GK dimension of the relatively free algebra for sl_2

Let \(sl_2(K)\) be the Lie algebra of the \(2\times 2\) traceless matrices over an infinite field \(K\) of characteristic different from 2, denote by \(R_m= R_m(sl_2(K))\) the relatively free (also called universal) algebra of rank \(m\) in the variety of Lie algebras generated by \(sl_2(K).\) In this paper we compute the Gelfand–Kirillov dimension of the Lie algebra \(R_m(sl_2(K)).\) It turns out that whenever \(m\ge 2\) one has \(\mathrm{GK}\dim R_m = 3(m-1).\) In order to compute it we use the explicit form of the Hilbert series of \(R_m\) described by Drensky. This result is new for \(m>2\) ; the case \(m=2\) was dealt with by Bahturin in 1979.     

Algorithms and Identities for(q,h)-Bernstein Polynomials and(q,h)-Bézier Curves–A Non-Blossoming Approach

We establish several fundamental identities,including recurrence relations,degree elevation formulas,partition of unity and Marsden identity,for quantum Bernstein bases and quantum Bézier curves.We also develop two term recurrence relations for quantum Bernstein bases and recursive evaluation algorithms for quantum Bézier curves.Our proofs use standard mathematical induction and other elementary techniques.     

-identities for the Grassmann algebra: The conjecture of Henke and Regev

Let be an algebraically closed field of characteristic 0, and let be the infinite dimensional Grassmann (or exterior) algebra over . Denote by the vector space of the multilinear polynomials of degree in , ..., in the free associative algebra . The symmetric group acts on the left-hand side on , thus turning it into an -module. This fact, although simple, plays an important role in the theory of PI algebras since one may study the identities satisfied by a given algebra by applying methods from the representation theory of the symmetric group. The -modules and are canonically isomorphic. Letting be the alternating group in , one may study and its isomorphic copy in with the corresponding action of . Henke and Regev described the -codimensions of the Grassmann algebra , and conjectured a finite generating set of the -identities for . Here we answer their conjecture in the affirmative.

     

Enhanced in-source fragmentation in MALDI-TOF-MS of oligonucleotides using 1,5-diaminonapthalene

The capability to rapidly and confidently determine or confirm the sequences of short oligonucleotides, including native and chemically-modified DNA and RNA, is important for a number of fields. While matrix-assisted laser desorption/ionization (MALDI) time-of-flight (TOF) mass spectrometry (MS) has been used previously to sequence short oligonucleotides, the typically low fragmentation efficiency of in-source or post-source decay processes necessitates the accumulation of a large number of spectra, thus limiting the throughput of these methods. Here we introduce a novel matrix, 1,5-diaminonapthalene (DAN), for facile in-source decay (ISD) of DNA and RNA molecular anions, which allows for rapid sequence confirmation. d-, w-, and y-series ions are prominent in the spectra, complementary to the (a-B)- and w- ions that are typically produced by MALDI post-source decay (PSD). Results are shown for several model DNA and RNA oligonucleotides, including combinations of DAN-induced fragmentation with true tandem TOF MS (MS/MS) for pseudo-MS³ and “activated-ion PSD.”     

Synthesis of Coenzyme Q<Subscript>10</Subscript> and β-carotene by Yeasts Isolated from Antarctic Soil and Lichen in Response to Ultraviolet and Visible Radiations

