Exploring the Coordination Properties of Phosphonium-Functionalized N-Heterocyclic Carbenes Towards Gold

Gold(I) complexes with N-heterocyclic carbene ligands functionalized with a pendant phosphonium moiety were synthesized by simple procedures. In particular, the simple addition of LiBr salt in the reaction media allows the formation of the NHC gold(I) mononuclear complexes, whilst in the absence of excess bromide ions the deprotonation of the methylene group in alpha position to the phosphonium group occurs, allowing the isolation of the dinuclear complexes with two C,C-bridging NHC-phosphonium ylide ligands. The complexes were characterized in solution with NMR spectroscopy and ESI-MS spectrometry, as well as in the solid state by means of single crystal X-ray diffraction analysis. Mononuclear gold(III) species were also isolated by Br₂ oxidative addition to the mononuclear gold(I) species and fully characterized. Preliminary results of the biological effects on MCF7 cancer cells are also reported.     

Nonlinear first order partial differential equations reducible to first order homogeneous and autonomous quasilinear ones

A theorem providing necessary conditions enabling one to map a nonlinear system of first order partial differential equations to an equivalent first order autonomous and homogeneous quasilinear system is given. The reduction to quasilinear form is performed by constructing the canonical variables associated to the Lie point symmetries admitted by the nonlinear system. Some applications to relevant partial differential equations are given.     

A fuzzy approach to using expert knowledge for tuning paper machines

Paper machines are very complex production systems, but their scope is simple: they consume materials and resources, called factors, to produce paper, which in turn can be described by its characteristics. In this paper, a decision support system is developed in cooperation with an industrial partner to help them with operational decision making when tuning a paper machine. The decision support system was developed in two phases. Firstly, the knowledge of experts is collected and stored in the form of a fuzzy ontology. Secondly, this knowledge is made usable so that a user of the decision support system can specify what characteristics of the produced paper to increase or to decrease and be returned with a recommendation on what factors to change. In this paper, we will work out the optimization problems on which the system is based. Additionally to a basic goal programming model, two extensions are explored, accounting for uncertainty and non-linearity, respectively.     

Symmetry for extremal functions in subcritical Caffarelli–Kohn–Nirenberg inequalities

We use the formalism of the Rényi entropies to establish the symmetry range of extremal functions in a family of subcritical Caffarelli–Kohn–Nirenberg inequalities. By extremal functions we mean functions that realize the equality case in the inequalities, written with optimal constants. The method extends recent results on critical Caffarelli–Kohn–Nirenberg inequalities. Using heuristics given by a nonlinear diffusion equation, we give a variational proof of a symmetry result, by establishing a rigidity theorem: in the symmetry region, all positive critical points have radial symmetry and are therefore equal to the unique positive, radial critical point, up to scalings and multiplications. This result is sharp. The condition on the parameters is indeed complementary of the condition that determines the region in which symmetry breaking holds as a consequence of the linear instability of radial optimal functions. Compared to the critical case, the subcritical range requires new tools. The Fisher information has to be replaced by Rényi entropy powers, and since some invariances are lost, the estimates based on the Emden–Fowler transformation have to be modified.     

New perspectives in hydrogenase direct electrochemistry

Electrochemical studies of hydrogenases, the biological catalysts of H₂ oxidation and production, have proven wrong the old saying that enzymes do not easily transfer electrons to electrodes in the absence of mediators. Many distinct hydrogenases have actually been directly connected to electrodes or particles, for studying their catalytic mechanism or for designing solar-fuels catalysts. In this review, we list the electrodes that have proved successful for direct electron transfer to hydrogenases, and we discuss recent results which illustrate new directions in this research field: the study of the biosynthesis of FeFe hydrogenase, the electrochemical characterization of non-standard NiFe or FeFe hydrogenases, the general discussion of what makes a catalyst better in one particular direction of the reaction, and the elucidation of the molecular mechanisms of hydrogenase catalysis by combining electrochemistry and theoretical chemistry, spectroscopy or photochemistry. The electrochemical methods described herein will probably prove useful for studying or using other redox enzymes.     

Core@shell Poly(n‐butylacrylate)@polystyrene Nanoparticles: Baroplastic Force‐Responsiveness in Presence of Strong Phase Separation

Poly(n‐butylacrylate)@polystyrene nanoparticles behaving as a capsule‐based sealing nanoadditive are synthesized through an optimized semicontinuous emulsion polymerization protocol. Solid state time‐domain ¹H‐NMR and ¹³C magic angle spinning (MAS) NMR analysis suggest strong phase separation. Line width of ¹³C resonances in cross polarization and single pulse experiment MAS‐NMR spectra indicates that the peculiar mobility of each phase is preserved at the nanoscale. Atomic force spectroscopy (AFM) shows the permanence of spherical shape in absence of solvent (i.e., subsequent to strong capillary and surface forces) up to moderate external load, as well as the possibility of plastically deforming the polystyrene shell and ultimately triggering the nanoparticle flow at higher force loads. The breakdown characteristic of the nanoparticle shows for the first time baroplastic behavior on a single particle with precise biphasic core@shell morphology.

     

A Priori Estimates for Fractional Nonlinear Degenerate Diffusion Equations on Bounded Domains

Archive for Rational Mechanics and Analysis - We investigate quantitative properties of the nonnegative solutions $${u(t,x)\geq 0}$$ to the nonlinear fractional diffusion equation, $${\partial_t u...     

On the classification of multidimensionally consistent 3D maps

We classify multidimensionally consistent maps given by (formal or convergent) series of the following kind:

$$\begin{aligned} T_k x_{ij}=x_{ij} + \sum _{m=2}^\infty A_{ij ; \, k}^{(m)}(x_{ij},x_{ik},x_{jk}), \end{aligned}$$

where \(A_{ij;\, k}^{(m)}\) are homogeneous polynomials of degree m of their respective arguments. The result of our classification is that the only non-trivial multidimensionally consistent map in this class is given by the well-known symmetric discrete Darboux system

$$\begin{aligned} T_k x_{ij}=\frac{x_{ij}+x_{ik}x_{jk}}{\sqrt{1-x_{ik}^2}\sqrt{1-x_{jk}^2}}. \end{aligned}$$