C–H⋅<Emphasis Type="Italic">s</Emphasis>O hydrogen bond networks in <Emphasis Type="Italic">E</Emphasis>- and Z-unsaturated esters of C-glycosides

Methyl E(Z)-4,7 anhydro-5-benzamido-6,8-di-O-benzoyl-2,3,5-trideoxy-d-allo-oct-2-enoate have been synthesized like intermediates and isolated as single crystals during the synthesis of pyrazole-related C nucleosides as synthetic product with cytotoxic activity.¹ Crystal structures of E(Z) isomers were determined by X-ray analysis. E isomer crystallizes in the triclinic crystal system, space group P1, a = 5.319(1) Å, b = 10.758(2) Å, c = 12.229(2) Å, α = 72.38(2)^∘, β = 89.97(2)^∘, γ = 87.07(2)^∘, D_x = 1.320 Mgm⁻³ and Z isomer in the orthorhombic crystal system, space group P2₁2₁2₁, a = 5.1297(13) Å, b = 19.667(5) Å, c = 25.871(6) Å, D_x = 1.348 Mgm⁻³. The molecular structure was solved by direct method on the basis of 2609 and 2727 unique reflections recorded at the temperature 293 K (E-isomer) and 173 K (Z-isomer) up to the final R-factor 0.0378 and 0.0435, respectively. C–H⋅sO contact networks were analyzed and the correlation established between the existence of the weak C–H⋅sO hydrogen bonds and the melting point of the single crystals.     

Advantages of simplicial partitioning for Lipschitz optimization problems with linear constraints

The well known DIRECT (DIviding RECTangles) algorithm for global optimization requires bound constraints on variables and does not naturally address additional linear or nonlinear constraints. A feasible region defined by linear constraints may be covered by simplices, therefore simplicial partitioning may tackle linear constraints in a very subtle way. In this paper we demonstrate this advantage of simplicial partitioning by applying a recently proposed deterministic simplicial partitions based DISIMPL algorithm for optimization problems defined by general linear constraints (Lc-DISIMPL). An extensive experimental investigation reveals advantages of this approach to such problems comparing with different constraint-handling methods, proposed for use with DIRECT. Furthermore the Lc-DISIMPL algorithm gives very competitive results compared to a derivative-free particle swarm algorithm (PSwarm) which was previously shown to give very promising results. Moreover, DISIMPL guarantees the convergence to the global solution, whereas the PSwarm algorithm sometimes fails to converge to the global minimum.     

Bifurcation of Nonlinear Bloch Waves from the Spectrum in the Gross–Pitaevskii Equation

We rigorously analyze the bifurcation of stationary so-called nonlinear Bloch waves (NLBs) from the spectrum in the Gross–Pitaevskii (GP) equation with a periodic potential, in arbitrary space dimensions. These are solutions which can be expressed as finite sums of quasiperiodic functions and which in a formal asymptotic expansion are obtained from solutions of the so-called algebraic coupled mode equations. Here we justify this expansion by proving the existence of NLBs and estimating the error of the formal asymptotics. The analysis is illustrated by numerical bifurcation diagrams, mostly in 2D. In addition, we illustrate some relations of NLBs to other classes of solutions of the GP equation, in particular to so-called out-of-gap solitons and truncated NLBs, and present some numerical experiments concerning the stability of these solutions.     

10.1007/s10973-006-8123-z

This work presents preparation and thermal characterization of three novel organomercurials: Hg₂(CF₃COCHCOCF₃)₂-μ₂-(CF₃COCCOCF₃)μ₂(CF₃C(OH)₂CH₂C(OH)₂CF₃) (I), Hg₂(CF₃COCHCOCF₃)₂-μ₂-(CF₃COCCOCF₃) (II) and Hg₂(CH₃COCHCOCF₃)₂-μ₂-(CH₃COCCOCF₃) (III) which means that they contain at least one direct mercury-to-carbon bond among the carbonyl groups of β-diketone molecules which are capable for chelating of metal ions. IR-spectra support the conclusion that mercury is most probably bound to the γ-carbon of fluorinated derivatives of acetylacetone and is not chelated through oxygen in any of the isolated compounds. The thermal decomposition of mercurated hexafluoro- and trifluoroacetylacetone in nitrogen occurs in a few steps. Each step was identified and studied by simultaneous DTA/TG analyzer. On the basis of dynamic heating experiments by TG applying Flynn-Wall method the activation energy for each of them was determined.     

Spectral synthesis for coadjoint orbits of nilpotent Lie groups

We determine the space of primary ideals in the group algebra \(L^{1}(G) \) of a connected nilpotent Lie group by identifying for every \(\pi \in \widehat{G} \) the family \(\mathcal I^\pi \) of primary ideals with hull \(\{\pi \} \) with the family of invariant subspaces of a certain finite dimensional sub-space \(\mathcal P_Q^\pi \) of the space of polynomials \(\mathcal P(G) \) on G.     

Simultaneous pH and Temperature Measurements Using Pyranine as a Molecular Probe

Steep variations in concentration and temperature frequently occur in small fluid compartments such as those found in cells or microfluidic devices. A quantitative characterization of concentration and temperature gradients is therefore required before these systems can be fully understood. Although different spatially resolved fluorescence methods have been developed to measure either the temperature or the concentration of ions such as proton or calcium, often concentration measurements depend on temperature and vice versa. Here, we describe a method allowing simultaneous measurement of pH and temperature. This method is based on the detection of the blinking of the fluorescent pH indicator pyranine, a process due to its alternating between a basic form and an acidic form. Fluorescence correlation spectroscopy allows measuring both the protonation and deprotonation rates of pyranine, and each pair of rates can be uniquely related to a pair of pH and temperature values. We show, however, that the relationship between rates, pH and temperature, is very sensitive to the presence of other acid-base molecules in solution. We also show that it is influenced by the overall ionic strength of the solution, in a manner that depends on buffer composition.     

Frictional contact problem of a rigid stamp and an elastic layer bonded to a homogeneous substrate

In this study, the frictional contact problem for a layer bonded to a homogeneous substrate is considered according to the theory of elasticity. The layer is indented by a rigid cylindrical stamp which is subjected to concentrated normal and tangential forces. The friction between the layer and the stamp is taken into account. The problem is reduced to a singular integral equation of the second kind in which the contact pressure function and the contact area are the unknown by using integral transform technique and the boundary conditions of the problem. The singular integral equation is solved numerically using both the Jacobi polynomials and the Gauss?CJacobi integration formula, considering equilibrium and consistency conditions. Numerical results for the contact pressures, the contact areas, the normal stresses, and the shear stresses are given, for both the frictional and the frictionless contacts.