Atmospheric chemistry of diazomethane – an experimental and theoretical study

The kinetics of the O₃, OH and NO₃ radical reactions with diazomethane were studied in smog chamber experiments employing long-path FTIR and PTR-ToF-MS detection. The rate coefficients were determined to be k _CH2NN+O3?=?(3.2?±?0.4)?×?10^?17 and k _CH2NN+OH?=?(1.68?±?0.12)?×?10^?10 cm³ molecule^?1 s^?1 at 295?±?3?K and 1013?±?30 hPa, whereas the CH₂NN?+?NO₃ reaction was too fast to be determined in the static smog chamber experiments. Formaldehyde was the sole product observed in all the reactions. The experimental results are supported by CCSD(T*)-F12a/aug-cc-pVTZ//M062X/aug-cc-pVTZ calculations showing the reactions to proceed exclusively via addition to the carbon atom. The atmospheric fate of diazomethane is discussed.     

In Vitro Calli Production Resulted in Different Profiles of Plant-Derived Medicinal Compounds in Phyllanthus amarus

The efficient production of plant-derived medicinal compounds (PDMCs) from in vitro plants requires improvements in knowledge about control of plant or organ development and factors affecting the biosynthesis pathway of specific PDMCs under in vitro conditions, leading to a realistic large-scale tool for in vitro secondary metabolite production. Thus, this study aimed to develop an in vitro technique, through the induction and proliferation of calli, for production of plant fresh weight, and to compare the PDMC profile obtained from the plants versus in vitro calli of Phyllanthus amarus. It was successfully possible to obtain and proliferate two types of calli, one with a beige color and a friable appearance, obtained in the dark using Murashige and Skoog (MS) medium plus 2,4-dichlorophenoxyacetic acid (2,4-D), and a second type with a green color, rigid consistency, and nonfriable appearance obtained under light conditions and MS medium plus 6-benzyladenine (6-BA). In vitro micropropagated plants that gave rise to calli were also acclimatized in a greenhouse and cultivated until obtaining the mass for PDMC analysis and used as a control. While the micropropagated-derived plants concentrated the lignans niranthin, nirtetralin, and phyllanthin, the Phyllanthus amarus calli proliferated in vitro concentrated a completely different biochemical profile and synthesis of compounds, such as betulone, squalene, stigmasterol, and β-sitosterol, in addition to others not identified by GC-MS database. These results demonstrate the possibility of applying the calli in vitro from Phyllanthus amarus for production of important PDMCs unlike those obtained in cultures of differentiated tissues from field plants.     

Synthesis of tertiary amine‐based pH‐responsive polymers by RAFT Polymerization

Well‐defined tertiary amine‐based pH‐responsive homopolymers and block copolymers were synthesized via reversible addition‐fragmentation chain transfer (RAFT) polymerization using 4‐cyanopentanoic acid dithiobenzoate (CPAD) as the RAFT agent for homopolymers and a poly(ethylene glycol) (PEG) macro‐RAFT agent for the block copolymers. ¹H NMR and gel permeation chromatography results confirmed the successful synthesis of these homopolymers and block copolymers. Kinetics studies indicated that the formation of both the homopolymers and the block copolymers were well defined. The pKa titration experiments suggested that the homopolymers and the related block copolymers have a similar pKa. The dynamic light scattering investigation showed that all of the block copolymers underwent a sharp transition from unimers to micelles around their pKa and the hydrodynamic diameter (D_h) was not only dependent on the molecular weight but also on the composition of the block copolymers. The polymer solution of PEG‐b‐PPPDEMA formed the largest micelle compare to the PEG‐b‐PDPAEMA and PEG‐b‐PDBAEMA with a similar molecular weight. © 2015 Wiley Periodicals, Inc. J. Polym. Sci., Part A: Polym. Chem. 2015 , 53, 1010–1022     

Asymptotic behavior toward nonlinear waves for radially symmetric solutions of the multi-dimensional Burgers equation

