On skew polynomial rings over locally nilpotent rings

We will show that skew polynomial rings in several variables over locally nilpotent rings cannot contain nonzero idempotent elements. We will also prove that such rings are Brown–McCoy radical.     

Tropical Hurwitz numbers

Hurwitz numbers count genus g, degree d covers of ℙ¹ with fixed branch locus. This equals the degree of a natural branch map defined on the Hurwitz space. In tropical geometry, algebraic curves are replaced by certain piece-wise linear objects called tropical curves. This paper develops a tropical counterpart of the branch map and shows that its degree recovers classical Hurwitz numbers. Further, the combinatorial techniques developed are applied to recover results of Goulden et al. (in Adv. Math. 198:43–92, 2005) and Shadrin et al. (in Adv. Math. 217(1):79–96, 2008) on the piecewise polynomial structure of double Hurwitz numbers in genus 0.     

Grünbaum colorings of toroidal triangulations

We prove that if G is a triangulation of the torus and χ(G)≠5, then there is a 3‐coloring of the edges of G so that the edges bounding every face are assigned three different colors. © 2009 Wiley Periodicals, Inc. J Graph Theory 63: 68–81, 2010     

Modeling of Al12N12, Mg12O12, Ca12O12, and C23N nanostructured as potential anode materials for sodium-ion battery

Journal of Solid State Electrochemistry - The rising costs of lithium and other versatile metals which are of electrochemical importance have sprouted concerns in the electrochemical world. Sodium...     

Sustainable Design of Structural and Functional Polymers for a Circular Economy

To achieve a sustainable circular economy, polymer production must start transitioning to recycled and biobased feedstock and accomplish CO₂ emission neutrality. This is not only true for structural polymers, such as in packaging or engineering applications, but also for functional polymers in liquid formulations, such as adhesives, lubricants, thickeners or dispersants. At their end of life, polymers must be either collected and recycled via a technical pathway, or be biodegradable if they are not collectable. Advances in polymer chemistry and applications, aided by computational material science, open the way to addressing these issues comprehensively by designing for recyclability and biodegradability. This Review explores how scientific progress, together with emerging regulatory frameworks, societal expectations and economic boundary conditions, paint pathways for the transformation towards a circular economy of polymers.     

Compartmentalized Polyampholyte Microgels by Depletion Flocculation and Coacervation of Nanogels in Emulsion Droplets

In pH-responsive drug carriers, the distribution of charges has been proven to affect delivery efficiency but is difficult to control and verify. Herein, we fabricate polyampholyte nanogel-in-microgel colloids (NiM−C) and show that the arrangement of the nanogels (NG) can easily be manipulated by adapting synthesis conditions. Positively and negatively charged pH-responsive NG are synthesized by precipitation polymerization and labelled with different fluorescent dyes. The obtained NG are integrated into microgel (MG) networks by subsequent inverse emulsion polymerization in droplet-based microfluidics. By confocal laser scanning microscopy (CLSM), we verify that depending on NG concentration, pH value and ionic strength, NiM−C with different NG arrangements are obtained, including Janus-like phase-separation of NG, statistical distribution of NG, and core–shell arrangements. Our approach is a major step towards uptake and release of oppositely charged (drug) molecules.