Lexicodes over rings

In this paper, we consider the construction of linear lexicodes over finite chain rings by using a \(B\) -ordering over these rings and a selection criterion. As examples we give lexicodes over \(\mathbb Z _4\) and \(\mathbb F _2+u\mathbb F _2\) . It is shown that this construction produces many optimal codes over rings and also good binary codes. Some of these codes meet the Gilbert bound. We also obtain optimal self-dual codes, in particular the octacode.     

Spinor methods in conformal Killing transport

The equations of conformal Killing transport are discussed using tensor and spinor methods. It is shown that, in Minkowski space-time, the equations for a null conformal Killing vector ξ ^a are completely determined by the corresponding spinor ω ^A and its covariant derivative, which defines a spinor π _A′ . In conformally flat space-time, the covariant derivative of π _A′ is also involved. Some applications to twistor theory are briefly mentioned.     

Antioxidant oligomeric proanthocyanidins from Cistus salvifolius

The purified proanthocyanidin oligomers of Cistus salvifolius herb extract accounted for 78% of the total proanthocyanidins and 73% of the total antioxidant activity of this extract. To elucidate the structure of the oligomer, it was depolymerized by acid catalysis in the presence of phloroglucinol. The structures of the resulting flavan-3-ols and phloroglucinol adducts were determined on the basis of 1D- and reverse 2D-NMR (HSQC, HMBC) experiments of their peracetylated derivatives, MALDI-TOF-MS and CD spectroscopy. These observations resulting from the degradation with phloroglucinol were confirmed by 13C NMR spectroscopy of the oligomer. The mean molecular weight of the higher oligomeric fraction was estimated to be 5-6 flavan-3-ol-units.     

Two-step synthesis of the bipyrrole precursor of prodigiosins

The key intermediate in the synthesis of prodigiosins, 4-methoxy-2,2′-bipyrrole-5-carboxaldehyde, has been prepared in two steps and 65% overall yield from the commercially available 4-methoxy-3-pyrrolin-2-one.     

MDS and self-dual codes over rings

In this paper we give the structure of constacyclic codes over formal power series and chain rings. We also present necessary and sufficient conditions on the existence of MDS codes over principal ideal rings. These results allow for the construction of infinite families of MDS self-dual codes over finite chain rings, formal power series and principal ideal rings. We also define the Reed–Solomon codes over principal ideal rings.     

On self-dual cyclic codes over finite chain rings

In this paper, we give necessary and sufficient conditions for the existence of non-trivial cyclic self-dual codes over finite chain rings. We prove that there are no free cyclic self-dual codes over finite chain rings with odd characteristic. It is also proven that a self-dual code over a finite chain ring cannot be the lift of a binary cyclic self-dual code. The number of cyclic self-dual codes over chain rings is also investigated as an extension of the number of cyclic self-dual codes over finite fields given recently by Jia et al.     

On some classes of linear codes over $${\mathbb {Z}}_{2}{\mathbb {Z}}_{4}$$ and their covering radii

In this paper, we define the simplex and MacDonald codes of types \(\alpha \) and \(\beta \) over \({\mathbb {Z}}_{2}{\mathbb {Z}}_{4}\). We also examine the covering radii of these codes. Further, we study the binary images of these codes and prove that the binary image of the simplex codes of type \(\alpha \) meets the Gilbert bound.     

On codes over $$\mathbb {F}_{q}+v\mathbb {F}_{q}+v^{2}\mathbb {F}_{q}$$

In this paper we investigate linear codes with complementary dual (LCD) codes and formally self-dual codes over the ring \(R=\mathbb {F}_{q}+v\mathbb {F}_{q}+v^{2}\mathbb {F}_{q}\), where \(v^{3}=v\), for q odd. We give conditions on the existence of LCD codes and present construction of formally self-dual codes over R. Further, we give bounds on the minimum distance of LCD codes over \(\mathbb {F}_q\) and extend these to codes over R.     

Densities and Volumetric Properties of Binary and Ternary Mixtures of Diisopropyl Ether, Fluorobenzene, α,α,α-Trifluorotoluene, and Ethanol at Temperature 298.15 K and Pressure 101 kPa

Excess molar volumes of binary mixtures of (fluorobenzene + ethanol), (fluorobenzene + diisopropyl ether), (α,α,α-trifluorotoluene + ethanol), (diisopropyl ether + ethanol), (α,α,α-trifluorotoluene + diisopropyl ether), and the ternary mixtures of (fluorobenzene + diisopropyl ether + ethanol), and (α,α,α-trifluorotoluene + diisopropyl ether + ethanol) were evaluated from density data. The densities were measured with a vibrating-tube densimeter at the temperature 298.15 K and the pressure 101 kPa.The values of the mixing volumes of the ternary systems were predicted in terms of empirical equations using binary solution data alone. The extent of chemical associations among the molecules forming the mixtures is discussed.     

Eco-Friendly Methodology for the Formation of Aromatic Carbon–Heteroatom Bonds by Using Green Ionic Liquids

A new sustainable method is reported for the formation of aromatic carbon–heteroatom bonds under solvent-free and mild conditions (no co-oxidant, no strong acid and no toxic reagents) by using a new type of green ionic liquid. The bromination of methoxy arenes was chosen as a model reaction. The reaction methodology is based on only using natural sodium bromine, which is transformed into an electrophilic brominating reagent within an ionic liquid, easily prepared from the melted salt FeCl₃ hexahydrate. Bromination reactions with this in-situ-generated reagent gave good yields and excellent regioselectivity under simple and environmentally friendly conditions. To understand the unusual bromine polarity reversal of sodium bromine without any strong oxidant, the molecular structure of the reaction medium was characterised by Raman and direct infusion electrospray ionisation mass spectroscopy (ESI-MS). An extensive computational investigation using density functional theory methods was performed to describe a mechanism that suggests indirect oxidation of Br⁻ through new iron adducts. The versatility of the methodology was successively applied to nitration and thiocyanation of methoxy arenes using KNO₃ and KSCN in melted hexahydrated FeCl₃.