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.     

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.     

Room-temperature ferromagnetism in amorphous In–Ga–Zn–O films fabricated by using pulsed-laser deposition

Room-temperature ferromagnetism (RTFM) was observed in pulsed-laser deposited amorphous In–Ga–Zn–O (a-IGZO) films undoped with impurities containing unpaired d or f electrons. The presence of oxygen vacancies in the prepared a-IGZO films was verified by X-ray photoelectron spectroscopy and suggested to be responsible for the observed RTFM. The electrical and optical properties of the a-IGZO films were also investigated.     

Field emission characteristics of carbon nanotubes post-treated with high-density Ar plasma

The field emission characteristics of carbon nanotubes (CNTs) grown by thermal chemical vapor deposition (CVD) and subsequently surface treated by high-density Ar plasma in an inductively coupled plasma reactive ion etching (ICP-RIE) with the various plasma powers were measured. Results indicate that, after treated by Ar plasma with power between 250 and 500 W, the emission current density of the CNTs is enhanced by nearly two orders of magnitude (increased from 0.65 to 48 mA/cm²) as compared to that of the as-grown ones. Scanning electron microscopy (SEM) and transmission electron microscopy (TEM) were employed to investigate the structural features relevant to the modified field emission properties of CNTs. The SEM images of CNTs subjected to a 500 W Ar plasma treatment exhibit obvious damages to the CNTs. Nevertheless, the turn-on fields decreased from 3.6 to 2.2 V/μm, indicating a remarkable field emission enhancement. Our results further suggest that the primary effect of Ar plasma treatment might be to modify the geometrical structures of the local emission region in CNTs. In any case, the Ar plasma treatment appears to be an efficient method to enhance the site density for electron emission and, hence markedly improving the electric characteristics of the CNTs.     

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.     

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.     

Abstract Riccati equations in an L1 space of finite measure and applications to transport theory

We consider operator-valued Riccati initial-value problems of the form R′(t) + TR(t) + R(t)T = TA(t) + TB(t)R(t) + R(t)TC(t) + R(t)TD(t)R(t), R(0) = R₀. Here A to D and R₀ have values as non-negative bounded linear operators in L¹ (μ), where μ is a finite measure, and T is a closed non-negative operator in L¹ (μ) satisfying additional technical conditions. For such problems the notion of strongly mild solutions is defined, and local existence and uniqueness theorems for such solutions are established. The results of the analysis are applied to the reflection kernels with both isotropically scattering homogeneous and anisotropically scattering inhomogeneous medium.     

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.     

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.