Fixed Points,Continuous Selections,and Existence of Solution of Optimization-Related Problems

We propose a definition of a generalized type of Knaster–Kuratowski–Mazurkiewicz (KKM) mappings, called a weak T-KKM mapping, and a corresponding weak KKM property. A new extension of the Fan–Glicksberg fixed-point theorem is established. Sufficient conditions for the existence of a continuous selection, a fixed point of a composition, and a coincidence point are also provided. Then, we use the obtained results to study the existence of solutions to various optimization-related problems. Discussions and detailed examples are included as well to compare our results with existing ones and to explain their advantages in many situations.     

12-Epi-9-deacetoxyxenicin,new cytotoxic diterpenoid from a Bornean soft coral,Xenia sp.

One new compound, 12-epi-9-deacetoxyxenicin (1) along with a hydroperoxide product, 12-epi-9-deacetoxy-8-hydroperoxyxenicin (2) and two known sesquiterpenoids (3–4) were isolated from a population of Bornean soft coral Xenia sp. The structures of these secondary metabolites were elucidated based on their spectroscopic data. Compounds 1 and 2 showed cytotoxic activity against ATL cell line, S1T. In addition, compound 3 exhibited hyphal inhibition of Lagenidium thermophilum.     

Plasmonic Hotspots in Air: An Omnidirectional Three‐Dimensional Platform for Stand‐Off In‐Air SERS Sensing of Airborne Species

Molecular‐level airborne sensing is critical for early prevention of disasters, diseases, and terrorism. Currently, most 2D surface‐enhanced Raman spectroscopy (SERS) substrates used for air sensing have only one functional surface and exhibit poor SERS‐active depth. “Aerosolized plasmonic colloidosomes” (APCs) are introduced as airborne plasmonic hotspots for direct in‐air SERS measurements. APCs function as a macroscale 3D and omnidirectional plasmonic cloud that receives laser irradiation and emits signals in all directions. Importantly, it brings about an effective plasmonic hotspot in a length scale of approximately 2.3 cm, which affords 100‐fold higher tolerance to laser misalignment along the z‐axis compared with 2D SERS substrates. APCs exhibit an extraordinary omnidirectional property and demonstrate consistent SERS performance that is independent of the laser and analyte introductory pathway. Furthermore, the first in‐air SERS detection is demonstrated in stand‐off conditions at a distance of 200 cm, highlighting the applicability of 3D omnidirectional plasmonic clouds for remote airborne sensing in threatening or inaccessible areas.     

Formation of a Macrocycles‐in‐a‐Macrocycle Superstructure with All‐gauche Conformation by Reversible Radical Association

The formation of an unprecedented macrocycles‐in‐a‐macrocycle (MIM) superstructure by reversible radical–radical association of a triphenylamine based monomer terminated with three dicyanomethyl radicals is presented. The reaction yield is nearly quantitative and the obtained macrocycle contains three small dimeric macrocycles according to X‐ray crystallographic analysis. The six monomer molecules are linked by nine long dynamic covalent C(sp³)?C(sp³) bonds that all adopt a gauche conformation. Such a conformation favors the formation of a MIM structure rather than a 2D network with an all‐anti conformation. Two enantiomers with left‐/ right‐handed chirality exist in the single crystals of the superstructure.     

On-line coupling of liquid chromatography at critical conditions with electrospray ionization tandem mass spectrometry for the characterization of a nitroxide-mediated poly(ethylene oxide)/polystyrene block copolymer

Coupling of liquid chromatography at critical conditions (LCCC) with on-line mass spectrometry (MS) detection was implemented via an electrospray ionization (ESI) interface, using a mobile phase containing the cationizing agent. Critical conditions established for poly(ethylene oxide) were used to characterize a poly(ethylene oxide)/polystyrene block copolymer (PEO-b-PS) in both MS and MS/MS modes. As co-oligomer molecules were successfully separated according to the PS block size, structural information could be reached from simplified MS spectra. The microstructure of this copolymer, synthesized by nitroxide-mediated polymerization, could further be unambiguously characterized in LCCC/ESI-MS/MS experiments since the PS block size could be reached by both the co-oligomer chromatographic behavior and its MS/MS pattern.     

