Logical Kronecker delta deconstruction of the absolute value function and the treatment of absolute deviations

A logical Kronecker delta reformulation of the absolute value function and the related discrete problem of the optimal absolute deviation are studied as the basic step towards applications of first order norms in theoretical chemistry. Absolute value function derivatives appear in the present context related to unit step function, Dirac delta function and its derivatives. The absolute value of the difference of two Minkowski normalized Gaussian functions is analyzed as an example. The proposed logical Kronecker delta deconstruction manner to express the absolute value function is also applied to the absolute deviation from the median of a set of numerical values, which looks to be just the optimal first order norm.     

Multifunctional microgel magnetic/optical traps for SERS ultradetection

We report on the fabrication of a SERS substrate comprising magnetic and silver particles encapsulated within a poly(N-isopropylacrylamide) (pNIPAM) thermoresponsive microgel. This colloidal substrate has the ability to adsorb analytes from solution while it is expanded (low temperature) and reversibly generate hot spots upon collapse (high temperature or drying). Additionally, the magnetic functionality permits concentration of the composite particles into small spatial regions, which can be exploited to decrease the amount of material per analysis while improving its SERS detection limit. Proof of concept for the sequestration of uncommon molecular systems is demonstrated through the first SERS analysis of pentachlorophenol (PCP), a chlorinated ubiquitous environmental pollutant.     

NMR methods for unravelling the spectra of complex mixtures

The main methods for the simplification of the NMR of complex mixtures by selective attenuation/suppression of the signals of certain components are presented. The application of relaxation, diffusion and PSR filters and other techniques to biological samples, pharmaceuticals, foods, living organisms and natural products are illustrated with examples.     

Translocation versus cyclisation in radicals derived from N-3-alkenyl trichloroacetamides

Under radical reaction conditions, two different and competitive reaction pathways were observed for N-(α-methylbenzyl)trichloroacetamides with a N-3-cyclohexenyl substituent: 1,4-hydrogen translocation and radical addition to a double bond. However, for radicals with an acyclic alkenyl side chain, the direct cyclisation process was exclusively observed. The dichotomy between translocation and direct radical cyclisation in these substrates has been theoretically studied using density functional theory (DFT) methods at the B3LYP/6-31G** computational level.     

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.     

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).     

Ueber eine allgemeinere Theorie der Adsorption von Lösungen

Ohne Zusammenfassung