A commutative generalization of complex numbers is called bicomplex numbers. A holomorphic function of bicomplex number corresponds to a holomorphic mapping on C2 which satisfies the complex Cauchy-Riemann equations. It is known that the holomorphic solutions of complex Cauchy-Riemann equations are essentially the direct product of two holomorphic functions of one complex variable. In this short note, we prove that in the complex Banach space, the holomorphic solutions of the Cauchy-Riemann equations have the same property.
We discuss a type of topological invariants on the infinite-dimensional manifolds, that is, Cr mapping degrees on Banach manifolds with orientable Fredholm structures. Our degree theory is an intrinsical extension and unification of the usual smooth mapping degrees on the finite-dimensional manifolds.
For a regular semigroup with an inverse transversal, we discuss here how the structure of congruence lattice affect the semigroup. We characterize the congruence-free regular semigroups with Q -inverse transversals.
It is disscused the strong consistency of M estimator of regression ametric in linear model. Some suitable sufficiency conditions are obtained. Comed to the corresponding result of Chen Xiru, Zhao Lincheng [1] , these greatly improve the moment conditions.
Let B be a p-block of a finite group G. We consider a free Abelian group with a basis of Brauer irreducible characters of the block B, and its factor group determined by Cartan matrix of the block B . Let C=(cij) and D=(dij) be the Cartan matrix and the decomposition matrix of B, respectively. We give some new results about the relations among C, defect group of B and the vertices of simple modules. We also get some new results about the decomposition numbers dij, the heights of ordinary irreducible characters of B and Cartan invariants.
Let G be a finite group and H its subgroup. Suppose that D(G) is the group double of G and F the field algebra of G-spin model. This paper considers the sub-Hopf algebra D(H)of D(G) and proves that the D(H)-invariant space AH in F is a C*-algebra. There is a C*-representation of D(H) so that D(H) and AH are commutants of each other.
We consider an curvature flows with boundary condition. In contradiction to the former works [1-4] and others,here the speed of flow of surfaces is in inversely proportional to curvature of surface. We show that the corresponding first initial-boundary problem admits a classical convex solution for all time and then investigate asymptotic behaviour of the solution.
If A is a completely distributive subspace lattice algebra on a Hilbert space, then the rank one subalgebra of A is weak dense in A if and only if, the weak closures of the first and the second preannihilators of A in the space of all trace class operators are reflexive. If A is a nest algebra, then Lat, A , the nest of all invariant subspaces of A, is maximal if and only if, all of the weak closed subspaces of A containing A-are reflexive.
In this paper, we discuss the T(1)Theorems by weakening the operator's kernels on spaces of homogeneous type and obtain the boundedness and endpoint estimates of the commutators of singular integral operators associated with the weaker kernels with BMO functions on Lp (1