Hexanes/acetonitrile: a binary solvent system for the efficient monosilylation of symmetric primary and secondary diols

Symmetric diols are useful compounds in the synthesis of natural products, their value often dependent on their successful monoprotection. A general and simple method for the monosilylation of symmetrical primary and secondary diols is reported. The method exploits the solubility differential of diols and their monosilylated counterparts in a binary hexanes/acetonitrile solvent system.     

On weighted spectral radius of unraveled balls and normalized Laplacian eigenvalues

For a graph G, the unraveled ball of radius r centered at a vertex v is the ball of radius r centered at v in the universal cover of G. We obtain a lower bound on the weighted spectral radius of unraveled balls of fixed radius in a graph with positive weights on edges, which is used to present an upper bound on the $s^{\text{th}}$ (where $s\ge 2$) smallest normalized Laplacian eigenvalue of irregular graphs under minor assumptions. Moreover, when $s=2$, the result may be regarded as an Alon–Boppana type bound for a class of irregular graphs.     

Connected cubic s-arc-regular Cayley graphs of finite nonabelian simple groups

A graph is said to be s-arc-regular if its full automorphism group acts regularly on the set of its s-arcs. In this paper, we investigate connected cubic s-arc-regular Cayley graphs of finite nonabelian simple groups. Two suffcient and necessary conditions for such graphs to be 1- or 2-arc-regular are given and based on the conditions, several infinite families of 1-or 2-arc-regular cubic Cayley graphs of alternating groups are constructed.     

Super-symmetric informationally complete measurements

Symmetric informationally complete measurements (SICs in short) are highly symmetric structures in the Hilbert space. They possess many nice properties which render them an ideal candidate for fiducial measurements. The symmetry of SICs is intimately connected with the geometry of the quantum state space and also has profound implications for foundational studies. Here we explore those SICs that are most symmetric according to a natural criterion and show that all of them are covariant with respect to the Heisenberg–Weyl groups, which are characterized by the discrete analog of the canonical commutation relation. Moreover, their symmetry groups are subgroups of the Clifford groups. In particular, we prove that the SIC in dimension 2, the Hesse SIC in dimension 3, and the set of Hoggar lines in dimension 8 are the only three SICs up to unitary equivalence whose symmetry groups act transitively on pairs of SIC projectors. Our work not only provides valuable insight about SICs, Heisenberg–Weyl groups, and Clifford groups, but also offers a new approach and perspective for studying many other discrete symmetric structures behind finite state quantum mechanics, such as mutually unbiased bases and discrete Wigner functions.     

Determination of asymmetric and symmetric dimethylarginines in human plasma by HPLC with electrochemical detection

A new HPLC method was developed and validated for the determination of asymmetric and symmetric dimethylarginines and l ‐arginine in human plasma. After SPE and evaporation of the eluate, the samples were derivatised with an o‐phthaldialdehyde reagent containing 3‐mercaptopropionic acid. The derivatives formed were analysed by isocratic RP‐HPLC with electrochemical detection at +320 mV. The mobile phase consisted of 50 mM phosphate buffer (pH 6.1) containing 10% v/v acetonitrile, the flow rate was 1 mL/min. The retention times of all compounds including monomethylarginine (internal standard) were <24 min. The LODs (S/N 3:1) were 0.012 μM for both dimethylarginines and 0.013 μM for l ‐arginine; the linearity of the method was from 0.1 to 20 μM for both dimethylarginines and from 1 to 200 μM for l ‐arginine. Absolute extraction recoveries measured for all analytes ranged from 85 to 88%.