Role of saturability of noncovalent interactions in the analysis of the three-dimensional structure—opioid activity relationship

The effect of the saturability of noncovalent interactions on the character of opioid activity of opioid receptor ligands belonging to different structural classes was investigated. A three-dimensional model for an opiate pharmacophore was used to show that the involvement of pharmacophore elements, which are responsible for the agonist ligand binding to opioid receptors, in intramolecular interactions gives rise to antagonistic properties.     

Some Norm Inequalities for Gaussian Wick Products

We provide several inequalities for the ? ^q (𝒫)-norm of the Wick product of random variables. These estimates are based on a Jensen's type inequality for the Wick multiplication, which we derive via a positivity argument. As an application we study a certain type of anticipating stochastic differential equation whose solution is shown to be an element of ? ^q (𝒫) for some q ≥ 1.     

The existence of positive solutions to a non‐local singular boundary value problem

We consider the non‐local singular boundary value problem (1) where q ∈ C⁰([0,1]) and f, h ∈ C⁰((0,∞)), limf(x)=?∞, limh(x)=∞. We present conditions guaranteeing the existence of a solution x ∈ C¹([0,1]) ∩ C²((0,1]) which is positive on (0,1]. The proof of the existence result is based on regularization and sequential techniques and on a non‐linear alternative of Leray–Schauder type. Copyright © 2005 John Wiley & Sons, Ltd.     

Bayesian evidence computation for model selection in non-linear geoacoustic inference problems

This paper applies a general Bayesian inference approach, based on Bayesian evidence computation, to geoacoustic inversion of interface-wave dispersion data. Quantitative model selection is carried out by computing the evidence (normalizing constants) for several model parameterizations using annealed importance sampling. The resulting posterior probability density estimate is compared to estimates obtained from Metropolis-Hastings sampling to ensure consistent results. The approach is applied to invert interface-wave dispersion data collected on the Scotian Shelf, off the east coast of Canada for the sediment shear-wave velocity profile. Results are consistent with previous work on these data but extend the analysis to a rigorous approach including model selection and uncertainty analysis. The results are also consistent with core samples and seismic reflection measurements carried out in the area.     

Comparison of Cu(II)-promoted leaving group stabilization of the cleavage of a homologous set of phosphate mono-, di-, and triesters in water, methanol, and ethanol

The cleavage of a set of phosphate mono-, di-, and triesters having a Cu(II)-complexed 2-phenanthrolyl group at the ortho-position of a departing phenoxide was studied in water and ethanol. Experimentally observed pH/rate profiles, solvent deuterium kinetic isotope effects, and activation parameters are compared with those obtained in methanol. The pH/rate profile in each solvent exhibits an extended plateau due to solvent attack on forms designated as [Cu(II):1b/c](0) for the monoester, [Cu(II):2b](+), for the diester, and [Cu(II):3a](2+) for the triester. The solvent dkie values (k(H)/k(D)) for the three complexes are 0.91, 0.95, and 0.83 for decomposition of [Cu(II):1b/c](0) in water (W), methanol (M), and ethanol (E), 1.22, 1.09, and 1.29 for [Cu(II):2b](+) in W, M, and E, and 1.94, 2.2, and 1.96 for [Cu(II):3a](2+) in W, M, and E. Near unit, or slightly inverse values for the monoester are taken as evidence for little involvement of solvent in a highly dissociative TS for P-OAr cleavage, with slightly higher solvent dkie values for the diester signifying the onset of some solvent participation in assisting the nucleophilic displacement. The larger primary dkie for the triester gives evidence for a solvent-assisted delivery of ROH in the cleavage through a more associative mechanism. Activation parameters for each substrate in the solvents are compared, indicating that the transition from methanol to ethanol for each substrate involves a near cancellation of the ΔΔH(?) and -TΔΔS(?) values (25 °C) so that the respective rates in both solvents are very similar. The transition from alcohol to water produces variable effects, with ΔΔH(?) and -TΔΔS(?) values canceling for cleavage of the triester and being additive for the mono and diester, explaining their 100-500 rate reduction in passing from methanol to water. The rate enhancing effects of the Cu(II)-promoted leaving group assistance in all three solvents are substantial and estimated at 10(12)-10(15) for the monoester, 10(12)-10(14) for the diester, and 10(5) for the triester relative to their background reactions.     

