Embedding Banach spaces into the space of bounded functions with countable support

We prove that a WLD subspace of the space consisting of all bounded, countably supported functions on a set Γ embeds isomorphically into if and only if it does not contain isometric copies of . Moreover, a subspace of is constructed that has an unconditional basis, does not embed into , and whose every weakly compact subset is separable (in particular, it cannot contain any isomorphic copies of ).     

Euler’s partition theorem for all moduli and new companions to Rogers–Ramanujan–Andrews–Gordon identities

The Ramanujan Journal - We generalise Euler’s partition theorem involving odd parts and distinct parts for all moduli and provide new companions to...     

Supervised learning via smoothed Polya trees

Advances in Data Analysis and Classification - We propose a generative classification model that extends Quadratic Discriminant Analysis (QDA) (Cox in J R Stat Soc Ser B (Methodol)...     

Self-assembly mechanism of PEG-b-PCL and PEG-b-PBO-b-PCL amphiphilic copolymer micelles in aqueous solution from coarse grain modeling

We followed the self-assembly of high-molecular weight MePEG- b -PCL (poly(methyl ethylene glycol)-block-poly(ε-caprolactone)) diblock and MePEG- b -PBO- b -PCL (poly(methyl ethylene glycol)-block-poly(1,2-butylene oxide)-block-poly(ε-caprolactone)) into micelles using molecular dynamics simulation with a coarse grain (CG) force field based on quantum mechanics (CGq FF). The triblock polymer included a short poly(1,2-butylene oxide) (PBO) at the hydrophilic-hydrophobic interface of these systems. Keeping the hydrophilic length fixed (MePEG₄₅), we considered 250 chains in which the hydrophobic length changed from PCL₄₄ or PBO₆- b -PCL₄₃ to PCL₆₂ or PBO₉- b -PCL₆₁. The polymers were solvated in explicit water for 2 μs of simulations at 310.15 K. We found that the longer diblock system undergoes a morphological transition from an intermediate rod-like micelle to a prolate-sphere, while the micelle formed from the longer triblock system is a stable rod-like micelle. The two shorter diblock and triblock systems show similar self-assembly processes, both resulting in slightly prolate-spheres. The dynamics of the self-assembly is quantified in terms of chain radius of gyration, shape anisotropy, and hydration of the micelle cores. The final micelle structures are analyzed in terms of the local density components. We conclude that the CG model accurately describes the molecular mechanisms of self-assembly and the equilibrium micellar structures of hydrophilic and hydrophobic chains, including the quantity of solvent trapped inside the micellar core.     

Multiple linear regression models for predicting the n‑octanol/water partition coefficients in the SAMPL7 blind challenge

Journal of Computer-Aided Molecular Design - A multiple linear regression model called MLR-3 is used for predicting the experimental n-octanol/water partition coefficient (log PN) of 22...     

Graph Theory Applied to Plasma Chemical Reaction Engineering

Plasma Chemistry and Plasma Processing - This work explores the following applications of graph theory to plasma chemical reaction engineering: assembly of a weighted directional graph with the key...