On the Fundamental Polymer Chemistry of Inverse Vulcanization for Statistical and Segmented Copolymers from Elemental Sulfur

In this concept review, the fundamental and polymerization chemistry of inverse vulcanization for the preparation of statistical and segmented sulfur copolymers, which have been actively developed and advanced in various applications over the past decade is discussed. This concept review delves into a discussion of step-growth polymerization constructs to describe the inverse vulcanization process and discuss prepolymer approaches for the synthesis of segmented sulfur polyurethanes. Furthermore, this concept review discusses the advantages of inverse vulcanization in conjunction with dynamic covalent polymerization and post-polymerization modifications to prepare segmented block copolymers with enhanced thermomechanical and flame retardant properties of these materials.     

Stochastic sensitivity analysis of coupled acoustic-structural systems under non-stationary random excitations

This paper presents a new sensitivity analysis method for coupled acoustic–structural systems subjected to non-stationary random excitations. The integral of the response power spectrum density (PSD) of the coupled system is taken as the objective function. The thickness of each structural element is used as a design variable. A time-domain algorithm integrating the pseudo excitation method (PEM), direct differentiation method (DDM) and high precision direct (HPD) integration method is proposed for the sensitivity analysis of the objective function with respect to design variables. Firstly, the PEM is adopted to transform the sensitivity analysis under non-stationary random excitations into the sensitivity analysis under pseudo transient excitations. Then, the sensitivity analysis equation of the coupled system under pseudo transient excitations is derived based on the DDM. Moreover, the HPD integration method is used to efficiently solve the sensitivity analysis equation under pseudo transient excitations in a reduced-order modal space. Numerical examples are presented to demonstrate the validity of the proposed method.     

Hitting probabilities and the Hausdorff dimension of the inverse images of a class of anisotropic random fields

Let X = {X(t):t ∈ R~N} be an anisotropic random field with values in R~d.Under certain conditions on X,we establish upper and lower bounds on the hitting probabilities of X in terms of respectively Hausdorff measure and Bessel-Riesz capacity.We also obtain the Hausdorff dimension of its inverse image,and the Hausdorff and packing dimensions of its level sets.These results are applicable to non-linear solutions of stochastic heat equations driven by a white in time and spatially homogeneous Gaussian noise and anisotropic Guassian random fields.     

Investigation of segmental reorganization within amphiphilic block polymer nanoparticles derived from shell crosslinked micelle templates: Shell crosslinked knedel-like inversion

The construction of nanoscopic materials by synthetic methodologies that iterate covalent and supramolecular interactions has been developed over the past three decades as a powerful method to afford complex functional materials. Indeed, the present study was nearly lost in the archives of dissertation research completed in 2001, which revealed nanoscale conformational dynamics in the segmental reorganization, and partial inversion, of topologically shell crosslinked knedel-like (SCK) nanoparticles. © 2019 Wiley Periodicals, Inc. J. Polym. Sci. 2020 , 58, 204–214     

High strength,acid-resistant composites from canola,sunflower, or linseed oils: Influence of triglyceride unsaturation on material properties

Here are reported composites made by crosslinking unsaturated units in canola, sunflower, or linseed oil with sulfur to yield CanS , SunS , and LinS , respectively. These plant oils were selected because the average number of crosslinkable unsaturated units per triglyceride vary from 1.3 for canola to 1.5 for sunflower and 1.8 for linseed oil. The remeltable composites show compressive strengths that increase with increasing unsaturation number from CanS (9.3 MPa) to SunS (17.9 MPa) to LinS (22.9 MPa). These values for SunS and LinS are competitive when compared with the value of 17 MPa required for residential building using traditional Portland cement. The plant oil composites are recyclable over many cycles and can retain up to 100% of strength after 24 hr in oxidizing acid under conditions where Portland cement is dissolved in under 30 min. Infusion of the composites into premade cement blocks affords them with significantly improved acid resistance as well. This work thus provides a simple, nearly 100% atom economical route to convert plant oils and waste sulfur to composites having enhanced performance over commercial structural materials.     

A problem of determining a special spatial part of 3D memory kernel in an integro‐differential hyperbolic equation

The inverse problem of determining 2D spatial part of integral member kernel in integro‐differential wave equation is considered. It is supposed that the unknown function is a trigonometric polynomial with respect to the spatial variable y with coefficients continuous with respect to the variable x. Herein, the direct problem is represented by the initial‐boundary value problem for the half‐space x>0 with the zero initial Cauchy data and Neumann boundary condition as Dirac delta function concentrated on the boundary of the domain . Local existence and uniqueness theorem for the solution to the inverse problem is obtained.     

On Characterizations of Special Elements in Rings with Involution

Let $R$ be a ring with involution. It is well-known that an EP element in $R$ is a core invertible element, but the question when a core invertible element is an EP element, the authors answer in this paper. Several new characterizations of star-core, normal and Hermitian elements in $R$ are also presented.