Hilbert space representations of decoherence functionals and quantum measures

We show that any decoherence functional D can be represented by a spanning vector-valued measure on a complex Hilbert space. Moreover, this representation is unique up to an isomorphism when the system is finite. We consider the natural map U from the history Hilbert space K to the standard Hilbert space H of the usual quantum formulation. We show that U is an isomorphism from K onto a closed subspace of H and that U is an isomorphism from K onto H if and only if the representation is spanning. We then apply this work to show that a quantum measure has a Hilbert space representation if and only if it is strongly positive. We also discuss classical decoherence functionals, operator-valued measures and quantum operator measures.     

Transition from concerted to stepwise processes as a function of leaving group ability: density functional theory and experimental study of lyoxide‐promoted cleavages of phosphorothioate and phosphate triesters in water and methanol

The base‐promoted solvolysis of a series of O,O‐dimethyl O‐aryl and O,O‐dimethyl O‐alkyl phosphorothioates (1) as well as O,O‐dimethyl O‐aryl and O,O‐dimethyl O‐alkyl phosphates (2) was studied computationally by density functional theory methods in methanol and water continuum media to determine the transition between concerted and stepwise processes. In addition, an experimental study was undertaken on the solvolysis of these series in basic methanol and water. The computations indicate that the solvolytic mechanism for series 1 involves lyoxide attack anti to the leaving group in a concerted manner with good leaving groups having pK_a^Lg values < 12.3 in methanol and in a stepwise fashion with the formation of a 5‐coordinate thiophosphorane intermediate when the pK_a^Lg > 12.3. A similar transition from concerted to stepwise mechanism occurs with series 2 in methanol as well as with series 1 and 2 in water, although for the aqueous solvolyses with hydroxide nucleophile, the transitions between concerted and stepwise mechanisms occur with better leaving groups than in the case in methanol. The computational data allow the construction of Brønsted plots of log k₂^?OS versus pK_a^Lg in methanol and water, which are compared with the experimental Brønsted plots determined with these series previously and with new data determined in this work. Both the computational and experimental Brønsted data reveal discontinuities in the plots between substrates bearing O‐aryl and O‐alkyl leaving groups, with the gradients of the plots being far steeper than, and non‐collinear with, the O‐aryl leaving groups for solvolysis of the O‐alkyl‐containing substrates. These discontinuities signify that care should be exercised in interpreting breaks in Brønsted plots in terms of changes in rate‐limiting steps that signify the formation of an intermediate during a solvolytic process. Copyright © 2011 John Wiley & Sons, Ltd.     

On Saint‐Venant's principle in a poroelastic arch‐like region

In this paper we consider the state of plane strain in an elastic material with voids occupying a curvilinear strip as an arch‐like region described by R: a<r<b, 0<θ<ω, where r and θ are polar coordinates and a, b, and ω (<2π) are prescribed positive constants. Such a curvilinear strip is maintained in equilibrium under self‐equilibrated traction and equilibrated force applied on one of the edges, whereas the other three edges are traction free and subjected to zero volumetric fraction or zero equilibrated force. In fact, we study the case when one right or curved edge is loaded. Our aim is to derive some explicit spatial estimates describing how some appropriate measures of a specific Airy stress function and volume fraction evolve with respect to the distance to the loaded edge. The results of the present paper prove how the spatial decay rate varies with the constitutive profile. For the problem corresponding to a loaded right edge, we are able to establish an exponential decay estimate with respect to the angle θ. Whereas for the problem corresponding to a loaded curved edge, we establish an algebraical spatial decay with respect to the polar distance r, provided the angle ω is lower than the critical value $\pi\sqrt{2}$. The intended applications of these results concern various branches of medicine as for example the bone implants. Copyright © 2010 John Wiley & Sons, Ltd.     

Spherical Particle in Nematic Liquid Crystal Under an External Field: The Saturn Ring Regime

We consider a nematic liquid crystal occupying the exterior region in \({\mathbb {R}}^3\) outside of a spherical particle, with radial strong anchoring. Within the context of the Landau-de Gennes theory, we study minimizers subject to an external field, modeled by an additional term which favors nematic alignment parallel to the field. When the external field is high enough, we obtain a scaling law for the energy. The energy scale corresponds to minimizers concentrating their energy in a boundary layer around the particle, with quadrupolar symmetry. This suggests the presence of a Saturn ring defect around the particle, rather than a dipolar director field typical of a point defect.