Context-free grammars for triangular arrays

We consider context-free grammars of the form G = {f → fb1+b2+1ga1+a2, g → fb1 ga1+1},where ai and bi are integers sub ject to certain positivity conditions. Such a grammar G gives rise to triangular arrays {T(n, k)}0≤k≤n satisfying a three-term recurrence relation. Many combinatorial sequences can be generated in this way. Let Tn (x) =∑nk=0T(n, k)xk. Based on the differential operator with respect to G, we define a sequence of linear operators Pn such that Tn+1(x) = Pn(Tn(x)). Applying the characterization of real stability preserving linear operators on the multivariate polynomials due to Borcea and Br?ndén, we obtain a necessary and sufficient condition for the operator Pn to be real stability preserving for any n. As a consequence, we are led to a sufficient condition for the real-rootedness of the polynomials defined by certain triangular arrays, obtained by Wang and Yeh.Moreover, as special cases we obtain grammars that lead to identities involving the Whitney numbers and the Bessel numbers.     

Are accurate computations of the 13C′ shielding feasible at the DFT level of theory?

The goal of this study is twofold. First, to investigate the relative influence of the main structural factors affecting the computation of the ¹³C′ shielding, namely, the conformation of the residue itself and the next nearest‐neighbor effects. Second, to determine whether calculation of the ¹³C′ shielding at the density functional level of theory (DFT), with an accuracy similar to that of the ¹³C^α shielding, is feasible with the existing computational resources. The DFT calculations, carried out for a large number of possible conformations of the tripeptide Ac‐G XY ‐NMe, with different combinations of X and Y residues, enable us to conclude that the accurate computation of the ¹³C′ shielding for a given residue X depends on the: (i) (?,ψ) backbone torsional angles of X ; (ii) side‐chain conformation of X ; (iii) (?,ψ) torsional angles of Y ; and (iv) identity of residue Y . Consequently, DFT‐based quantum mechanical calculations of the ¹³C′ shielding, with all these factors taken into account, are two orders of magnitude more CPU demanding than the computation, with similar accuracy, of the ¹³C^α shielding. Despite not considering the effect of the possible hydrogen bond interaction of the carbonyl oxygen, this work contributes to our general understanding of the main structural factors affecting the accurate computation of the ¹³C′ shielding in proteins and may spur significant progress in effort to develop new validation methods for protein structures. © 2013 Wiley Periodicals, Inc.     

Resilient quantum computation in correlated environments: a quantum phase transition perspective

We analyze the problem of a quantum computer in a correlated environment protected from decoherence by quantum error correction using a perturbative renormalization group approach. The scaling equation obtained reflects the competition between the dimension of the computer and the scaling dimension of the correlations. For an irrelevant flow, the error probability is reduced to a stochastic form for a long time and/or a large number of qubits; thus, the traditional derivation of the threshold theorem holds for these error models. In this way, the "threshold theorem" of quantum computing is rephrased as a dimensional criterion.     

Identification of Semiconductive Patches in Thermally Processed Monolayer Oxo‐Functionalized Graphene

The thermal decomposition of graphene oxide (GO) is a complex process at the atomic level and not fully understood. Here, a subclass of GO, oxo‐functionalized graphene (oxo‐G), was used to study its thermal disproportionation. We present the impact of annealing on the electronic properties of a monolayer oxo‐G flake and correlated the chemical composition and topography corrugation by two‐probe transport measurements, XPS, TEM, FTIR and STM. Surprisingly, we found that oxo‐G, processed at 300 °C, displays C?C sp³‐patches and possibly C?O?C bonds, next to graphene domains and holes. It is striking that those C?O?C/C?C sp³‐separated sp²‐patches a few nanometers in diameter possess semiconducting properties with a band gap of about 0.4 eV. We propose that sp³‐patches confine conjugated sp²‐C atoms, which leads to the local semiconductor properties. Accordingly, graphene with sp³‐C in double layer areas is a potential class of semiconductors and a potential target for future chemical modifications.     

Enynones in organic synthesis. I. Spiroannulation by tandem oxy-cope rearrangement-electrocyclic ring closure

Bis-acetylenic alcohols of proper design undergo a facile oxy-Cope rearrangement to afford mixtures of E- and Z-enynones. These latter compounds afford methylenecyclopentenones upon enolization and electrocyclic ring closure.     

N-Acetylneuraminic Acid: Neoglycoproteins and Pseudopolysaccharides

Abstract

A simplified procedure for the synthesis of acetochloroneuraminic acid is described starting from the methyl ester. N-acetyl neuraminic acid α-allyl glycoside was prepared in high yield using silver salicylate as catalyst. Reductive ozonolysis of the allyl group, followed by direct reductive ami nation to protein carriers, gave immunogenic neoglycoproteins. Copolymerization of the α-allyl glycoside with acrylamide produced a water-soluble pseudopolysaccharide useful for the EL ISA technique.     

Efficient and library-friendly synthesis of furo- and thieno[2,3-d] pyrimidin-4-amine derivatives by microwave irradiation

A new, divergent, efficient, and selective synthesis of furo- and thieno[2,3-d]pyrimidin-4-amine derivatives by microwave irradiation has been developed starting from readily available amines and substituted 2-aminofuran-3-carbonitrile or 2-aminothiophene-3-carbonitrile, which are converted into corresponding formamidines in DMF using benzenesulfonyl chloride.     

The periodic table and the intrinsic barrier in s(n)2 reactions

The identity S(N)2 reactions on nitrogen (see eq 3) with nucleophiles having the general structure H(n)()X(-) where X belongs to the group of nonmetallic elements which do not border the line separating them from the metallic elements (X = F, Cl, Br, I, O, S, Se, N, P, and C) were studied at the G2+ level. The results show that, similarly to the previously observed phenomenon for S(N)2 reaction on carbon (J. Am. Chem. Soc. 1999, 121, 7724), the Periodic Table, through the valence of the element X, controls the intrinsic barrier for the reaction. The average intrinsic barriers obtained for nitrogen substrates were 20, 27, 39, and 57 kcal/mol for the mono-, di-, tri-, and tetravalent X's, respectively. It is also concluded that the intrinsic barriers are similar for N- and C-based substrates and dimethyl substitution on both raises the intrinsic barrier by ca. 10 kcal/mol.