Urban sprawl is threatening the limited highly fertile land in the Nile delta of Egypt. Landsat TM satellite images of 1984, 1992 and ETM+ of 2006 have been used to study the impact of urban sprawl on agricultural lan...Urban sprawl is threatening the limited highly fertile land in the Nile delta of Egypt. Landsat TM satellite images of 1984, 1992 and ETM+ of 2006 have been used to study the impact of urban sprawl on agricultural land of the Northern Nile delta, Egypt. Visual interpretation using on screen digitizing and change detection techniques were applied for monitoring the urban sprawl. Combining the land capability map and the urban thematic layer using GIS made it possible to point out the risk of urban expansion on the expense of the highly capable soil class. The results show that a total expansion of urban area amounted to 689.20 km2(6.3% of total area) during the study period 1984–2006. The urban expansion during the 1984–2006 was on the expense of the most fertile soils where, the high capable soils(Class I) lost 247.14 km2(2.26 % of total area) and the moderate capable soils lost 32.73 km2(0.3% of total area), while the low capable soils lost only 57.39 km2(0.53% of total area). The urban encroachment over the non capable soils was very limited during the study period 1984–1992, where 7.33 km2 only was lost. The pattern of urban sprawl has been changed during the 1992 to 2006 whereas much larger area(50.64 km2) of the non capable soils was converted to urban. It can be concluded that the urban sprawl is one of the dominant degradation process on the land of Nile Delta.展开更多
Let H be a cosemisimple Hopf algebra over a field k, and π ： A→ H be a surjective cocentral bialgebra homomorphism of bialgebras. The authors prove that if A is Galois over its coinvariants B=LH Ker π and B is a s...Let H be a cosemisimple Hopf algebra over a field k, and π ： A→ H be a surjective cocentral bialgebra homomorphism of bialgebras. The authors prove that if A is Galois over its coinvariants B=LH Ker π and B is a sub-Hopf algebra of A, then A is itself a Hopf algebra. This generalizes a result of Cegarra [3] on group-graded algebras.展开更多
The period of a monic polynomial over an arbitrary Galois ring GR(pe,d) is theoretically determined by using its classical factorization and Galois extensions of rings. For a polynomial f(x) the modulo p remainder of ...The period of a monic polynomial over an arbitrary Galois ring GR(pe,d) is theoretically determined by using its classical factorization and Galois extensions of rings. For a polynomial f(x) the modulo p remainder of which is a power of an irreducible polynomial over the residue field of the Galois ring, the period of f(x) is characterized by the periods of the irreducible polynomial and an associated polynomial of the form (x-1)m+pg(x). Further results on the periods of such associated polynomials are obtained, in particular, their periods are proved to achieve an upper bound value in most cases. As a consequence, the period of a monic polynomial over GR(pe,d) is equal to pe-1 times the period of its modulo p remainder polynomial with a probability close to 1, and an expression of this probability is given.展开更多
A finite group G is called exceptional if for a Galois extension F/k of number fields with the Galois group G,in the Brauer-Kuroda relation of the Dedekind zeta functions of fields between k and F,the zeta function of...A finite group G is called exceptional if for a Galois extension F/k of number fields with the Galois group G,in the Brauer-Kuroda relation of the Dedekind zeta functions of fields between k and F,the zeta function of F does not appear.In the present paper we describe effectively all exceptional groups of orders divisible by exactly two prime numbers p and q,which have unique subgroups of orders p and q.展开更多
In this paper, the classical Galois theory to the H＊-Galois case is developed. Let H be a semisimple and cosemisimple Hopf algebra over a field k, A a left H-module algebra, and A/An a right H＊-Galois extension. The...In this paper, the classical Galois theory to the H＊-Galois case is developed. Let H be a semisimple and cosemisimple Hopf algebra over a field k, A a left H-module algebra, and A/An a right H＊-Galois extension. The authors prove that, if An is a separable kalgebra, then for any right coideal subalgebra B of H, the B-invariants AB = {a ∈ A ｜ b · a = ε（b）a, Ab ε B} is a separable k-algebra. They also establish a Galois connection between right coideal subalgebras of H and separable subalgebras of A containing AH as in the classical case. The results are applied to the case H = （kG）＊ for a finite group G to get a Galois 1-1 correspondence.展开更多
