Simplexes in spaces of constant curvature

In hyperbolic, Euclidean and spherical n-space, we determine, for each positive number l, the largest interval of the form _n (l)l _ijl which guarantees the existence of an n-simplex p ₁ p ₂ ... p _n+1 with edge-lengths p _ip_j=l _ij. (In spherical geometry of curvature 1 the interval is empty unless l2 arcsin ) The assertion that these intervals are as large as possible is justified because each of them allows certain degenerate simplexes. We determine explicitly all of these critical configurations.This work was supported by Canadian NSERC grants.     

An optimized protocol for anthraquinones isolation from Rhamnus frangula L.

Different from works described in the literature, which use expansive analytical methods to separation of anthraquinones derivatives (AQs), this communication reported a simple and inexpensive methodology to get them. In this way, the expensive commercial AQs: Chrysophanol, physcione and emodine were extracted from plant material (Rhamnus frangula L.) and isolated by classical column chromatography technique under optimised binary mobile phase gradients (CHCl₃ : AcOEt(a), a = 1 to 5%) in excellent yields.     

The view-obstruction problem for spheres in ℝ5

In the view-obstruction problem, congruent, closed convex bodies centred at the points in ⁿ are expanded uniformly until they block all rays from the origin into the open positive cone. The central problem is to determine the minimal blocking size. In the case of spheres of diameter 1 and cubes of side 1 these values are known forn=2, 3 and 4. Here we show that in ⁵, this value for the sphere of diameter 1 is .     

The elusive vanadate (V(3)O(9))(3-): isolation, crystal structure, and nonaqueous solution behavior.

The isolation, crystal structure, and nonaqueous solution characteristics of the first trinuclear vanadate are presented. The crystal structure reveals a six-membered cyclic arrangement of alternating vanadium and oxygen atoms for the anion of [(C(4)H(9))(4)N](3)(V(3)O(9)). The (51)V NMR spectrum of this compound in CD(3)CN exhibits multiple peaks. The relative intensities of each resonance can be altered by concentration and temperature changes, the later of which are reversible. Addition of [(C(4)H(9))(4)N]Br and NaClO(4) also perturbs the equilibria between species observed. Conductivity data for [(C(4)H(9))(4)N](3)(V(3)O(9)) in CH(3)CN as a function of concentration display pronounced curvature and indicate formation of a neutral species in solution at the highest concentrations studied. Stoichiometric mixtures of [(C(4)H(9))(4)N](3)(V(3)O(9)) with the known vanadates [(C(4)H(9))(4)N](3)(HV(4)O(12)), [(C(4)H(9))(4)N](3)(V(5)O(14)), and [(C(4)H(9))(4)N](3)(H(3)V(10)O(28)) are prepared and examined by (51)V NMR. Equilibration between the various vanadates is observed and characterized. Resonances for these known vanadates, however, cannot be used to identify the peaks found for [(C(4)H(9))(4)N](3)(V(3)O(9)), alone, in solution. The existence of ion pairs in acetonitrile is the only interpretation for the solution behavior of [(C(4)H(9))(4)N](3)(V(3)O(9)) consistent with all data. As such, we can directly observe each possible ion pairing state by (51)V NMR: (V(3)O(9))(3-) at -555 ppm, [[(C(4)H(9))(4)N](V(3)O(9))] (2-) at -569 ppm, [[(C(4)H(9))(4)N](2)(V(3)O(9))](-) at -576 ppm, and [(C(4)H(9))(4)N](3)(V(3)O(9)) at -628 ppm. To the best of our knowledge, [(C(4)H(9))(4)N](3)(V(3)O(9)) presents the first case in which every possible ion paired state can be observed directly from a parent polyion. Isolation and characterization of this simple metal oxo moiety may now facilitate efforts to design functional polyoxometalates.     

Acetylcholinesterase Immobilization on 3‐Mercaptopropionic Acid Self Assembled Monolayer for Determination of Pesticides

Studies on the immobilization of acetylcholinesterase onto a SAM gold electrode and the use of the fabricated biosensor for the determination of carbaryl and parathion are presented. The influence of pH, ionic strength, enzyme loading and concentration of glutaraldehyde on the response of the biosensor was investigated . The amperometric biosensor developed in this study provided linearity to parathion and carbaryl in the 2.0 a 30.0×10^?6 mol L^?1 concentration range. The detection limits under the optimum working conditions were found to be 9.3 μg L^?1 for parathion and 9.0 μg L^?1 for carbaryl. The enzyme electrode was found to be stable for 7 days.     

