An adaptive multilevel wavelet framework for scale‐selective WENO reconstruction schemes

We put forth a dynamic computing framework for scale‐selective adaptation of weighted essential nonoscillatory (WENO) schemes for the simulation of hyperbolic conservation laws exhibiting strong discontinuities. A multilevel wavelet‐based multiresolution procedure, embedded in a conservative finite volume formulation, is used for a twofold purpose. (i) a dynamic grid adaptation of the solution field for redistributing grid points optimally (in some sense) according to the underlying flow structures, and (ii) a dynamic minimization of the in built artificial dissipation of WENO schemes. Taking advantage of the structure detection properties of this multiresolution algorithm, the nonlinear weights of the conventional WENO implementation are selectively modified to ensure lower dissipation in smoother areas. This modification is implemented through a linear transition from the fifth‐order upwind stencil at the coarsest regions of the adaptive grid to a fully nonlinear fifth‐order WENO scheme at areas of high irregularity. Therefore, our computing algorithm consists of a dynamic grid adaptation strategy, a scale‐selective state reconstruction, a conservative flux calculation, and a total variation diminishing Runge‐Kutta scheme for time advancement. Results are presented for canonical examples drawn from the inviscid Burgers, shallow water, Euler, and magnetohydrodynamic equations. Our findings represent a novel direction for providing a scale‐selective dissipation process without a compromise on shock capturing behavior for conservation laws, which would be a strong contender for dynamic implicit large eddy simulation approaches.     

New Perspectives for Old Clusters: Anderson–Evans Anions as Building Blocks of Large Polyoxometalate Frameworks in a Series of Heterometallic 3 d–4 f Species

A series of nine [Sb₇W₃₆O₁₃₃Ln₃M₂(OAc)(H₂O)₈]^17? heterometallic anions ( Ln₃M₂ ; Ln=La–Gd, M=Co; Ln=Ce, M=Ni and Zn) have been obtained by reacting 3 d metal disubstituted Krebs‐type tungstoantimonates(III) with early lanthanides. Their unique tetrameric structure contains a novel {MW₉O₃₃} capping unit formed by a planar {MW₆O₂₄} fragment to which three {WO₂} groups are condensed to form a tungstate skeleton identical to that of a hypothetical trilacunary derivative of the ?‐Keggin cluster. It is shown, for the first time, that classical Anderson–Evans {MW₆O₂₄} anions can act as building blocks to construct purely inorganic large frameworks. Unprecedented reactivity in the outer ring of these disk‐shaped species is also revealed. The Ln₃M₂ anions possess chirality owing to a {Sb₄O₄} cluster being encapsulated in left‐ or right‐handed orientations. Their ability to self‐associate in blackberry‐type vesicles in solution has been assessed for the Ce₃Co₂ derivative.     

Word problems and ceers

This note addresses the issue as to which ceers can be realized by word problems of computably enumerable (or, simply, c.e.) structures (such as c.e. semigroups, groups, and rings), where being realized means to fall in the same reducibility degree (under the notion of reducibility for equivalence relations usually called “computable reducibility”), or in the same isomorphism type (with the isomorphism induced by a computable function), or in the same strong isomorphism type (with the isomorphism induced by a computable permutation of the natural numbers). We observe, e.g., that every ceer is isomorphic to the word problem of some c.e. semigroup, but (answering a question of Gao and Gerdes) not every ceer is in the same reducibility degree of the word problem of some finitely presented semigroup, nor is it in the same reducibility degree of some non-periodic semigroup. We also show that the ceer provided by provable equivalence of Peano Arithmetic is in the same strong isomorphism type as the word problem of some non-commutative and non-Boolean c.e. ring.     

Direct On‐Surface Patterning of a Crystalline Laminar Covalent Organic Framework Synthesized at Room Temperature

We report herein an efficient, fast, and simple synthesis of an imine‐based covalent organic framework (COF) at room temperature (hereafter, RT‐COF‐1 ). RT‐COF‐1 shows a layered hexagonal structure exhibiting channels, is robust, and is porous to N₂ and CO₂. The room‐temperature synthesis has enabled us to fabricate and position low‐cost micro‐ and submicropatterns of RT‐COF‐1 on several surfaces, including solid SiO₂ substrates and flexible acetate paper, by using lithographically controlled wetting and conventional ink‐jet printing.     

