Effective metastability of Halpern iterates in CAT(0) spaces

This paper provides an effective uniform rate of metastability (in the sense of Tao) on the strong convergence of Halpern iterations of nonexpansive mappings in CAT(0) spaces. The extraction of this rate from an ineffective proof due to Saejung is an instance of the general proof mining program which uses tools from mathematical logic to uncover hidden computational content from proofs. This methodology is applied here for the first time to a proof that uses Banach limits and hence makes a substantial reference to the axiom of choice.     

Design of optical triangulation devices

This paper presents the derivation of the precise relation between the displacement of a light spot on an object's surface and the displacement of its image on the detector in an optical triangulation device, along with applications of the design of triangulation devices. Based on this relation, improved designs of optical triangulation devices, including devices of adjustable configurations, are proposed and discussed.     

Multi-resolution analysis of wavelet transform on pressure fluctuations in an L-valve

A novel diagnostic method to characterize the flow patterns in an 80 mm-i.d. L-valve had been developed by using multi-resolution analysis (MRA) of wavelet transformation on the pressure fluctuation signals which were acquired from the standpipe and the horizontal part of L-valve. Parameters including the aeration rate, aeration positions, riser gas velocity and composition of binary particle mixture (194-μm and 937-μm sand particles) were used to investigate the relationship of performance of L-valve and its pressure fluctuations. By means of MRA, the original pressure fluctuations were divided into multi-scale signals. They were macro-scale, meso-scale and micro-scale successfully described the structures of gas–solid flow in the L-valve, such as the gas bubbles/slugs, dune-ripple flow, suspension particle flow, etc.     

<!?tlsb=‐0.06pt>Bromido(η5‐carboxycyclopentadienyl)dinitrosylchromium(0) and (η5‐benzoylcyclopentadienyl)bromidodinitrosylchromium(0)

In the structures of each of the title compounds, [CrBr(C₆H₅O₂)(NO)₂], (I), and [CrBr(C₁₂H₉O)(NO)₂], (II), one of the nitrosyl groups is located at a site away from the exocyclic carbonyl C atom of the cyclopentadienyl (Cp) ring, with twist angles of 174.5 (3) and 172.5 (1)°. The observed orientation is surprising, since the NO group is expected to be situated trans to an electron‐rich C atom in the ring. The organic carbonyl plane is turned away from the Cp ring plane by 5.6 (8) and 15.2 (3)°in (I) and (II), respectively. The exocyclic C—C bond in (I) is bent out of the Cp ring plane towards the Cr atom by 2.8 (3)°, but is coplanar with the Cp ring in (II); the angle is 0.1 (1)°.     

On vortex shedding behind a circular disk

Abtract  Experiments were performed for individual realizations of the vortex shedding process behind a circular disk at Reynolds numbers of 10³–10⁵, at which periodic vortex shedding prevails in the wake. The phase differences regarding the individual vortex shedding structures detected at multiple circumferential locations in the wake were obtained by analyzing the hot-wire signals with a conditional-sampling scheme. The phase differences of vortex shedding detected at circumferential positions 90° apart show a wide scatter, but the anti-phase character is largely preserved in the individual vortex shedding process as detected at circumferential locations 180° apart. The randomness of phase differences involved in the vortex shedding process is noted to be essential in order to satisfy the axisymmetric property of the global flow. Received: 4 April 19969/Accepted: 29 January 1997     

Self-organization of ZnO wrinkles oriented by patterned PMMA templates

In this study, well-ordered ZnO wrinkles were fabricated by sol–gel derived ZnO films via heat treatment at 400 °C for 2 h with the assistance of polymethymethacrylate (PMMA) templates. PMMA templates with various patterns were employed to investigate the effects of template geometries on arrangements of the formed ZnO wrinkles. The influence of thickness on the transformation of the entire resulting structures of the spin-coated ZnO sol–gel films is discussed. With 2-dimensional arrangement of PMMA patterns, more than two orientations of wrinkled ZnO can be induced in one template. By controlling the arrangement of PMMA patterns and thickness of ZnO sol–gel films, specific circular, hexagonal, triangular and triangular-star complex structures were produced due to the constrained shrinkage force of the ZnO films applied toward the PMMA side walls during drying. By this technique, we can obtain 3-dimensional ZnO structures that conventional photolithography and nano-imprinting lithography are hard to achieve in few process steps.     

