The length function and matrix algebras

By the length of a finite system of generators for a finite-dimensional associative algebra over an arbitrary field we mean the least positive integer k such that words of length not exceeding k span this algebra (as a vector space). The maximum length for the systems of generators of an algebra is referred to as the length of the algebra. In the present paper, we study the main ring-theoretical properties of the length function: the behavior of the length under unity adjunction, direct sum of algebras, passage to subalgebras and homomorphic images. We give an upper bound for the length of the algebra as a function of the nilpotency index of its Jacobson radical and the length of the quotient algebra. We also provide examples of length computation for certain algebras, in particular, for the following classical matrix subalgebras: the algebra of upper triangular matrices, the algebra of diagonal matrices, the Schur algebra, Courter’s algebra, and for the classes of local and commutative algebras.     

Shining Light on the Secreted Luciferases of Marine Copepods: Current Knowledge and Applications

Copepod luciferases—a family of small secretory proteins of 18.4–24.3 kDa, including a signal peptide—are responsible for bright secreted bioluminescence of some marine copepods. The copepod luciferases use coelenterazine as a substrate to produce blue light in a simple oxidation reaction without any additional cofactors. They do not share sequence or structural similarity with other identified bioluminescent proteins including coelenterazine‐dependent Renilla and Oplophorus luciferases. The small size, strong luminescence activity and high stability, including thermostability, make secreted copepod luciferases very attractive candidates as reporter proteins which are particularly useful for nondisruptive reporter assays and for high‐throughput format. The most known and extensively investigated representatives of this family are the first cloned GpLuc and MLuc luciferases from copepods Gaussia princeps and Metridia longa, respectively. Immediately after cloning, these homologous luciferases were successfully applied as bioluminescent reporters in vivo and in vitro, and since then, the scope of their applications continues to grow. This review is an attempt to systemize and critically evaluate the data scattered through numerous articles regarding the main structural features of copepod luciferases, their luminescent and physicochemical properties. We also review the main trends of their application as bioluminescent reporters in cell and molecular biology.     

Vapour permeation and sorption in fluoropolymer gel membrane based on ionic liquid 1-ethyl-3-methylimidazolium bis(trifluoromethylsulphonyl)imide

The emissions of hydrocarbons from fossil fuels into atmosphere entail both an economic loss and an environmental pollution. Membrane separations can be used for vapour recovery and/or vapour removal from the permanent gas stream, given that the appropriate membrane is identified. A neat poly(vinylidene fluoride-co-hexafluoropropylene) membrane is impermeable to both the representatives of aliphatic hydrocarbons and branched hydrocarbons, namely hexane and isooctane, whereas the permeation flux is enhanced by the presence of 80 mass % of the ionic liquid 1-ethyl-3-methylimidazolium bis(trifluoromethylsulphonyl)imide in the membrane, as detailed in this work. The permeabilities of hydrocarbon vapours were determined from the binary mixture containing hydrocarbon and nitrogen to simulate the real input of an air stream containing a condensable hydrocarbon. The diffusion coefficient determined from sorption measurements was higher for hexane, as would be expected for a smaller molecule, whereas both the sorption isotherms and permeabilities of the hydrocarbons studied were found to be almost identical. It is possible that the sorption effect predominates in the transport mechanism for VOCs/N₂ separations.