The Synthesis of Some Fused Pyrazolo‐1,4‐Naphthoquinones

New fused pyrazolo‐1,4‐naphthoquinones were prepared from the reaction of hydrazines with 6‐(4‐methyl‐3‐pentenyl)‐1,4‐naphthoquinone. The reaction was extended to hydroxylamine to afford the corresponding isoxazolo‐1,4‐napthoquinone compound.     

Four Novel Phenanthrene Derivatives with α-Glucosidase Inhibitory Activity from Gastrochilus bellinus

Four new phenanthrene derivatives, gastrobellinols A-D (1–4), were isolated from the methanolic extract of Gastrochilus bellinus (Rchb.f.) Kuntze, along with eleven known phenolic compounds including agrostophyllin (5), agrostophyllidin (6), coniferyl aldehyde (7), 4-hydroxybenzaldehyde (8), agrostophyllone (9), gigantol (10), 4-(methoxylmethyl)phenol (11), syringaldehyde (12), 1-(4′-hydroxybenzyl)-imbricartin (13), 6-methoxycoelonin (14), and imbricatin (15). Their structures were determined by spectroscopic methods. Each isolate was evaluated for α-glucosidase inhibitory activity. Compounds 1, 2, 3, 7, 9, 13, and 15 showed higher activity than the drug acarbose. Gastrobellinol C (3) exhibited the strongest α-glucosidase inhibition with an IC₅₀ value of 45.92 μM. A kinetic study of 3 showed competitive inhibition on the α-glucosidase enzyme. This is the first report on the phytochemical constituents and α-glucosidase inhibitory activity of G. bellinus.     

Novel Amphiphilic Block Copolymers for the Formation of Stimuli-Responsive Non-Lamellar Lipid Nanoparticles

Non-lamellar lyotropic liquid crystalline (LLC) lipid nanoparticles contain internal multidimensional nanostructures such as the inverse bicontinuous cubic and the inverse hexagonal mesophases, which can respond to external stimuli and have the potential of controlling drug release. To date, the internal LLC mesophase responsiveness of these lipid nanoparticles is largely achieved by adding ionizable small molecules to the parent lipid such as monoolein (MO), the mixture of which is then dispersed into nanoparticle suspensions by commercially available poly(ethylene oxide)–poly(propylene oxide) block copolymers. In this study, the Reversible Addition-Fragmentation chain Transfer (RAFT) technique was used to synthesize a series of novel amphiphilic block copolymers (ABCs) containing a hydrophilic poly(ethylene glycol) (PEG) block, a hydrophobic block and one or two responsive blocks, i.e., poly(4-(4,4,5,5-tetramethyl-1,3,2-dioxaborolan-2-yl)benzyl acrylate) (PTBA) and/or poly(2-(dimethylamino)ethyl methacrylate) (PDMAEMA). High throughput small angle X-ray scattering studies demonstrated that the synthesized ABCs could simultaneously stabilize a range of LLC MO nanoparticles (vesicles, cubosomes, hexosomes, inverse micelles) and provide internal particle nanostructure responsiveness to changes of hydrogen peroxide (H₂O₂) concentrations, pH and temperature. It was found that the novel functional ABCs can substitute for the commercial polymer stabilizer and the ionizable additive in the formation of next generation non-lamellar lipid nanoparticles. These novel formulations have the potential to control drug release in the tumor microenvironment with endogenous H₂O₂ and acidic pH conditions.     

Effect of Concentration on the Photophysics of Dyes in Light‐Scattering Materials.

Photoactive materials based on dye molecules incorporated into thin films or bulk solids are useful for applications as photosensitization, photocatalysis, solar cell sensitization and fluorescent labeling, among others. In most cases, high concentrations of dyes are desirable to maximize light absorption. Under these circumstances, the proximity of dye molecules leads to the formation of aggregates and statistical traps, which dissipate the excitation energy and lower the population of excited states. The search for enhancement of light collection, avoiding energy wasting requires accounting the photophysical parameters quantitatively, including the determination of quantum yields, complicated by the presence of light scattering when particulate materials are considered. In this work we summarize recent advances on the photophysics of dyes in light‐scattering materials, with particular focus on the effect of dye concentration. We show how experimental reflectance, fluorescence and laser‐induced optoacoustic spectroscopy data can be used together with theoretical models for the quantitative evaluation of inner filter effects, fluorescence and triplet formation quantum yields and energy transfer efficiencies.