Employing isomorphisms between their ambient rings, we propose new definitions of equivalence and isometry for skew polycyclic codes that will lead to tighter classifications than existing ones. This reduces the number of previously known isometry and equivalence classes. In the process, we classify classes of skew (f, sigma, delta)-polycyclic codes with the same performance parameters, to avoid duplicating already existing codes, and state precisely when different notions of equivalence coincide. The generator of a skew polycyclic code is in one-one correspondence with the generator of a principal left ideal in its nonassociative unital ambient ring. By allowing the ambient rings to be nonassociative, we eliminate the need on restrictions on the length of the codes. Ring isomorphisms that preserve the Hamming distance (called isometries) map generators of principal left ideals to generators of principal left ideals and preserve length, dimension, and Hamming distance of the corresponding isometric skew polycyclic codes. (c) 2026 The Author(s). Published by Elsevier Inc. This is an open access article under the CC BY license (http:// creativecommons.org/licenses/by/4.0/).
In this paper, we propose a domain decomposition dynamical low-rank method to solve high-dimensional radiative transfer problems and similar kinetic equations. The algorithm uses a separate low-rank approximation on each spatial subdomain, which means that, for a given accuracy, we can often use fewer degrees of freedom compared to classic dynamical low-rank methods. In particular, we can solve problems with point sources efficiently, that for classic algorithms require almost full rank. Our algorithm only transfers boundary data between subdomains and is thus very attractive for distributed memory parallelization, where classic dynamical low-rank algorithms suffer from global data dependency. We demonstrate the efficiency of our algorithm by a number of challenging test examples that have both very optical thin and thick regions.
We study the local well-posedness of the solution to a coupled nonlinear elliptic-parabolic system which models electrical discharge in a Micro-Electro-Mechanical System (MEMS). A simple MEMS capacitor device contains two plates acting as the capacitor's electrodes, one of which is flexible, and which are separated by a narrow gas-filled gap. In the event of the flexible plate approaching the other, electrical discharge can occur. This is modelled here by two parabolic equations, for densities of electrons and positive ions, and an elliptic equation for electric potential. We show the local-in-time existence of a weak solution for the coupled system. Compactness techniques, used previously in the study of drift-diffusion equations, are employed in our proof.
By work of Howlett and Muraleedaran–Taylor, a parabolic subgroup of a real or complex reflection group always admits a complement in its normalizer. In this note, we investigate this phenomenon for quaternionic reflection groups. Here, in contrast to the real and complex setting, we find that complements of parabolic subgroups do not exist in general. Indeed, there are infinitely many examples of quaternionic reflection groups in arbitrary rank greater than 2 with a parabolic subgroup that does not admit a complement in its normalizer. We give a full classification of parabolic subgroups of irreducible quaternionic reflection groups and describe their complements, if the latter exist.
Prevalent supramolecular constructs in the stable anhydrate and solvates of daprodustat were investigated on the basis of structural data, molecular packing, and intermolecular energy calculations. Three previously reported polymorphs (Forms I-III), alongside six solvates have been (re)produced and characterized using complementary techniques, including hot-stage microscopy, differential scanning calorimetry, and variable-temperature powder X-ray diffraction. A monotropic relationship between Form II and the thermodynamically stable Form I has been confirmed. The crystal structures of Form I and five solvates are reported, with three of the solvates exhibiting isostructurality. The six solvates all desolvate to Form I upon heating. In contrast, an additional transient phase was found to transform into Form II. The title compound was also found to decompose upon prolonged exposure to temperatures above its sublimation temperature. Using pairwise intermolecular energy calculations, supramolecular columns propagating along the shortest crystallographic axis were identified as the predominant interaction in each daprodustat solid-state form. The findings of this study provide valuable insight into the challenges associated with suitable single crystal growth and the needle morphology consistently observed in daprodustat polymorphs and solvates. The thermal stability behaviour of solid-state forms of daprodustat and associated desolvation pathways established in this work can guide the selection of the most suitable form for processing.
