The representation of weak Hopf algebras is studied by investigating the Gorenstein dimensions of weak Hopf algebras and weak Hopf-Galois extensions.Let H be a weak Hopf algebra with a bijective antipode,A a weak righ...The representation of weak Hopf algebras is studied by investigating the Gorenstein dimensions of weak Hopf algebras and weak Hopf-Galois extensions.Let H be a weak Hopf algebra with a bijective antipode,A a weak right H-comodule algebra and B the H-coinvariant subalgebra of A.First,some properties of Gorenstein projective H-modules in the representation category are studied,and the fact that Gorenstein global dimension of H is the same as the Gorenstein projective dimension of its left unital subalgebra is demonstrated.Secondly,by applying the integral theory of weak Hopf algebras,on the one hand,a sufficient and necessary condition that a projective A-module is a projective B-module is given;on the other hand,the separability of the functor AB-and that of the restriction of scalar function B(-)are described,respectively.Finally,as a mean result,the Gorenstein global dimension of a weak Hopf-Galois extension is investigated under the condition that H is both semisimple and cosemisimple.展开更多
A creepy photoelectric endoscopy system with good performance is studied, and anexpansion and correction algorithm for a compressed photoelectric image with serious geometricdistortion is presented. The algorithm can ...A creepy photoelectric endoscopy system with good performance is studied, and anexpansion and correction algorithm for a compressed photoelectric image with serious geometricdistortion is presented. The algorithm can not only correct the geometric distortion, but alsorestore the gray-level distribution by means of ternary convolution algorithm. The details andthe outline in the image are very clear. It is proved to be of high performance in practice.展开更多
Based on the Mach＇s principle and the characteristic mass of the present universe, Mo a c3/2GHo, it is noticed that, ＇rate of decrease in the laboratory fine structure ratio＇ is a measure of the cosmic rate of expa...Based on the Mach＇s principle and the characteristic mass of the present universe, Mo a c3/2GHo, it is noticed that, ＇rate of decrease in the laboratory fine structure ratio＇ is a measure of the cosmic rate of expansion. If the observed laboratory fine structure ratio is a constant, then, independent of the cosmic red shift and CMBR observations, it can be suggested that, at present there is no cosmic acceleration. Obtained value of the present Hubble constant is 70.75 Km/sec/Mpc. If it is true that, rate of decrease in temperature is a measure of cosmic rate of expansion, then from the observed cosmic isotropy it can also be suggested that, at present there is no cosmic acceleration. At present if the characteristic mass of the universe is, Mo = c3/2GHo and if the primordial universe is a natural setting for the creation of black holes and other non-perturbative gravitational entities, it is also possible to assume that throughout its journey, the whole universe is a primordial growing and light speed rotating black hole. At any time, if cot is the angular velocity, then cosmic radius is c/ω1 and cosmic mass is c3/2Gω1 Instead of the Planck mass, initial conditions can be addressed with the Coulomb mass = Mc = √/4xeoG At present, if ω1= H0 the cosmic black hole＇s volume density, observed matter density and the thermal energy density are in geometric series and the geometric ratio is 1 ＋ ln（M0 ＋Mc）.展开更多
Based on their Euler poles, we calculated the relative velocities between every two plates in the typical global plate motion models, respectively, and estimated the area change along these boundaries. In our calculat...Based on their Euler poles, we calculated the relative velocities between every two plates in the typical global plate motion models, respectively, and estimated the area change along these boundaries. In our calculations, plates on both sides accommodated area changes depending on the boundary types： extensional, convergent or transform, so we can estimate area change of each plate and then globally. Our preliminary results show that the area of the southern hemisphere increased while that of the northern hemisphere decreased over the past I million years, and global area has increased by 26,000km^2 to 36,000km^2, which corresponds to the 160m - 250m increment on the Earth＇s radius if all these area increments are attributed to Earth＇s expansion. Taking the NUVEL-1 model as an example, of the 14 plates in this model, 11 are decreasing, but the global area has increased because of the larger increment amount from Africa, North America and Antarctica. Finally, we also discussed factors affecting the global area change such as subduction zone retreating and back-arc spreading.展开更多
Let π and π′ be unitary automorphic cuspidal representations of GL_n(A_E) and GL_m(A_F), and let E and F be solvable Galois extensions of Q of degrees ? and ?′, respectively. Using the fact that the automorphic in...Let π and π′ be unitary automorphic cuspidal representations of GL_n(A_E) and GL_m(A_F), and let E and F be solvable Galois extensions of Q of degrees ? and ?′, respectively. Using the fact that the automorphic induction and base change maps exist for E and F, and assuming an invariance condition under the actions of the Galois groups, we attach to the pair(π, π′) a Rankin-Selberg L-function L(s, π×E,Fπ′) for which we prove a prime number theorem. This gives a method for comparing two representations that could be defined over completely different extensions, and the main results give a measure of how many cuspidal components the two representations π and π′ have in common when automorphically induced down to the rational numbers. The proof uses the structure of the Galois group of the composite extension EF and the character groups attached to the fields via class field theory. The second main theorem also gives an indication of when the base change of π up to the composite extension EF remains cuspidal.展开更多
基金The National Natural Science Foundation of China(No.11601203)the China Postdoctoral Science Foundation(No.2018M642128)Qing Lan Project of Jiangsu Province,the Natural Science Foundation of Jiangsu Province(No.BK20150113).