文摘Urban sprawl is threatening the limited highly fertile land in the Nile delta of Egypt. Landsat TM satellite images of 1984, 1992 and ETM+ of 2006 have been used to study the impact of urban sprawl on agricultural land of the Northern Nile delta, Egypt. Visual interpretation using on screen digitizing and change detection techniques were applied for monitoring the urban sprawl. Combining the land capability map and the urban thematic layer using GIS made it possible to point out the risk of urban expansion on the expense of the highly capable soil class. The results show that a total expansion of urban area amounted to 689.20 km2(6.3% of total area) during the study period 1984–2006. The urban expansion during the 1984–2006 was on the expense of the most fertile soils where, the high capable soils(Class I) lost 247.14 km2(2.26 % of total area) and the moderate capable soils lost 32.73 km2(0.3% of total area), while the low capable soils lost only 57.39 km2(0.53% of total area). The urban encroachment over the non capable soils was very limited during the study period 1984–1992, where 7.33 km2 only was lost. The pattern of urban sprawl has been changed during the 1992 to 2006 whereas much larger area(50.64 km2) of the non capable soils was converted to urban. It can be concluded that the urban sprawl is one of the dominant degradation process on the land of Nile Delta.
文摘Let H be a cosemisimple Hopf algebra over a field k, and π ： A→ H be a surjective cocentral bialgebra homomorphism of bialgebras. The authors prove that if A is Galois over its coinvariants B=LH Ker π and B is a sub-Hopf algebra of A, then A is itself a Hopf algebra. This generalizes a result of Cegarra [3] on group-graded algebras.
基金National Natural Science Foundation of China (Grant Nos. 61070172 and 10990011)the Strategic Priority Research Program of Chinese Academy of Sciences (Grant No. XDA06010702)the State Key Laboratory of Information Security, Chinese Academy of Sciences
文摘The period of a monic polynomial over an arbitrary Galois ring GR(pe,d) is theoretically determined by using its classical factorization and Galois extensions of rings. For a polynomial f(x) the modulo p remainder of which is a power of an irreducible polynomial over the residue field of the Galois ring, the period of f(x) is characterized by the periods of the irreducible polynomial and an associated polynomial of the form (x-1)m+pg(x). Further results on the periods of such associated polynomials are obtained, in particular, their periods are proved to achieve an upper bound value in most cases. As a consequence, the period of a monic polynomial over GR(pe,d) is equal to pe-1 times the period of its modulo p remainder polynomial with a probability close to 1, and an expression of this probability is given.
基金supported by National Natural Science Foundation of China (Grant No. 10871106)
文摘A finite group G is called exceptional if for a Galois extension F/k of number fields with the Galois group G,in the Brauer-Kuroda relation of the Dedekind zeta functions of fields between k and F,the zeta function of F does not appear.In the present paper we describe effectively all exceptional groups of orders divisible by exactly two prime numbers p and q,which have unique subgroups of orders p and q.
基金supported by the National Natural Science Foundation of China(No.11331006)
文摘In this paper, the classical Galois theory to the H＊-Galois case is developed. Let H be a semisimple and cosemisimple Hopf algebra over a field k, A a left H-module algebra, and A/An a right H＊-Galois extension. The authors prove that, if An is a separable kalgebra, then for any right coideal subalgebra B of H, the B-invariants AB = {a ∈ A ｜ b · a = ε（b）a, Ab ε B} is a separable k-algebra. They also establish a Galois connection between right coideal subalgebras of H and separable subalgebras of A containing AH as in the classical case. The results are applied to the case H = （kG）＊ for a finite group G to get a Galois 1-1 correspondence.
