Maximizing the distance between center,centroid and characteristic set of a tree

Consider a tree P_n-g,g , n≥ 2, 1≤ g≤ n-1 on n vertices which is obtained from a path on [1,2,?…?,n-g] vertices by adding g pendant vertices to the pendant vertex n-g. We prove that over all trees on n?≥?5 vertices, the distance between center and characteristic set, centroid and characteristic set, and center and centroid is maximized by trees of the form P_n-g,g , 2?≤?g?≤?n-3. For n≥ 5, we also supply the precise location of the characteristic set of the tree P_n-g,g , 2?≤?g?≤?n-3.     

Photochemical Conjugation and One‐Pot Radiolabelling of Antibodies for Immuno‐PET

Monoclonal antibodies (mAbs), immunoglobulin fragments, and other proteins are important scaffolds in the development of radiopharmaceuticals for diagnostic immuno‐positron emission tomography (immuno‐PET) and targeted radioimmunotherapy (RIT). Conventional methods for radiolabelling proteins with metal ions such as ⁶⁸Ga, ⁶⁴Cu, ⁸⁹Zr, and ⁹⁰Y require multi‐step procedures involving pre‐purification, functionalisation with a chelate, and subsequent radiolabelling. Standard coupling chemistries are time‐consuming, difficult to automate, and involve synthesis, isolation, and storage of an intermediate, new molecular entity (the conjugated mAb) whose biochemical properties can differ from those of the parent protein. To circumvent these issues, we developed a photoradiochemical approach that uses fast, chemoselective, light‐induced protein modification under mild conditions with novel metal‐ion‐binding chelates derivatised with aryl azide (ArN₃) groups. Experiments show that one‐pot photochemical conjugation and radiolabelling of formulated mAbs can be achieved in <20 min.     

Room-Temperature Synthesis of Germanium Oxide Nanofilaments and Their Potential Use as Luminescent Self-Cleaning Surfaces

Germanium oxide nanofilaments (GNFs) have been synthesized under ambient conditions from the gas phase using germanium tetrachloride as a precursor. Non-crystalline GNFs synthesized by this procedure are 1–10 μm in length and 80–110 nm in diameter applying Droplet Assisted Growth and Shaping (DAGS) Chemistry. The relative humidity has been adjusted at various values in order to demonstrate the crucial role of humidity in the gas phase for the nanofilament synthesis. The novel GNFs show a strong luminescence emission in the ultra-violet and light blue region. In addition, a self-cleaning and superhydrophobic properties could be introduced in the luminescent GNF nanofilaments by simple treatment with silane molecules.     

Solvent- and Substrate-Induced Chiroptical Inversion in Amphiphilic,Biocompatible Glycoconjugate Supramolecules: Shape-Persistent Gelation,Self-Healing,and Antibacterial Activity

We have shown solvent- and substrate-dependent chiral inversion of a few glycoconjugate supramolecules. (Z)-F-Gluco, in which d -glucosamine has been attached chemically to Cbz-protected l -phenylalanine at the C terminus, forms a self-healing hydrogel through intertwining of the nanofibers wherein the gelators undergo lamellar packing in the β-sheet secondary structures with a single chiral handedness. Dihybrid (Z)-F-gluco nanocomposite gel was prepared by in-situ formation of silver nanoparticles AgNPs in the gel; this enhances the mechanical properties of the composite gel through physical crosslinking without altering the packing pattern. In contrast, (Z)-L-gluco bearing an l -leucine moiety does not form a hydrogel but an organogel. Interestingly, the chiral handedness of the aggregates of (Z)-L-gluco can be reversed by choosing suitable solvents. In addition to self-healing behavior, (Z)-L-gluco gel revealed shape persistency. Further, (Z)-F-gluco hydrogel is benign, nontoxic, non-immunogenic, and non-allergenic in animal cells. AgNP-loaded (Z)-F-gluco hydrogel showed antibacterial activity against both Gram-positive and Gram-negative bacteria.     

Water extract of red mud: an efficient and renewable medium for environmentally benign synthesis of 2-amino-4H-chromenes

Molecular Diversity - In this study, an efficient and convenient domino Michael addition/intramolecular cyclization protocol is presented for the synthesis of biologically relevant...     

Synthesis,X-ray crystal structure,DFT calculations,spectroscopic characterization and redox behaviour of a rhodium(III) complex of an anthracene–pyridylhydrazone ligand

Transition Metal Chemistry - A pyridylhydrazone incorporating an anthracene moiety, designated as HLAnc, has been synthesized in order to examine its coordination behaviour towards rhodium(III)....     

NHC-Pd complex heterogenized on graphene oxide for cross-coupling reactions and supercapacitor applications

N-heterocyclic carbene (NHC)-palladium(II) complex (GO@NHC-Pd) was synthesized on graphene oxide (GO) support via a simple and cost-effective multistep approach. The spectroscopic, microscopic, thermal, and surface analyses of GO@NHC-Pd confirmed the successful formation of the catalyst. The investigation of catalytic activity showed that GO@NHC-Pd was very effective in Suzuki–Miyaura as well as Hiyama cross-coupling. Being heterogeneous in nature, GO@NHC-Pd was recovered after each reaction cycle easily and reused for up to nine and six cycles in Suzuki–Miyaura and Hiyama cross-coupling, respectively, without significant loss of activity. Further exploration of the supercapacitor performance of GO@NHC-Pd catalyst assembled in a two-electrode cell configuration shown a maximum attained capacitance of 105.26 F/g at a current density of 0.1 A/g with good cycling stability of 96.89% over 2,500 cycles.     

Mechanical behaviour of a hydrogel film with embedded voids under the tensile load

The behaviour of alginate gel film in response to the tensile load is analysed in this paper. The bubbles of 0.5?mm diameter were embedded in the film by the fluidic method prior to gelation, thus providing uniform voidage over the entire film. Further, the intrinsic porosity of the gel matrix around the voids was varied by removing water through either evaporation under vacuum, or employing lyophilisation. The Poisson’s ratio and the modulus of elasticity were estimated from direct measurements. The viscoelasticity of the gel matrix was characterized from stress-relaxation measurement. The transient response to tensile loading and the evolution of stress contours were studied through numerical simulation in ANSYS. The ultimate strength was studied for the gel films with embedded voids of different sizes. The numerical simulations were validated by experimental measurements.

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