On the uniqueness of semi-wavefronts for non-local delayed reaction–diffusion equations

We establish the uniqueness of semi-wavefront solution for a non-local delayed reaction–diffusion equation. This result is obtained by using a generalization of the Diekmann–Kaper theory for a nonlinear convolution equation. Several applications to the systems of non-local reaction–diffusion equations with distributed time delay are also considered.     

Specific Design of Titanium(IV) Phenolato Chelates Yields Stable and Accessible,Effective and Selective Anticancer Agents

Octahedral titanium(IV) complexes of phenolato hexadentate ligands were developed and showed very high stability for days in water solutions. In vitro cytotoxicity studies showed that, whereas tetrakis(phenolato) systems are generally of low activity presumably due to inaccessibility, smaller bis(phenolato)bis(alkoxo) complexes feature high anticancer activity and accessibility even without formulations, also toward a cisplatin‐resistant cell line. An all‐aliphatic control complex was unstable and inactive. A leading phenolato complex also revealed: 1) high durability in fully aqueous solutions; accordingly, negligible loss of activity after preincubation for three days in medium or in serum; 2) maximal cellular accumulation and induction of apoptosis following 24–48 h of administration; 3) reduced impact on noncancerous fibroblast cells; 4) in vivo efficacy toward lymphoma cells in murine model; 5) high activity in NCI‐60 panel, with average GI₅₀ of 4.6±2 μm . This newly developed family of Ti^IV complexes is thus of great potential for anticancer therapy.     

Is it True That the Normal Valence‐Length Correlation Is Irrelevant for Metal–Metal Bonds?

The most intriguing feature of metal–metal bonds in inorganic compounds is an apparent lack of correlation between the bond order and the bond length. In this study, we combine a variety of literature data obtained by quantum chemistry and our results based on the empirical bond valence model (BVM), to confirm for the first time the existence of a normal exponential correlation between the effective bond order (EBO) and the length of the metal–metal bonds. The difference between the EBO and the formal bond order is attributed to steric conflict between the (TM)_n cluster (TM=transition metal) and its environment. This conflict, affected mainly by structural type, should cause high lattice strains, but electron redistribution around TM atoms, evident from the BVM calculations, results in a full or partial strain relaxation.     

A new nonlinear optical silicate carbonate K2Ca[Si2O5](CO3) with a hybrid structure of kalsilite and soda-like layered fragments

Single crystals of a new silicate carbonate, K₂Ca[Si₂O₅](CO₃), have been synthesized in a multi-components hydrothermal solution with a pH value close to neutral and a high concentration of a carbonate mineralizer. The new compound has an axial structure (s.g. P6₃22) with unit cell parameters a = 5.04789 (15), c = 17.8668 (6) Å. Pseudosymmetry of the structure corresponds to s.g. P6₃/mmc which is broken only by one oxygen position. The structure consists of two layered fragments: one of the type of the mineral kalsilite (KAlSiO₄) and the other of the high-temperature soda-like α-Na₂CO₃, Ca substituting for Na. The electro-neutral layer K₂[Si₂O₅] (denoted K) as well as the layer Ca(CO₃) (denoted S) may separately correspond to individual structures. In K₂Ca[Si₂O₅](CO₃) the S-K layers are connected together via Ca-O interactions between Ca atoms from the carbonate layer and apical O atoms from the silicate one, and also via K-O interlayer interactions. A hypothetical acentric structure, sp.gr. P-62c, is predicted on the basis of the order-disorder theory. It presents another symmetrical option for the arrangement of K-layers relative to S-layers. The K,Ca-silicate-carbonate powder produces a moderate SHG signal that is two times larger that of the α-quartz powder standard and close to other silicates with acentric structures and low electronic polarizability.     

Site‐Resolved Two‐Step Relaxation Process in an Asymmetric Dy2 Single‐Molecule Magnet

Elaborate chemical design is of utmost importance in order to slow down the relaxation dynamics in single‐molecule magnets (SMMs) and hence improve their potential applications. Much interest was devoted to the study of distinct relaxation processes related to the different crystal fields of crystallographically independent lanthanide ions. However, the assignment of the relaxation processes to specific metal sites remains a challenging task. To address this challenge, a new asymmetric Dy₂ SMM displaying a well‐separated two‐step relaxation process with the anisotropic centers in fine‐tuned local environments was elaborately designed. For the first time a one‐to‐one relationship between the metal sites and the relaxation processes was evidenced. This work sheds light on complex multiple relaxation and may direct the rational design of lanthanide SMMs with enhanced magnetic properties.     

A study of the effect of step excrescences and free‐stream disturbances on boundary layer stability

In this work, a study of the mechanism by which free‐stream acoustic and vorticity disturbances interact with a boundary layer flow developing over a flat plate featuring a step excrescence located at a certain distance from a blunt leading edge is included. The numerical tool is a high‐fidelity implicit numerical algorithm solving for the unsteady, compressible form of the Navier–Stokes equations in a body‐fitted curvilinear coordinates and employing high‐accurate compact differencing schemes with Pade‐type filters. Acoustic and vorticity waves are generated using a source term in the momentum and energy equations, as opposed to using inflow boundary conditions, to avoid spurious waves that may propagate from boundaries. The results show that the receptivity to surface step excrescences is largely the result of an overall adverse pressure gradient posed by the step, and that the free‐stream disturbances accelerate the generation of instabilities in the downstream. As expected, it is found that the acoustic disturbance interacting with the surface imperfection is more efficient in exciting the Tollmien–Schlichting waves than the vorticity disturbance. The latter generates Tollmien–Schlichting waves that are grouped in wave packets consistent with the wavelength of the free‐stream disturbance. Copyright © 2015 John Wiley & Sons, Ltd.     

Stability of equilibrium solutions of a double power reaction-diffusion equation with a Dirac interaction

In this paper, information about the instability of equilibrium solutions of a nonlinear family of localized reaction-diffusion equations in dimension one is provided. More precisely, explicit formulas to the equilibrium solutions are computed and, via analytic perturbation theory, the exact number of positive eigenvalues of the linear operator associated to the stability problem is analyzed. In addition, sufficient conditions for blow up of the solutions of the equation are also discussed.