The Precambrian basement complex in the southernmost part of North-Central Nigeria is underlain by migmatitic banded gneisses, granitic intrusions and dykes of dolerite, rhyolite porphyry and pegmatite. The rocks are ...The Precambrian basement complex in the southernmost part of North-Central Nigeria is underlain by migmatitic banded gneisses, granitic intrusions and dykes of dolerite, rhyolite porphyry and pegmatite. The rocks are generally felsic, containing modal and normative hypersthene, as well as normative corundum. The basement complex has experienced high-grade regional metamorphism as indicated by the presence of hypersthene and plagioclase of andesine composition. Anatectic melting is suggested by the occurrence of ptygmatic folds, folded gneissose foliation, numerous quartzo-feldspathic veins and lenses of dark-colured, micaceous schistose rocks. Geochemically, the rocks have magnesian, calc-alkalic and strongly peraluminous characteristics. Their overall characteristics suggest derivation from progressive (fractional) partial melting of pelitic rocks during high-grade regional metamorphism, possibly associated with intense hydrothermal activities. The magnesian characteristics reflect close affinity to relatively hydrous, oxidizing melts and source regions in settings broadly related to subduction.展开更多
William Paul Thurston是低维拓扑学的开拓者之一，1982年因其在叶状结构、几何化猜想等方面的纲领式工作荣获菲尔兹奖．同年另外两位获奖者是AlainConnes和丘成桐．菲尔兹奖得主中有些以博学多才闻名，有些因其非同寻常的刻苦执著而为...William Paul Thurston是低维拓扑学的开拓者之一，1982年因其在叶状结构、几何化猜想等方面的纲领式工作荣获菲尔兹奖．同年另外两位获奖者是AlainConnes和丘成桐．菲尔兹奖得主中有些以博学多才闻名，有些因其非同寻常的刻苦执著而为人称道，Thurston先生却是公认为“天才”的．展开更多
The author surveys Connes' results on the longitudinal Laplace operator along a(regular) foliation and its spectrum, and discusses their generalization to any singular foliation on a compact manifold. Namely, it i...The author surveys Connes' results on the longitudinal Laplace operator along a(regular) foliation and its spectrum, and discusses their generalization to any singular foliation on a compact manifold. Namely, it is proved that the Laplacian of a singular foliation is an essentially self-adjoint operator(unbounded) and has the same spectrum in every(faithful) representation, in particular, in L2 of the manifold and L2 of a leaf.The author also discusses briefly the relation of the Baum-Connes assembly map with the calculation of the spectrum.展开更多
We consider the functional separation of variables to the nonlinear diffusion equation with source and convection term： ut = （A（x）D（u）ux）x ＋ B（x）Q（u）, Ax ≠ 0. The functional separation of variables to thi...We consider the functional separation of variables to the nonlinear diffusion equation with source and convection term： ut = （A（x）D（u）ux）x ＋ B（x）Q（u）, Ax ≠ 0. The functional separation of variables to this equation is studied by using the group foliation method. A classification is carried out for the equations which admit the function separable solutions. As a consequence, some solutions to the resulting equations are obtained.展开更多
文摘The Precambrian basement complex in the southernmost part of North-Central Nigeria is underlain by migmatitic banded gneisses, granitic intrusions and dykes of dolerite, rhyolite porphyry and pegmatite. The rocks are generally felsic, containing modal and normative hypersthene, as well as normative corundum. The basement complex has experienced high-grade regional metamorphism as indicated by the presence of hypersthene and plagioclase of andesine composition. Anatectic melting is suggested by the occurrence of ptygmatic folds, folded gneissose foliation, numerous quartzo-feldspathic veins and lenses of dark-colured, micaceous schistose rocks. Geochemically, the rocks have magnesian, calc-alkalic and strongly peraluminous characteristics. Their overall characteristics suggest derivation from progressive (fractional) partial melting of pelitic rocks during high-grade regional metamorphism, possibly associated with intense hydrothermal activities. The magnesian characteristics reflect close affinity to relatively hydrous, oxidizing melts and source regions in settings broadly related to subduction.
文摘William Paul Thurston是低维拓扑学的开拓者之一，1982年因其在叶状结构、几何化猜想等方面的纲领式工作荣获菲尔兹奖．同年另外两位获奖者是AlainConnes和丘成桐．菲尔兹奖得主中有些以博学多才闻名，有些因其非同寻常的刻苦执著而为人称道，Thurston先生却是公认为“天才”的．
基金supported by a Marie Curie Career Integration Grant(No.FP7-PEOPLE-2011-CIG,No.PCI09-GA-2011-290823)the FCT(Portugal)with European Regional Development Fund(COMPETE)national funds through the project PTDC/MAT/098770/2008
文摘The author surveys Connes' results on the longitudinal Laplace operator along a(regular) foliation and its spectrum, and discusses their generalization to any singular foliation on a compact manifold. Namely, it is proved that the Laplacian of a singular foliation is an essentially self-adjoint operator(unbounded) and has the same spectrum in every(faithful) representation, in particular, in L2 of the manifold and L2 of a leaf.The author also discusses briefly the relation of the Baum-Connes assembly map with the calculation of the spectrum.
基金The project supported by National Natural Science Foundation of China under Grant No. 10371098 and the Program for New Century Excellent Talents in Universities under Grant No. NCET-04-0968
文摘We consider the functional separation of variables to the nonlinear diffusion equation with source and convection term： ut = （A（x）D（u）ux）x ＋ B（x）Q（u）, Ax ≠ 0. The functional separation of variables to this equation is studied by using the group foliation method. A classification is carried out for the equations which admit the function separable solutions. As a consequence, some solutions to the resulting equations are obtained.
