The smallest enclosing ball problem and the smallest intersecting ball problem: existence and uniqueness of solutions

In this paper we study the following problems and their further generalizations: given a finite number of nonempty closed subsets of a normed space, find a ball with the smallest radius that encloses all of the sets, and find a ball with the smallest radius that intersects all of the sets. These problems can be viewed as generalized versions of the smallest enclosing circle problem introduced in the nineteenth century by Sylvester which asks for the circle of smallest radius enclosing a given set of finite points in the plane. We will focus on sufficient conditions for the existence and uniqueness of an optimal solution for each problem, while the study of optimality conditions and numerical implementation will be addressed in our next projects.     

Multifarious injection chamber for molecular structure study (MICOSS) system: development and application for serial femtosecond crystallography at Pohang Accelerator Laboratory X‐ray Free‐Electron Laser

The multifarious injection chamber for molecular structure study (MICOSS) experimental system has been developed at the Pohang Accelerator Laboratory X‐ray Free‐Electron Laser for conducting serial femtosecond crystallography. This system comprises several instruments such as a dedicated sample chamber, sample injectors, sample environment diagnostic system and detector stage for convenient distance manipulation. Serial femtosecond crystallography experiments of lysozyme crystals have been conducted successfully. The diffraction peaks have reached to ～1.8 Å resolution at the photon energy of 9.785 keV.     

An improved stability criterion for a class of neutral differential equations

This work gives an improved criterion for asymptotical stability of a class of neutral differential equations. By introducing a new Lyapunov functional, we avoid the use of the stability assumption on the main operators and derive a novel stability criterion given in terms of a LMI, which is less restricted than that given by Park [J.H. Park, Delay-dependent criterion for asymptotic stability of a class of neutral equations, Appl. Math. Lett. 17 (2004) 1203–1206] and Sun et al. [Y.G. Sun, L. Wang, Note on asymptotic stability of a class of neutral differential equations, Appl. Math. Lett. 19 (2006) 949–953].     

2‐[(Diphenylphosphino)methyl]pyridine as ligand for iron‐based atom transfer radical polymerization

2‐[(Diphenylphosphino)methyl]pyridine (DPPMP) was successfully used as a bidentate ligand in the iron‐mediated atom transfer radical polymerization (ATRP) of methyl methacrylate (MMA) with various initiators and solvents. The effect of the catalytic system on ATRP was studied systematically. Most of the polymerizations with DPPMP ligand were well controlled with a linear increase in the number‐average molecular weights (M_n) versus conversion and relatively low molecular weight distributions (M_w/M_n = 1.10–1.3) being observed throughout the reactions, and the measured molecular weights matched the predicted values. Initially added iron(III) bromide improved the controllability of the polymerization reactions in terms of molecular weight control. The ratio of ligand to metal influenced the controllability of ATRP system, and the optimum ratio was found to be 2:1. It was shown that ATRP of MMA with FeX₂/DPPMP catalytic system (X = Cl, Br) initiated by 2‐bromopropionitrile (BPN) was controlled more effectively in toluene than in polar solvents. The rate of polymerization increased with increasing the polymerization temperature and the apparent activation energy was calculated to be 56.7 KJ mol^?1. In addition, reverse ATRP of MMA was able to be successfully carried out using AIBN in toluene at 80 °C. Polymerization of styrene (St) was found to be controlled well by using the PEBr/FeBr₂/DPPMP system in DMF at 110 °C. © 2008 Wiley Periodicals, Inc. J Polym Sci Part A: Polym Chem 46: 2922–2935, 2008     

带阻尼项一维非等熵流方程组初边值问题解的收敛速度

研究了带阻尼项一维非等熵流方程组的初边值问题，利用能量估计的办法证明了整体解的存在性和得到在L2－模及L∞－模意义下解的大时间状态稳定性估计。     

Biological functionalization of the amine-terminated Si(100) surface by glycine

A peptide reaction of glycine on an amine-terminated Si(100) surface was investigated using C 1s, N 1s, O 1s, and Si 2p core-level spectroscopy, where the amine-terminated Si(100) surface was prepared using NH₃. In-situ thermal treatments at a mild temperature of 50 °C after the adsorption of glycine on a room-temperature amine-terminated Si(100) surface induced the peptide reaction between the carboxyl group of glycine and the amine group of the surface. This suggests that the amine-terminated Si(100) surface can be an excellent template for constructing a junction between a biomaterial and a Si surface using a dry process.     

