Modeling of the glycine tripeptide cyclization in the Ser65Gly/Tyr66Gly mutant of green fluorescent protein

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Reductions on equivalence relations generated by universal sets

Let X, Y be Polish spaces, , . We say A is universal for Γ provided that each x‐section of A is in Γ and each element of Γ occurs as an x‐section of A. An equivalence relation generated by a set is denoted by , where . The following results are shown:

• (1) If A is a set universal for all nonempty closed subsets of Y, then is a equivalence relation and .
• (2) If A is a set universal for all countable subsets of Y, then is a equivalence relation, and
  • (i) and ;
  • (ii) if , then ;
  • (iii) if every set is Lebesgue measurable or has the Baire property, then .
  • (iv) for , if every set has the Baire property, and E is any equivalence relation, then .

     

Graphs are (1,Δ+1)-choosable

A graph $G$ is $(k,k^{\prime })$-choosable if the following holds: For any list assignment $L$ which assigns to each vertex $v$ a set $L\left(v\right)$ of $k$ real numbers, and assigns to each edge $e$ a set $L\left(e\right)$ of $k^{\prime }$ real numbers, there is a total weighting $?:V\left(G\right)\cup E\left(G\right)\to R$ such that $?\left(z\right)\in L\left(z\right)$ for $z\in V\cup E$, and ${\sum }_{e\in E\left(u\right)}?\left(e\right)+?\left(u\right)\ne {\sum }_{e\in E\left(v\right)}?\left(e\right)+?\left(v\right)$ for every edge $uv$. This paper proves that if $G$ is a connected graph of maximum degree $\Delta \ge 2$, then $G$ is $(1,\Delta +1)$-choosable.     

Syntheses of chiral fused 4,5-diazafluorene–bis(nopinane) derivatives

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Cyclometallated 1,2,3-triazol-5-ylidene iridium(III) complexes: synthesis,structure, and photoluminescence properties

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Binuclear copper(II) complex with 2-imidazolylbenzothiazole and bridged chloride ligands

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Separation technique based on electrophoresis,chromatography and magnetism phenomena: the migration time and peak broadening

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Light-intensity switch enabled nonsynchronous growth of fluorinated raspberry-like nanoparticles

Raspberry-like (RB) nanoparticles hold potential for diverse applications due to their hierarchical morphology. Here we developed a novel tandem synthetic approach of nonsynchronous growth based on photo-mediated reversible-deactivation radical polymerization, enabling simple, efficient and bottom-up synthesis of RB nanoparticles of uniform sizes at quantitative conversions of fluorinated monomers. Chain transfer agents of different chain lengths, concentrations and chemical compositions were varied to tune the diameter of RB particles. Importantly, fluorinated RB nanoparticles obtained with this method allow facile post modifications via both covalent bond formation and intermolecular physical interactions without disrupting the RB morphology. The facile nature of this method and versatility of the obtained fluorinated RB materials open new opportunities for the development of functional materials using nanoparticles.

Nonsynchronous growth of raspberry-like (RB) nanoparticles in a one-pot and bottom-up fashion, enabling simple post-modification of RB colloids through both covalent bond formation and supramolecular interaction.