Left dihedral codes over finite chain rings

Let R be a finite commutative chain ring, $D_{2n}$ be the dihedral group of size 2n and $R[D_{2n}]$ be the dihedral group ring. In this paper, we completely characterize left ideals of $R[D_{2n}]$ (called left $D_{2n}$-codes) when $\gcd (char(R),n)=1$. In this way, we explore the structure of some skew-cyclic codes of length 2 over R and also over $R\times S$, where S is an isomorphic copy of R. As a particular result, we give the structure of cyclic codes of length 2 over R. In the case where $R={\mathbb{F}}_{p^m}$ is a Galois field, we give a classification for left $D_{2N}$-codes over ${\mathbb{F}}_{p^m}$, for any positive integer N. In both cases we determine dual codes and identify self-dual ones.     

Chiral separation of lansoprazole and rabeprazole by capillary electrophoresis using dual cyclodextrin systems

Novel capillary electrophoresis methods using CDs as chiral selectors were developed and validated for the chiral separation of lansoprazole and rabeprazole, two proton pump inhibitors. Fourteen different neutral and anionic CDs were screened at pH 4 and 7 in the preliminary analysis. Sulfobutyl‐ether‐β‐CD with a degree of substitution of 6.5 and 10 at neutral pH proved to be the most suitable chiral selector for both compounds. Various dual CD systems were also compared, and the possible mechanisms of enantiomer separation were investigated. A dual selector system containing sulfobutyl‐ether‐β‐CD degree of substitution 6.5 and native γ‐CD proved to be the most adequate system for the separations. Method optimization was carried out using an experimental design approach, performing an initial fractional factorial screening design, followed by a central composite design to establish the optimal analytical conditions. The optimized methods (25 mM phosphate buffer, pH 7, 10 mM sulfobutyl‐ether‐β‐CD/20 mM γ‐CD, +20 kV voltage; 17°C temperature; 50 mbar/3 s injection, detection at 210 nm for lansoprazole; 25 mM phosphate buffer, pH 7, 15 mM sulfobutyl‐ether‐β‐CD/30 mM γ‐CD, +20 kV voltage; 18°C temperature; 50 mbar/3 s injection, detection at 210 nm for rabeprazole) provided baseline separation for lansoprazole (R_s = 2.91) and rabeprazole (R_s = 2.53) enantiomers with favorable migration order (in both cases the S‐enantiomers migrates first). The optimized methods were validated according to current guidelines and proved to be reliable, linear, precise, and accurate for the determination of 0.15% distomer as chiral impurity in dexlansoprazole and dexrabeprazole samples.     

Increasing the antioxidant capability via the synergistic effect of coupling diphenylamine with sterically hindered phenol

A series of novel diphenylamine-phenol antioxidants were synthesised that combined the two antioxidant types into a single molecule. These antioxidants were then functionalised with alkyl chains to aid their solubility in hydrocarbon media. As part of a structure-activity study, diphenylamine derivatives were also generated bearing carboxylic acid functionalities in either the ortho, meta or para position with respect to the secondary amine. Methyl or ethyl spacers were also incorporated between the carboxylic acid and the aromatic ring. The antioxidant ability of the diphenylamine-phenols was evaluated using Differential Scanning Calorimetry (DSC) and compared to commercially available antioxidants Irganox L135 and Irganox L57 both as individual components and when blended together. The diphenylamine-phenol antioxidant with an ethyl spacer between the diphenylamine and carboxylic acid in the meta position with respect to the secondary amine functionality showed an impressive oxidation induction time of ca. 24 min in direct comparison with the blend of Irganox L135 and Irganox L57 (ca. 16 min).     

A ratio-metric fluorescent sensor design platform with red emission of Europium(III) as built-in fluorescence correction

A Eu^III-containing single molecule BCR-Eu as design platform for ratio-metric fluorescent sensor which includes a blue-emitting coumarin dye, a green-emitting BODIPY fluorophore and a Eu^III moiety as the origin of red light has been designed and synthesized. The compound BCR shows only green emission with large stoke shift when excited in 400 nm due to good fluorescence resonance energy transfer from coumarin to BODIPY. After embedding Eu^III complexes in the molecule, BCR-Eu exhibits dual emission which is equal in magnitude and independent of each other, when excited at the range of 305–365 nm. An emission from Lanthanide complexes as the stable built-in standard fluorescence peak offers a promising opportunity to enhance the precision of bioimaging and also an ideal design platform for future ratio-metric fluorescent sensor.     

Local linear convergence analysis of Primal–Dual splitting methods

In this paper, we study the local linear convergence properties of a versatile class of Primal–Dual splitting methods for minimizing composite non-smooth convex optimization problems. Under the assumption that the non-smooth components of the problem are partly smooth relative to smooth manifolds, we present a unified local convergence analysis framework for these methods. More precisely, in our framework, we first show that (i) the sequences generated by Primal–Dual splitting methods identify a pair of primal and dual smooth manifolds in a finite number of iterations, and then (ii) enter a local linear convergence regime, which is characterized based on the structure of the underlying active smooth manifolds. We also show how our results for Primal–Dual splitting can be specialized to cover existing ones on Forward–Backward splitting and Douglas–Rachford splitting/ADMM (alternating direction methods of multipliers). Moreover, based on these obtained local convergence analysis result, several practical acceleration techniques are discussed. To exemplify the usefulness of the obtained result, we consider several concrete numerical experiments arising from fields including signal/image processing, inverse problems and machine learning. The demonstration not only verifies the local linear convergence behaviour of Primal–Dual splitting methods, but also the insights on how to accelerate them in practice.     

The dual code of any (δ+αu2)-constacyclic code over F2m[u]∕〈u4〉 of oddly even length

Let ${\mathbb{F}}_{2^m}$ be a finite field of cardinality $2^m$, $R={\mathbb{F}}_{2^m}\left[u\right]∕〈u^4〉={\mathbb{F}}_{2^m}+u{\mathbb{F}}_{2^m}+u^2{\mathbb{F}}_{2^m}+u^3{\mathbb{F}}_{2^m}$ $(u^4=0)$ which is a finite chain ring, and $n$ is an odd positive integer. For any $\delta ,\alpha \in {\mathbb{F}}_{2^m}^{\times }$, an explicit representation for the dual code of any $(\delta +\alpha u^2)$-constacyclic code over $R$ of length $2n$ is given. And some dual codes of $(1+u^2)$-constacyclic codes over $R$ of length 14 are constructed. For the case of $\delta =1$, all distinct self-dual $(1+\alpha u^2)$-constacyclic codes over $R$ of length $2n$ are determined.     

An efficient approach for dual sourcing inventory systems with Tailored Base-Surge policies

Nowadays most companies use dual sourcing strategies to manage supply chains. Recently, a practical policy called the Tailored Base-Surge (TBS) policy has been proposed to manage the system, and shown to perform well. We study a dual sourcing inventory system with i.i.d. demands and TBS policies. Using the techniques of MacLaurin series analysis, we develop an efficient method to calculate the moments of the inventory position, the bullwhip effect, and performance measures. Numerical experiments show that our method works well.