The effect of ferulic acid ethyl ester on leptin-induced proliferation and migration of aortic smooth muscle cells

Leptin is a peptide hormone, which has a central role in the regulation of body weight; it also exerts many potentially atherogenic effects. Ferulic acid ethyl ester (FAEE) has been approved for antioxidant properties. The aim of this study was to investigate whether FAEE can inhibit the atherogenic effects of leptin and the possible molecular mechanism of its action. Both of cell proliferation and migration were measured when the aortic smooth muscle cell (A10 cell) treated with leptin and/or FAEE. Phosphorylated p44/42MAPK, cell cycle-regulatory protein (for example, cyclin D1, p21, p27), β-catenin and matrix metalloproteinase-9 (MMP-9) proteins levels were also measured. Results demonstrated that leptin (10, 100 ng ml⁻¹) significantly increased the proliferation of cells and the phosphorylation of p44/42MAPK in A10 cells. The proliferative effect of leptin was significantly reduced by the pretreatment of U0126 (0.5 μM), a MEK inhibitor, in A10 cells. Meanwhile, leptin significantly increased the protein expression of cyclin D1, p21, β-catenin and decreased the expression of p27 in A10 cells. In addition, leptin (10 ng ml⁻¹) significantly increased the migration of A10 cells and the expression of MMP-9 protein. Above effects of leptin were significantly reduced by the pretreatment of FAEE (1 and 10 μM) in A10 cells. In conclusion, FAEE exerts multiple effects on leptin-induced cell proliferation and migration, including the inhibition of p44/42MAPK phosphorylation, cell cycle-regulatory proteins and MMP-9, thereby suggesting that FAEE may be a possible therapeutic approach to the inhibition of obese vascular disease.     

Nonlinear rheological behavior of a concentrated spherical silica suspension

Linear and nonlinear viscoelastic properties were examined for a 50 wt% suspension of spherical silica particles (with radius of 40 nm) in a viscous medium, 2.27/1 (wt/wt) ethylene glycol/glycerol mixture. The effective volume fraction of the particles evaluated from zero-shear viscosities of the suspension and medium was 0.53. At a quiescent state the particles had a liquid-like, isotropic spatial distribution in the medium. Dynamic moduli G^* obtained for small oscillatory strain (in the linear viscoelastic regime) exhibited a relaxation process that reflected the equilibrium Brownian motion of those particles. In the stress relaxation experiments, the linear relaxation modulus G(t) was obtained for small step strain (0.2) while the nonlinear relaxation modulus G(t, ) characterizing strong stress damping behavior was obtained for large (>0.2). G(t, ) obeyed the time-strain separability at long time scales, and the damping function h() (–G(t, )/G(t)) was determined. Steady flow measurements revealed shear-thinning of the steady state viscosity () for small shear rates (< ^–1; = linear viscoelastic relaxation time) and shear-thickening for larger (>^–1). Corresponding changes were observed also for the viscosity growth and decay functions on start up and cessation of flow, + (t, ) and _– (t, ). In the shear-thinning regime, the and dependence of ₊(t,) and _–(t,) as well as the dependence of () were well described by a BKZ-type constitutive equation using the G(t) and h() data. On the other hand, this equation completely failed in describing the behavior in the shear-thickening regime. These applicabilities of the BKZ equation were utilized to discuss the shearthinning and shear-thickening mechanisms in relation to shear effects on the structure (spatial distribution) and motion of the suspended particles.Dedicated to the memory of Prof. Dale S. Parson     

Influence of organoclay dispersed state of poly(ethylene glycol‐co‐1,3/1,4‐cyclohexanedimethanol terephthalate)/organoclay nanocomposites on their characteristics

This work prepared poly(ethylene glycol‐co‐1,3/1,4‐cyclohexanedimethanol terephthalate) (PETG)/organoclay nanocomposites via a melt intercalation process and investigated the influences of organoclay aspect ratio and organoclay content on the dispersed state, mechanical, thermal, gas barrier, and heat recovery properties of PETG/organoclay nanocomposites. X‐ray diffraction (XRD) and transmission electron microscopic analyses showed that the organoclay dispersed in the polymer matrix with intercalation in the nanometer scale range. Differential scanning calorimetry (DSC) analysis demonstrated that all of the obtained nanocomposites were amorphous, indicating that the addition of organoclay did not affect the amorphous nature of PETG. The gas barrier properties of the nanocomposites improved with organoclay content and the properties were also affected by the organoclay aspect ratio. Water vapor and oxygen transmission rates (OTRs) of PETG/organoclay nanocomposites containing 3 phr Cloisite 15A, and 3 phr modified polymer grade Na‐montmorillonites (MPGN) were the lowest among the samples tested, and were 41.7 and 44.3%, respectively, of those of neat PETG. Similar organoclay content‐ and aspect ratio‐related effects were observed in the mechanical and heat recovery properties of the tested nanocomposites. Copyright © 2010 John Wiley & Sons, Ltd.     

Vision system for three-dimensional position measurement based on stereo disparity

A stereo disparity-based range finding technique was developed for measuring three-dimensional coordinates of object points. It used an image-matching algorithm which functionally consisted of scene reduction, epipolar line selection, and features matching. Experiments implementing this technique were performed on an industrial vision system. An error analysis indicated that image resolution was the major source of measurement inaccuracy.