On stationary Navier-Stokes flows in 2D semi-infinite channel involving the general outflow condition

Summary We consider the stationary Navier-Stokes equations in a certain type of semi-infinite channel under the general outflow condition. Assuming that the domain and the data are symmetric with respect to a straight line, the axis of symmetry, and that the axis intersects every component of the boundary, we show the existence of solutions and certain regularity properties of the solutions.

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Sunto In questo lavoro consideriamo le equazioni di Navier-Stokes stazionarie in un certo tipo di canali semi-infiniti sotto la condizione generale di outflow. Assumendo che sia il dominio sia i dati siano simmetrici rispetto ad una retta, l’asse di simmetria, e che questa retta intersechi ogni componente del bordo, mostriamo esistenza di soluzioni ed alcune proprietà di regolarità delle stesse.

     

Lattice Points on Similar Figures and Conics

Let us say that a plane figure F satisfies Steinhaus’ condition if for any positive integer n, there exists a figure F _n similar to F which satisfies the condition |F_n?mathbb Z²|=n{|F_ncap{mathbb Z}^2|=n}. For example, the circular disc satisfies Steinhaus’ condition. We prove that every compact convex region in the plane mathbb R²{mathbb R^2} satisfies Steinhaus’ condition. As for plane curves, it is known that the circle satisfies Steinhaus’ condition. We consider Steinhaus’ condition for other conics, and present several results.     

Comment on ‘A comparison theorem of the SOR iterative method’

In this work, we point out that there are incorrect assertions in the article by Li-Ying Sun (Li-Ying Sun, A comparison theorem for the SOR iterative method, J. Comput. Appl. Math. 181 (2005) 336-341). Moreover, we answer an open problem.     

BRDF color mapping using line scan camera

Optical Review - An optical imaging system for color mapping of the bidirectional reflectance distribution function (BRDF) using a line scan camera is proposed here that can detect slight BRDF...     

Ultrasonic irradiation effect in the quenched benzene

On slow cooling, a precursor phenomenon in supercooled benzene was probed by longitudinal absorption. On quenching, in-situ observation of ultrasonic measurements was carried out at the fixed temperature. Sequence of the transmitted waves was multiple scattered in quenched benzene. The dynamic ultrasound scattering is sensitive to the local strain and dynamic inhomogeneous fluctuations. The quenched benzene shows the maximum value of longitudinal absorption at incubation time, t_inc. Crystal domain growth/coarsening is promoted by the ultrasonic irradiation at t_inc < t. In addition, t_inc depends on the quenching temperature. Ultrasonic irradiation and quenching effects dominate the extraordinal nucleation and growth process of benzene in spite of simple and non-polar molecular liquid.     

Yaequinolones J1 and J2, novel insecticidal antibiotics from Penicillium sp. FKI-2140

[chemical reaction: see text]. Two novel insecticidal antibiotics with a p-methoxyphenylquinolinone skeleton fused with a pyran ring, yaequinolones J1 (1) and J2 (2), have been isolated from Penicillium sp. FKI-2140, and structures were elucidated by spectroscopic studies including various NMR experiments. The relative stereochemistries were assigned by NOE experiments. Yaequinolones J1 and J2 showed toxicity against Artemia salina (brine shrimp) with the MIC value of 6.25 microg/mL.     

Synthesis and toxicity assay of ceramic nanophosphors for bioimaging with near-infrared excitation

Yttrium hydroxyl carbonate (Y(OH)CO₃) precursors were synthesized by the homogeneous co-precipitation method in the presence of polyacrylic acid (PAAc). Resultant precursor particle size is about 15–20 nm with narrow size distribution whereas the particle size is smaller than those acquired by the conventional homogeneous precipitation method. Effective decrease of Y(OH)CO₃ particle size was found to be higher for the presence of weak polyanionic ionomer such as PAAc than the presence of strong polyanionic ionomer such as sodium polystyrene sulfonate (PSS). It was observed that the morphology and size of the precursors are almost unchanged after the calcination process. Er³⁺ doped Y₂O₃ nanoparticles were synthesized by PAAc assisted homogeneous co-precipitation method showed bright green (550 nm) and red (660 nm) upconversion (UC) as well as near-infrared (NIR) fluorescence (1550 nm) under 980-nm excitation. UC and NIR fluorescence bioimaging and in-vitro cytotoxicity assay of Er³⁺ doped Y₂O₃ nanoparticles were successfully attempted with commercially available macrophages and B-cell hybridomas. Cellular uptake of nanoparticles is evidenced from bright field, UC and NIR fluorescence images of macrophages.     

Preparation and characterization of conducting trimetallic nickel-dithiolene complexes with bridging tetrathiooxalate ligands

Trimetallic nickel dithiolene complexes with two tetrathiooxalate (tto) ligands were obtained by a reaction monitored by ESI-mass spectrometry followed by HPLC separation and were characterized by elemental or crystal structural analysis, MO calculations, and electrical conductivity measurements.