Three-pencil lattices on triangulations

In this paper, three-pencil lattices on triangulations are studied. The explicit representation of a lattice, based upon barycentric coordinates, enables us to construct lattice points in a simple and numerically stable way. Further, this representation carries over to triangulations in a natural way. The construction is based upon group action of S ₃ on triangle vertices, and it is shown that the number of degrees of freedom is equal to the number of vertices of the triangulation.      

Parallel solution-phase synthesis of (Z)-3-(arylamino)-2,3-dehydroalanine derivatives and solid-phase synthesis of fused pyrimidones

N-Protected (Z)-3-(arylamino)-2,3-dehydroalanine esters 5 and 10 were prepared in one step from methyl (Z)-2-acylamino-3-(dimethylamino)prop-2-enoates 3 and 9 and anilines 4 employing a parallel solution-phase synthetic approach. In most cases, analytically pure products 5 and 10 were obtained. On the other hand, a three-step parallel solid-phase synthesis of 2-acetylamino-4H-azino[1,2-x]pyrimidin-4-ones 15 via the polymer-bound methyl (Z)-2-acetylamino-3-(dimethylamino)prop-2-enoate (12) was also developed.     

Enaminone‐Based Synthesis of Dipodazine Derivatives

A series of racemic dipodazine analogues 9 were prepared in 22–80% yield from (3Z,6RS)‐3‐[(dimethylamino)methylidene]‐6‐methyl‐1‐(phenylmethyl)piperazine‐2,5‐dione ( 7 ) (Scheme 1), which was prepared in four steps from (RS)‐alanine methyl ester hydrochloride. The preparation of nonracemic 7 from (S)‐alanine methyl ester hydrochloride failed, since the introduction of the enamino functionality at position 3 of the precursor 6 was accompanied by almost complete racemization.     

Implications of the LHCb evidence for charm CP violation

The LHCb collaboration recently announced preliminary evidence for CP violation in D meson decays. We discuss this result in the context of the standard model (SM), as well as its extensions. In the absence of reliable methods to evaluate the hadronic matrix elements involved, we can only estimate qualitatively the magnitude of the non-SM tree level operators required to generate the observed central value. In the context of an effective theory, we list the operators that can give rise to the measured CP violation and investigate constraints on them from other processes.     

Use of a fluorous bridge for diffusion controlled uptake of molecular chlorine in chlorine addition to alkenes

Fluorous solvent was used for passive transport of molecular chlorine from one side of the U-tube to the other, where addition of chlorine to alkenes was quantitative and diffusion controlled.     

Lattices on simplicial partitions

In this paper, (d+1)-pencil lattices on simplicial partitions in R^d are studied. The barycentric approach naturally extends the lattice from a simplex to a simplicial partition, providing a continuous piecewise polynomial interpolant over the extended lattice. The number of degrees of freedom is equal to the number of vertices of the simplicial partition. The constructive proof of this fact leads to an efficient computer algorithm for the design of a lattice.     

There is no (95, 40, 12, 20) strongly regular graph

We show that there is no (95, 40, 12, 20) strongly regular graph and, consequently, there is no (96, 45, 24, 18) strongly regular graph, no nontrivial regular two‐graph on 96 vertices, and no partial geometry pg(4, 9, 2). The main idea of the result is based on the star complement technique and requires a moderate amount of computation.