Singular perturbed Markov chains and exact behaviors of simulated annealing processes

We study asymptotic properties of discrete and continuous time generalized simulated annealing processesX(·) by considering a class of singular perturbed Markov chains which are closely related to the large deviation of perturbed diffusion processes. Convergence ofX(t) in probability to a setS ₀ of desired states, e.g., the set of global minima, and in distribution to a probability concentrated onS ₀ are studied. The corresponding two critical constants denoted byd and withd are given explicitly. When the cooling schedule is of the formc/logt, X(t) converges weakly forc>0. Whether the weak limit depends onX(0) or concentrates onS ₀ is determined by the relation betweenc, d, and . Whenc>, the expression for the rate of convergence for each state is also derived.     

Substitution-Inert Metal Complex Mobile Phases in Non-Suppressed Cation Chromatography

Substitution-inert metal complexes, [Co(edda)(H₂O)₂]⁺, (Co(edda)(en)]⁺, [Co(edda)(dmen)]⁺, [Co(en)₂-(gly)]²⁺, [Co(en)₂(acac)]²⁺, and [Co(trien)(gly)]²⁺ in their nitrate salt solutions are used as eluents in nonsuppressed cation chromatography (where edda = ethylenediamine-N,N′-diacetic acid, en = ethylenediamine, dmen = N,N′-dime-thylethylenediamine, gly = glycine, acac = acetylacetone, and trien = triethylenetetraamine). It is found that all the mono- and di-valent charged complexes can be used to separate alkali and alkaline earth metal cations, respectively. The separations for monovalent cations are sometimes comparable to those using ultrapure HNO₃ solutions. However, the divalent Ca²⁺ and Sr²⁺ ions cannot be resolved using the metal complex eluents. On the other hand, a selected, direct non-suppressed IC separation of zinc(II) and cadmium(II) ions is demonstrated for the first time using a substitution-inert metal complex eluent and a conductivity detector. Comparisons of these eluents with those reported previously, i. e. HNO₃ and ethylenediammonium salt solution are made and explanations are proposed to account for the different selectivities observed where possible. The future development of this technique is also briefly discussed.     

An Efficient Method for Preparing the α-Deuterated-α,β-Unsaturated Carbonyl Compounds by Reaction of Stable Phosphonium Ylides with Carbonyl Compounds in Deuterium Oxide

Carbonyl compounds reacted with stable phosphonium ylides in D₂O to give α-deuterated-α,β-unsaturated carbonyl compounds in the same flask. The chemical yield and deuterium incorporation are excellent under our procedure. The fragile group like ozonide was compatible with our reaction condition.     

An exact,finite, gauge-invariant,non-perturbative approach to QCD renormalization

A particular choice of renormalization, within the simplifications provided by the non-perturbative property of Effective Locality, leads to a completely finite, non-perturbative approach to renormalized QCD, in which all correlation functions can, in principle, be defined and calculated. In this Model of renormalization, only the Bundle chain-Graphs of the cluster expansion are non-zero. All Bundle graphs connecting to closed quark loops of whatever complexity, and attached to a single quark line, provided no ‘self-energy’ to that quark line, and hence no effective renormalization. However, the exchange of momentum between one quark line and another, involves only the cluster-expansion’s chain graphs, and yields a set of contributions which can be summed and provide a finite color-charge renormalization that can be incorporated into all other QCD processes. An application to High Energy elastic pp scattering is now underway.     

STUDIES OF ADHESION OF METAL PARTICLES TO SILICA PARTICLES BASED ON ZETA POTENTIAL MEASUREMENTS

The zeta-potentials of silica, copper, platinum and gold particles have been measured as a function of pH. The isoelectric points were found to be at pH 3.0, 5.8, 3.0 and 3.5, respectively. In the pH range 3.0 to 5.8 copper and silica particles are oppositely charged and accordingly the coating of silica with copper particles could be demonstrated. In the case of gold and platinum the sign of the charge is such that direct adhesion to silica particles cannot be expected and this was also demonstrated in the case of platinum.     

