Viscosity of liquid mixtures: the Vesovic-Wakeham method for chain molecules

New expressions for the viscosity of liquid mixtures, consisting of chain-like molecules, are derived by means of Enskog-type analysis. The molecules of the fluid are modelled as chains of equally sized, tangentially joined, and rigid spheres. It is assumed that the collision dynamics in such a fluid can be approximated by instantaneous collisions. We determine the molecular size parameters from the viscosity of each pure species and show how the different effective parameters can be evaluated by extending the Vesovic-Wakeham (VW) method. We propose and implement a number of thermodynamically consistent mixing rules, taking advantage of SAFT-type analysis, in order to develop the VW method for chain molecules. The predictions of the VW-chain model have been compared in the first instance with experimental viscosity data for octane-dodecane and methane-decane mixtures, thus, illustrating that the resulting VW-chain model is capable of accurately representing the viscosity of real liquid mixtures.     

CXCR4 Stimulates Macropinocytosis: Implications for Cellular Uptake of Arginine-Rich Cell-Penetrating Peptides and HIV

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Highlights? CXCR4 was identified as a receptor to stimulate cellular uptake of R12 peptide ? Interaction with R12 stimulates internalization of CXCR4 via macropinocytosis ? SDF-1α and HIV-1 gp120 protein also induce macropinocytosis ? Macropinocytic uptake of HIV-1 diminished the infection of host cells     

3‐Deoxy‐β‐d‐ribo‐hexopyranose (3‐deoxy‐β‐d‐glucopyranose)

The β‐pyranose form, (III), of 3‐deoxy‐d ‐ribo‐hexose (3‐deoxy‐d ‐glucose), C₆H₁₂O₅, crystallizes from water at 298 K in a slightly distorted ⁴C₁ chair conformation. Structural analyses of (III), β‐d ‐glucopyranose, (IV), and 2‐deoxy‐β‐d ‐arabino‐hexopyranose (2‐deoxy‐β‐d ‐glucopyranose), (V), show significantly different C—O bond torsions involving the anomeric carbon, with the H—C—O—H torsion angle approaching an eclipsed conformation in (III) (−10.9°) compared with 32.8 and 32.5° in (IV) and (V), respectively. Ring carbon deoxygenation significantly affects the endo‐ and exocyclic C—C and C—O bond lengths throughout the pyranose ring, with longer bonds generally observed in the monodeoxygenated species (III) and (V) compared with (IV). These structural changes are attributed to differences in exocyclic C—O bond conformations and/or hydrogen‐bonding patterns superimposed on the direct (intrinsic) effect of monodeoxygenation. The exocyclic hydroxymethyl conformation in (III) (gt) differs from that observed in (IV) and (V) (gg).     

Hydrating the Bispropionate Notch in Malaria Pigment: A New Structural Motif in the Iron(III)(deuteroporphyrin) Dimer

Treating deuterohemin, chloro(deuteroporphyrinato)iron(III), with a non-coordinating base in DMSO/methanol allows for the isolation of [(deuteroporphyrinato)iron(III)]₂, deuterohematin anhydride (DHA), an analogue of malaria pigment, the natural product of heme detoxification by malaria. The structure of DHA obtained from this solvent system has been solved by X-ray powder diffraction analysis and displays many similarities, yet important structural differences, to malaria pigment. Most notably, a water molecule of solvation occupies a notch created by the propionate side chains and stabilizes a markedly bent propionate ligand coordinated with a long Fe−O bond, and a carboxylate cluster associated with water molecules is generated. Together, these features account for its increased solubility and more open structure, with an increased porphyrin–porphyrin separation. The IR spectroscopic signature associated with this structure also accounts for the strong IR band at 1587 cm⁻¹ seen for many amorphous preparations of synthetic malaria pigment, and it is proposed that stabilizing these structures may be a new objective for antimalarial drugs. The important role of the vinyl substituents in this biochemistry is further demonstrated by the structure of deuterohemin obtained by single-crystal X-ray diffraction analysis.     

Projektive Skalen,Tschebyscheff-Polynome und Fibonacci-Zahlen

Summary. Let $\widehat{\widehat T}_n$ and $\overline U_n$ denote the modified Chebyshev polynomials defined by $\widehat{\widehat T}_n (x) = {T_{2n + 1} \left(\sqrt{x + 3 \over 4} \right) \over \sqrt{x + 3 \over 4}}, \quad \overline U_{n}(x) = U_{n} \left({x + 1 \over 2}\right) \qquad (n \in \mathbb{N}_{0},\ x \in \mathbb{R}).$ For all $n \in \mathbb{N}_{0}$ define $\widehat{\widehat T}_{-(n + 1)} = \widehat{\widehat T}_n$ and $\overline U_{-(n + 2)} = - \overline U_n$, furthermore $\overline U_{-1} = 0$. In this paper, summation formulae for sums of type $\sum\limits^{+\infty}_{k = -\infty} \mathbf a_{\mathbf k}(\nu; x)$ are given, where $\bigl(\mathbf a_{\mathbf k}(\nu; x)\bigr)^{-1} = (-1)^k \cdot \Bigl( x \cdot \widehat{\widehat T}_{\left[k + 1 \over 2\right] - 1} (\nu) +\widehat{\widehat T}_{\left[k + 1 \over 2\right]}(\nu)\Bigr) \cdot \Bigl(x \cdot \overline U_{\left[k \over 2\right] - 1} (\nu) + \overline U_{\left[k \over 2\right]} (\nu)\Bigr)$ with real constants $ x, \nu $. The above sums will turn out to be telescope sums. They appear in connection with projective geometry. The directed euclidean measures of the line segments of a projective scale form a sequence of type $(\mathbf a_{\mathbf k} (\nu;x))_{k \in \mathbb{Z}}$ where $ \nu $ is the cross-ratio of the scale, and x is the ratio of two consecutive line segments once chosen. In case of hyperbolic $(\nu \in \mathbb{R} \setminus] - 3,1[)$ and parabolic $\nu = -3$ scales, the formula $\sum\limits^{+\infty}_{k = -\infty} \mathbf a_{\mathbf k} (\nu; x) = {\frac{1}{x - q_{{+}\atop(-)}}} - {\frac{1}{x - q_{{-}\atop(+)}}} \eqno (1)$ holds for $\nu > 1$ (resp. $\nu \leq - 3$), unless the scale is geometric, that is unless $x = q_+$ or $x = q_-$. By $q_{\pm} = {-(\nu + 1) \pm \sqrt{(\nu - 1)(\nu + 3)} \over 2}$ we denote the quotient of the associated geometric sequence.

     

Orthocomplemented complete lattices and graphs

The problem I consider originates from Dörfler, who found a construction to assign an Orthocomplemented latticeH(G) to a graphG. By Dörfler it is known that for every finite Orthocomplemented latticeL there exists a graphG such thatH(G)=L. Unfortunately, we can find more than one graphG with this property, i.e., orthocomplemented lattices which belong to different graphs can be isomorphic. I show some conditions under which two graphs have the same orthocomplemented lattice.     

Sandwich Theorem und offene Zerlegungen in schwachK-analytischen Banachräumen

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