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.     

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.     

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.     

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.      

Alpha-substituted organic peroxides: synthetic strategies for a biologically important class of gem-dihydroperoxide and perketal derivatives

In this paper we review the recent developments in the synthesis of alpha-substituted hydroperoxides. Alpha-substituted hydroperoxides are interesting compounds due to their chemistry and bioactivity and as intermediates for the synthesis of other peroxides, of which cyclic peroxides are of major importance. Although the emphasis of this report will be on the derivatives of gem-dihydroperoxides, perketals, as well as the less studied nitrogen and sulfur derivatives, will also be covered.     

Infrared spectrum of 4-methoxypicolinic acid N-oxide: computation of asymmetric O-H stretching band

In this article we studied the strong intramolecularly hydrogen-bonded system 4-methoxypicolinic acid N-oxide. The potential energy surface V = V(rOH,rOO) and the corresponding dipole moment function were calculated using the DFT B3LYP/6-31+G(d,p) level of approximation. The time-independent vibrational Schr?dinger equation was solved using a rectangular grid basis set and shifted Gaussian basis set. The vibrational spectrum and metric parameters were also calculated. Effects of deuteration were considered. The calculated vibrational spectra were compared with the experimental spectra. The vibrational transition corresponding to asymmetric O-H stretching that occurs at about 1400 cm-1 compares well with the experimentally assigned O-H asymmetric stretching band centered at 1380 cm-1. The corresponding asymmetric O-D stretching band was predicted to be at 1154 cm-1, while the experimental O-D band was not assigned due to its very low intensity. Several overtones and hot transitions of significant intensities were located in the vicinity of the fundamental O-H stretching frequency, effectively broadening the infrared absorption attributed to the O-H stretching mode. This is in a good agreement with the observed broad protonic absorptions found in the infrared spectra of the title compound and its analogs. We have shown that the Gaussian basis set is the method of choice for a two-dimensional vibrational problem that requires several hundreds of vibrational basis functions and when high accuracy of the eigenvalues is required or when extending the calculations to more vibrational degrees of freedom. We have also demonstrated that for a large number of basis functions the Gramm-Schmidt orthogonalization procedure outperforms symmetric and canonical orthogonalization schemes.