Recovery of An Unknown Flux in Parabolic Problems with Nonstandard Boundary Conditions: Error Estimates

In this paper, we consider a 2nd order semilinear parabolic initial boundary value problem (IBVP) on a bounded domain ^N, with nonstandard boundary conditions (BCs). More precisely, at some part of the boundary we impose a Neumann BC containing an unknown additive space-constant (t), accompanied with a nonlocal (integral) Dirichlet side condition.We design a numerical scheme for the approximation of a weak solution to the IBVP and derive error estimates for the approximation of the solution u and also of the unknown function .     

Hydrogenation of poly(myrcene) and poly(farnesene) using diimide reduction at ambient pressure

Ambient pressure chemical hydrogenation using p-toluene sulfonyl hydrazide (TSH) via thermal diimide formation (N₂H₂) permitted reduction of double bonds of poly(myrcene) (poly[Myr]) and poly(farnesene) (poly[Far]). Both pendent and backbone double bonds in poly(Myr) (M_n = 56 kg/mol) and poly(Far) (M_n = 62 kg/mol) synthesized by conventional free radical polymerization were hydrogenated to almost completion. Furthermore, TSH semi-batch addition efficiently hydrogenated double bonds, while avoiding undesired autohydrogenation of diimides that occurred in batch mode. Thermal stability improved for hydrogenated poly(Myr) and poly(Far), where temperature at 10% weight loss (T_10%) increased from 188 to 404°C for poly(Myr) and from 310 to 379°C for poly(Far). T_gs of poly(Myr) and poly(Far) also increased by about 10–25°C, indicating increased stiffness after hydrogenation. Finally, viscosities of poly(Myr) and poly(Far) were also increased after hydrogenation, and a greater increase was observed for poly(Myr) (by two orders of magnitude from 10² to 10⁴ Pa s) due to its M_n being much higher than its entanglement molecular weight. Poly(Far) viscosity only increased by 1.5 times after hydrogenation (~10⁴ Pa s), comparable to the poly(Myr) after hydrogenation, suggesting unsaturated poly(Far) was more entangled than unsaturated poly(Myr) because of its longer side chains.     

Utilization of carbohydrates by radiation processing

Upgrading and utilization of carbohydrates such as chitosan, sodium alginate, carrageenan, cellulose, pectin have been investigated for recycling these bio-resources and reducing the environmental pollution. These carbohydrates were easily degraded by irradiation and various kinds of biological activities such as anti-microbial activity, promotion of plant growth, suppression of heavy metal stress, phytoalexins induction, etc. were induced. On the other hand, some carbohydrate derivatives, carboxymethylcellulose and carboxymethylstarch, could be crosslinked under certain radiation condition and produce the biodegradable hydrogel for medical and agricultural use.     

Molecular dynamics study of solubilization of cyclohexane,benzene, and phenol into mixed micelles composed of sodium dodecyl sulfate and octaethylene glycol monododecyl ether

Molecular dynamics calculations of a mixed micelle composed of sodium dodecyl sulfate (SDS) and octaethylene glycol monododecyl ether (C₁₂E₈) were performed for six compositions (SDS/C₁₂E₈ = 100/0, 80/20, 60/40, 40/60, 20/80, and 0/100) to investigate the composition dependence of the mixed micelle structure and solubilization of cyclohexane, benzene, and phenol molecules by the micelle. The radial density distribution of the hydrophilic polyoxyethylene (POE) group of C₁₂E₈ as a function of distance from the micelle center is very sharp for micelles with high SDS content because the POE group captures a Na⁺ ion in solution and wraps around it to form a compact crown-ether-like complex. The hydrophobic dodecyl groups of SDS and C₁₂E₈ were separately distributed in the mixed micelle core. ΔG(r) evaluated for each solute showed that despite the structural changes of the micelle the binding strength of the solute molecules to the micelle did not change significantly. © 2019 Wiley Periodicals, Inc.     

Biopolymer Skeleton Produced by Rhizobium radiobacter: Stoichiometric Alternation of Glycosidic and Amidic Bonds in the Lipopolysaccharide O‐Antigen

The lipopolysaccharide (LPS) O‐antigen structure of the plant pathogen Rhizobium radiobacter strain TT9 and its possible role in a plant‐microbe interaction was investigated. The analyses disclosed the presence of two O‐antigens, named Poly1 and Poly2. The repetitive unit of Poly2 constitutes a 4‐α‐l ‐rhamnose linked to a 3‐α‐d ‐fucose residue. Surprisingly, Poly1 turned out to be a novel type of biopolymer in which the repeating unit is formed by a monosaccharide and an amino‐acid derivative, so that the polymer has alternating glycosidic and amidic bonds joining the two units: 4‐amino‐4‐deoxy‐3‐O‐methyl‐d ‐fucose and (2′R,3′R,4′S)‐N‐methyl‐3′,4′‐dihydroxy‐3′‐methyl‐5′‐oxoproline). Differently from the O‐antigens of LPSs from other pathogenic Gram‐negative bacteria, these two O‐antigens do not activate the oxidative burst, an early innate immune response in the model plant Arabidopsis thaliana, explaining at least in part the ability of this R. radiobacter strain to avoid host defenses during a plant infection process.     

