Some essential properties ofQ p (∂Δ)-spaces

For p∈(?∞, ∞) letQ _p (?Δ) be the space of all complex-valued functions f on the unit circle ?Δ satisfying $\mathop {\sup }\limits_{I \subset \partial \Delta } \left| I \right|^{ - p} \int_I {\int_I {\frac{{\left| {f(z) - f(w)} \right|^2 }}{{\left| {z - w} \right|^{2 - p} }}\left| {dz} \right|\left| {dw} \right|< \infty } } $ , where the supremum is taken over all subarcs I ? ?Δ with the arclength |I|. In this paper, we consider some essential properties ofQ _p (?Δ). We first show that if p>1, thenQ _p (?Δ)=BMO(?Δ), the space of complex-valued functions with bounded mean oscillation on ?Δ. Second, we prove that a function belongs toQ _p (?Δ) if and only if it is Möbius bounded in the Sobolev spaceL _p ² (?Δ). Finally, a characterization ofQ _p (?Δ) is given via wavelets.     

Strong monotonicity of operator functions

LetA, B be bounded selfadjoint operators on a Hilbert space. We will give a formula to get the maximum subspace such that is invariant forA andB, and . We will use this to show strong monotonicity or strong convexity of operator functions. We will see that when 0≤A≤B, andB−A is of finite rank,A ^t ≤B ^t for somet>1 if and only if the null space ofB−A is invariant forA.     

Remarks on a unified theory for classical and generalized interpolation and extrapolation

A unified theory for generalized interpolation, as developed by Mühlbach, and classical polynomial interpolation is discussed. A fundamental theorem for generalized linear iterative interpolation is given and used to derive generalizations of the classical formulae due to Neville, Aitken and Lagrange. Using Mühlbach's definition of generalized divided differences, Newton's generalized interpolation formula, including an expression for the error term, is derived as a pure identity.     

Sigma-compact,nowhere locally compact metric spaces can be densely imbedded in Hilbert space

It is shown that if H is a connected, locally contractible, separable, topologically complete metric space with the property that mappings of separable metric spaces into H are approximable by imbeddings (in particular, if H is Hilbert space), then every sigma-compact, nowhere locally compact metric space can be densely imbedded in H.     

Wild double tangent ball embeddings of spheres in En

It has been known for years that a 2-sphere Σ in E³ must be flatly embedded if it has double tangent balls on opposite sides of Σ at each of its points. However, when the double tangent balls are not required to be on opposite sides of Σ, pathological embeddings exist. This paper details the allowable wild embeddings of spheres having these indiscrete double tangent balls and discusses the higher dimensional analogues.     

大容量串行Flash的快速编程

介绍一种通过51系列单片机事行口对AT45Dxxx系列F1ash芯片编程的方法。此方法程序简单，运行速度高，是一种值得推荐的编程方法。     

A space with maximal discrepancy between its Katêtov and covering dimension

It is shown, using a non-measurable partition of the real line, that the covering dimension of a modified Niemytzki space is infinite while its Katêtov dimension is zero.     

The evaluation identification in function spaces

A study is made of the natural function which maps each point x of a space X to the evaluation function e_x:Y^x→Y defined by $\text{e}{}_{\mathrm{x}}\text{(?)=?(x)}$. A consequence of the results is that βX and υX can both be considered as subspaces of spaces of continous functions from appropriate domain spaces into I or R, respectively.