PAN composite membrane with different solvent affinities controlled by surface modification methods

Polyacrylonitrile (PAN) composite membranes with surface properties designed by either a chemical modification with ethylenediamine (EDA), or layer‐by‐layer (LbL) polyelectrolyte adsorption were investigated in this paper. Fourier‐transformed infrared (FTIR) spectroscopy and streaming potential measurements showed that the first step of the reaction with EDA in gas phase was the formation of ammonium salts with the reactive carboxylic groups present on the surface of the starting membrane. Part of the ammonium carboxylate groups was transformed in secondary amide linkages by a heat‐induced reaction. Poly(sodium styrenesulfonate) (NaPSS) and a polycation containing about 95 mol % of N,N‐dimethyl‐2‐hydroxypropyleneammonium chloride units in the backbone (PCA₅) were used as opposite polyions in the LbL film construction. The adsorbed polyion amount per every layer was controlled by the nature and concentration of the supporting electrolyte in polyelectrolyte deposition solution (NaBr and KBr). An almost linear increase of the adsorbed polyion amount versus the layer pair number was observed. The swelling degree (SD) in pure alcohols of the LbL‐modified PAN composite membrane decreased with the increase of the solvent polarity and with the decrease of the pore volume by pore filling with polyelectrolyte complex multilayer. © 2005 Wiley Periodicals, Inc. J Polym Sci Part A: Polym Chem 43: 4161–4171, 2005     

Observation of nonlinear self-trapping in triangular photonic lattices

We experimentally study light self-trapping in triangular photonic lattices induced optically in nonlinear photorefractive crystals. We observe the formation of two-dimensional discrete and gap spatial solitons originating from the first and second bands of the linear transmission spectrum.     

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.     

Gravitational Field Equations on Fefferman Space–Times

The total space \({\mathfrak M} \approx {\mathbb H}_1 \times S^1\) of the canonical circle bundle over the 3-dimensional Heisenberg group \({\mathbb H}_1\) is a space–time with the Lorentzian metric \(F_{\theta _0}\) (Fefferman’s metric) associated to the canonical Tanaka–Webster flat contact form \(\theta _0\) on \({\mathbb H}_1\). The matter and energy content of \(\mathfrak M\) is described by the energy-momentum tensor \({T}_{\mu \nu }\) (the trace-less Ricci tensor of \(F_{\theta _0}\)) as an effect of the non flat nature of Feferman’s metric \(F_{\theta _0}\). We study the gravitational field equations \(R_{\mu \nu } - (1/2) \, R \, g_{\mu \nu } = {T}_{\mu \nu }\) on \({\mathfrak M}\). We consider the first order perturbation \(g = F_{\theta _0} + \epsilon \, h\), \(\epsilon<< 1\), and linearize the field equations about \(F_{\theta _0}\). We determine a Lorentzian metric g on \({\mathfrak M}\) which solves the linearized field equations corresponding to a diagonal perturbation h.     

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.     

A Buzano type inequality for two Hermitian forms and applications

A Buzano type inequality for two nonnegative Hermitian forms is obtained. Applications to inequalities for norm and numerical radius of bounded linear operators in complex Hilbert spaces are given.     

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.     

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].