Reaction of [Cp12W2O5] with mercaptocarboxylic acids: Addition rather than reduction. Isolation and characterization of Cp1WO2(SCH2CH2COOH)

The reaction of Cp¹₂W₂O₅ with HS(CH₂)_nCOOH (n = 1, 2) in MeOH or in CH₂Cl₂ solutions at room temperature proceeds in slightly different ways depending on the value of n. For n = 2, it selectively yields compound Cp¹WO₂(SCH₂CH₂CO₂H), which has been isolated and characterized by elemental analysis, NMR and single crystal X-ray diffraction. The reaction is equilibrated, being shifted to the product by absorption of water by anhydrous Na₂SO₄ in CH₂Cl₂, and to the reactants by addition of water. Contrary to the Mo analogue, no products resulting from metal reduction are obtained. The corresponding reaction for n = 1 occurs similarly at low substrate/W ratios (<0.5), but proceeds further to several uncharacterized products for greater substrate amounts. The primary product could not be isolated, but its ¹H NMR spectrum suggests a different, asymmetric structure.     

N-acylbenzotriazole mediated microwave assisted synthesis of protected and novel unprotected ferrocenoylamidoamino acids

In this study, crystalline and chirally stable carboxyl-protected and novel unprotected N-ferrocenoyl amino acid derivatives of Ser, Cys, Ala, Phe, Trp, Asp and Asn have been prepared. These amino acids undergo substitution reaction with 1-(ferrocenylcarbonyl)-1H-benzotriazole, 1, in partially aqueous media under microwave irradiation.     

Speciation of [Cp*2M2O5] in Polar and Donor Solvents

The speciation of compounds [Cp*₂M₂O₅] (M=Mo, W; Cp*=pentamethylcyclopentadienyl) in different protic and aprotic polar solvents (methanol, dimethyl sulfoxide, acetone, acetonitrile), in the presence of variable amounts of water or acid/base, has been investigated by ¹H NMR spectrometry and electrical conductivity. Specific hypotheses suggested by the experimental results have been further probed by DFT calculations. The solvent (S)‐assisted ionic dissociation to generate [Cp*MO₂(S)]⁺ and [Cp*MO₃]^? takes place extensively for both metals only in water/methanol mixtures. Equilibrium amounts of the neutral hydroxido species [Cp*MO₂(OH)] are generated in the presence of water, with the relative amount increasing in the order MeCN≈acetone<MeOH<DMSO. Addition of a base (Et₃N) converts [Cp*₂M₂O₅] into [Et₃NH]⁺[Cp*MO₃]^?, for which the presence of a N? H???O?M interaction is revealed by ¹H NMR spectroscopy in comparison with the sodium salts, Na⁺[Cp*MO₃]^?. These are fully dissociated in DMSO and MeOH, but display a slow equilibrium between free ions and the ion pair in MeCN and acetone. Only one resonance is observed for mixtures of [Cp*MO₃]^? and [Cp*MO₂(OH)] because of a rapid self‐exchange. In the presence of extensive ionic dissociation, only one resonance is observed for mixtures of the cationic [Cp*MO₂(S)]⁺ product and the residual undissociated [Cp*₂M₂O₅] because of a rapid associative exchange via the trinuclear [Cp*₃M₃O₇]⁺ intermediate. In neat methanol, complex [Cp*₂W₂O₅] reacts to yield extensive amounts of a new species, formulated as the mononuclear methoxido complex [Cp*WO₂(OMe)] on the basis of the DFT study. An equivalent product is not observed for the Mo system. The addition of increasing amounts of water results in the rapid decrease of this product in favor of [Cp*₂W₂O₅] and [Cp*WO₂(OH)].     

On the additive cyclic structure of quasi-cyclic codes

An index $?$, length $m?$ quasi-cyclic code can be viewed as a cyclic code of length $m$ over the field ${\mathbb{F}}_{q^{?}}$ via a basis of the extension ${\mathbb{F}}_{q^{?}}∕{\mathbb{F}}_q$. However, this cyclic code is only linear over ${\mathbb{F}}_q$, making it an additive cyclic code, or an ${\mathbb{F}}_q$-linear cyclic code, over the alphabet ${\mathbb{F}}_{q^{?}}$. This approach was recently used in Shi et al. (2017) [16] to study a class of quasi-cyclic codes, and more importantly in Shi et al. (2017) [17] to settle a long-standing question on the asymptotic performance of cyclic codes. Here, we answer one of the problems posed in these two articles, and characterize those quasi-cyclic codes which have ${\mathbb{F}}_{q^{?}}$-linear cyclic images under a basis of the extension ${\mathbb{F}}_{q^{?}}∕{\mathbb{F}}_q$. Our characterizations are based on the module structure of quasi-cyclic codes, as well as on their CRT decompositions into constituents. In the case of a polynomial basis, we characterize the constituents by using the theory of invariant subspaces of operators. We also observe that analogous results extend to the case of quasi-twisted codes.     

Effect of titanium source on structural properties and acidity of Ti-pillared bentonite

Ti-pillared bentonites (Ti-PBs) were synthesised using bentonite from the Hanç?l? region in Turkey. Ti(IV) chloride, Ti(IV) ethoxide and Ti(IV) propoxide were used as the titanium sources; the syntheses were carried out using different H⁺/Ti ratios, bentonite suspension percentages and calcination temperatures. Titanium was found in the form of titanium dioxide for all the sources. The Ti(IV) chloride source afforded a sample with a significantly higher specific BET surface area (by 323 m² g^?1), TiO₂ content of 50.5 mass % and a more microporous structure with a micropore volume of 0.112 cm³ g^?1; the Ti(IV) propoxide source afforded a more mesoporous structure with a higher total pore volume. The micropore region showed the formation of pores of different sizes, while prominent narrow peaks were obtained in the mesopore region. Ti-PBs, which exhibited only the anatase phase of titanium dioxide, yielded high Brønsted and Lewis acidities. When the rutile phase and the anatase phase occurred together, as a result of the lower TiO₂ content, the Brønsted and Lewis acidities of the Ti-PBs decreased. The use of Ti(IV) chloride and Ti(IV) propoxide sources at H⁺/Ti ratios of 4.0 and a bentonite suspension percentage of 2.0 resulted in samples exhibiting strong Brønsted acidity.     

Rough convergence of double sequences of fuzzy numbers

In this paper, we define the concepts of rough convergence and rough Cauchy sequence of double sequences of fuzzy numbers. Then, we investigate some relations between rough limit set and extreme limit points of such sequences.