Chemical constituents from the leaves of Manglietia phuthoensis and their effects on osteoblastic MC3T3-E1 cells

Two new phenyl glycosides, mangliesides A and B (1, 2), a new ionol glycoside, manglieside C (3), two new lignan glycosides, mangliesides D and E (4, 5), were isolated from the leaves of Manglietia phuthoensis, along with two known lignans, 3-methoxymagnolol (6) and obovatol (7). Their structures were established by means of 1D and 2D NMR, electrospray ionization (ESI)-MS and HR-ESI-MS experiments. Among them, compounds 2 and 5 significantly (p<0.05) increased the growth and differentiation of osteoblastic MC3T3-E1 cells in vitro.     

Electrochemical and spectroscopic characterization of a series of mixed-ligand diruthenium compounds

The electrochemistry and spectroelectrochemistry of a novel series of mixed-ligand diruthenium compounds were examined. The investigated compounds having the formula Ru(2)(CH(3)CO(2))(x)(Fap)(4-x)Cl where x = 1-3 and Fap is 2-(2-fluoroanilino)pyridinate anion were made from the reaction of Ru(2)(CH(3)CO(2))(4)Cl with 2-(2-fluoroanilino)pyridine (HFap) in refluxing methanol. The previously characterized Ru(2)(Fap)(4)Cl as well as the three newly isolated compounds represented as Ru(2)(CH(3)CO(2))(Fap)(3)Cl (1), Ru(2)(CH(3)CO(2))(2)(Fap)(2)Cl (2), and Ru(2)(CH(3)CO(2))(3)(Fap)Cl (3) possess three unpaired electrons with a Ru(2)(5+) dimetal core. Complexes 1 and 2 have well-defined Ru(2)(5+/4+) and Ru(2)(5+/6+) redox couples in CH(2)Cl(2), but 3 exhibits a more complicated electrochemical behavior due to equilibria involving association or dissociation of the anionic chloride axial ligand on the initial and oxidized or reduced forms of the compound. The E(1/2) values for the Ru(2)(5+/4+) and Ru(2)(5+/6+) processes vary linearly with the number of CH(3)CO(2)(-) bridging ligands on Ru(2)(CH(3)CO(2))(x)(Fap)(4-x)Cl and plots of reversible half-wave potentials vs the number of acetate groups follow linear free energy relationships with the largest substituent effect being observed for the oxidation. The major UV-visible band of the examined compounds in their neutral Ru(2)(5+) form is located between 550 and 800 nm in CH(2)Cl(2) and also varies linearly with the number of CH(3)CO(2)(-) ligands on Ru(2)(CH(3)CO(2))(x)(Fap)(4-x)Cl. The electronic spectra of the singly oxidized and singly reduced forms of each diruthenium species were characterized by UV-visible spectroelectrochemistry in CH(2)Cl(2).     

Dry Reforming of Methane on a Highly‐Active Ni‐CeO2 Catalyst: Effects of Metal‐Support Interactions on C−H Bond Breaking

Ni‐CeO₂ is a highly efficient, stable and non‐expensive catalyst for methane dry reforming at relative low temperatures (700 K). The active phase of the catalyst consists of small nanoparticles of nickel dispersed on partially reduced ceria. Experiments of ambient pressure XPS indicate that methane dissociates on Ni/CeO₂ at temperatures as low as 300 K, generating CH_x and CO_x species on the surface of the catalyst. Strong metal–support interactions activate Ni for the dissociation of methane. The results of density‐functional calculations show a drop in the effective barrier for methane activation from 0.9 eV on Ni(111) to only 0.15 eV on Ni/CeO_2?x(111). At 700 K, under methane dry reforming conditions, no signals for adsorbed CH_x or C species are detected in the C 1s XPS region. The reforming of methane proceeds in a clean and efficient way.     

Isolating Reactions at the Picoliter Scale: Parallel Control of Reaction Kinetics at the Liquid–Liquid Interface

Miniaturized liquid–liquid interfacial reactors offer enhanced surface area and rapid confinement of compounds of opposite solubility, yet they are unable to provide in situ reaction monitoring at a molecular level at the interface. A picoreactor operative at the liquid–liquid interface is described, comprising plasmonic colloidosomes containing Ag octahedra strategically assembled at the water‐in‐decane emulsion interface. The plasmonic colloidosomes isolate ultrasmall amounts of solutions (<200 pL), allowing parallel monitoring of multiple reactions simultaneously. Using the surface‐enhanced Raman spectroscopy (SERS) technique, in situ monitoring of the interfacial protonation of dimethyl yellow (p‐dimethylaminoazobenzene (DY)) is performed, revealing an apparent rate constant of 0.09 min^?1 for the first‐order reaction. The presence of isomeric products with similar physical properties is resolved, which would otherwise be indiscernible by other analytical methods.