Cochran's statistical theorem for outer inverses of matrices and matrix quadratic forms

We extend the matrix version of Cochran's statistical theorem to outer inverses of a matrix. As applications, we investigate the Wishartness and independence of matrix quadratic forms for Kronecker product covariance structures.     

On the pivot structure for the weighing matrix W(12,11)

In the present article we concentrate our study on the growth problem for the weighing matrix W(12,11) and show that the unique W(12,11) has three pivot structures. An improved algorithm for extending a k × k (0,+,-) matrix to a W(n,n-1), if possible, has been developed to simplify the proof. For the implementation of the algorithm special emphasis is given to the notions of data structures and parallel processing.     

Crack path instabilities in DCDC experiments in the low speed regime

We studied the low speed fracture regime (10⁻⁴-10⁻⁹ m s⁻¹) in different glassy materials (soda-lime glass, glass ceramics) with variable but controlled length scale of heterogeneity. The chosen mechanical system enabled us to work in pure mode I (tensile) and at a fixed load on double cleavage drilled compression specimen. The internal residual stresses of studied samples were carefully relaxed by appropriate thermal treatment. By means of optical and atomic force microscopy techniques fracture surfaces have been examined. We have shown for the first time that the crack front line underwent an out-of-plane oscillating behavior as a result of a reproducible sequence of instabilities. The wavelength of such a phenomenon is in the micrometer range and its amplitude in the nanometer range. These features were observed for different glassy materials providing that a typical length scale characterizing internal heterogeneities was lower than a threshold limit estimated to few nanometers. This effect is the first clear experimental evidence of crack path instabilities in the low speed regime in a uniaxial loading experiment. This phenomenon has been interpreted by referring to the stability criterion for a straight crack propagation as presented by Adda-Bedia et al. [Phys. Rev. Lett. 76 (1996) 1497].     

On perfectly normal dense subspaces of products

Let M be a separable metric space consisting of more than one point. We construct perfectly normal dense subspaces Z⊂Mc² and (under additional set-theoretic assumption) Y⊂Mc which are not collectionwise Hausdorff.     

Continuous time collocation methods for Volterra-Fredholm integral equations

Summary Integral equations of mixed Volterra-Fredholm type arise in various physical and biological problems. In the present paper we study continuous time collocation, time discretization and their global and discrete convergence properties.     

Tchebychev acceleration technique for large scale nonsymmetric matrices

Summary The acceleration by Tchebychev iteration for solving nonsymmetric eigenvalue problems is dicussed. A simple algorithm is derived to obtain the optimal ellipse which passes through two eigenvalues in a complex plane relative to a reference complex eigenvalue. New criteria are established to identify the optimal ellipse of the eigenspectrum. The algorithm is fast, reliable and does not require a search for all possible ellipses which enclose the spectrum. The procedure is applicable to nonsymmetric linear systems as well.     

Bioengineering functional copolymers. III. Synthesis of biocompatible poly[(N‐isopropylacrylamide‐co‐maleic anhydride)‐g‐poly(ethylene oxide)]/poly(ethylene imine) macrocomplexes and their thermostabilization effect on the activity of the enzyme penicillin G acylase

Stimuli‐responsive poly[(N‐isopropylacrylamide‐co‐maleic anhydride)‐g‐poly(ethylene oxide)]/poly(ethylene imine) macrobranched macrocomplexes were synthesized by (1) the radical copolymerization of N‐isopropylacrylamide and maleic anhydride with α,α′‐azobisisobutyronitrile as an initiator in 1,4‐dioxane at 65 °C under a nitrogen atmosphere, (2) the polyesterification (grafting) of prepared poly(N‐isopropylacrylamide‐co‐maleic anhydride) containing less than 20 mol % anhydride units with α‐hydroxy‐ω‐methoxy‐poly(ethylene oxide)s having different number‐average molecular weights (M_n = 4000, 10,000, or 20,000), and (3) the incorporation of macrobranched copolymers with poly(ethylene imine) (M_n = 60,000). The composition and structure of the synthesized copolymer systems were determined by Fourier transform infrared, ¹H and ¹³C NMR spectroscopy, and chemical and elemental analyses. The important properties of the copolymer systems (e.g., the viscosity, thermal and pH sensitivities, and lower critical solution temperature behavior) changed with increases in the molecular weight, composition, and length of the macrobranched hydrophobic domains. These copolymers with reactive anhydride and carboxylic groups were used for the stabilization of penicillin G acylase (PGA). The conjugation of the enzyme with the copolymers significantly increased the thermal stability of PGA (three times at 45 °C and two times at 65 °C). © 2003 Wiley Periodicals, Inc. J Polym Sci Part A: Polym Chem 41: 1580–1593, 2003     

Application of coupling methods to the Neumann eigenvalue problem

Summary By using coupling methods, some lower bounds are obtained for the first Neumann eigenvalue on Riemannian manifolds. This method is new and the results improve some known estimates. An example shows that our estimates can be sharp.Research supported in part by the Foundation of Beijing Normal University     

Observation of p(1×1)-type rows on TiO2(110)-p(1×2) surface by scanning tunneling microscope (STM)

The TiO₂(110) surfaces were observed by a Scanning Tunneling Microscope (STM). We found two types of bright p(1×1)-type rows on the p(1×2) surface. One p(1×1)-type formed independently and corresponds to the bridging oxygen rows. The second p(1×1)-type appeared in a bright grouping, forming narrow rows, and corresponds to the five-fold titanium rows. The above results suggest the following two conclusions. First, the density of state (DOS) on the bridging oxygen rows becomes higher than that on the five-fold titanium atom rows when a bridging oxygen row exists independently on the p(1×2) surface. Second, the bright rows on a TiO₂(110)-p(1×1) surface correspond to the five-fold titanium atom rows. The results further show the validity of DOS calculations on the TiO₂(110)-p(1×1) surface by Diebold et al. [Phys. Rev. Lett. 77 (1996) 1322]. The difference of width for Ti₂O₃ unit rows on the p(1×2) and p(1×3) surfaces in STM images are also discussed.     

Symmetries and conservation laws of Navier-Stokes equations

All the symmetries and conservation laws of Navier-Stokes equations are calculated.