Di­chloro­bis(1,2‐phenyl­enedi­amine)­nickel(II)

The title compound, [NiCl₂(C₆H₈N₂)₂], contains centrosymmetric mol­ecules with two phenyl­ene­di­amine ligands coordinated in a bidentate fashion. The Ni—N distances are 2.088 (1) and 2.096 (1) Å, and the Ni—Cl distance of 2.4635 (4) Å. The plane of each phenyl­enedi­amine mol­ecule makes a dihedral angle of 26.53 (7)° with the NiN₄ plane. Extensive hydrogen bonding leads to distinct cleavage in the bc plane.     

A novel metal iodide promoted three-component synthesis of substituted pyrrolidines

[reaction: see text] A new one-pot procedure for the synthesis of substituted pyrrolidine derivatives with commercially available cyclopropyl ketones, aldehydes, and amines by a metal iodide promoted three-component reaction was developed.     

Cultivating <Emphasis Type="BoldItalic">Chlorella</Emphasis> sp. in a Pilot-Scale Photobioreactor Using Centrate Wastewater for Microalgae Biomass Production and Wastewater Nutrient Removal

This study is concerned with a novel mass microalgae production system which, for the first time, uses “centrate”, a concentrated wastewater stream, to produce microalgal biomass for energy production. Centrate contains a high level of nutrients that support algal growth. The objective of this study was to investigate the growth characteristics of a locally isolated microalgae strain Chlorella sp. in centrate and its ability to remove nutrients from centrate. A pilot-scale photobioreactor (PBR) was constructed at a local wastewater treatment plant. The system was tested under different harvesting rates and exogenous CO₂ levels with the local strain of Chlorella sp. Under low light conditions (25 μmol·m^-2s^-1) the system can produce 34.6 and 17.7 g·m^-2day^-1 biomass in terms of total suspended solids and volatile suspended solids, respectively. At a one fourth harvesting rate, reduction of chemical oxygen demand, total Kjeldahl nitrogen, and soluble total phosphorus were 70%, 61%, and 61%, respectively. The addition of CO₂ to the system did not exhibit a positive effect on biomass productivity or nutrient removal in centrate which is an organic carbon rich medium. The unique PBR system is highly scalable and provides a great opportunity for biomass production coupled with wastewater treatment.     

Stereoselective approaches to 2,3,6-trisubstituted piperidines. An enantiospecific synthesis of quinolizidine (-)-217A

The enantiospecific and diastereocontrolled total synthesis of alkaloid (-)-217A is described that employs a stepwise [3+3] annelation strategy and a piperidine 2,3-cyclopropanation-ring opening reaction as the key steps.     

Perturbation and bifurcation in a free boundary problem

We study the equation with a discontinuous nonlinearity: ?Δu = λH(u ? 1) (H is Heaviside's unit function) in a square subject to various boundary conditions. We expect to find a curve dividing the harmonic (Δu = 0) region from the superharmonic (Δu = ?λ) region, defined by the equation u(x, y) = 1. This curve is called the free boundary since its location is determined by the solution to the problem. We use the implicit function theorem to study the effect of perturbation of the boundary conditions on known families of solutions. This justifies rigorously a formal scheme derived previously by Fleishman and Mahar. Our method also discovers bifurcations from previously known solution families.     

Crossed products and entropy of automorphisms

Let be an exact C∗-algebra, let G be a locally compact group, and let be a C∗-dynamical system. Each automorphism α_g induces a spatial automorphism Ad_λg on the reduced crossed product . In this paper we examine the question, first raised by E. Størmer, of when the topological entropies of α_g and Ad_λg coincide. This had been answered by N. Brown for the particular case of discrete abelian groups. Using different methods, we extend his result to preservation of entropy for α_g when the subgroup of Aut(G) generated by the corresponding inner automorphism Ad_g has compact closure. This property is satisfied by all elements of a wide class of groups called locally [FIA]⁻. This class includes all abelian groups, both discrete and continuous, as well as all compact groups.     

A note on the stability of solutions of the Hill equation with a square-wave coefficient

The results of Van der Pol and Strutt [Phil. Mag.5, 18 (1928)] on the stability of solutions to the Hill equation for a square-wave coefficient have been re-examined. More accurate and extensive results for the stability boundaries are presented, with emphasis on the closed unstable regions which are imbedded in the stable regions.     

Three‐dimensional boundary element analysis of drop deformation in confined flow for Newtonian and viscoelastic systems

An adaptive (Lagrangian) boundary element approach is proposed for the general three‐dimensional drop deformation in confined flow. The adaptive method is stable as it includes remeshing capabilities of the deforming interface between drop and suspending fluid, and thus can handle large deformations. Both drop and surrounding fluid are viscous incompressible and can be Newtonian or viscoelastic. A boundary‐only formulation is implemented for fluids obeying the linear Jeffrey's constitutive equation. Similarly to the formulation for two‐dimensional Newtonian fluids (Khayat RE, Luciani A, Utracki LA. Boundary element analysis of planar drop deformation in confined flow. Part I. Newtonian fluids. Engineering Analysis of Boundary Elements 1997; 19 : 279), the method requires the solution of two simultaneous integral equations on the interface between the two fluids and the confining solid boundary. Although the problem is formulated for any confining geometry, the method is illustrated for a deforming drop as it is driven by the ambient flow inside a cylindrical tube. The accuracy of the method is assessed by comparison with the analytical solution for two‐phase radial spherical flow, leading to good agreement. The influence of mesh refinement is examined for a drop in simple shear flow. Copyright © 2000 John Wiley & Sons, Ltd.     

Pontryagin’s principle for state-constrained evolutionary differential complementarity system

This paper is devoted to the state-constrained optimal control problem of evolutionary variational inequality. In this paper, the control domain is not necessarily convex. Moreover, since our state constraint is quite general and, in many cases, it requires pointwise behavior of the state, the framework of the partial differential equation (instead of the abstract framework) is used. Some optimality conditions (in the form of Pontryagin’s principle) for optimal controls are established.