Degenerate riccati equations with unbounded coefficients arising in transport theory

Of concern is the degenerate Riccati equation of the form TR+RT=TA+TBR+RTC+RTDR (?). This models a certain transport equation in the half-space. Our first result will concern a unique, positive solution of the operator equation SR+RT=K in a anach space equipped with a cone structure. We then proceed to prove existence of positive solutions for (?) on an L¹ space of σ-finite measure and a Banach space X, respectively, under different assumptions. Some estimates of the solution with respect to certain norms are obtained.     

The wavelet transform method applied to a coupled chaotic system with asymmetric coupling schemes

The wavelet transform method originated by Wei et al. (2002) [19] is an effective tool for enhancing the transverse stability of the synchronous manifold of a coupled chaotic system. Much of the theoretical study on this matter is centered on networks that are symmetrically coupled. However, in real applications, the coupling topology of a network is often asymmetric; see Belykh et al. (2006)  [23], [24], Chavez et al. (2005)  [25], Hwang et al. (2005)  [26], Juang et al. (2007)  [17], and Wu (2003)  [13]. In this work, a certain type of asymmetric sparse connection topology for networks of coupled chaotic systems is presented. Moreover, our work here represents the first step in understanding how to actually control the stability of global synchronization from dynamical chaos for asymmetrically connected networks of coupled chaotic systems via the wavelet transform method. In particular, we obtain the following results. First, it is shown that the lower bound for achieving synchrony of the coupled chaotic system with the wavelet transform method is independent of the number of nodes. Second, we demonstrate that the wavelet transform method as applied to networks of coupled chaotic systems is even more effective and controllable for asymmetric coupling schemes as compared to the symmetric cases.     

Biochemical and biomedical applications of multifunctional magnetic nanoparticles: a review

Nanotechnology offers tremendous potential for future medical diagnosis and therapy. Various types of nanoparticles have been extensively studied for numerous biochemical and biomedical applications. Magnetic nanoparticles are well-established nanomaterials that offer controlled size, ability to be manipulated by an external magnetic field, and enhancement of contrast in magnetic resonance imaging. As a result, these nanoparticles could have many applications including bacterial detection, protein purification, enzyme immobilization, contamination decorporation, drug delivery, hyperthermia, etc. All these biochemical and biomedical applications require that these nanoparticles should satisfy some prerequisites including high magnetization, good stability, biocompatibility, and biodegradability. Because of the potential benefits of multimodal functionality in biomedical applications, in this account highlights some general strategies to generate magnetic nanoparticle-based multifunctional nanostructures. After these magnetic nanoparticles are conjugated with proper ligands (e.g., nitrilotriacetate), polymers (e.g., polyacrylic acid, chitosan, temperature- and pH-sensitive polymers), antibodies, enzymes, and inorganic metals (e.g., gold), such biofunctional magnetic nanoparticles exhibit many advantages in biomedical applications. In addition, the multifunctional magnetic nanoparticles have been widely applied in biochemical fields including enzyme immobilization and protein purification.     

50 Years of CORDIC: Algorithms, Architectures, and Applications

Year 2009 marks the completion of 50 years of the invention of CORDIC (coordinate rotation digital computer) by Jack E. Volder. The beauty of CORDIC lies in the fact that by simple shift-add operations, it can perform several computing tasks such as the calculation of trigonometric, hyperbolic and logarithmic functions, real and complex multiplications, division, square-root, solution of linear systems, eigenvalue estimation, singular value decomposition, QR factorization and many others. As a consequence, CORDIC has been utilized for applications in diverse areas such as signal and image processing, communication systems, robotics and 3-D graphics apart from general scientific and technical computation. In this article, we present a brief overview of the key developments in the CORDIC algorithms and architectures along with their potential and upcoming applications.     