Polyoxygenated Klysimplexane- and Eunicellin-Based Diterpenoids from the Gorgonian Briareum violaceum

Three new polyoxygenated diterpenoids with a rare 4-isopropyl-1,5,8a-trimethylperhydrophenanthrane structure of the klysimplexane skeleton, briarols A‒C (1‒3), and one eunicellin-based diterpenoid, briarol D (4), were isolated from Briareum violaceum, a gorgonian inhabiting Taiwanese waters. The chemical structures of these compounds were determined by employing extensive analyses of NMR and high-resolution electrospray ionization mass spectrometry (HRESIMS) data. Metabolites 1‒3 were found to possess the rarely found skeleton of the diterpenoid klysimplexin T. All isolated compounds showed very weak cytotoxic activity against the growth of three cancer cell lines. A plausible biosynthetic pathway for briarols A‒C from the coexisting eunicellin diterpenoid briarol D (4) was postulated.     

On the development of a triple‐preserving Maxwell's equations solver in non‐staggered grids

We present in this paper a finite difference solver for Maxwell's equations in non‐staggered grids. The scheme formulated in time domain theoretically preserves the properties of zero‐divergence, symplecticity, and dispersion relation. The mathematically inherent Hamiltonian can be also retained all the time. Moreover, both spatial and temporal terms are approximated to yield the equal fourth‐order spatial and temporal accuracies. Through the computational exercises, modified equation analysis and Fourier analysis, it can be clearly demonstrated that the proposed triple‐preserving solver is computationally accurate and efficient for use to predict the Maxwell's solutions. Copyright © 2009 John Wiley & Sons, Ltd.     

Percolation phenomenon of calcium bis(2-ethylhexyl) sulfosuccinate water-in-oil microemulsions by conductivity and dielectric spectroscopy measurements

The sodium counterion (Na+) of the sodium bis(2-ethylhexyl) sulfosuccinate (AOT) surfactant was exchanged with calcium Ca2+ to investigate the counterion charge effect on the structure of water in normal decane microemulsions. Ohmic conductivity and dielectric permittivity measurements were performed on samples at constant water to surfactant mole ratio [water]/[Ca(AOT)(2)]=26.6. Increasing the volume fraction of the dispersed phase phi, a percolation phenomenon was observed at the constant temperature of 25 degrees C. The percolation threshold was found at phi approximately 15% by Ohmic conductivity and static dielectric permittivity studied as a function of phi, and by the frequency dependence of the complex permittivity. Critical exponents typical of the static percolation mechanism (formation of bicontinuous microemulsions) were found below and above threshold. The comparison of these results obtained for the two different counterions, Ca2+ and Na+, in AOT surfactant water in normal decane microemulsions allows detection of an important difference. The percolation below threshold is dynamic for the sodium-based microemulsions, accounting for the formation of clusters of droplets, whereas calcium-based microemulsions show a static percolation. For this system, the coalescence of droplets begins to occur below threshold at phi approximately 12%.     

Determination of 12 pueraria components by high-performance liquid chromatography-mass spectrometry

Puerariae radix, a commonly used Chinese herb drug derived from the dried root of legume plant, contains a series of isoflavones as its chief pharmacologically active constituents. Using 12 pueraria components as markers, an LC-UV-MS method requiring less than 60 min, was developed for estimating the quality of pueraria samples within 60 min. Extracts were analyzed using a Cosmosil 5C18-MS column, by gradient elution with an aqueous solution of acetic acid and methanol-ACN at a flow-rate of 1.0 mL/min. Peaks were detected at 254 nm and each peak was identified by LC/MS. The reproducibilities (RSD) of this proposed method, on the basis of peak-area ratios from six replicate injections, were 0.93-1.42% (intraday) and 1.05-1.63% (interday) at a detection limit of 0.12-0.78 microg/mL. Most of the markers used in this study can be classified, respectively, into three major categories, namely, isoflavones, O-glycosidic isoflavones, and C-glycosidic isoflavones. The structures of the compounds were determined from LC-MS fragmentation data and data from the literature.