A second order numerical scheme for the solution of the one-dimensional Boussinesq equation

A predictor–corrector (P-C) scheme is applied successfully to a nonlinear method arising from the use of rational approximants to the matrix-exponential term in a three-time level recurrence relation. The resulting nonlinear finite-difference scheme, which is analyzed for local truncation error and stability, is solved using a P-C scheme, in which the predictor and the corrector are explicit schemes of order 2. This scheme is accelerated by using a modification (MPC) in which the already evaluated values are used for the corrector. The behaviour of the P-C/MPC schemes is tested numerically on the Boussinesq equation already known from the bibliography free of boundary conditions. The numerical results are derived for both the bad and the good Boussinesq equation and conclusions from the relevant known results are derived.      

Small molecules as inhibitors of cyclin-dependent kinases

Cell division (mitosis) is one of the basic requirements for multicellular oranisms. The capability of a cell to replicate enables a complex assembly to be created. Faulty regulation of the control mechanism in the cell cycle leads to an excessive cell proliferation and is the cause of cancer. The key position of the cyclin-dependent kinases (CDKs) and their direct partners, as well as the fact that the majority of malign illnesses show defects in at least one of these key players of the cell cycle, is of great interest for the development of low-molecular-weight CDK inhibitors. In this Review an overview of the different structural classes of ATP-competitive inhibitors of CDKs are given, whose devlopment was aimed at battling cancer. The Review shows how far the development of selective CDK inhibitors has progressed and to what extent the expectations for such drugs have so far been fulfilled.     

o-Phenylene halocarbenonitrenes and o-phenylene chlorocarbenocarbene: a combined experimental and computational approach

[reaction: see text] Computations find that o-phenylene(halo)carbenonitrenes 2-XN, X = F, Cl, Br, have quinoidal singlet biradical ground states such as the parent o-phenylenecarbenonitrene (2-HN). Compared to the parent 2-HN, halogen substitution stabilizes the A' states relative to the A' ones. Halogen substitution also affects the barrier and exothermicity of the ring-opening reaction (to form unsaturated nitriles 4-XN, X = F, Cl, Br), but it has a smaller effect on the ring-closing reaction (to form benzo(aza)cyclobutadiene 3-XN, X = F, Cl, Br). Attempts to generate and observe the o-phenylene(halo)carbenonitrenes 2-XN, X = F, Cl, Br, using matrix isolation spectroscopy under conditions similar to those of the successful observation of 2-HN failed. Instead, the observed photoproducts were a mixture of 3-XN and 4-XN. In each case, the major product of the mixture appears to be the thermodynamically more stable one. In the case of X = Br, the observed mixture contains an additional component that is postulated to be Z-6-BrN. o-Phenylenechlorocarbenocarbene is also computed to have a quinoidal singlet biradical ground state and relatively stabilized A' excited states. Attempts to generate the biscarbene under matrix isolation conditions led to the detection of benzochlorocyclobutadiene (3-ClC), small amounts of the ring-open product (dienediyne 4-ClC), and cycloalkyne 5-ClC. Computations suggest that the formation of 5-ClC implies the generation of Z-6-ClC, which is analogous to the formation of Z-6-BrN from 2-BrN.     

Singlet hydrocarbon carbenes with high barriers toward isomerization: a computational investigation

A prerequisite for a stable singlet hydrocarbon carbene is the existence of high barriers toward isomerization. Four derivatives of cyclopentylidene (1-4) with rigid and varying carbon cages are examined computationally at the B3LYP/6-311+G(d,p) level of theory. Singlet ground states are predicted for carbenes 1-4, with DeltaE(ST)'s = 7-22 kcal/mol. The rearrangement paths considered are 1,3-hydrogen shift, 1,2-carbon shift and beta-CC bond-cleavage. Carbenes 3 and 4 lie in relatively shallow potential-energy wells (around 4 and 6 kcal/mol, respectively) and are expected to rearrange via 1,3-hydrogen shifts to cyclopropane derivatives. For 1 and 2, the lowest energy rearrangement path is beta-CC bond-cleavage requiring about 12 and 20 kcal/mol, respectively, placing 2 in the deepest potential-energy well among the four carbenes.     

Data hiding based on image texture classification

In this paper, a new pattern-based fragile, semi-blind, spatial domain data hiding scheme is proposed. The Local Binary Pattern texture classification approach is used, in order to transparently and securely embed secret data into an image. Pixel values are modified in such a way that the texture satisfies the message requirements. The method is thoroughly studied and compared to other techniques in spatial domain in terms of capacity and image quality. The scheme performs well in images with smooth areas and can be used for authentication, tamper proofing, and secret communications.