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

The problem of uniqueness of meromorphic functions is discussed, the following theorem is proved: there exists a set S with 8 elements such that any two nonconstant meromorphic functions f and g satisfying E(S,f)=E(S,g) and E({∞},f)=E({∞},g) must be identical.

In this paper, by means of comparison theorem and Liapunov functionals, we consider the global attractivity of positive periodic solution of multispecies ecological competition-predator system with several delays. Some new results are obtained. Example shows that our conditions are feasible.

In this paper, we first establish a basic theorem on zeros of general transcendental functions. Based on the basic theorem, combining the global Hopf bifurcation theorem for general functional differential equations, which was established by Wu J. H. al using degree theory methods, we investigate the stability and global Hopf bifurcation for a lossless transmission line network which is described by a one delay differential-difference equation of neutral type.

In this paper, we investigate the comparability structure over exchange rings. This provides a new class of exchange rings satisfying the comparability and generalizes the corresponding results of Goodearl and Chen.

In this note we analyze the exact controllability of singularly perturbed damped wave equation with homogeneous Dirichlet boundary conditions under more general geometric control condition than that of [1]. We show that the null controllability of the heat equation can be obtained as a singular limit of the exact controllability of such sort of wave equations.

In this paper, based on large deviation formulas established in stronger topology generated by H lder norm, we obtain the functional limit theorems for C-R increments of k-dimensional Brownian motion in H lder norm.

In this paper, the notion of (minimal)approximation extensions is introduced, the existence and uniqueness of minimal approximation extensions over Gorenstein algebras are established, an application to minimal approximation extensions is given.

In this paper, we defined universally the tensor product of semimodules, and constructed the direct lim rlim Ci for any directed set of indices and an arbitrary directed direct system in the category C of semimodules over a semiring R , also the cokernel of any morphism f. We discussed some properties of the tensor product of semimodules. The main results are as the following: the tensor functor preserves right exactness of semimodules and coproduct, and also coproduct preserves flatness of semimodules, the tensor functor preserves direct limits and cokernel.

A note by Wang and Shao (1992), in which the constrained Kantorovich inequalities are considered in matrix versions expressed in terms of the loewner tial ordering, is extended to cover nonnegative Hermitian matrices by the singular value decomposition of matrix. Furthermore, the constrained Wielandt inequalities are also investigated.

Let f: Mn→RN be an affine immersion of a Riemannian manifold into Euclidean space, we establish the condition under which there exists another affine immersion overline f:Mn→RN with the same Gauss map as that of f. Furthermore, using this condition, we give the answer for the question: what extent does the Gauss map of an affine immersion determine the affine immersion up to.

This paper uses the theory of Lie groups and their representations to discuss the equivariant isometric minimal immersions of compact Riemannian symmetric spaces to the Grassmann manifold.

This paper deals with the discounted cost model for coutinuous time Markov decision processes with arbitrary transition rates and possible unbounded costs. Getting rid of the traditional condition that the Q -process deduced from a given policy is needed to be unique, we first consider the case of the Q-processes being not unique, of the costs possibly being unbounded, and of the action space being arbitrary. By first using the "α-discounted cost optimality inequality"instead of the traditional optimality equation, we not only prove the existence of optimal stationary policies, but also derive the existence of (∈>0) -optimal stationary policies, of the monotone optimal stationary policies, and of the (∈≥0) -optimal decision processes. Moreover, some new results are obtained. Finally, a substantial applied example of birth and death processes witn controlled migration rates is used to show that our assumptions here are satisfied, whereas the conditions in [1-14] fail to hold.

In this paper, some Ou-Iang type discrete inequalities defined on Nn are established, which are natural generalization and improvement of some known results obtained by Yang E. H.

For odd square-free n>1, the cyclotomic polynomial φn(x) satisfies the identity of Schinzel, φn(x)=P2n,m(x)-(-1/m)mxQ2n, m(x), where Pn,m(x)and Qn,m(x) are polynomials with integer coefficients and m|n . We give two simple identities to compute Pn,m(x) and Qn,m(x).

The reverse H lder inequality, Lp integrability and weak monotonicity of the component function of weakly quasiregular mappings are obtained by using Hodge decomposition.

This paper is devoted to the study of perturbations of nest subalgebras in factor von Neumann algebras. A sufficient condition is given for the similarity of nests in factor von Neumann algebras. is proved that close nest subalgebras in arbitrary factor von Neumann algebras are similar via an invertible operator close to the identity.

the adjacent lattice methods of Kneser are generalized, some adjacent lattice properties of the positive definite unimodular genera of rank 4n and determinant 1 over Z[/d] are given, and the classification of all the positive unimodular lattices of rank 4 over Z[/3]are obtained.

