Radon measure-valued solutions of nonlinear strongly degenerate parabolic equations

We prove the existence of suitably defined weak Radon measure-valued solutions of the homogeneous Dirichlet initial-boundary value problem for a class of strongly degenerate quasilinear parabolic equations. We also prove that: \((i)\) the concentrated part of the solution with respect to the Newtonian capacity is constant; \((ii)\) the total variation of the singular part of the solution (with respect to the Lebesgue measure) is nonincreasing in time. Conditions under which Radon measure-valued solutions of problem \((P)\) are in fact function-valued (depending both on the initial data and on the strength of degeneracy) are also given.     

Ambazone salt with p-aminobenzoic acid

In this study, we obtained a novel salt of ambazone (AMB) with p-aminobenzoic acid (PABA) that exhibits improved solubility and antibacterial activity. The salt was produced by solvent-drop grinding and characterized by powder X-ray diffraction, thermal analysis and Fourier transform infrared spectroscopy. The salt nature of the new form was confirmed by infrared spectroscopy based on the characteristic vibrational band of the protonated amino group. Based on the X-ray powder diffraction data, the compound crystallizes in the triclinic P_-1 space group with the following unit cell parameters: a = 14.294 Å, b = 9.162 Å, c = 8.777 Å, α = 95.90°, β = 100.63°, γ = 91.73°. Thermal analysis reveals the thermal events and different decomposition steps of this solid form as compared to the starting compounds. Powder dissolution measurements showed solubility improvement compared with pure ambazone of 2 and 3.3 times in water and phosphate buffer, respectively. Antibacterial tests showed higher activity of the salt to Gram-negative Escherichia coli and Salmonella bacteria as compared to AMB and PABA. The study demonstrates that the pharmaceutical salt of ambazone with p-aminobenzoic acid (AMB–PABA) can be a possible alternative to ambazone in the treatment of infections with Gram-negative bacteria.     

Some classes of operators with symbol on the Lipschitz space of a tree

In this paper, we expand the study of the multiplication operators on the Lipschitz space of a tree begun in Colonna and Easley (Integral Equ Oper Theory 68:391–411, 2010) by focusing on their adjoint acting on a certain separable subspace of the Lipschitz space whose dual is isometrically isomorphic to \(\mathbf L^1\). We then study the properties of two useful operators \(\nabla \) and \(\Delta \) and use them (along with the multiplicative symbol \(\psi \)) to define the Toeplitz operator \(T_\psi \) on the space \(\mathbf L^p\) for \(1\le p \le \infty \). We give conditions for its boundedness and study its point spectrum.     

Synthesis of a Benzannulated Pyrrolizidine by a Copper‐Catalyzed Intramolecular α‐Arylation Reaction

A synthetic route to the pyrrolo[1,2‐a]indole ring system (benzannulated pyrrolizidine) involving a base‐induced intramolecular aza‐Michael reaction as the key C? N bond‐forming penultimate step, followed by a Cu‐catalyzed intramolecular α‐arylation reaction, to provide the tricyclic framework over six steps is described.     

Chemical basis of peptidoglycan discrimination by PrkC, a key kinase involved in bacterial resuscitation from dormancy

Bacterial Ser/Thr kinases modulate a wide number of cellular processes. In Bacillus subtilis , the Ser/Thr kinase PrkC has been shown to induce germination of bacterial spores in response to DAP-type but not Lys-type cell wall muropeptides. Muropeptides are a clear molecular signal that growing conditions are promising, since they are produced during cell wall peptidoglycan remodeling associated with cell growth and division of neighboring bacteria. However, whether muropeptides are able to bind the protein physically and how the extracellular region is able to distinguish the two types of muropeptides remains unclear. Here we tackled the important question of how the extracellular region of PrkC (EC-PrkC) senses muropeptides. By coupling NMR techniques and protein mutagenesis, we exploited the structural requirements necessary for recognition and binding and proved that muropeptides physically bind to EC-PrkC through DAP-moiety-mediated interactions with an arginine residue, Arg500, belonging to the protein C-terminal PASTA domain. Notably, mutation of this arginine completely suppresses muropeptide binding. Our data provide the first molecular clues into the mechanism of sensing of muropeptides by PrkC.     

Photophysical and Primary Self-Referencing Thermometric Properties of Europium Hydrogen-Bonded Triazine Frameworks

Lanthanide hydrogen-bonded organic frameworks (LnHOFs) are recently emerging as a novel versatile class of multicomponent luminescent materials with promising potential applications in optics and photonics. Trivalent europium (Eu³⁺) incorporated polymeric hydrogen-bonded triazine frameworks (PHTF:Eu) have been successfully obtained via a facile and low-cost thermal pyrolysis route. The PHTF:Eu material shows a porous frame structure principally composed of isocyanuric acid and ammelide as a minor constituent. Intense red luminescence with high colour-purity from Eu³⁺ is obtained by exciting over a broad absorption band peaked at 300 nm either at room or low temperature. The triazine-based host works as excellent optical antenna towards Eu³⁺, yielding ~42% sensitization efficiency (η_sens) and an intrinsic quantum yield of Eu³⁺ emission (Φ_Eu) as high as ~46%. Temperature-dependent emission studies show that PHTF:Eu displays relatively high optical stability at elevated temperatures in comparison to traditional inorganic phosphors. The retrieved activation energy of 89 meV indicates that thermal quenching mechanisms are attributed to the intrinsic energy level structure of the metal-triazine assembly, possibly via a thermally activated back transfer to ligand triplet or CT states. Finally, by using an innovative approach based on excitation spectra, we demonstrate that PHTF:Eu can work as a universal primary self-referencing thermometer based on a single-emitting center with excellent relative sensitivity in the cryogenic temperature range.     

Optimization of a 2D photonic crystal add/drop multiplexer based on contra-directional coupling

We present a highly integrated add/drop multiplexer, where the contra-directional coupling is realized by phase matching two photonic crystal waveguides. The device band structure, the corresponding transmission and drop spectra, and the coupling length are carefully analysed. Different device configurations are discussed and by tailoring the coupling factor, we optimize the frequency response of the filter, obtaining a -sized channel selector, characterized by a very high drop efficiency.     

Structural features responsible for GFPuv and S147P-GFP’s improved fluorescence

Green fluorescent protein (GFP) is used as a biological marker. It is a protein in the jellyfish, Aequorea victorea, which is found in the cold Pacific Northwest. Mature GFP, i.e. fully fluorescent GFP, is most efficiently formed at temperatures well below 37 °C. The GFPuv (F99S/M153T/V163A) and S147P-GFP mutants mature more efficiently at room temperature than wild-type GFP, and therefore result in increased fluorescence at room temperature. Computational methods have been used to examine whether the low-energy precyclized forms of these improved GFP-mutants are preorganized so that they can more efficiently form the chromophore than the wild-type and S65T-GFP. All mutations examined (S147P, F99S, M153T, V163A and F99S/M153T/V163A) more efficiently preorganize the immature precyclized forms of GFP for chromophore formation than immature wild-type GFP. It has been proposed that Arg96 is involved in chromophore formation. Our calculations suggest that the M153T and V163A mutations in GFPuv maybe partially responsible for the increased maturation efficiency observed in GFPuv because they improve the Arg96–Tyr66 interaction. The same is true for the S147P mutation in S147P-GFP.     

Bi-Sobolev mappings with differential matrices in Orlicz Zygmund classes

Bi-Sobolev mappings have been defined as those homeomorphisms such that f and f−1 belong to . We deduce regularity properties of the distortion of f from the regularity of the differential matrix Df−1 and conversely.