The four-dimensional character of Einstein’s spacetime is generally accepted in mainstream physics as beyond reasonable doubt correct. However the real problem is when we require scale invariance and that this spacet...The four-dimensional character of Einstein’s spacetime is generally accepted in mainstream physics as beyond reasonable doubt correct. However the real problem is when we require scale invariance and that this spacetime be four-dimensional on all scales. It is true that on our classical scale, the 4D decouples into 3D plus one time dimension and that on very large scale only the curvature of spacetime becomes noticeable. However the critical problem is that such spacetime must remain 4D no matter how small the scale we are probing is. This is something of crucial importance for quantum physics. The present work addresses this basic, natural and logical requirement and shows how many contradictory results and shortcomings of relativity and quantum gravity could be eliminated when we “complete” Einstein’s spacetime in such a geometrical gauge invariant way. Concurrently the work serves also as a review of the vast Literature on E-Infinity theory used here.展开更多
A new robust watermarking approach was proposed in 2D continuous wavelet domain (CWT). The watermark is embedded into the large coefficients in the middle band of wavelet transform modulus maxima (WTMM) of the hos...A new robust watermarking approach was proposed in 2D continuous wavelet domain (CWT). The watermark is embedded into the large coefficients in the middle band of wavelet transform modulus maxima (WTMM) of the host image. After possible attacks, the watermark is then detected and extracted by correlation analysis. Compared with other wavelet domain watermarking approaches, the WTMM approach can endow the image with beth rotation and shift invariant properties. On the other hand, scale invariance is achieved with the geometric normalization during watermark detection. Case studies involve various attacks such as shifting, lossy compression, scaling, rotation and median filtering on the watermarked image, and the result shows that the approach is robust to these attacks.展开更多
Let K be a compact group.For a symplectic quotient M_(λ) of a compact Hamiltonian Kahler K-manifold,we show that the induced complex structure on M_(λ) is locally invariant when the parameter λ varies in Lie(K)^(*)...Let K be a compact group.For a symplectic quotient M_(λ) of a compact Hamiltonian Kahler K-manifold,we show that the induced complex structure on M_(λ) is locally invariant when the parameter λ varies in Lie(K)^(*).To prove such a result,we take two di erent approaches:(i)use the complex geometry properties of the symplectic implosion construction;(ii)investigate the variation of geometric invariant theory(GIT)quotients.展开更多
In this paper,the invariant geometric flows for hypersurfaces in centro-affine geometry are explored.We first present evolution equations of the centro-affine invariants corresponding to the geometric flows.Based on t...In this paper,the invariant geometric flows for hypersurfaces in centro-affine geometry are explored.We first present evolution equations of the centro-affine invariants corresponding to the geometric flows.Based on these fundamental evolution equations,we show that the centro-affine heat flow for hypersurfaces is equivalent to a system of ordinary differential equations,which can be solved explicitly.Finally,the centro-affine invariant normal flows for hypersurfaces are investigated,and two specific flows are provided to illustrate the behaviour of the flows.展开更多
文摘The four-dimensional character of Einstein’s spacetime is generally accepted in mainstream physics as beyond reasonable doubt correct. However the real problem is when we require scale invariance and that this spacetime be four-dimensional on all scales. It is true that on our classical scale, the 4D decouples into 3D plus one time dimension and that on very large scale only the curvature of spacetime becomes noticeable. However the critical problem is that such spacetime must remain 4D no matter how small the scale we are probing is. This is something of crucial importance for quantum physics. The present work addresses this basic, natural and logical requirement and shows how many contradictory results and shortcomings of relativity and quantum gravity could be eliminated when we “complete” Einstein’s spacetime in such a geometrical gauge invariant way. Concurrently the work serves also as a review of the vast Literature on E-Infinity theory used here.
基金The National Natural Science Foundation of China (No.60703048)the Natural Science Foundation of Hubei Province (No.2007ABA303)
文摘A new robust watermarking approach was proposed in 2D continuous wavelet domain (CWT). The watermark is embedded into the large coefficients in the middle band of wavelet transform modulus maxima (WTMM) of the host image. After possible attacks, the watermark is then detected and extracted by correlation analysis. Compared with other wavelet domain watermarking approaches, the WTMM approach can endow the image with beth rotation and shift invariant properties. On the other hand, scale invariance is achieved with the geometric normalization during watermark detection. Case studies involve various attacks such as shifting, lossy compression, scaling, rotation and median filtering on the watermarked image, and the result shows that the approach is robust to these attacks.
基金supported by China Postdoctoral Science Foundation(Grant No.BX201700008).
文摘Let K be a compact group.For a symplectic quotient M_(λ) of a compact Hamiltonian Kahler K-manifold,we show that the induced complex structure on M_(λ) is locally invariant when the parameter λ varies in Lie(K)^(*).To prove such a result,we take two di erent approaches:(i)use the complex geometry properties of the symplectic implosion construction;(ii)investigate the variation of geometric invariant theory(GIT)quotients.
基金This work was supported by National Natural Science Foundation of China(Grant Nos.11631007 and 11971251).
文摘In this paper,the invariant geometric flows for hypersurfaces in centro-affine geometry are explored.We first present evolution equations of the centro-affine invariants corresponding to the geometric flows.Based on these fundamental evolution equations,we show that the centro-affine heat flow for hypersurfaces is equivalent to a system of ordinary differential equations,which can be solved explicitly.Finally,the centro-affine invariant normal flows for hypersurfaces are investigated,and two specific flows are provided to illustrate the behaviour of the flows.