Two simple constant ratio approximation algorithms for minimizing the total weighted completion time on a single machine with a fixed non-availability interval

In this note, we consider the scheduling problem of minimizing the sum of the weighted completion times on a single machine with one non-availability interval on the machine under the non-resumable scenario. Together with a recent 2-approximation algorithm designed by Kacem [I. Kacem, Approximation algorithm for the weighted flow-time minimization on a single machine with a fixed non-availability interval, Computers & Industrial Engineering 54 (2008) 401–410], this paper is the first successful attempt to develop a constant ratio approximation algorithm for this problem. We present two approaches to designing such an algorithm. Our best algorithm guarantees a worst-case performance ratio of 2+ε$2+\epsilon$.     

Local flux mimetic finite difference methods

We develop a local flux mimetic finite difference method for second order elliptic equations with full tensor coefficients on polyhedral meshes. To approximate the velocity (vector variable), the method uses two degrees of freedom per element edge in two dimensions and n degrees of freedom per n-gonal mesh face in three dimensions. To approximate the pressure (scalar variable), the method uses one degree of freedom per element. A specially chosen quadrature rule for the L ²-product of vector-functions allows for a local flux elimination and reduction of the method to a cell-centered finite difference scheme for the pressure unknowns. Under certain assumptions, first-order convergence is proved for both variables and second-order convergence is proved for the pressure. The assumptions are verified on simplicial meshes for a particular quadrature rule that leads to a symmetric method. For general polyhedral meshes, non-symmetric methods are constructed based on quadrature rules that are shown to satisfy some of the assumptions. Numerical results confirm the theory.     

Streamlined access to 2,3-dihydropyrazino[1,2-a]indole-1,4-diones via Ugi reaction followed by microwave-assisted cyclization

An efficient method is developed to construct drug-like 2,3-dihydropyrazino[1,2-a]indole-1,4-diones from 1H-indole-2-carboxylic acids, ethyl pyruvate, isocyanides, and primary amines via a one-pot, two-step procedure involving Ugi reaction and microwave-assisted cyclization.     

Synthesis of fluorine containing glycolurils and oxazolines from oxides of internal perfluoroolefins

The reaction of oxides of internal perfluoroolefins 1-3 with urea gave two kinds of novel fluorine containing N-heterocyclic compounds depending on the solvent nature: 1,5-bis(perfluoroalkyl)tetraazabicyclo[3.3.0]octane-3,7-diones 4a-c and 2-amino-5-fluoro-4,5-bis(perfluoroalkyl)-4,5-dihydrooxazol-4-ols 7a-d. Use of polar dimethylsulfoxide, N,N-dimethylacetamide and acetonitrile afforded glycolurils 4a-c in moderate yields. In dioxane, unexpected cyclization occurred resulting in oxazolines 7a-d in high yields. A similar reaction of oxiranes 2, 3 with urea in aqueous dioxane gave mixtures of 4,5-dihydroxy-4,5-bis(perfluoroalkyl)imidazolidine-2-ones 9b, c, glycolurils 4b, c and oxazolines 7b-d. The molecular structure of trans-isomers of oxazoline 7b and imidazolidine 9b has been established by X-ray crystallography.     

ReALE: A reconnection-based arbitrary-Lagrangian–Eulerian method

We present a new reconnection-based arbitrary-Lagrangian–Eulerian (ALE) method. The main elements in a standard ALE simulation are an explicit Lagrangian phase in which the solution and grid are updated, a rezoning phase in which a new grid is defined, and a remapping phase in which the Lagrangian solution is transferred (conservatively interpolated) onto the new grid. In standard ALE methods the new mesh from the rezone phase is obtained by moving grid nodes without changing connectivity of the mesh. Such rezone strategy has its limitation due to the fixed topology of the mesh. In our new method we allow connectivity of the mesh to change in rezone phase, which leads to general polygonal mesh and allows to follow Lagrangian features of the mesh much better than for standard ALE methods. Rezone strategy with reconnection is based on using Voronoi tessellation. We demonstrate performance of our new method on series of numerical examples and show it superiority in comparison with standard ALE methods without reconnection.     

Solution of time-convolutionary Maxwell’s equations using parameter-dependent Krylov subspace reduction

We suggest a new algorithm for the solution of the time domain Maxwell equations in dispersive media. After spacial discretization we obtain a large system of time-convolution equations. Then this system is projected onto a small subspace consisting of the Laplace domain solutions for a preselected set of Laplace parameters. This approach is a generalization of the rational Krylov subspace approach for the solution of non-dispersive Maxwell’s systems. We show that the projected system preserves such properties of the initial system as stability and passivity. As an example we consider the 3D quasistationary induced polarization problem with the Cole–Cole conductivity model important for geophysical oil exploration. Our numerical experiments show that the introduction of the induced polarization does not have significant effect on convergence.     

BioCores: identification of a drug/natural product-based privileged structural motif for small-molecule lead discovery

The analysis of known drugs (Comprehensive Medicinal Chemistry database (2008 version): ) and natural products (Koch et al., Proc Natl Acad Sci USA 102:17272–17277, 2008) has led to the identification of privileged saturated and aromatic heterocyclic ring pairs that we have termed as “BioCores.” This article explains how the BioCores can be used for the design of novel lead-like scaffolds.     

Radiative decays of scalar mesons σ(600), f 0(980) and a 0(980) in the local Nambu-Jona-Lasinio model

The two-photon decay widths of scalar mesons σ(600), f ₀(980) and a ₀(980) as well a ₀ → ju(ω)γ and f ₀ → ju(ω)γ are calculated in the framework of the local Nambu-Jona-Lasinio model. The contributions of the quark loops (Hartree-Fock approximation) and the meson loops (next 1/N _c -approximation where N _c is the number of colors) are taken into account. The values of these contributions, as we show, are of the same order of magnitude. For the f ₀ decay the K-loop contribution plays the dominant role. The results for two-gamma decays are in satisfactory agreement with modern experimental data. The predictions for a ₀ → ju(ω)γ and f ₀ → ju(ω)γ widths are given.     

Mixed convection heat transfer of a nanofluid in a lid-driven enclosure with two adherent porous blocks

Journal of Thermal Analysis and Calorimetry - Convective flow and heat transfer in an alumina/water nanofluid enclosure having two centered adherent porous blocks under the effect of moving upper...     

Naphthalene derivatives of a conformationally locked GFP chromophore with large stokes shifts

The active development of fluorescence microscopy requires an increase in the variety of the dyes and their characteristics. Compounds with a large Stokes shift, i.e., a large difference between the positions of the absorption and emission maxima, have attracted the interest of researchers as a tool that can be used for multicolor labeling. One of the known approaches to increase the Stokes shift is the introduction of additional polycyclic fragments. Herein, we report novel derivatives of a conformationally locked GFP chromophore containing the naphthalene ring. The proposed modification leads not only to the enhancement of the Stokes shift up to 100 nm but also leads to the noticeable red-shift of the emission and absorption spectra in contrast with the corresponding derivatives with one benzene ring.