渐近保持PIC算法在等离子体粒子模拟中的应用

针对准中性Vlasov-Poisson系统中多尺度物理参数共存的问题开展研究,采用渐近保持格式推导出与Vlasov方程相耦合的Poisson方程。数值模拟了一维等离子体在真空中的膨胀,比较了渐近保持PIC算法与传统PIC算法模拟结果的异同。结果表明：两种算法在满足多尺度中小尺度量限制的前提下,其结果保持高度一致;且在克服小尺度量束缚时,渐近保持PIC算法依然可以正确地模拟等离子体的物理行为,大大节省了计算时间。     

Liquid-phase adsorption and desorption of phenol onto activated carbons with ultrasound

The effect of 48-kHz ultrasound on the adsorption and desorption of phenol from aqueous solutions onto coconut shell-based granular activated carbons was studied at 25 degrees C. Experiments were performed at different carbon particle sizes (1.15, 2.5, 4.0 mm), initial phenol concentrations (1.06-10.6 mol/m3), and ultrasonic powers (46-133 W). Regardless of the absence and presence of ultrasound, the adsorption isotherms were well obeyed by the Langmuir equation. When ultrasound was applied in the whole adsorption process, the adsorption capacity decreased but the Langmuir constant increased with increasing ultrasonic power. According to the analysis of kinetic data by the Elovich equation, it was shown that the initial rate of adsorption was enhanced after sonication and the number of sites available for adsorption was reduced. The effect of ultrasonic intensity on the initial rate and final amount of desorption of phenol from the loaded carbons using 0.1 mol/dm3 of NaOH were also evaluated and compared.     

Synthesis and evaluation of in vitro bioactivity for polysubstituted N-arylpyrazole derivatives

New polysubstituted N-arylpyrazole derivatives were synthesized from N1-arylsydnone with acetylene and boronic acid, including 2-thiophenyl, 3-thiophenyl, 2-benzo[b]thiophenyl, or dibenzothiophenyl-4-boronic acid, via 1,3-dipolar cycloaddition and Suzuki coupling reaction. Based on the growth inhibitory activity results against lung carcinoma (NCI-H226), nasopharyngeal (NPC-TW01), and T-cell leukemia (Jurkat) cancer cells, compounds 5d and 7d with dibenzothiophenyl bioisostere possessed the significant inhibitory activity for NPC-TW01 (32 μM and 16 μM) and NCI-H226 (16 μM and 8.9 μM), respectively.     

A dedicated small‐angle X‐ray scattering beamline with a superconducting wiggler source at the NSRRC

At the National Synchrotron Radiation Research Center (NSRRC), which operates a 1.5 GeV storage ring, a dedicated small‐angle X‐ray scattering (SAXS) beamline has been installed with an in‐achromat superconducting wiggler insertion device of peak magnetic field 3.1 T. The vertical beam divergence from the X‐ray source is reduced significantly by a collimating mirror. Subsequently the beam is selectively monochromated by a double Si(111) crystal monochromator with high energy resolution (ΔE/E? 2 × 10^?4) in the energy range 5–23 keV, or by a double Mo/B₄C multilayer monochromator for 10–30 times higher flux (～10¹¹ photons s^?1) in the 6–15 keV range. These two monochromators are incorporated into one rotating cradle for fast exchange. The monochromated beam is focused by a toroidal mirror with 1:1 focusing for a small beam divergence and a beam size of ～0.9 mm × 0.3 mm (horizontal × vertical) at the focus point located 26.5 m from the radiation source. A plane mirror installed after the toroidal mirror is selectively used to deflect the beam downwards for grazing‐incidence SAXS (GISAXS) from liquid surfaces. Two online beam‐position monitors separated by 8 m provide an efficient feedback control for an overall beam‐position stability in the 10 µm range. The beam features measured, including the flux density, energy resolution, size and divergence, are consistent with those calculated using the ray‐tracing program SHADOW. With the deflectable beam of relatively high energy resolution and high flux, the new beamline meets the requirements for a wide range of SAXS applications, including anomalous SAXS for multiphase nanoparticles (e.g. semiconductor core‐shell quantum dots) and GISAXS from liquid surfaces.     

Optical Non‐Linearity from Montmorillonite Intercalated with a Chromophore‐Containing Dendritic Structure: A Self‐Assembly Approach

Chromophore‐containing dendritic structures (G1, G2) are utilized to intercalate layered silicates, which results in a large d‐spacing up to 126 Å. An exfoliated morphology is obtained by mixing the dendritic structure intercalated layered silicates with polyimide in N,N‐dimethylacetamide solution. The dendritic structures attached on the clay template would arrange in a non‐centrosymmetric manner. This self‐assembled arrangement brought about the electro‐optical coefficients of 5–6 pm · V⁻¹ for these relatively low chromophore‐containing organic/inorganic nanocomposites without resorting to poling. Excellent temporal stability (100 °C) is also achieved.