An Extremal Problem Arising in the Dynamics of Two-Phase Materials That Directly Reveals Information about the Internal Geometry

In two-phase materials, each phase having a non-local response in time, it has been found that for some driving fields the response somehow untangles at specific times, and allows one to directly infer useful information about the geometry of the material, such as the volume fractions of the phases. Motivated by this, and to obtain an algorithm for designing appropriate driving fields, we find approximate, measure independent, linear relations between the values that Markov functions take at a given set of possibly complex points, not belonging to the interval [-1,1] where the measure is supported. The problem is reduced to simply one of polynomial approximation of a given function on the interval [-1,1] and, to simplify the analysis, Chebyshev approximation is used. This allows one to obtain explicit estimates of the error of the approximation, in terms of the number of points and the minimum distance of the points to the interval [-1,1]. Assuming this minimum distance is bounded below by a number greater than 1/2, the error converges exponentially to zero as the number of points is increased. Approximate linear relations are also obtained that incorporate a set of moments of the measure. In the context of the motivating problem, the analysis also yields bounds on the response at any particular time for any driving field, and allows one to estimate the response at a given frequency using an appropriately designed driving field that effectively is turned on only for a fixed interval of time. The approximation extends directly to Markov-type functions with a positive semidefinite operator valued measure, and this has applications to determining the shape of an inclusion in a body from boundary flux measurements at a specific time, when the time-dependent boundary potentials are suitably tailored. © 2022 Wiley Periodicals, Inc.     

A Generalization of the Univalence on the Boundary Theorem with Applications to Sobolev Mappings

We give a generalization of a known theorem from classical complex analysis, namely the univalence on the boundary theorem. We apply this result to obtain some univalence conditions for Sobolev mappings \(f\in C({\overline{D}},{\mathbb {R}}^n)\bigcap W_{loc}^{1,q}(D,{\mathbb {R}}^n)\) which are injective on \(\partial D\), in connection with a known result of Ball from (Proc R Soc Edinb Sect A 88(3–4):315–328, 1981) modeling nonlinear elasticity.     

Transfer, amplification, and inversion of helical chirality mediated by concerted interactions of C3-supramolecular dendrimers

The synthesis, structural, and retrostructural analysis of two libraries containing 16 first and second generation C(3)-symmetric self-assembling dendrimers based on dendrons connected at their apex via trisesters and trisamides of 1,3,5-benzenetricarboxylic acid is reported. A combination of X-ray diffraction and CD/UV analysis methods demonstrated that their C(3)-symmetry modulates different degrees of packing on the periphery of supramolecular structures that are responsible for the formation of chiral helical supramolecular columns and spheres self-organizable in a diversity of three-dimensional (3D) columnar, tetragonal, and cubic lattices. Two of these periodic arrays, a 3D columnar hexagonal superlattice and a 3D columnar simple orthorhombic chiral lattice with P222(1) symmetry, are unprecedented for supramolecular dendrimers. A thermal-reversible inversion of chirality was discovered in helical supramolecular columns. This inversion is induced, on heating, by the change in symmetry from a 3D columnar simple orthorhombic chiral lattice to a 3D columnar hexagonal array and, on cooling, by the change in symmetry from a 2D hexagonal to a 2D centered rectangular lattice, both exhibiting intracolumnar order. A first-order transition from coupled columns with long helical pitch, to weakly or uncorrelated columns with short helical pitch that generates a molecular rotator, was also discovered. The torsion angles of the molecular rotator are proportional to the change in temperature, and this effect is amplified in the case of the C(3)-symmetric trisamide supramolecular dendrimers forming H-bonds along their column. The structural changes reported here can be used to design complex functions based on helical supramolecular dendrimers with different degree of packing on their periphery.     

Enumerative Properties of NC (B) (p,q)

We determine the rank generating function, the zeta polynomial and the M?bius function for the poset NC ^(B) (p, q) of annular non-crossing partitions of type B, where p and q are two positive integers. We give an alternative treatment of some of these results in the case q = 1, for which this poset is a lattice. We also consider the general case of multiannular noncrossing partitions of type B, and prove that this reduces to the cases of non-crossing partitions of type B in the annulus and the disc.     

