Derivation of Hartreeʼs theory for generic mean-field Bose systems

In this paper we provide a novel strategy to prove the validity of Hartree?s theory for the ground state energy of bosonic quantum systems in the mean-field regime. For the known case of trapped Bose gases, this can be shown using the strong quantum de Finetti theorem, which gives the structure of infinite hierarchies of k-particles density matrices. Here we deal with the case where some particles are allowed to escape to infinity, leading to a lack of compactness. Our approach is based on two ingredients: (1) a weak version of the quantum de Finetti theorem, and (2) geometric techniques for many-body systems. Our strategy does not rely on any special property of the interaction between the particles. In particular, our results cover those of Benguria–Lieb and Lieb–Yau for, respectively, bosonic atoms and boson stars.     

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.     

Cocrystals of the antibiotic trimethoprim with glutarimide and 3,3‐dimethylglutarimide held together by three hydrogen bonds

The antibiotic trimethoprim [5‐(3,4,5‐trimethoxybenzyl)pyrimidine‐2,4‐diamine] was cocrystallized with glutarimide (piperidine‐2,6‐dione) and its 3,3‐dimethyl derivative (4,4‐dimethylpiperidine‐2,6‐dione). The cocrystals, viz. trimethoprim–glutarimide (1/1), C₁₄H₁₈N₄O₃·C₅H₇NO₂, (I), and trimethoprim–3,3‐dimethylglutarimide (1/1), C₁₄H₁₈N₄O₃·C₇H₁₁NO₂, (II), are held together by three neighbouring hydrogen bonds (one central N—H...N and two N—H...O) between the pyrimidine ring of trimethoprim and the imide group of glutarimide, with an ADA/DAD pattern (A = acceptor and D = donor). These heterodimers resemble two known cocrystals of trimethoprim with barbituric acid and its 5,5‐diethyl derivative. Trimethoprim shows a conformation in which the planes of the pyrimidine and benzene rings are approximately perpendicular to one another. In its glutarimide coformer, five of the six ring atoms lie in a common plane; the C atom opposite the N atom deviates by about 0.6 Å. The crystal packing of each of the two cocrystals is characterized by an extended network of hydrogen bonds and contains centrosymmetrically related trimethoprim homodimers formed by a pair of N—H...N hydrogen bonds. This structural motif occurs in five of the nine published crystal structures in which neutral trimethoprim is present.     

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.     

Density functional theory study on sensing properties of g-C3N4 sheet to atmospheric gasses: Role of zigzag and armchair edges

The ability of the polymer-based graphitic carbon nitride (g-C₃N₄) as a gas sensor toward NO, NO₂, CO, CO₂, SO₂, SO₃, and O₂ gasses is assessed using density functional theory (DFT) calculations in terms of energetic and electronic transport characteristics. In particular, this study is aimed to explore the role of zigzag and armchair edges of the g-C₃N₄ sheet on sensing performances. The electronic properties of adsorption systems, such as Bader charge analysis, band gaps, work function, and density of states (DOS), are used to understand the interaction between the adsorbed gas molecules and the g-C₃N₄ sheet. Our calculated results indicate that SOx (SO₃ and SO₂) gasses have higher adsorption energies on the g-C₃N₄ sheet than other gasses. Furthermore, the transport properties, such as current–voltage (I-V) and resistance-voltage (R-V) curves along the zigzag and armchair directions are calculated using the non-equilibrium Green's function (NEGF) method to understand the performance of the g-C₃N₄ sheet as a prominent conductive/resistive sensor. The I-V/R-V results indicate that the zigzag g-C₃N₄ sheet has excellent sensing ability toward SOx gasses at low applied voltages. However, the presence of H₂O degrades the sensing performance of the armchair g-C₃N₄ sheet. Theoretical recovery time has also been calculated to evaluate the reusability of g-C₃N₄ sheet-based gas sensors. Our results reveal that the zigzag g-C₃N₄ sheet-based sensing device has a remarkably high sensitivity (>300%) and selectivity toward SOx gasses and has the potential to work in a complex environment.     

Quantitative Nanoscale Secondary Ion Mass Spectrometry (NanoSIMS) Imaging of Individual Vesicles to Investigate the Relation between Fraction of Chemical Release and Vesicle Size

We used correlative transmission electron microscopy (TEM) and nanoscale secondary ion mass spectrometry (NanoSIMS) imaging to quantify the contents of subvesicular compartments, and to measure the partial release fraction of ¹³C-dopamine in cellular nanovesicles as a function of size. Three modes of exocytosis comprise full release, kiss-and-run, and partial release. The latter has been subject to scientific debate, despite a growing amount of supporting literature. We tailored culturing procedures to alter vesicle size and definitively show no size correlation with the fraction of partial release. In NanoSIMS images, vesicle content was indicated by the presence of isotopic dopamine, while vesicles which underwent partial release were identified by the presence of an ¹²⁷I-labelled drug, to which they were exposed during exocytosis allowing entry into the open vesicle prior to its closing again. Demonstration of similar partial release fractions indicates that this mode of exocytosis is predominant across a wide range of vesicle sizes.     

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.