Distributive Lattices with a Generalized Implication: Topological Duality

In this paper we introduce the notion of generalized implication for lattices, as a binary function ⇒ that maps every pair of elements of a lattice to an ideal. We prove that a bounded lattice A is distributive if and only if there exists a generalized implication ⇒ defined in A satisfying certain conditions, and we study the class of bounded distributive lattices A endowed with a generalized implication as a common abstraction of the notions of annihilator (Mandelker, Duke Math J 37:377–386, 1970), Quasi-modal algebras (Celani, Math Bohem 126:721–736, 2001), and weakly Heyting algebras (Celani and Jansana, Math Log Q 51:219–246, 2005). We introduce the suitable notions of morphisms in order to obtain a category, as well as the corresponding notion of congruence. We develop a Priestley style topological duality for the bounded distributive lattices with a generalized implication. This duality generalizes the duality given in Celani and Jansana (Math Log Q 51:219–246, 2005) for weakly Heyting algebras and the duality given in Celani (Math Bohem 126:721–736, 2001) for Quasi-modal algebras.     

How accurate are the nonlinear chemical Fokker-Planck and chemical Langevin equations?

The chemical Fokker-Planck equation and the corresponding chemical Langevin equation are commonly used approximations of the chemical master equation. These equations are derived from an uncontrolled, second-order truncation of the Kramers-Moyal expansion of the chemical master equation and hence their accuracy remains to be clarified. We use the system-size expansion to show that chemical Fokker-Planck estimates of the mean concentrations and of the variance of the concentration fluctuations about the mean are accurate to order Ω(-3∕2) for reaction systems which do not obey detailed balance and at least accurate to order Ω(-2) for systems obeying detailed balance, where Ω is the characteristic size of the system. Hence, the chemical Fokker-Planck equation turns out to be more accurate than the linear-noise approximation of the chemical master equation (the linear Fokker-Planck equation) which leads to mean concentration estimates accurate to order Ω(-1∕2) and variance estimates accurate to order Ω(-3∕2). This higher accuracy is particularly conspicuous for chemical systems realized in small volumes such as biochemical reactions inside cells. A formula is also obtained for the approximate size of the relative errors in the concentration and variance predictions of the chemical Fokker-Planck equation, where the relative error is defined as the difference between the predictions of the chemical Fokker-Planck equation and the master equation divided by the prediction of the master equation. For dimerization and enzyme-catalyzed reactions, the errors are typically less than few percent even when the steady-state is characterized by merely few tens of molecules.     

Theoretical Development of a Novel Equation for Dynamic Spontaneous Imbibition with Variable Inlet Saturation and Interfacial Coupling Effects

In oil recovery from fractured reservoirs, dynamic spontaneous imbibition (DSI) plays an important role. Conventional equations used for characterizing dynamic spontaneous imbibition neglect the effects of the driving forces acting across the wetting and non-wetting phases which are flowing in opposite directions. Such effects, defined as interfacial coupling effects (ICE), are known to cause a decrease in the calculated flow rate in drainage processes. Moreover, none of the numerical models have considered a variable inlet saturation (S*) for DSI. A new theoretical model has been developed using generalized transport equations to describe dynamic spontaneous imbibition for immiscible two-phase flow processes. The inclusion of interfacial coupling effects provides a more accurate way to describe dynamic spontaneous imbibition. Furthermore, the addition of variable inlet saturation allows one to establish whether the inlet-face saturation (S*) increases from the initial saturation to 1−Sro, or whether it can remain constant and equal to one minus the residual saturation to the non-wetting phase (1−Sro).     

Cracking in polylactide spherulites

A polylactide of high optical purity was crystallized between 100 and 140 °C, in‐between two glass slides, and its morphology was investigated by polarizing optical microscopy, scanning electron microscopy, and atomic force microscopy, during subsequent heating and cooling cycles between ?15 °C and the crystallization temperature. It was found that dark circular rings show up on cooling on top of the spherulites and represent cracks of about 300 nm in width. This phenomenon is completely reversible, and the heating–cooling curves are centered at about 56 °C, which coincide with the T_g of polylactide. © 2005 Wiley Periodicals, Inc. J Polym Sci Part B: Polym Phys 43: 3308–3315, 2005     

Hétérocycles contenant du phosphore. XXII—Etude par RMP de dérivés de l'oxazaphospholane-1,3,2: II—Analyse des spectres de composés monosubstitués en 5 ou disubstitués en 4 et 5.

The influence of various factors (temperature, nature and concentration of solvent) or the utilisation of various physical methods (tickling or INDOR experiments, for example) are employed to analyse the PMR spectra of some 5-monosubstituted or 4,5-disubstituted 1,3,2-oxazaphospholane derivatives.     

Vibrational relaxation of ortho and para-H2 in the range 400-50 K

The vibrational relaxation of ortho-para-H₂ mixtures was studied in the interval 400-50 K. At and above 300 K the ortho and para self-relaxation rates, k_oo and k_pp, are identical within experimental error. In the low temperature range, k_oo >k_pp and k_oo is found to vary slowly with temperature.     

Discovery of powerful uranyl ligands from efficient synthesis and screening

New tripodal gem-(bis-phosphonates) uranophiles were discovered by a screening method that allowed for the selection of ligands with strong uranyl-binding properties in a convenient microtiter-plate format. The method is based on competitive uranium binding by using Sulfochlorophenol S as chromogenic chelate. This dye compound was found to present high uranyl complexation properties and allowed to highlight ligands presenting association constants for UO(2+)(2) up to 10(18) at pH 7.4 and 10(20) at pH 9. A collection of 40 known ligands including polycarboxylate, hydroxamate, catecholate, hydroxypyridonate and hydroxyquinoline derivatives was tested. Also screened was a combinatorial library prepared from seven amine scaffolds and eight acrylates bearing diverse chelating moieties. Among these 96 tested candidates, a tripod derivative bearing gem-bis-phosphonates moieties was found to present the highest complexation properties over a wide range of pH and was further studied.     

Computer simulation of a nitrogen ICP discharge

A theoretical model for calculating radial and axial temperature profiles in a nitrogen ICP discharge was improved to include the normal distribution of magnetic flux density and a three-gas flow pattern commonly used in spectrochemical applications. Calculated radial temperature and particle velocity distributions for nitrogen ICP discharges compare well with experimentally obtained data.