Nonlinear versions of a vector maximal principle

Some nonlinear extensions of the vector maximality statement established by Goepfert et al. [A. Goepfert, C. Tammer, C. Z?linescu, On the vectorial Ekeland’s variational principle and minimal points in product spaces, Nonlinear Anal. 39 (2000) 909-922] are given. Basic instruments for these are the Brezis-Browder ordering principle [H. Brezis, F.E. Browder, A general principle on ordered sets in nonlinear functional analysis, Adv. Math. 21 (1976) 355-364] and its logical equivalent in Turinici [M. Turinici, Variational principles on semi-metric structures, Libertas Math. 20 (2000) 161-171].     

High dilution of anionic vacancies in Sr(0.8)Ba(0.2)Fe(O,F)(~2.5)

The (Ba,Sr)FeO(3-δ) system is known for its strong tendency for oxygen and vacancies to order into several forms including fully ordered pseudobrownmillerites, hexagonal perovskites with segregation of the vacancies in particular anionic layers and low deficient (pseudo)cubic compounds (generally δ < 0.27, Fe(3/4+)). We show for the first time, using a simple chemical process, the easy access to a large amount of vacancies (δ ≈ 0.5, Fe(3+)) within the room-temperature stable tetragonal (pseudocubic) Sr(0.8)Ba(0.2)FeF(~0.1)(O,F)(~2.5.) The drastic effect of the incorporation of a minor amount of fluoride passes through the repartition of local O/F/□ constraints shifting the tolerance factor into the pseudocubic range for highly deficient compounds. It is stable up to 670 K, where an irreversible reoxidation process occurs, leading to the cubic-form. The comparison with the cubic oxide Sr(0.8)Ba(0.2)FeO(~2.7) shows the increase of the resistivity (3D-VRH model) by two decades due to the almost single valent Fe(3+) of the oxofluoride. In addition, the G-type magnetic ordering shows relatively weak moment for Fe(3+) cations (M(Fe) ≈ 2.64(1) μB at room temperature) attributed to incoherent magnetic components expected from local disorder in such anionic-deficient compounds.     

New link between conceptual density functional theory and electron delocalization

In this paper we give a new definition of the softness kernel based on the exchange-correlation density. This new kernel is shown to correspond to the change of electron fluctuation upon external perturbation, thus helping to bridge the gap between conceptual density functional theory and some tools describing electron localization in molecules. With the aid of a few computational calculations on diatomics we illustrate the performance of this new computational tool.     

Selection of a synthetic glycan oligomer from a library of DNA-templated fragments against DC-SIGN and inhibition of HIV gp120 binding to dendritic cells

We report the synthesis of a nucleic acid-encoded carbohydrate library, its combinatorial self-assembly into 37,485 pairs and a screen against DC-SIGN leading to the identification of consensus ligand motifs. A prototypical example from the selected pairs was shown to have enhanced binding. A dendrimer incorporating the selected motifs inhibited gp120's binding to dendritic cells with higher efficiency than mannan.     

A multipurpose gold(I) precatalyst

[Au(tmbn)(2)](SbF(6)) is the first gold(I) complex supported by two nitrile ligands that is indefinitely stable at room temperature. This is a highly versatile precatalyst that can be used for the preparation of active and robust solid-supported gold(I) catalysts.     

Thermal behavior of some vanadyl complexes with flavone derivatives as potential insulin-mimetic agents

Two new complexes having general formula VOL₂·nH₂O [(1) L: 5-hydroxyflavone, n = 1; (2) L: chrysin, n = 4] were synthesized and characterized. Based on IR and electronic data we concluded that studied flavones act as bidentate ligands in complexes with metallic ion coordinated in a square-pyramidal stereochemistry. The thermal analysis (TG, DTA) elucidated the composition and also the number and nature of the water molecules. The thermal behavior also indicated strong interactions between oxovanadium (IV) and these oxygen donor ligands.