Synthesis of C12-Keto Saxitoxin Derivatives with Unusual Inhibitory Activity Against Voltage-Gated Sodium Channels

A novel series of C12-keto-type saxitoxin (STX) derivatives bearing an unusual nonhydrated form of the ketone at C12 has been synthesized, and their Na_V-inhibitory activity has been evaluated in a cell-based assay as well as whole-cell patch-clamp recording. Among these compounds, 11-benzylidene STX ( 3 a ) showed potent inhibitory activity against neuroblastoma Neuro 2A in both cell-based and electrophysiological analyses, with EC₅₀ and IC₅₀ values of 8.5 and 30.7 nm , respectively. Interestingly, the compound showed potent inhibitory activity against tetrodotoxin-resistant subtype of Na_V1.5, with an IC₅₀ value of 94.1 nm . Derivatives 3 a – d and 3 f showed low recovery rates from Na_V1.2 subtype (ca 45–79 %) compared to natural dcSTX ( 2 ), strongly suggesting an irreversible mode of interaction. We propose an interaction model for the C12-keto derivatives with Na_V in which the enone moiety in the STX derivatives 3 works as Michael acceptor for the carboxylate of Asp¹⁷¹⁷.     

Fast multipole method for three-dimensional systems with periodic boundary condition in two directions

We derived a new expression for the electrostatic interaction of three-dimensional charge-neutral systems with two-dimensional periodic boundary conditions (slab geometry) using a fast multipole method (FMM). Contributions from all the image cells are expressed as a sum of real and reciprocal space terms, and a self-interaction term. The reciprocal space contribution consists of two parts: zero and nonzero terms of the absolute value of the reciprocal lattice vector. To test the new expressions, electrostatic interactions were calculated for a randomly placed charge distribution in a cubic box and liquid water produced by molecular dynamics calculation. The accuracy could be controlled by the degree of expansion of the FMM. In the present expression, the computational complexity of the electrostatic interaction of N-particle systems is order N, which is superior to that of the conventional two-dimensional periodic Ewald method for a slab geometry and the particle mesh Ewald method with a large empty space at an interface of the unit cell. © 2020 Wiley Periodicals, Inc.     

Enhanced optical sensing of anions with amide-functionalized gold nanoparticles

A gold nanoparticle surface-modified with amide ligands shows enhanced optical sensing of anions: the detection limit is increased by about three orders of magnitude higher than that originally expected from the anion binding ability of neutral amide ligands.     

Salicylaldoxime in manganese(III) carboxylate chemistry: Synthesis, structural characterization and physical studies of hexanuclear and polymeric complexes

The use of salicylaldehyde oxime (H₂salox) in manganese(III) carboxylate chemistry has yielded new members of the family of hexanuclear compounds presenting the [Mn₆(μ₃-O)₂(μ₂-OR)₂]¹²⁺ core, complexes [Mn^III₆(μ₃-O)₂(O₂CPh)₂(salox)₆(L₁)₂(L₂)₂] (L₁ = py, L₂ = H₂O (1); L₁ = Me₂CO, L₂ = H₂O (2); L₁ = L₂ = MeOH (3)). Addition of NaOMe to the acetonitrile reaction mixture, afforded the 1D complex [Mn^III₃Na(μ₃-O)(O₂CPh)₂(salox)₃(MeCN)]_n (4), whereas addition of NaClO₄ to the acetone reaction mixture afforded an analogous 1D complex [Mn^III₃Na(μ₃-O)(O₂CPh)₂(salox)₃(Me₂CO)]_n (5). The structures of 1–3 present the [Mn₆(μ₃-O)₂(μ₂-OR)₂]¹²⁺ core and can be described as two [Mn₃(μ₃-O)]⁷⁺ triangular subunits linked by two μ₂-oximato oxygen atoms of the salox²⁻ ligands, which show the less common μ₃-κ²O:κO′:κN coordination mode. The benzoato ligands are coordinated through the usual syn,syn-μ₂-κO:κO′ mode. The 1D polymeric structures of 4 and 5 consist of alternating [Mn₃(μ₃-O)]⁷⁺ subunits and Na⁺ atoms linked through two μ₃-κ²O:κO′:κN and one μ₄-κ²O:κ²O′:κN salox²⁻ ligands as well as one syn,anti-μ₂-κO:κO′ benzoato ligand. DC and AC magnetic susceptibility studies on 1 revealed the stabilization of an S = 4 ground state, and indications of single-molecule magnetism behavior, whereas the DC experimental data from polycrystalline sample of 5 are indicative of antiferromagnetic interactions within the [Mn₃] subunit. Solid state ¹H NMR data of 1 were used to probe the spin-lattice relaxation of the system.