The present paper is concerned with the asymptotic behaviors of radially symmetric solutions for the multi-dimensional Burgers equation on the exterior domain in ${\mathbb{R}}^n,n\ge 3$, where the boundary and far field conditions are prescribed. We show that in some case where the corresponding 1-D Riemann problem for the non-viscous part admits a shock wave, the solution tends toward a linear superposition of stationary and rarefaction waves as time goes to infinity, and also show the decay rate estimates. Furthermore, we improve the results on the asymptotic stability of the stationary waves which are treated in the previous papers [2], [3]. Finally, for the case of $n=3$, we give the complete classification of the asymptotic behaviors, which includes even a linear superposition of stationary and viscous shock waves.     

System bandwidth and the existence of generalized shift-invariant frames

We consider the question whether, given a countable family of lattices ${({\mathrm{\Gamma }}_j)}_{j\in J}$ in a locally compact abelian group G, there exist functions ${(g_j)}_{j\in J}$ such that the resulting generalized shift-invariant system ${(g_j(??\gamma ))}_{j\in J,\gamma \in {\mathrm{\Gamma }}_j}$ is a tight frame of $L^2(G)$. This paper develops a new approach to the study of generalized shift-invariant system via almost periodic functions, based on a novel unconditional convergence property. From this theory, we derive characterizing relations for tight and dual frame generators, we introduce the system bandwidth as a measure of the total bandwidth a generalized shift-invariant system can carry, and we show that the so-called Calderón sum is uniformly bounded from below for generalized shift-invariant frames. Without the unconditional convergence property, we show, counter intuitively, that even orthonormal bases can have arbitrary small system bandwidth. Our results show that the question of existence of frame generators for a general lattice system is rather subtle and depends on analytical and algebraic properties of the lattice system.     

Uniqueness of isometric immersions with the same mean curvature

Motivated by the quasi-local mass problem in general relativity, we study the rigidity of isometric immersions with the same mean curvature into a warped product space. As a corollary of our main result, two star-shaped hypersurfaces in a spatial Schwarzschild or AdS-Schwarzschild manifold with nonzero mass differ only by a rotation if they are isometric and have the same mean curvature. We also prove similar results if the mean curvature condition is replaced by an ${\sigma }_2$-curvature condition.     

PtII-Catalyzed Hydroxylation of Terminal Aliphatic C(sp3)−H Bonds with Molecular Oxygen

The practical application of Shilov-type Pt catalysis to the selective hydroxylation of terminal aliphatic C−H bonds remains a formidable challenge, due to difficulties in replacing Pt^IV with a more economically viable oxidant, particularly O₂. We report the potential of employing FeCl₂ as a suitable redox mediator to overcome the kinetic hurdles related to the direct use of O₂ in the Pt reoxidation. For the selective conversion of butyric acid to γ-hydroxybutyric acid (GHB), a significantly enhanced catalyst activity and stability (turnover numbers (TON)>30) were achieved under 20 bar O₂ in comparison to current state-of-the-art systems (TON<10). In this regard, essential reaction parameters affecting the overall activity were identified, along with specific additives to attain catalyst stability at longer reaction times. Notably, deactivation by reduction to Pt⁰ was prevented by the addition of monodentate pyridine derivatives, such as 2-fluoropyridine, but also by introducing varying partial pressures of N₂ in the gaseous atmosphere. Finally, stability tests revealed the involvement of Pt^II and FeCl₂ in catalyzing the non-selective overoxidation of GHB. Accordingly, in situ esterification with boric acid proved to be a suitable strategy to maintain enhanced selectivities at much higher conversions (TON>60). Altogether, a useful catalytic system for the selective hydroxylation of primary aliphatic C−H bonds with O₂ is presented.     

Regularity results of the thin obstacle problem for the p(x)-Laplacian

We study thin obstacle problems involving the energy functional with $p(x)$-growth. We prove higher integrability and Hölder regularity for the gradient of minimizers of the thin obstacle problems under the assumption that the variable exponent $p(x)$ is Hölder continuous.