Application of Time Series Analysis Methods to Assess the impact of COVID-19 on Carbon Dioxide Emission Reduction in Connecticut - Kiernan, Katherine A.; Wu, Hao; Mugno, Ray; Pang, Yulei (2022 IEEE International Conference on Big Data (Big Data), 2022)
The primary goals of this study are to determine if the datasets of positive COVID-19 test cases and CO2 emissions from Connecticut over the span of March 24th, 2020-October 31, 2021 are in any ways correlated. With climate change a prominent issue facing the entire world today, it is important to explore methods of providing records of past patterns of greenhouse gas emissions in order to inform decision making that could reduce future ones. Autoregressive integrated moving average (ARIMA) modeling is also implemented in this paper to provide forecasting based on CO2 emissions in CT starting from 2019. The most significant results from this paper are as follows: the CO2 emission data of transportation sectors including ground transportation, domestics aviation, and international aviation and weekly COVID-19 positive test cases data has a strong relationship during the first 28 weeks of the pandemic with a correlation of -86.34%. The CO2 emissions experienced on average a -22.96% change of pre-pandemic vs during initial quarantine conditions and at most a - 44.48% change when comparing the pre-pandemic mean to the during initial quarantine minimum value. Lastly, the ARIMA model found to have the lowest Akaike information criterion (AIC) was ARIMA (4,0,4). In conclusion, in the event of a collective global pandemic and lockdown conditions, less traveling resulting in a correlated decrease of CO2 emissions. This means that perhaps concentrated efforts on reducing unnecessary travel could help mitigate the levels of carbon dioxide emissions as a more long-term solution to climate change opposed to the pandemic’s short-term example.
Keywords: ARIMA; CO2 emission; COVID-19; Carbon dioxide; Change points detection; Climate change; Correlation coefficient; Decision making; Greenhouse effect; Pandemics; Time series analysis; dept.csc; dept.mat

A norm functor for quadratic algebras - Biesel, Owen (Beiträge zur Algebra und Geometrie / Contributions to Algebra and Geometry, 2022)
Given commutative, unital rings $$\mathcal {A}$$and $$\mathcal {B}$$with a ring homomorphism $$\mathcal {A}\rightarrow \mathcal {B}$$making $$\mathcal {B}$$free of finite rank as an $$\mathcal {A}$$-module, we can ask for a “trace” or “norm” homomorphism taking algebraic data over $$\mathcal {B}$$to algebraic data over $$\mathcal {A}$$. In this paper we we construct a norm functor for the data of a quadratic algebra: given a locally-free rank-2 $$\mathcal {B}$$-algebra $$\mathcal {D}$$, we produce a locally-free rank-2 $$\mathcal {A}$$-algebra $$\textrm{Nm}_{\mathcal {B}/\mathcal {A}}(\mathcal {D})$$in a way that is compatible with other norm functors and which extends a known construction for étale quadratic algebras. We also conjecture a relationship between discriminant algebras and this new norm functor.
Keywords: 11R11; 13B02; 13B40; 13C10; 14B25; Algebra of finite rank; Norm functor; Quadratic algebra; Ring extension; dept.mat; Étale algebra

Deformations of reducible SL(n, C) representations of fibered 3-manifold groups - Kozai, K. (Osaka Journal of Mathematics, 2022)
Let Mφ be a surface bundle over a circle with monodromy φ: S → S. We study deformations of certain reducible representations of π1(Mφ)intoSL(n, C), obtained by composing a reducible representation into SL(2, C) with the irreducible representation SL(2, C) → SL(n, C). In particular, we show that under certain conditions on the eigenvalues of φ∗, the reducible representation is contained in a (n + 1 + k)(n − 1) dimensional component of the representation variety, where k is the number of components of ∂Mφ . This result applies to mapping tori of pseudo-Anosov maps with orientable invariant foliations whenever 1 is not an eigenvalue of the induced map on homology, where the reducible representation is also a limit of irreducible representations. © 2022, Osaka University. All rights reserved.
Keywords: dept.mat; ⛔ No DOI found

Comparative assessment of shell properties in eight species of cohabiting unionid bivalves - Prezant, Robert S.; Dickinson, Gary H.; Chapman, Eric J.; Mugno, Raymond; Rosen, Miranda N.; Cadmus, Maxx B. (Freshwater Mollusk Biology and Conservation, 2022)
Freshwater unionid mussels produce a bilayered shell with the mineral proportion comprising an outer prismatic and an inner nacreous layer. The shell is the animals’ primary structural means of protection from predators and environmental challenges; therefore, variations in shell strength and properties may lead to differences in survival. Few studies have systematically assessed shell properties in unionids. A major challenge in such work is separating effects of environment from those of evolutionary history, because ultimately, both can affect shell properties. We collected eight species of unionids within a small area of the Allegheny River, Pennsylvania, that was relatively homogeneous in substratum type and other environmental characteristics. For each species, we quantified shell thickness, including thickness of the prismatic and nacreous layers, and shell micromechanical properties (microhardness and crack propagation, a measure of fracture resistance) in three regions of the shell. Shell thickness varied dramatically among species and was about five times greater in the thickest-shelled species, Pleurobema sintoxia, than in the thinnest-shelled species, Villosa iris. Because all species experienced similar environmental conditions, variation in shell thickness can be attributed largely to evolutionary history. In contrast, microhardness and crack propagation showed little variation among species. Given that micromechanical properties are similar among species, shell strength may be largely a function of thickness. These results have conservation implications, as differences in shell thickness could reflect relative vulnerability to predators and physical conditions
Keywords: dept.aa; dept.mat; peer-reviewed

Constructing (3, B)-sudoku pair latin squares - Carrigan, Braxton; Diaz, David; Hammer, James; Lorch, John (Australasian Journal of Combinatorics, 2022)
An (a, b)-Sudoku pair Latin square is a Latin square that is simult-aneously an (a, b)-Sudoku Latin square and a (b, a)-Sudoku Latin square. While (a, b)-Sudoku Latin squares are known to exist for any positive integers a and b, the pairs a, b for which an (a, b)-Sudoku pair Latin square exists are largely unknown. In this article we establish the existence of (a, b)-Sudoku pair Latin squares for an infinite collection of pairs (a, b). Our results show that a (3, b)-Sudoku pair Latin square can be constructed for any positive integer b. ©The author(s).
Keywords: dept.mat; peer-reviewed; ⛔ No DOI found