Field‐effect transistors based on PPV derivatives as a semiconducting layer

A series of modified thiophene groups containing PPV‐based semiconducting materials, poly[(2,5‐bis(octyloxy)‐1,4‐phenylenevinylene)‐alt‐(2,2′bithienylenevinylene)] ( PPBT ), poly[(2,5‐bis(octyloxy)‐1,4‐phenylenevinylene)‐alt‐(5,5‐thiostilylenevinylene)] ( PPTVT ), have been synthesized through a Horner coupling reaction. From the FTIR and ¹H NMR spectroscopy, the configuration of the vinylene groups in the polymers was all trans (E) geometry. The weight‐average molecular weights (M_w) of PPBT and PPTVT were found to be 11,700 and 11,800, with polydispersity indices of 2.51 and 2.53, respectively. PPBT and PPTVT thin films exhibit UV–visible absorption maxima at 538 and 558 nm, respectively, and the strong absorption shoulder peaks at 578 and 602 nm, respectively. Solution processed field‐effect transistors (FET) fabricated using all the polymers showed p‐type OTFT characteristics. The field‐effect mobility of the PPTVT was obtained up to 2.3 × 10^?3 cm² V^?1 s^?1, an on/off ratio of 1.0 × 10⁵ with ambient air stability. Studies of the atomic force microscopy (AFM) and X‐ray diffraction (XRD) analysis of the polymer thin films revealed that all the polymers were amorphous structure. The greater planarity and rigidity of PPTVT compared to PPBT results in elongation of conjugation length and better π–π stacking of polymer chains in amorphous region, which leads to improved FET performance. © 2008 Wiley Periodicals, Inc. J Polym Sci Part A: Polym Chem 47: 111–120, 2009     

Study of Internal Linear Inductively Coupled Plasma Source for Ultra Large-Scale Flat Panel Display Processing

An internal-type linear inductive antenna, which is referred to as “double comb-type antenna”, was used as a large-area inductively coupled plasma (ICP) source with a substrate area of 2,300 mm × 2,000 mm. The characteristics of the ICP source were investigated for potential applications to flat panel display (FPD) processing. The source showed higher power transfer efficiency at higher RF power and higher operating pressures. The power transfer efficiency was approximately 88.1% at 9 kW of RF power and a pressure of 20 mTorr Ar. This source showed increasing plasma density and improved plasma uniformity with increasing RF power at a given operating pressure. A plasma density >1.5 × 10¹¹/cm³ and a plasma uniformity of approximately 11% was obtained at 9 kW of RF power and 15 mTor Ar using this internal ICP source, which is applicable to FPD processing.     

Acid–base and coordination properties of <Emphasis Type="Italic">Meso</Emphasis>-substituted porphyrins in nonaqueous solutions

Acid–base and coordination properties of alkyl and aryl meso-substituted porphyrins are studied spectrophotometrically in nonaqueous solutions. It is found that the nature of the substituent greatly affects the basicity of ligands for porphyrins characterized by a flat structure of macrocycle. The electronic effects of substituents have a much weaker influence on the kinetics of complexing. These effects could be due to the opposite orientation of some factors: an increase in the basicity and stability of the N–H bonds of porphyrin reaction centers. Dissociation constants pK _b of the cationic forms of meso-substituted derivatives of porphyrin are measured. The values of pK _b are in good agreement with classic concepts of the nature of substituents, particularly those indirectly included in the macrocycle through phenyl buffer rings.     

Copper ferrite superparamagnetic nanoparticles as a heterogeneous catalyst for directed phenol/formamide coupling

The copper ferrite-catalyzed, directed coupling of ortho-arylated phenols and dialkylformamides in the presence of a peroxide oxidant is described. Acyclic and cyclic amides were compatible with the reaction conditions. The copper ferrite catalyst is heterogeneous since substantial leaching was not detected and re-use of the catalyst for 9 consecutive reactions proceeded without a significant decrease in yield. To the best of our knowledge, this transformation has not been previously performed under heterogeneous catalysis conditions.