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Let A be a Noetherian local ring with canonical module KA. We characterize A when KA is a torsionless, reflexive, or q-torsionfree module for an integer q ≥ 3. If A is a Cohen–Macaulay ring, H.-B. Foxby proved in 1974 that the A-module KA is q-torsionfree if and only if the ring A is q-Gorenstein. With mild assumptions, we provide a generalization of Foxby’s result to arbitrary Noetherian local rings admitting the canonical module. In particular, since the reflexivity of the canonical module is closely related to the ring being Gorenstein in low codimension, we also explore quasinormal rings, introduced by W. V. Vasconcelos. We provide several examples as well. ©2025 Walter de Gruyter GmbH,Berlin/Boston.

This paper surveys and summarizes Wolmer Vasconcelos’ results surrounding multiplicities, Hilbert coefficients, and their extensions. We particularly focus on Vasconcelos’ results regarding multiplicities and Chern coefficients, and other invariants which they bound. The Sally module is an important instrument introduced by Vasconcelos for this study, which naturally relates Hilbert coefficients to reduction numbers. ©2025 Walter de Gruyter GmbH,Berlin/Boston.

A degree of a module M is a numerical measure of information carried by M. We highlight some of Vasconcelos’ outstanding contributions to the theory of degrees, bridging commutative algebra and computational algebra. We present several degrees he introduced and developed, including arithmetic degree, jdeg, homological degree, cohomological degrees, canonical degree, and bicanonical degree. For the canonical and bicanonical degrees, we discuss recent developments motivated by our joint works [25, 19, 9]. ©2025 Walter de Gruyter GmbH,Berlin/Boston.

The Alder–Andrews Theorem, a partition inequality generalizing Euler’s partition identity, the first Rogers–Ramanujan identity, and a theorem of Schur to d-distinct partitions of n, was proved successively by Andrews in 1971, Yee in 2008, and Alfes, Jameson, and Lemke Oliver in 2010. While Andrews and Yee utilized q-series and combinatorial methods, Alfes et al. proved the finite number of remaining cases using asymptotics originating with Meinardus together with high-performance computing. In 2020, Kang and Park conjectured a “level 2” Alder–Andrews type partition inequality which relates to the second Rogers–Ramanujan identity. Duncan, Khunger, the second author, and Tamura proved Kang and Park’s conjecture for all but finitely many cases using a combinatorial shift identity. Here, we generalize the methods of Alfes et al. to resolve nearly all of the remaining cases of Kang and Park’s conjecture. © The Author(s), under exclusive licence to Springer Science+Business Media, LLC, part of Springer Nature 2026.

A proper Skolem labelling of a graph G is a function assigning a positive integer to each vertex of G such that any two vertices assigned the same integer are that distance apart in the graph. The Skolem number of a graph is smallest number n such that there exists a proper Skolem labelling only using the positive integers less than or equal to n. In this paper, we will begin by proving the Skolem number for another family of subgraphs of the hexagonal lattice and then prove the Skolem number for two families of subgraphs of the Kagome Lattice. © 2025 Georgia Southern University. All rights reserved.

The λ-fold complete 3-uniform hypergraph on v vertices has the edge multiset consisting of λ copies of each 3-element subset of its vertex set. A tight 6-cycle, denoted TC6, is a hypergraph with vertex set {a,b,c,d,e,f} and edge set {{a,b,c},{b,c,d},{c,d,e},{d,e,f},{e,f,a},{f,a,b}}. We give necessary and sufficient conditions on v for the existence of a TC6-decomposition of the λ-fold complete 3-uniform hypergraph on v vertices for any positive integer λ. © The Author(s), under exclusive license to Springer Nature Switzerland AG 2025.

