On the asymptotic solution of the Graetz‐Nusselt problem for short x → 0 and large x → ∞ with partial usage of finite differences

The principal goal of this article is to present two asymptotic solutions for the classical Graetz‐Nusselt problem. The method of lines (MOL) has been adopted for solving the governing partial differential energy equation in two independent variables in an asymptotic manner. Two temperature subfields are determined semianalytically: one for small x (x → 0) and the other for large x (x → ∞). Later, the two asymptotic mean Nusselt number subdistributions, Nu _X→0(x) and Nu _X→∞(x), blend themselves into a generalized correlation equation for the mean Nusselt number distribution Nu (x) covering the entire x‐domain. The simplicity of the MOL procedure, combined with the high quality asymptotic mean Nusselt number subdistributions, provides an alternative methodology for solving the Graetz‐Nusselt problem without using higher level mathematics. © 2004 Wiley Periodicals, Inc. Numer Methods Partial Differential Eq, 2004.     

On toric h-vectors of centrally symmetric polytopes

We prove tight lower bounds for the coefficients of the toric h-vector of an arbitrary centrally symmetric polytope generalizing previous results due to R. Stanley and the author using toric varieties. Our proof here is based on the theory of combinatorial intersection cohomology for normal fans of polytopes developed by G. Barthel, J.-P. Brasselet, K. Fieseler and L. Kaup, and independently by P. Bressler and V. Lunts. This theory is also valid for nonrational polytopes when there is no standard correspondence with toric varieties. In this way we can establish our bounds for centrally symmetric polytopes even without requiring them to be rational. Received: 24 March 2004     

Laminar forced convection in vertical pipes exposed to external natural convection and external radiation: uncoupled/lumped solution

This paper is concerned with the laminar forced convection flow in a vertical pipe exposed to either natural convection or simultaneous natural convection and thermal radiation external to the pipe. An uncoupled/lumped formulation enabled the determination of the mean bulk temperature distribution of the internal flow and the total rate of heat transfer. Average values for both internal and external Nusselt numbers have been taken from standard correlations reported in the literature, leading to the calculation of an effective average Nusselt number, which controls the thermal interaction process. Typical results for a selected combination of internal and external fluids are discussed at length and they compared favorably with others based on a conjugate/numerical formulation. This formulation necessitated a finite difference methodology where information was transferred between the two flows (internal and external), via their respective heat transfer coefficients. On the other hand, attention was focused on the uncoupled/lumped formulation in order to examine in detail the effects of the thermal boundary conditions, and consequently the important role of radiation as an enhancing heat transfer mechanism.     

Pickering Interfacial Catalysis for Biphasic Systems: From Emulsion Design to Green Reactions

Pickering emulsions are surfactant‐free dispersions of two immiscible fluids that are kinetically stabilized by colloidal particles. For ecological reasons, these systems have undergone a resurgence of interest to mitigate the use of synthetic surfactants and solvents. Moreover, the use of colloidal particles as stabilizers provides emulsions with original properties compared to surfactant‐stabilized emulsions, microemulsions, and micellar systems. Despite these specific advantages, the application of Pickering emulsions to catalysis has been rarely explored. This Minireview describes very recent examples of hybrid and composite amphiphilic materials for the design of interfacial catalysts in Pickering emulsions with special emphasis on their assets and challenges for industrially relevant biphasic reactions in fine chemistry, biofuel upgrading, and depollution.     

Synthesis,Characterization, and Biological Evaluation of a Dual-Action Ligand Targeting αvβ3 Integrin and VEGF Receptors

A dual-action ligand targeting both integrin α_Vβ₃ and vascular endothelial growth factor receptors (VEGFRs), was synthesized via conjugation of a cyclic peptidomimetic α_Vβ₃ Arg-Gly-Asp (RGD) ligand with a decapentapeptide. The latter was obtained from a known VEGFR antagonist by acetylation at the Lys13 side chain. Functionalization of the precursor ligands was carried out in solution and in the solid phase, affording two fragments: an alkyne VEGFR ligand and the azide integrin α_Vβ₃ ligand, which were conjugated by click chemistry. Circular dichroism studies confirmed that both the RGD and VEGFR ligand portions of the dual-action compound substantially adopt the biologically active conformation. In vitro binding assays on isolated integrin α_Vβ₃ and VEGFR-1 showed that the dual-action conjugate retains a good level of affinity for both its target receptors, although with one order of magnitude (10/20 times) decrease in potency. The dual-action ligand strongly inhibited the VEGF-induced morphogenesis in Human Umbilical Vein Endothelial Cells (HUVECs). Remarkably, its efficiency in preventing the formation of new blood vessels was similar to that of the original individual ligands, despite the worse affinity towards integrin α_Vβ₃ and VEGFR-1.     

Mechanism of Thyroxine Deiodination by Naphthyl‐Based Iodothyronine Deiodinase Mimics and the Halogen Bonding Role: A DFT Investigation

This paper deals with a systematic density functional theory (DFT) study aiming to unravel the mechanism of the thyroxine (T4) conversion into 3,3′,5‐triiodothyronine (rT3) by using different bio‐inspired naphthyl‐based models, which are able to reproduce the catalytic functions of the type‐3 deiodinase ID‐3. Such naphthalenes, having two selenols, two thiols, and a selenol–thiol pair in peri positions, which were previously synthesized and tested in their deiodinase activity, are able to remove iodine selectively from the inner ring of T4 to produce rT3. Calculations were performed including also an imidazole ring that, mimicking the role of the His residue, plays an essential role deprotonating the selenol/thiol moiety. For all the used complexes, the calculated potential energy surfaces show that the reaction proceeds via an intermediate, characterized by the presence of a X?I?C (X=Se, S) halogen bond, whose transformation into a subsequent intermediate in which the C?I bond is definitively cleaved and the incipient X?I bond is formed represents the rate‐determining step of the whole process. The calculated trend in the barrier heights of the corresponding transition states allows us to rationalize the experimentally observed superior deiodinase activity of the naphthyl‐based compound with two selenol groups. The role of the peri interactions between chalcogen atoms appears to be less prominent in determining the deiodination activity.