On free subgroups of units of rings

We prove that if for elements of a ring of characteristic zero and is not nilpotent, then there exists such that the group generated by and is free nonabelian. This is used to prove that a noncommutative positive-definite algebra with involution over an uncountable field contains a free nonabelian subsemigroup.

     

Physico-chemical properties of Tecoma stans Linn. seed oil: a new crop for vegetable oil

Tecoma stans Linn. is known to have various medicinal and therapeutic properties. However, to our knowledge, no information is available regarding their seed oils. In this study, the fatty acid (FA) compositions, physico-chemical properties and antioxidant capacities of T. stans seed oils (TSOs) were investigated. The oil content of the seeds was 15%. The FAs of the TSOs were analysed by GC–MS. α-Linolenic (45.47%), oleic (23.56%), linoleic (11.48%), palmitic (6.09%) and stearic (4.12%) acids were the major detected FAs. γ-Linolenic acid and stearidonic acid, unusually FAs, were also present (1.04% and 6.65%, respectively). The total tocol content in the TSOs was found to be 266.06 mg/100 g. The main component was γ-tocopherol (78.93%). The total phenolic content (168.69 mg GAE/100 g oil) and total flavonoid content (5.54 mg CE/g oil) were also determined in the TSOs.     

Functionalized nanohybrid materials obtained from the interlayer grafting of aminoalcohols on kaolinite

New robust functionalized nanohybrid materials were prepared by the interlayer covalent attachment of aminoalcohols to the octahedral sheets of kaolinite.     

A new steroid glycoside and furochromones from Cyperus rotundus L

Further phytochemical investigation of the aerial parts of Cyperus rotundus L. afforded a new steroid glycoside named sitosteryl (6'-hentriacontanoyl)-beta-D-galactopyranoside (4) in addition to three furochromones, khellin (2), visnagin (3) and ammiol (9). Furthermore, benzo-alpha-pyrone (coumarin) (1), salicylic acid (5), caffeic acid (6), protocatechuic acid (7), p-coumaric acid (8), tricin (10) and isorhamnetin (11) were isolated. The structures of these compounds were established by spectroscopic methods. The isolated furochromones were tested for insect antifeedant activity against larvae Spodoptera littoralis when incorporated in artificial diet and offered to larvae in a chronic feeding bioassay. Also, visnagin, khellin and sitosteryl (6'-hentriacontanoyl)-beta-D-galactopyranoside showed strong cytotoxic activity against L5178y mouse lymphoma cells and were also active in the brine shrimp lethality test.     

Lipase-catalyzed esterification of selected phenolic acids with linolenyl alcohols in organic solvent media

Lipase-catalyzed esterification of selected phenolic acids with linolenyl alcohols was investigated in selected organic solvent media. The enzyme activity for the esterification of dihydrocaffeic acid with linolenyl alcohol in solvent mixtures of hexane/2-butanone of 75∶25 (v/v) and 65∶35 (v/v) was 0.88 and 0.47 μmol of esterified dihydrocaffeic acid/(g of solid enzyme·min), respectively, with a corresponding esterification yield of 76 and 58%, respectively. However, the esterification of ferulic acid with linolenyl alcohol in the reaction medium of hexane/2-butanone of 65∶35 (v/v) resulted in a low yield (16%). Using the reaction medium of hexane/2-butanone of 75∶25 (v/v), an increase in linolenyl alcohol concentration with a concomitant use of a constant amount of dihydrocaffeic acid resulted in an increase in esterification yield. The highest esterification yield of 99% was obtained with a ratio of dihydrocaffeic acid to linolenyl alcohol of 1∶8 after 7 d of reaction. Biosynthesis of the end product, linolenyl dihydrocaffeate, was confirmed by electrospray ionization mass spectroscopy structural analysis; the esterproduct demonstrated an antiradical activity close to that of α-tocopherol.     

CMRH: A new method for solving nonsymmetric linear systems based on the Hessenberg reduction algorithm

The Generalized Minimal Residual (GMRES) method and the Quasi-Minimal Residual (QMR) method are two Krylov methods for solving linear systems. The main difference between these methods is the generation of the basis vectors for the Krylov subspace. The GMRES method uses the Arnoldi process while QMR uses the Lanczos algorithm for constructing a basis of the Krylov subspace. In this paper we give a new method similar to QMR but based on the Hessenberg process instead of the Lanczos process. We call the new method the CMRH method. The CMRH method is less expensive and requires slightly less storage than GMRES. Numerical experiments suggest that it has behaviour similar to GMRES. This revised version was published online in June 2006 with corrections to the Cover Date.     

Multidimensional upwind convection schemes for flow in porous media on structured and unstructured quadrilateral grids

Standard reservoir simulation schemes employ first order upwind schemes for approximation of the convective fluxes when multiple phases or components are present. These convective flux schemes rely upon upwind information that is determined according to grid geometry. As a consequence directional diffusion is introduced into the solution that is grid dependent. The effect can be particularly important for cases where the flow is across grid coordinate lines and is known as cross-wind diffusion.Truly higher dimensional upwind schemes that minimize cross-wind diffusion are presented for convective flow approximation on quadrilateral unstructured grids. The schemes are locally conservative and yield improved results that are essentially free of spurious oscillations. The higher dimensional schemes are coupled with full tensor Darcy flux approximations.The benefits of the resulting schemes are demonstrated for classical test problems in reservoir simulation including cases with full tensor permeability fields. The test cases involve a range of structured and unstructured grids with variations in orientation and permeability that lead to flow fields that are poorly resolved by standard simulation methods. The higher dimensional formulations are shown to effectively reduce the numerical cross-wind diffusion effect, leading to improved resolution of concentration and saturation fronts.     

Activation and Stabilization of The Hydroperoxide Lyase Enzymatic Extract from Mint Leaves (Mentha spicata) Using Selected Chemical Additives

The effects of selected lyoprotecting excipients and chemical additives on the specific activity and the thermal stability of the hydroperoxide lyase (HPL) enzymatic extract from mint leaves were investigated. The addition of KCl (5%, w/w) and dextran (2.5%, w/w) to the enzymatic extract, prior to lyophilization, increased the HPL specific activity by 2.0- and 1.2-fold, respectively, compared to the control lyophilized extract. From half-life time (t _1/2), it can be seen that KCl has enhanced the HPL stability by 1.3- to 2.3-fold, during long-period storage at ?20 °C and 4 °C. Among the selected additives used throughout this study, glycine appeared to be the most effective one. In addition to the activation effect conferred by glycine, it also enhanced the HPL thermal stability. In contrast, polyhydroxyl-containing additives were not effective for stabilizing the HPL enzymatic extract. On the other hand, there was no signification increase in HPL activity and its thermal stability with the presence of Triton X-100. The results also showed that in the presence of glycine (10%), the catalytic efficiency of HPL was increased by 2.45-fold than that without additive.     

A new look at CMRH and its relation to GMRES

CMRH is a Krylov subspace method which uses the Hessenberg process to produce a basis of a Krylov method, and minimizes a quasiresidual. This method produces convergence curves which are very close to those of GMRES, but using fewer operations and storage. In this paper we present new analysis which explains why CMRH has this good convergence behavior. Numerical examples illustrate the new bounds.