On polynomial symbols for subdivision schemes

Given a dilation matrix A :ℤ^d→ℤ^d, and G a complete set of coset representatives of 2π(A ^−Tℤ^d/ℤ^d), we consider polynomial solutions M to the equation ∑ _g∈G M(ξ+g)=1 with the constraints that M≥0 and M(0)=1. We prove that the full class of such functions can be generated using polynomial convolution kernels. Trigonometric polynomials of this type play an important role as symbols for interpolatory subdivision schemes. For isotropic dilation matrices, we use the method introduced to construct symbols for interpolatory subdivision schemes satisfying Strang–Fix conditions of arbitrary order. Research partially supported by the Danish Technical Science Foundation, Grant No. 9701481, and by the Danish SNF-PDE network.     

Solid codes and the uniform density of fd-domains

By means of further investigation of solid codes,the problem“Is every fd-domain uni- formly dense”proposed by Yuqi Guo,C.M.Reis and G.Thierrin in 1988 is solved in this paper.     

Testing for additivity with B-splines

Regression splines are often used for fitting nonparametric functions, and they work especially well for additivity models. In this paper, we consider two simple tests of additivity: an adaptation of Tukey's one degree of freedom test and a nonparametric version of Rao's score test. While the Tukey-type test can detect most forms of the local non-additivity at the parametric rate of O(n-1/2), the score test is consistent for all alternative at a nonparametric rate. The asymptotic distribution of these test statistics is derived under both the null and local alternative hypotheses. A simulation study is conducted to compare their finite-sample performances with some existing kernel-based tests. The score test is found to have a good overall performance.     

Covalent functionalization of multi-walled carbon nanotubes by lipase

Lipase from Candida rugosa was covalently anchored onto acid-treated multi-walled carbon nanotubes (MWNTs) through a self-catalytic mechanism. A variety of characterization techniques including FTIR, Raman spectroscopy, and XPS were employed to demonstrate the formation of the ester linkage between lipase and MWNTs. The MWNTs-lipase biocomposites showed significantly increased solubility in some common-used organic solvents, such as THF, DMF and chloroform. This study may offer a novel and facile route for covalent modification of carbon nanotubes, and expand the potential utilization of both lipases and MWNTs in the fields of biocatalyst and biosensor.     

Specific heat and related thermophysical properties of liquid Fe-Cu-Mo alloy

The specific heat and related thermophysical properties of liquid Fe77.5Cu13Mo9.5 monotectic alloy were investigated by an electromagnetic levitation drop calorimeter over a wide temperature range from 1482 to 1818 K. A maximum undercooling of 221 K (0.13 Tm) was achieved and the specific heat was determined as 44.71 J·mol-1·K-1. The excess specific heat, enthalpy change, entropy change and Gibbs free energy difference of this alloy were calculated on the basis of experimental results. It was found that the calculated results by traditional estimating methods can only describe the solidification process under low undercooling conditions. Only the experimental results can reflect the reality under high undercooling conditions. Meanwhile, the thermal diffusivity, thermal conductivity, and sound speed were derived from the present experimental results. Furthermore, the solidified microstructural morphology was examined, which consists of (Fe) and (Cu) phases. The calculated interface energy was applied to exploring the correlation between competitive nucleation and solidification microstructure within monotectic alloy.     

Thermal conductance for single wall carbon nanotubes

We report a theoretical analysis of the phonon thermal conductance, κ(T), for single wall carbon nanotubes (SWCN). In a range of low temperatues up to 100 K, κ(T) of perfect SWCN is found to increase with temperature, approximately, in a parabolic fashion. This is qualitatively consistent with recent experimental measurements where the tube-tube interactions are negligibly weak. When the carbon-carbon bond length is slightly varied, κ(T) is found to be qualitatively unaltered which implies that the anharmonic effect does not change the qualitative behavior of κ(T). Received 12 June 2001     

Nonnegative curvature and cobordism type

We show that in each dimension n = 4k, k≥ 2, there exist infinite sequences of closed simply connected Riemannian n-manifolds with nonnegative sectional curvature and mutually distinct oriented cobordism type. W. Tuschmann’s research was supported in part by a DFG Heisenberg Fellowship.     

The equations of a holomorphic subspace in a complex Finsler space

In [Mu1] we underlined the motifs of holomorphic subspaces in a complex Finsler space: induced nonlinear connection, coupling connections, and the induced tangent and normal connections. In the present paper we investigate the equations of Gauss, H-and A-Codazzi, and Ricci equations of a holomorphic subspace. We deduce the link between the holomorphic curvatures of the Chern-Finsler connection and its induced tangent connection. Conditions for totally geodesic holomorphic subspaces are obtained. Communicated by János Szenthe     

Barycentric coordinates for convex sets

In this paper we provide an extension of barycentric coordinates from simplices to arbitrary convex sets. Barycentric coordinates over convex 2D polygons have found numerous applications in various fields as they allow smooth interpolation of data located on vertices. However, no explicit formulation valid for arbitrary convex polytopes has been proposed to extend this interpolation in higher dimensions. Moreover, there has been no attempt to extend these functions into the continuous domain, where barycentric coordinates are related to Green’s functions and construct functions that satisfy a boundary value problem. First, we review the properties and construction of barycentric coordinates in the discrete domain for convex polytopes. Next, we show how these concepts extend into the continuous domain to yield barycentric coordinates for continuous functions. We then provide a proof that our functions satisfy all the desirable properties of barycentric coordinates in arbitrary dimensions. Finally, we provide an example of constructing such barycentric functions over regions bounded by parametric curves and show how they can be used to perform freeform deformations.