Objective To compare the incidence and natural course of reactive axillary lymph nodes (RAL) between mRNA and attenuated whole-virus vaccines using Deauville criteria. Methods In this multi-institutional PET-CT study comprising multiple vaccine types (Pfizer-BioNTech/Comirnaty, Moderna/Spikevax, Sinovac/CoronaVac and Janssen vaccines), we evaluated the incidence and natural course of RAL in a large cohort of oncological patients utilizing a standardized Deauville scaling system (n=522; 293 Female, Deauville 3-5 positive for RAL). Univariate and multivariate analyses were conducted to evaluate the predictive value of clinical parameters (absolute neutrophil count [ANC], platelets, age, sex, tumor type, and vaccine-to-PET interval) for PET positivity. Results Pfizer-BioNTech/Comirnaty and Moderna vaccines revealed similar RAL incidences for the first 20 days after the second dose of vaccine administration (44% for the first 10 days for both groups, 26% vs. 20% for 10-20 days, respectively for Moderna and Pfizer). However, Moderna recipients revealed significantly higher incidences of RAL after 20 days compared to Pfizer-BioNTech/Comirnaty, with nodal reactivity spanning up to the 9th week post-vaccination (15% vs. 4%, respectively P<0.001). No RAL was observed in patients who received either a single dose of J&J vaccine or two doses of CroronaVac. Younger patients showed increased likelihood of RAL, otherwise, clinical/demographic parameters were not predictive of RAL (P=0.014 for age, P>0.05 for additional clinical/demographic parameters). Conclusion RAL based on strict PET criteria was observed with mRNA but not with attenuated whole-virus vaccines, in line with higher immunogenicity and stronger protection offered by mRNA vaccines. © 2024 Wolters Kluwer Health. All rights reserved.

Human mesenchymal stem cells (hMSCs) have great potential in cell-based therapies and regenerative medicine due to their self-renewal and multipotency. hMSCs can be differentiated into several cell types, including adipocytes and osteblast. Conventional approaches for determining adipocyte formation include staining of lipid droplets (i.e., oil-red-O) during adipogenesis, which is time-consuming and uneconomical. Thus, there is an emerging need for a more effective and accurate approach to the prediction of adipogenic differentiation. Here, by combining live-cell imaging with a deep learning method, we developed a convolutional neural network-based approach to precisely predict lipid droplet formation during adipogenic differentiation of hMSCs. © 2023 IEEE.

In L1 attrition research, it's recognized that a previously acquired language can transform under the influence of a newly acquired one. However, the precise L1-L2 relationship is intricate and warrants further study. Some research suggest that L2 mastery might reduce L1 proficiency, while others show that both languages can be maintained. Age of onset and L1 use are the factors that have been discussed in the debate surrounding L1 attrition. The study aims to contribute to the ongoing discussion by examining L1 and L2 proficiency of Russian-English bilingual speakers (N = 35). The participants with comparable L2 proficiency but various degrees of L1 attrition who arrived at different ages and differed in their frequency of L1 use were recruited for the study. This diverse group provided an ideal quality sample for investigating the role of age of onset and L1 use, as well as the interplay between L1 and L2. By comparing L1 and L2 lexical diversity, syntactic complexity, and fluency, the study revealed that higher L2 proficiency was not associated with lower levels of L1 proficiency, suggesting that L1 retention is possible amidst L2 acquisition. L1 use played a more significant role in the L1 maintenance of these bilingual individuals. © 2024 Association for Language Learning.

Impaired autonomic modulation and baroreflex sensitivity (BRS) have been reported during and after COVID-19. Both impairments are associated with negative cardiovascular outcomes. If these impairments were to exist undetected in young men after COVID-19, they could lead to negative cardiovascular outcomes. Fatigue is associated with autonomic dysfunction during and after COVID-19. It is unclear if fatigue can be used as an indicator of impaired autonomic modulation and BRS after COVID-19. This study aims to compare parasympathetic modulation, sympathetic modulation, and BRS between young men who had COVID-19 versus controls and to determine if fatigue is associated with impaired autonomic modulation and BRS. Parasympathetic modulation as the high-frequency power of R-R intervals (lnHFR-R), sympathetic modulation as the low-frequency power of systolic blood pressure variability (LFSBP), and BRS as the -index were measured by power spectral density analysis. These variables were compared between 20 young men who had COVID-19 and 24 controls. Independent t-tests and Mann-Whitney U tests indicated no significant difference between the COVID-19 and the control group in: lnHFR-R, P=0.20; LFSBP, P=0.11, and -index, P=0.20. Fatigue was not associated with impaired autonomic modulation or BRS. There is no difference in autonomic modulations or BRS between young men who had COVID-19 compared to controls. Fatigue did not seem to be associated with impaired autonomic modulation or impaired BRS in young men after COVID-19. Findings suggest that young men might not be at increased cardiovascular risk from COVID-19-related dysautonomia and impaired BRS.

Wrote the online, open source numerical analysis textbook "Tea Time Numerical Analysis" hosted at github.com. Report describes the process of writing, publishing the text. Includes information about review process and statement of success towards goals.