In this paper, we prove that every Smyth power semilattice is isomorphic to the Smyth power domain of a continuous dcpo, each continuous dcpo is isomorphic to the way below spetrum of its Smyth power domain, and these two categories are equivalent through the upper power functor, which shows the close connection between upper and lower power domain constructions.

In this paper. we give the relation between the weighted Plancherel formula and the Plancherel formula on homogeneous line bundles over hermitian symmetric spaces, from which we get the weighted Plancherel formula on general bounded sym metric domains.

We construct a counterexample showing that the necessary and sufficient condition given in [7] for inductive limits to be uniformly β－regular is mistaken. More- over, we give some correct necessary and sufficient conditions for inductive limits to be β－regular and uniformly β－regular respectively.

This paper first discusses the structure of abstract interpolating splines (T- splines) associated with bounded linear operators. The projective property and the representation of T-spline are obtained by introducing a new inner product. Then the projective approximate solution and T-spline approximate solution of operator equation Tx=y are studied, and the relationships between the error estimates of the two approximate solutions are given.

Suppose that H is a complex separable infinite dimensional Hilbert space, a bounded operator T is said to be strongly irreducible if the only idempotents that commute with T are be 0 or I. Wang Zongyao, Jiang Chunlan and Ji Youqing have proved that there are a lot of strongly irreducible operators in the nest algebra of any nests and have got the closure of the unitary orbit of them. This paper discusses the existence of strongly irreducible operators in the algebra of the tensor product of finitely many nests. We prove that for any connected perfect set a in the complex plane, there exists a diagonal operator N and its compact perturbation T= N + K, the norm of K can be arbitrarily small, such that T is a strongly irreducible operator. T is in the algebra of the tensor product of finitely many well-ordered nests and σ(T) = σlr(T)=σ(N)=σlre(N) = σ. Furthermore. this paper discusses the operator with singleton spectrum and the algebra of the tensor product of well-ordered nests and the nests whose orthogonal complement is well-ordered, and obtains some results.

Let T be a tree, f: T → T be a continuous self-map, n be the number of the end points of T, and x ∈ T. In this paper, we prove that: (1) if there exists z ∈ ω(x, f) ∩ F(f) such that z is an unilateral accumulation point of ω(x, f), then there etists r ∈ Nn-1 such that fr has turbulent, (2) if ω(x, f) is an infinite set having the fixed points, then there exists r ∈ Nn such that fr has turbulent.

The sufficient and necessary conditions of the upper (lower) monotone point and upper (lower) locally uniformly monotone point in Musielak-Orlicz sequence spaces with Orlicz norm are given.

In this paper, the residuated lattices are further studied because of their wide applications, and a kind of new fuzzy logic algebra structure-regular residuated lattices are introduced. The concepts and properties of residuated lattices and regular residuated lattices are discussed, and some characteristic theorems are obtained. In them, there are the equational characterization of residuated lattices and regular residuated lattices. This shows that the classes of all residuated lattices and all regular residuated lattices form varieties. In this paper, the independence problem of axiom systems of residuated lattices and regular residuated lattices also are studied.

In this paper, we introduce and discuss nonlinear Lipschitz-α operators (shortly, Lip-α operators). At first, we define Lip-αoperators and obtain some basic properties of them. Secondly, the invertibility of these op erators is discussed and the conditional number of order a of a Lip-αoperator is defined and is used for dealing with "the Nonlinear Perturbation-Problem" of a nonlinear operator equation. Thirdly, the convergence of a sequence of Lip-αoperators is studied, and the Lip-αlimit and Lip-αCauchy sequence are introduced and discussed. We also prove that the space of all pass-zero Lip-αoperators from a set into a Banach space is a Banach space.

In this paper, we investigated the best simultaneous approximation problems from suns. Some results on characterization and uniqueness are established.

In this paper, the essential selfadjointness of the generalized Schrodinger operator H = (-Δ)m+ V(x) on C~∞_0 is established under a class of Lp potentials, and the distribution of the essential spectrum of H is given.

Some results of existence of positive solutions for the Dirichlet boundary value problems y″- f(t, y) =0, y(0) = c > 0 and y(1)=0 have been given in this paper, where f(t, y) may change sign and be singular at y=0.

In this paper, let Ω be a domain of Rn，s ∈R. 0

In this paper, From the blossom approach, a new proof of the theorem on the dimension of the bivariate spline space for the corss-cut partition is given.