In this paper,we mainly prove that everyn-dimensional Lip microbundle over a locally finite simplicial complex is micro-identical to a Lip-Sn(Rn)-bundle,and any two such are micro-identical,isomorphic Sn(Rn)-bundles.
This paper is devoted to study Cauchy problems of multidimensional semilinear strictly hyperbolic equations of second order with strongly singular initial data,where the derivatives of the initial data have discontinuity on two smooth curves transversally intersecting each other.The existence of the solution is proved,meanwhile,it is precisely discribed the flowery structure of the singularity of the solution.
This paper includes two parts.In the first part,we deal with the relations between the orders,the lower orders and the number of Julia directions of entire functions.In the second part,we deal with the existence of the zeros of a class of meromorphic functions.This class of meromorphic functions has an interesting physical background.
In this paper,we explicitly describe all the inverses and pseudo-inverses of a strong endomorphism of a graph.The number of them is determined.In addition,we give a characterization of a strong endomorphism whose pseudo-inverse set coincides with its inverse set.The graph,each strong endomorphism of which has this property,is also investigated.
In this paper,we show that a topologically irreducible * representation of a real C*-algebra is also algebraically irreducible.Moreover,the properties of pure real states on a real C*-algebra and their left kernels are discussed.
We show that a multiplication operator Φ(T)=ATB is normality preserving if and only if it is hyponormality preserving,if and only if it is either of the form A=f⊕g,B=h ⊕ f,or A=D,B=λD* for some λ∈C and D* D=I.Also we show that Φ is (semi-) Fredholmness prserving if and only if A and B are (semi-) Fredholm operators.
The object of this paper is to establish an expansion theorem for a regular right-definite eigenvalue problem with an eigenvalue parameter λ which is contained in the Schrödinger partial differential equation and in a general type of boundary conditions on the boundary of an arbitrary multiply connected bounded domain in Rn(n≥2).We associate with this problem an essentially self-adjoint operator in a suitably defined Hilbert space and then we develop an associated eigenfunction expansion theorem.
If T is an isomorphism of L∞(A,μ) into L∞(B,ν) which satisfies the condition ‖T‖‖T-1‖≤1+ε,where (A,μ) is a σ-finite measure space,then T/‖T‖ is close to an isometry with an error less than 4ε.
In the present paper a general formula for exact calculation of the discrepancy of an arbitrary finite point set of dimension d≥2 is explicitly given only in terms of the components of the points.
The concern of this paper is to derive formulas for the injective dimension of the n-th Weyl algebra An(R) in case k is a field of characteristic zero and R is a commutative affine k-algebra of finite injective dimension.For the case n=1 we prove a more general result from which the above result follows.Such formulas can be viewed as generalizations of the corresponding results given by J.C.McConnell in the case R has finite global dimension.
In this paper we consider the periodic solutions of nonlinear parabolic systems with nonlinear boundary conditions.By constructing the Poincare operator,we obtain the existence of -periodic weak solutions under some reasonable assumptions.
