The nature of phase separation in binary oxide melts and glasses. III. Borate and germanate systems

A review of immiscibility data in binary borate and germanate systems was performed in order to compare miscibility gap consolute temperatures with ionic potentials and radii of their associated cations. The trends obtained demonstrate that a selective solution mechanism similar to the one identified for the binary silicate systems is present in the borate and germanate binaries. More importantly, the borate and germanate immiscibility data permitted the identification of a new group of cations depicting an immiscibility behaviour different from the ones identified in binary silicate systems. The new group involves highly polarizable cations possessing a lone pair of electrons. This lone pair of electrons together with oxygen bonded by strong covalent bonds to modifier cations provides efficient shielding to the cations' nuclei which considerably reduces the coulombic repulsions and produces miscibility gaps with very low consolute temperatures. A new group of cations having an homogenizing effect on melts (i.e. a capacity to make immiscible melts single phase) is thus reported. Experimental and spectroscopic data suggest that miscibility gaps associated with cations having a lone pair of electrons exist in binary silicate systems such as TlO_1/2-SiO₂, PbO-SiO₂, SnO-SiO₂ and Bi₂O₃-SiO₂. The consolute temperature of their miscibility gaps is expected to be relatively low and metastable.     

Rigidity of the scattering length spectrum

In this paper we consider properties of obstacles satisfying some non-degeneracy conditions that can be recovered from the scattering length spectrum (SLS). Clearly the latter tells us whether the obstacle K is trapping or non-trapping. If the set of trapped points is relatively small, then the SLS also determines the volume of the obstacle, the number of its connected components, and whether its boundary is convex everywhere or it has non-trivial concavities. Under the additional assumption that the curvature of the obstacle does not vanish of infinite order, it is proved that from the SLS one can recover certain information about the number of reflection points of any simply reflecting ray in the exterior of the obstacle. Finally, for some special classes of obstacles (e.g. star-shaped ones), it is shown that the SLS completely determines the obstacle. Received: 2 March 1999 / Revised version: 16 January 2001 / Published online: 5 September 2002     

Permanence and stability of a predator–prey system with stage structure for predator

A stage-structured predator–prey system with delays for prey and predator, respectively, is proposed and analyzed. Mathematical analysis of the model equations with regard to boundedness of solutions, permanence and stability are analyzed. Some sufficient conditions which guarantee the permanence of the system and the global asymptotic stability of the boundary and positive equilibrium, respectively, are obtained.     

Microlocal study of topological Radon transforms and real projective duality

Various topological properties of projective duality between real projective varieties and their duals are obtained by making use of the microlocal theory of (subanalytically) constructible sheaves developed by Kashiwara [M. Kashiwara, Index theorem for constructible sheaves, Astérisque 130 (1985) 193-209] and Kashiwara-Schapira [M. Kashiwara, P. Schapira, Sheaves on Manifolds, Grundlehren Math. Wiss., vol. 292, Springer, Berlin-Heidelberg-New York, 1990]. In particular, we prove in the real setting some results similar to the ones proved by Ernström in the complex case [L. Ernström, Topological Radon transforms and the local Euler obstruction, Duke Math. J. 76 (1994) 1-21]. For this purpose, we describe the characteristic cycles of topological Radon transforms of constructible functions in terms of curvatures of strata in real projective spaces.     

Proof of semialgebraic covering mapping cylinder conjecture with semialgebraic covering homotopy theorem

In this paper we prove the semialgebraic version of Palais' covering homotopy theorem, and use this to prove Bredon's covering mapping cylinder conjecture positively in the semialgebraic category. Bredon's conjecture was originally stated in the topological category, and a topological version of our semialgebraic proof of the conjecture answers the original topological conjecture for topological G-spaces over “simplicial” mapping cylinders.     

