Enantioselective total synthesis of the potent anti-HIV nucleoside EFdA

A concise enantioselective total synthesis of 4'-ethynyl-2-fluoro-2'-deoxyadenosine (EFdA), an extremely potent anti-HIV agent, has been accomplished from (R)-glyceraldehyde acetonide in 18% overall yield by a 12-step sequence involving a highly diastereoselective ethynylation of an α-alkoxy ketone intermediate.     

Total synthesis of citridone A

The first total synthesis of citridone A has been achieved through regioselective intramolecular iodocyclization and regio- and stereoselective Pd(0)-catalyzed coupling as key reactions.     

1,5]-H shift of aldehyde hydrogen in dienal compounds to produce ketenes

In 3-ethoxycarbonyl-2,4-dienal compounds, a thermal [1,5]-H shift of aldehyde hydrogen easily proceeded to produce the corresponding vinyl ketenes due to the remarkable substituent effect caused by the C3 ester group. The produced ketenes were captured by an alcohol and olefins to afford the corresponding esters and four-membered ring compounds, respectively.     

Functionalization of a simple dithienylethene via palladium-catalyzed regioselective direct arylation

The direct arylation on the thienyl groups of a diarylethene with various aryl iodides efficiently provided arylated dithienylethenes under palladium catalysis. Unsymmetrically substituted dithienylethenes were also synthesized by this protocol. This procedure allows a rapid access to a variety of aryl-substituted dithienylethenes from a single substrate of a simple dithienylethene.     

High-throughput and simultaneous analysis of eight central-acting muscle relaxants in human plasma by ultra-performance liquid chromatography–tandem mass spectrometry in the positive and negative ionization modes

In this report, a high-throughput and sensitive method for analysis of eight central-acting muscle relaxants in human plasma by ultra-performance liquid chromatography–tandem mass spectrometry (UPLC-MS/MS) in the positive and negative ionization modes using tolbutamide as internal standard is presented. After pretreatment of a plasma sample by solid-phase extraction with an Oasis HLB cartridge, muscle relaxants were analyzed by UPLC with Acquity UPLC BEH C₁₈ column and Acquity TQD tandem quadrupole mass spectrometer equipped with an electrospray ionization interface. The calibration curves for muscle relaxants spiked into human plasma equally showed good linearities in the nanogram per milliliter order range. The detection limits (signal-to-noise ratio = 3) was as low as 0.1–2 ng/mL. The method gave satisfactory recovery rates, accuracy, and precision for quality control samples spiked with muscle relaxants. To further validate the present method, 250 mg of chlorphenesin carbamate was orally administered to a healthy male volunteer, and the concentrations of chlorphenesin carbamate in plasma were measured 0.5, 1, 2, 4, 6, and 8 h after dosing; their concentrations in human plasma were between 0.62 and 2.44 μg/mL. To our knowledge, this is the first report describing simultaneous analysis of over more than two central-acting muscle relaxants by liquid chromatography–tandem mass spectrometry. This has been realized by the capability of our instrument for simultaneous multiple reaction monitoring of the target compounds in both positive and negative ionization modes. Therefore, the present method seems very useful in forensic and clinical toxicology and pharmacokinetic studies.     

Reduction of the c-numerical range to the classical numerical range

Let A be an n×n complex matrix and c=(c₁,c₂,…,c_n) a real n-tuple. The c-numerical range of A is defined as the set

     

Construction of determinantal representation of trigonometric polynomials

For a pair of n×n Hermitian matrices H and K, a real ternary homogeneous polynomial defined by F(t,x,y)=det(tI_n+xH+yK) is hyperbolic with respect to (1,0,0). The Fiedler conjecture (or Lax conjecture) is recently affirmed, namely, for any real ternary hyperbolic polynomial F(t,x,y), there exist real symmetric matrices S₁ and S₂ such that F(t,x,y)=det(tI_n+xS₁+yS₂). In this paper, we give a constructive proof of the existence of symmetric matrices for the ternary forms associated with trigonometric polynomials.     

The boundary of higher rank numerical ranges

The rank-k-numerical range of an n×n matrix A is defined as

     

Abelian quotients of monoids of homology cylinders

A homology cylinder over a surface consists of a homology cobordism between two copies of the surface and markings of its boundary. The set of isomorphism classes of homology cylinders over a fixed surface has a natural monoid structure and it is known that this monoid can be seen as an enlargement of the mapping class group of the surface. We now focus on abelian quotients of this monoid. We show that both the monoid of all homology cylinders and that of irreducible homology cylinders are not finitely generated and moreover they have big abelian quotients. These properties contrast with the fact that the mapping class group is perfect in general. The proof is given by applying sutured Floer homology theory to homologically fibered knots studied in a previous paper.     

Principal points of a multivariate mixture distribution

A set of n-principal points of a distribution is defined as a set of n points that optimally represent the distribution in terms of mean squared distance. It provides an optimal n-point-approximation of the distribution. However, it is in general difficult to find a set of principal points of a multivariate distribution. Tarpey et al. [T. Tarpey, L. Li, B. Flury, Principal points and self-consistent points of elliptical distributions, Ann. Statist. 23 (1995) 103-112] established a theorem which states that any set of n-principal points of an elliptically symmetric distribution is in the linear subspace spanned by some principal eigenvectors of the covariance matrix. This theorem, called a “principal subspace theorem”, is a strong tool for the calculation of principal points. In practice, we often come across distributions consisting of several subgroups. Hence it is of interest to know whether the principal subspace theorem remains valid even under such complex distributions. In this paper, we define a multivariate location mixture model. A theorem is established that clarifies a linear subspace in which n-principal points exist.