Netizens raise information literacy,families reestablish new relationship between parents and children,schools improve ideological and political work,governments construct comprehensive control system and the international society carry out cooperation and global governance.
In the case of 4-dimensional anticommutative algebras a construction is given that links the associated cubic surface and the 27 lines on it with the structure of subalgebras of the algebra.
Using the properties ofn-Hopf algebras we show that certain spaces do not admit the structure of ann-valued group and that certain commutativen-valued groups do not arise by applying then-coset construction to any commutative group.
We construct essentially all the irreducible modules for the multiparameter quantum function algebraF?φ[G], whereG is a simple simply connected complex algebraic group, and ? is a root of unity.
For each compact Lie algebra g and each real representationV of g we construct a two-step nilpotent Lie groupN(g, V), endowed with a natural left-invariant riemannian metric.
We give the classification of all finite dimensional Levi-Tanaka algebras of CR codimension two and construct the corresponding standard homogeneous CR manifolds.
These transformations are based on the multiresolution analysis paradigm of Mallat and Meyer and give rise to a method for constructing multiresolution analyses and orthogonal wavelets on an interval.
We also obtain a way of constructing an arbitrary number of non-Gaussian continuous time processes whose second order properties are the same as those of fractional Brownian motion.
The first part of this paper describes the construction of pseudo-Riemannian homogeneous spaces with special curvature properties such as Einstein spaces, using corresponding known compact Riemannian ones.