Rebuilding of metal components with laser cladding forming

Laser cladding forming (LCF) is a novel powerful tool for the repairing of metal components. Rebuilding of V-grooves on medium carbon steel substrates has been carried out with laser cladding forming technique using stainless steel powder as the cladding material. Microstructure of the deposited layers has been characterized using optical microscopy (OM), scanning electron microscopy (SEM), energy dispersive X-ray microanalysis (EDAX), electron probe microanalysis (EPMA) and X-ray diffraction (XRD). Mechanical properties of the rebuilt V-groove samples have been evaluated by tensile and impacting tests and microhardness measurement. Experimental results show that good fusion bonding between the rebuilt layers and the substrate has been formed, and the microstructure of the cladding layers is mainly composed of fine, dense and defect-free epitaxial columnar dendrites. Due to the effect of grain size refinement, the tensile strength, impacting toughness, elongation and microhardness of the rebuilt samples have been greatly enhanced compared to those of the substrate. Microhardness is also very uniform throughout the rebuilt regions. With the growth of the deposited layers, the microhardness increases gradually. The good ductility of the deposited regions is verified by the SEM fracture analysis.     

Synergistic effect between 4-(2-pyridylazo) resorcin and chloride ion on the corrosion of cold rolled steel in 0.5 M sulfuric acid

The corrosion inhibition of 1-(2-pyridylazo)-2-naphthol (PAR) on the corrosion of cold rolled steel in 0.5 M sulfuric acid (H₂SO₄) was studied using weight loss method and potentiodynamic polarization method. Results obtained revealed that together with chloride ion, PAR is an effective corrosion inhibitor for steel corrosion in sulfuric acid. It was found that for steel corrosion inhibition in the presence of single PAR in sulfuric acid the Temkin adsorption isotherm may be used to explain the adsorption phenomenon. For the mixture of PAR and NaCl used as corrosion inhibitor, however, the Langmuir adsorption isotherm can be used to satisfactorily elucidate the adsorption of mixture of PAR and NaCl. Potentiodynamic polarization studies showed that single PAR mainly acts as a cathodic inhibitor for the corrosion of steel in 0.5 M sulfuric acid. The mixture of PAR and chloride ion, however, acts as a mixed type inhibitor that mainly inhibits cathodic reaction of the steel corrosion in sulfuric acid. By means of electrochemical polarization tests, a desorption potential at ca. −370 mV was observed for the adsorption of mixture of PAR and chloride ion, when potential reaches this value, adsorbed inhibitor molecule heavily departs from the steel surface. For the mixture of PAR and chloride ion, thermodynamic parameters such as adsorption heat, adsorption entropy and adsorption free energy were obtained from experimental data of the temperature studies of the inhibition process at four temperatures ranging from 30 to 45 °C, the kinetic data such as apparent activation energies and pre-exponential factors at different concentrations of the inhibitor were calculated, and the effect of the apparent activation energies and pre-exponential factors on the corrosion rates of cold rolled steel was discussed. The most suitable range of inhibitor concentration was discussed. The inhibitive action was satisfactorily explained by using both thermodynamic and kinetic models. Synergism between chloride ion and PAR was proposed. The results obtained from weight loss and potentiodynamic polarization were in good agreement.     

Asymptotic robustness of standard errors in multilevel structural equation models

Data in social and behavioral sciences are often hierarchically organized. Multilevel statistical methodology was developed to analyze such data. Most of the procedures for analyzing multilevel data are derived from maximum likelihood based on the normal distribution assumption. Standard errors for parameter estimates in these procedures are obtained from the corresponding information matrix. Because practical data typically contain heterogeneous marginal skewnesses and kurtoses, this paper studies how nonnormally distributed data affect the standard errors of parameter estimates in a two-level structural equation model. Specifically, we study how skewness and kurtosis in one level affect standard errors of parameter estimates within its level and outside its level. We also show that, parallel to asymptotic robustness theory in conventional factor analysis, conditions exist for asymptotic robustness of standard errors in a multilevel factor analysis model.     

A fiberwise analogue of the Borsuk-Ulam theorem for sphere bundles over a 2-cell complex II

We describe a finite complex B as I-trivial if there does not exist a Z₂-map from Si−1 to S(α) for any vector bundle α over B and any integer i with i>dimα. We prove that the m-fold suspension of projective plane FP² is I-trivial if and only if m≠0,2,4 for F=C, m≠0,4 for F=H. In the case where F is the Cayley algebra, the m-fold suspension is shown to be I-trivial for every m>0.