文摘The representation of weak Hopf algebras is studied by investigating the Gorenstein dimensions of weak Hopf algebras and weak Hopf-Galois extensions.Let H be a weak Hopf algebra with a bijective antipode,A a weak right H-comodule algebra and B the H-coinvariant subalgebra of A.First,some properties of Gorenstein projective H-modules in the representation category are studied,and the fact that Gorenstein global dimension of H is the same as the Gorenstein projective dimension of its left unital subalgebra is demonstrated.Secondly,by applying the integral theory of weak Hopf algebras,on the one hand,a sufficient and necessary condition that a projective A-module is a projective B-module is given;on the other hand,the separability of the functor AB-and that of the restriction of scalar function B(-)are described,respectively.Finally,as a mean result,the Gorenstein global dimension of a weak Hopf-Galois extension is investigated under the condition that H is both semisimple and cosemisimple.
文摘A creepy photoelectric endoscopy system with good performance is studied, and anexpansion and correction algorithm for a compressed photoelectric image with serious geometricdistortion is presented. The algorithm can not only correct the geometric distortion, but alsorestore the gray-level distribution by means of ternary convolution algorithm. The details andthe outline in the image are very clear. It is proved to be of high performance in practice.
文摘Based on the Mach＇s principle and the characteristic mass of the present universe, Mo a c3/2GHo, it is noticed that, ＇rate of decrease in the laboratory fine structure ratio＇ is a measure of the cosmic rate of expansion. If the observed laboratory fine structure ratio is a constant, then, independent of the cosmic red shift and CMBR observations, it can be suggested that, at present there is no cosmic acceleration. Obtained value of the present Hubble constant is 70.75 Km/sec/Mpc. If it is true that, rate of decrease in temperature is a measure of cosmic rate of expansion, then from the observed cosmic isotropy it can also be suggested that, at present there is no cosmic acceleration. At present if the characteristic mass of the universe is, Mo = c3/2GHo and if the primordial universe is a natural setting for the creation of black holes and other non-perturbative gravitational entities, it is also possible to assume that throughout its journey, the whole universe is a primordial growing and light speed rotating black hole. At any time, if cot is the angular velocity, then cosmic radius is c/ω1 and cosmic mass is c3/2Gω1 Instead of the Planck mass, initial conditions can be addressed with the Coulomb mass = Mc = √/4xeoG At present, if ω1= H0 the cosmic black hole＇s volume density, observed matter density and the thermal energy density are in geometric series and the geometric ratio is 1 ＋ ln（M0 ＋Mc）.
基金sponsored by the National Natural Science Foundation (40574047),China
文摘Based on their Euler poles, we calculated the relative velocities between every two plates in the typical global plate motion models, respectively, and estimated the area change along these boundaries. In our calculations, plates on both sides accommodated area changes depending on the boundary types： extensional, convergent or transform, so we can estimate area change of each plate and then globally. Our preliminary results show that the area of the southern hemisphere increased while that of the northern hemisphere decreased over the past I million years, and global area has increased by 26,000km^2 to 36,000km^2, which corresponds to the 160m - 250m increment on the Earth＇s radius if all these area increments are attributed to Earth＇s expansion. Taking the NUVEL-1 model as an example, of the 14 plates in this model, 11 are decreasing, but the global area has increased because of the larger increment amount from Africa, North America and Antarctica. Finally, we also discussed factors affecting the global area change such as subduction zone retreating and back-arc spreading.
文摘Let π and π′ be unitary automorphic cuspidal representations of GL_n(A_E) and GL_m(A_F), and let E and F be solvable Galois extensions of Q of degrees ? and ?′, respectively. Using the fact that the automorphic induction and base change maps exist for E and F, and assuming an invariance condition under the actions of the Galois groups, we attach to the pair(π, π′) a Rankin-Selberg L-function L(s, π×E,Fπ′) for which we prove a prime number theorem. This gives a method for comparing two representations that could be defined over completely different extensions, and the main results give a measure of how many cuspidal components the two representations π and π′ have in common when automorphically induced down to the rational numbers. The proof uses the structure of the Galois group of the composite extension EF and the character groups attached to the fields via class field theory. The second main theorem also gives an indication of when the base change of π up to the composite extension EF remains cuspidal.