The effect of different doses of visible (Vis), ultraviolet-А (UVA), and mixed light (UVA + Vis) upon coenzyme Q₁₀ (CoQ₁₀) and β-carotene synthesis and biomass yield by the Sporobolomyces salmonicolor AL₁, Cryptococcus albidus AS₅₅, Cryptococcus laurentii AS₅₆, and C. laurentii AS₅₈ strains isolated from Antarctic samples was investigated. The β-carotene concentration in the red strain biomass increased by 52% under irradiation with 11 J/cm² Vis, and the CoQ₁₀ concentration rose by 37% in relation to the control quantity obtained through dark cultivation. Under irradiation with 6 J/cm² UVA, the S. salmonicolor AL₁ strain synthesized 15% more β-carotene; C. albidus AS₅₅, 22%; C. laurentii AS₅₆, 44%; and C. laurentii AS₅₈, 35% in relation to the control quantity. Irradiation with a low UVА + Vis dose significantly stimulated β-carotene biosynthesis by the strains of the Cryptococcus genus (87%, 138%, and 100%), whereas S. salmonicolor AL₁ increased the β-carotene content to a smaller degree (55%). Higher doses of all three irradiation types inhibited β-carotene accumulation. Vis suppressed CoQ₁₀ biosynthesis in the Cryptococcus strains, whereas UVА and UVА + Vis inhibited it in all four strains. The S. salmonicolor AL₁ strain pre-treated with 0.02 J/cm² UVA synthesized twice as much CoQ₁₀ and β-carotene when cultivated in the presence of Vis light in an 11-J/cm² dose.     

Linearizing non-linear inverse problems and an application to inverse backscattering

We propose an abstract approach to prove local uniqueness and conditional Hölder stability to non-linear inverse problems by linearization. The main condition is that, in addition to the injectivity of the linearization A, we need a stability estimate for A as well. That condition is satisfied in particular, if A^∗A is an elliptic pseudo-differential operator. We apply this scheme to show uniqueness and Hölder stability for the inverse backscattering problem for the acoustic equation near a constant sound speed.     

Electrochemical DNA Hybridization Assay: Enzyme‐Labeled Detection of Mutation in p53 Gene

This paper discusses a new electrochemical DNA hybridization sensing approach based on the detection of a linked enzyme label. In this method we employ enzyme that is attached to a tethered ssDNA oligomer on the surface and the target analyte is a complementary ssDNA oligomer that does not require any pre‐treatment. The advantage of using of enzyme label is in its amplification of the registration of the hybridization event due to the catalytic reaction facilitated in the process. One particular novelty is associated with the use of enzymes that directly communicate with the electrode surface thus allowing for minimizing the need of additional reagents in the assay. The electrochemical assay was demonstrated when using mixed self‐assembled monolayers from thiolated oligonucleotide and 6‐mercapto 1‐hexanol on gold surfaces. Horseradish peroxidase (HRP) is attached to the surface tethered oligonucleotide using streptavidin‐biotin chemistry, and the enzyme successfully established direct electron transfer (DET) with the electrode or mediated electron transfer (MET) using a mediator. Hybridization results in increasing the angle of contact between electrode and DNA and also the stiffness of the ds DNA, which results in displacing the enzyme away from the electrode surface, and thereby reducing the occurrence of direct electron transfer between the enzyme and the electrode. The cyclic voltammetry showed a clear distinction in response between the complete complementary sequence and the two‐base mismatch sequence. Ellipsometric measurements show that the thickness of the thiol modified oligonucleotide on gold surfaces changes before and after hybridization for the complementary sequence, where as a minimal change in thickness was observed for the noncomplementary sequence. The model target analyte in this study was TP53 gene where a specific mutation is a marker for a list of cancers. Mutations of the TP53 gene have been demonstrated in tumors of the colon, breast, lung, ovary, bladder, and many other organs. Analysis of p53 mutations may provide useful information for the diagnosis, prognosis and therapy of cancer.     

Platinum group metal-free Fe-based (FeNC) oxygen reduction electrocatalysts for direct alcohol fuel cells

In direct alcohol fuel cells (DAFCs), the oxidation of alcohols happens at the expenses of the oxygen reduction reaction at the cathode. DAFCs' cathodes use a significant amount of platinum that is an expensive critical raw material. Moreover, platinum oxidizes alcohols, a fact that combined with alcohol crossover, decreases significantly the performance of the cells. The use of Fe-based (FeNC) platinum group metal–free (PGM-free) cathodes is a convenient strategy to overcome these limitations. This review analyzes the application of PGM-free cathodes to DAFCs. The discussion focuses on acidic systems and covers the following subjects: (i) the breakdown of DAFC potential in its components, (ii) the analysis of the advantages from the use of the PGM-free cathode, and (iii) a review of the performance and durability of DAFCs. The review closes with a view of the authors of the future perspective for the research.