A financial indicator for mid-term tendencies

This work proposes an heuristic indicator for mid-term tendencies of stock prices based on non-linear dynamic equations combined with a graphical method inspired on cell morphology analysis. The model consists of ordinary differential equations with parameters that are fitted by means of the actual data history of stock prices using Extended Kalman Filter. The model structures are to be chosen so as to adequately represent the specific microeconomic condition, such as oligopoly with leader and follower, economic clusters, firms producing complementary products and others. The equations are solved numerically and the trajectories in the phase plane are associated with cell membranes. In an analogy with the increase in the cell volume when its internal pressure rises, the new financial indicator expresses the increase of the stress in a stock market by means of expanding phase portraits.     

Synthesis of Nb2O5·nH2O nanoparticles by water-in-oil microemulsion

Hydrous niobium oxide (Nb₂O₅·nH₂O) nanoparticles had been successfully prepared by water-in-oil microemulsion. They were characterized by X-ray diffraction (XRD), thermal analysis (TG/DTG), Fourier transform infrared spectroscopy (FTIR), BET surface area measurement, transmission electron microscopy (TEM), scanning electron microscopy (SEM) and energy dispersive spectroscopy (EDS). The results showed that the nanoparticle was exactly Nb₂O₅·nH₂O with spherical shape. Their BET surface area was 60 m² g⁻¹. XRD results showed that Nb₂O₅·nH₂O nanoparticles with crystallite size in nanometer scale were formed. The crystallinity and crystallity size increased with increasing annealing temperature. TT-phase of Nb₂O₅ was obtained when the sample is annealed at 550 °C.     

Self-accumulation of aromatics at the oil-water interface through weak hydrogen bonding

It is well-known that the amphiphilic solutes are surface-active and can accumulate at the oil-water interface. Here, we have investigated the water and a light-oil model interface by using molecular dynamic simulations. It was found that aromatics concentrated in the interfacial region, whereas the other hydrocarbons were uniformly distributed throughout the oil phase. Similar to previous studies, such concentrations were not observed at pure aromatics-water interfaces. We show that the self-accumulation of aromatics at the oil-water interface is driven by differences in the interfacial tension, which is lower for aromatics-water than between the others. The weak hydrogen bonding between the aromatic rings and the water protons provides the mechanism for lowering the interfacial tension.     

Infrared and Raman spectra of silica polymorphs from an ab initio parametrized polarizable force field

The general aim of this study is to test the reliability of polarizable model potentials for the prediction of vibrational (infrared and Raman) spectra in highly anharmonic systems such as high temperature crystalline phases. By using an ab initio parametrized interatomic potential for SiO2 and molecular dynamics simulations, we calculate the infrared and Raman spectra for quartz, cristobalite, and stishovite at various thermodynamic conditions. The model is found to perform very well in the prediction of infrared spectra. Raman peak positions are also reproduced very well by the model; however, Raman intensities calculated by explicitly taking the derivative of the polarizability with respect to the atomic displacements are found to be in poorer agreement than intensities calculated using a parametrized "bond polarizability" model. Calculated spectra for the high temperature beta phases, where the role of dynamical disorder and anharmonicities is predominant, are found to be in excellent agreement with experiments. For the octahedral phases, our simulations are able to reproduce changes in the Raman spectra across the rutile-to-CaCl2 transition around 50 GPa, including the observed phonon softening.     

Absorption spectroscopy and binding constants for first-row transition metal complexes of a DOPA-containing peptide

A diverse array of biological systems incorporate 3,4-dihydroxyphenlyalanine (DOPA) into proteins and small molecules for cross-linking and material generation. Marine worm eggshells, sea squirt wound plugs, and marine mussel adhesives may all be formed by combining DOPA-containing molecules with high levels of metals. In order to provide model systems for characterizing these biomaterials, we carried out a study on metal binding to a DOPA-containing peptide. Ultraviolet-visible absorption spectra are presented for the AdopaTP peptide binding to Fe3+, V3+, VO2+, Mn3+, Ti4+, Cu2+, Co2+, and Ni2+ in mono, bis, and where applicable, tris coordination modes. Association constants were determined for selected metal ions binding to the peptide. In general, the spectroscopic and binding properties of this DOPA-containing peptide were found to be similar to those of catechol.