MBT,p-MBT),and successfully established their single crystal structures that remain unknown prior to this work.Interestingly,it is revealed that the position of the substituent methyl group has an obvious steric effect on the arrangement of the ligand around the[4Fe–4S]core,which further influences their overall packing patterns in single crystals.In addition,this work unveils two new structure transformation behaviors for the[Fe_(4)S_(4)(SR)_(4)]^(2–)system:i)the monomeric[Fe(SR)_(4)]^(2–)and tetrameric[Fe_(4)S_(4)(SR)_(4)]^(2–)can be interconverted,and ii)[Fe_(4)S_(4)(SR)_(4)]^(2–)can be transferred into an intriguing iron-oxide complex Na_(2)Fe_(6)O(OMe)_(18)·6MeOH in a well-controlled oxidizing environment.展开更多
文摘Ensuring digital media security through robust image watermarking is essential to prevent unauthorized distribution,tampering,and copyright infringement.This study introduces a novel hybrid watermarking framework that integrates Discrete Wavelet Transform(DWT),Redundant Discrete Wavelet Transform(RDWT),and Möbius Transformations(MT),with optimization of transformation parameters achieved via a Genetic Algorithm(GA).By combining frequency and spatial domain techniques,the proposed method significantly enhances both the imper-ceptibility and robustness of watermark embedding.The approach leverages DWT and RDWT for multi-resolution decomposition,enabling watermark insertion in frequency subbands that balance visibility and resistance to attacks.RDWT,in particular,offers shift-invariance,which improves performance under geometric transformations.Möbius transformations are employed for spatial manipulation,providing conformal mapping and spatial dispersion that fortify watermark resilience against rotation,scaling,and translation.The GA dynamically optimizes the Möbius parameters,selecting configurations that maximize robustness metrics such as Peak Signal-to-Noise Ratio(PSNR),Structural Similarity Index Measure(SSIM),Bit Error Rate(BER),and Normalized Cross-Correlation(NCC).Extensive experiments conducted on medical and standard benchmark images demonstrate the efficacy of the proposed RDWT-MT scheme.Results show that PSNR exceeds 68 dB,SSIM approaches 1.0,and BER remains at 0.0000,indicating excellent imperceptibility and perfect watermark recovery.Moreover,the method exhibits exceptional resilience to a wide range of image processing attacks,including Gaussian noise,JPEG compression,histogram equalization,and cropping,achieving NCC values close to or equal to 1.0.Comparative evaluations with state-of-the-art watermarking techniques highlight the superiority of the proposed method in terms of robustness,fidelity,and computational efficiency.The hybrid framework ensures secure,adaptive watermark embedding,making it highly suitable for applications in digital rights management,content authentication,and medical image protection.The integration of spatial and frequency domain features with evolutionary optimization presents a promising direction for future watermarking technologies.
基金financially supported by the Scientific Research Foundation of North China University of Technology(Grant Nos.11005136024XN147-87 and 110051360024XN151-86).
文摘With respect to oceanic fluid dynamics,certain models have appeared,e.g.,an extended time-dependent(3+1)-dimensional shallow water wave equation in an ocean or a river,which we investigate in this paper.Using symbolic computation,we find out,on one hand,a set of bilinear auto-Backlund transformations,which could connect certain solutions of that equation with other solutions of that equation itself,and on the other hand,a set of similarity reductions,which could go from that equation to a known ordinary differential equation.The results in this paper depend on all the oceanic variable coefficients in that equation.
基金supported by the Science Foundation of China University of Petroleum,Beijing(2462023SZBH013)the China Postdoctoral Science Foundation(2023M743878)+2 种基金the Postdoctoral Fellowship Program of CPSF(GZB20240848)supported partially by the NSFC(12271176)the Guangdong Natural Science Foundation(2024A1515010946).
文摘Let T:T^(d)→T^(d),defined by Tx=AX(mod 1),where A is a d×d integer matrix with eigenvalues 1<|λ_(1)|≤|λ_(2)|≤…≤|λ_(d)|,We investigate the Hausdorff dimension of the recurrence set R(ψ)={x∈T^(d):T^(n)x∈B(x,ψ(n))for infinitely many n}forα≥log|λ_(d)/λ_(1)|,whereψis a positive decreasing function defined onℕand its lower order at infinity isα=lim inf_(n→∞)-logψ(n)/n.In the case that A is diagonalizable overℚwith integral eigenvalues,we obtain the dimension formula.
基金supported by the Fundamental Research Funds for the Central Universities(22120240204 and 22120240039)the National Natural Science Foundation of China(22301219,Z.Z.,22101205,H.H.)。
文摘The synthesized molecular clusters featuring the cubic[4Fe–4S]core have been studied for several decades,as they serve as true analogs of the active components in ferritin within biological systems.Such a model cluster has been extensively investigated in various fields,including structural modulation,catalysis,and self-assembly under laboratory conditions,with the aim of gaining an in-depth understanding of their roles in biological functions.Herein,we revisited three well-known[Fe_(4)S_(4)(SR)_(4)]^(2–)molecules,namely[Me_(4)N]_(2)[Fe_(4)S_(4)(SR)_(4)](R=o-MBT,m-MBT,p-MBT),and successfully established their single crystal structures that remain unknown prior to this work.Interestingly,it is revealed that the position of the substituent methyl group has an obvious steric effect on the arrangement of the ligand around the[4Fe–4S]core,which further influences their overall packing patterns in single crystals.In addition,this work unveils two new structure transformation behaviors for the[Fe_(4)S_(4)(SR)_(4)]^(2–)system:i)the monomeric[Fe(SR)_(4)]^(2–)and tetrameric[Fe_(4)S_(4)(SR)_(4)]^(2–)can be interconverted,and ii)[Fe_(4)S_(4)(SR)_(4)]^(2–)can be transferred into an intriguing iron-oxide complex Na_(2)Fe_(6)O(OMe)_(18)·6MeOH in a well-controlled oxidizing environment.
