Is bismuth subsalicylate an effective nontoxic catalyst for plga synthesis?

Poly(d,l ‐lactide‐co‐glycolide) (PLGA) copolyesters are commonly used in biomedical applications. Researches were carried out on nontoxic or low‐toxic catalysts that are enough efficient to provide short polymerization times, adequate microstructure chains and similar properties than the commercial PLGA materials. In this study, PLGA were synthesized by ring‐opening copolymerization (ROP) using three different catalysts. Stannous octoate is the first catalyst we used, as it is very efficient, even its toxicity is still on debate. Two others low‐toxic catalysts [zinc lactate and bismuth subsalicylate (BiSS)] were also evaluated. The comparison of these ROP was realized in terms of kinetics and control of the polymerization. Then, the influence of the catalyst on the PLGA microstructure chains is reported. Finally, abiotic hydrolytic degradation rate is studied. Results described in this article show that BiSS is one very attractive catalyst to produce low toxic PLGA for biomedical applications. © 2014 Wiley Periodicals, Inc. J. Polym. Sci., Part A: Polym. Chem. 2014 , 52, 1130–1138     

Improved Bohr’s inequality for locally univalent harmonic mappings

We prove several improved versions of Bohr’s inequality for the harmonic mappings of the form $f=h+\overline{g}$, where $h$ is bounded by 1 and $\left|g^{\prime }\left(z\right)\right|\le \left|h^{\prime }\left(z\right)\right|$. The improvements are obtained along the lines of an earlier work of Kayumov and Ponnusamy, i.e. (Kayumov and Ponnusamy, 2018) for example a term related to the area of the image of the disk $D(0,r)$ under the mapping $f$ is considered. Our results are sharp. In addition, further improvements of the main results for certain special classes of harmonic mappings are provided.     

A generalization of the Leibnitz rule of successive differentiation

This note generalizes the well-known Leibnitz rule of successive differentiation for the product of two functions to a similar result for the product of three functions.     

Tuning the Reactivity of a Substrate for SNAP-Tag Expands Its Application for Recognition-Driven DNA-Protein Conjugation

Recognition-driven modification has been emerging as a novel approach to modifying biomolecular targets of interest site-specifically and efficiently. To this end, protein modular adaptors (MAs) are the ideal reaction model for recognition-driven modification of DNA as they consist of both a sequence-specific DNA-binding domain (DBD) and a self-ligating protein-tag. Coupling DNA recognition by DBD and the chemoselective reaction of the protein tag could provide a highly efficient sequence-specific reaction. However, combining an MA consisting of a reactive protein-tag and its substrate, for example, SNAP-tag and benzyl guanine (BG), revealed rather nonselective reaction with DNA. Therefore new substrates of SNAP-tag have been designed to realize sequence-selective rapid crosslinking reactions of MAs with SNAP-tag. The reactions of substrates with SNAP-tag were verified by kinetic analyses to enable the sequence-selective crosslinking reaction of MA. The new substrate enables the distinctive orthogonality of SNAP-tag against CLIP-tag to achieve orthogonal DNA-protein crosslinking by six unique MAs.     

The Almost Split Sequences for Trivial Extensions of Hereditary Algebras

Let A be a basic hereditary artin algebra and R = A Q be the trivial extension of A by its minimal injective cogenerator Q. We construct some right （left） almost split morphisms and irreducible morphisms in modR through the corresponding morphisms in modA. Furthermore, we can determine its almost split sequences in modR.     

RAFT polymerization of alternating styrene‐pentafluorostyrene copolymers

Reversible addition‐fragmentation chain‐transfer (RAFT) polymerization was used to control the alternating copolymerization of styrene and 2,3,4,5,6‐pentaflurostyrene. The RAFT polymerization yields a high degree of control over the molecular weight of the polymers and does not significantly influence the reactivity ratios of the monomers. The controlled free‐radical polymerization could be initiated using AIBN at elevated temperatures or using a redox couple (benzoyl peroxide/N,N‐dimethylaniline) at room temperature, while maintaining control over molecular weight and dispersity. The influence of temperature and solvent on the molecular weight distribution and reactivity ratios were investigated. © 2014 Wiley Periodicals, Inc. J. Polym. Sci., Part A: Polym. Chem. 2014 , 52, 1555–1559     

Strong approximation for ρ-mixing sequences

We establish strong invariance principles for sums of stationary ρ-mixing random variables with finite and infinite second moments under weaker mixing rates.Some earlier results are improved.As applications,some results of the law of the iterated logarithm with finite and infinite variance are obtained,also a conjecture raised by Shao in 1993 is solved.     

G-Frame and Riesz Sequences in Hilbert Spaces

G-frames generalize frames in Hilbert spaces. The literatures show that g-frames and frames share many similar properties, while they behave differently in redundancy and perturbation properties. Interestingly, g-frames have been extensively studied, but g-frame sequences have not. This problem is nontrivial since a g-frame and a frame both involve all vectors in the same Hilbert space, while a g-frame sequence and a frame sequence do not. They involve different linear spans. Using the synthesis and Gram matrix methods, we in this paper characterize g-frame sequences and g-Riesz sequences; obtain the Pythagorean theorem for g-orthonormal systems. These results recover several known results and lead to some new results on g-frames.