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1. Structural Properties of the Stability of Jamitons

   https://doi.org/10.1007/978-3-030-66560-9_3  

   Ramadan, R. A.; Rosales, R. R.; Seibold, B. (December 2020, Mathematical Descriptions of Traffic Flow: Micro, Macro and Kinetic Models. SEMA SIMAI Springer Series)

   null; null (Ed.)

   It is known that inhomogeneous second-order macroscopic traffic models can reproduce the phantom traffic jam phenomenon: whenever the sub-characteristic condition is violated, uniform traffic flow is unstable, and small perturbations grow into nonlinear traveling waves, called jamitons. In contrast, what is essentially unstudied is the question: which jamiton solutions are dynamically stable? To understand which stop-and-go traffic waves can arise through the dynamics of the model, this question is critical. This paper first presents a computational study demonstrating which types of jamitons do arise dynamically, and which do not. Then, a procedure is presented that characterizes the stability of jamitons. The study reveals that a critical component of this analysis is the proper treatment of the perturbations to the shocks, and of the neighborhood of the sonic points. 

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2. The size of the class of countable sequences of ordinals

   https://doi.org/10.1090/tran/8573  

   Chan, William; Jackson, Stephen; Trang, Nam (January 2021, Transactions of the American Mathematical Society)

   Assume . There is no injection of (the set of countable length sequences of countable ordinals) into (the class of length sequences of ordinals). There is no injection of (the powerset of ) into (the class of countable length sequences of ordinals). 

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3. Supercooling of the A phase of 3He

   https://doi.org/10.1038/s41467-022-35532-7  

   Tian, Y.; Lotnyk, D.; Eyal, A.; Zhang, K.; Zhelev, N.; Abhilash, T. S.; Chavez, A.; Smith, E. N.; Hindmarsh, M.; Saunders, J.; et al (December 2023, Nature Communications)

   Abstract Because of the extreme purity, lack of disorder, and complex order parameter, the first-order superfluid 3 He A–B transition is the leading model system for first order transitions in the early universe. Here we report on the path dependence of the supercooling of the A phase over a wide range of pressures below 29.3 bar at nearly zero magnetic field. The A phase can be cooled significantly below the thermodynamic A–B transition temperature. While the extent of supercooling is highly reproducible, it depends strongly upon the cooling trajectory: The metastability of the A phase is enhanced by transiting through regions where the A phase is more stable. We provide evidence that some of the additional supercooling is due to the elimination of B phase nucleation precursors formed upon passage through the superfluid transition. A greater understanding of the physics is essential before 3 He can be exploited to model transitions in the early universe. 

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4. Projectivity of the moduli of curves

   https://doi.org/10.1017/9781009051897.003  

   Cheng, Raymond; Lian, Carl; Murayama, Takumi (October 2022, Cambridge University Press)

   Belmans, Pieter; Ho, Wei; de_Jong, Aise Johan (Ed.)

   In this expository paper, we show that the Deligne–Mumford moduli space of stable curves is projective over Spec(Z). The proof we present is due to Kollár. Ampleness of a line bundle is deduced from the nefness of a related vector bundle via the ampleness lemma, a classifying map construction. The main positivity result concerns the pushforward of relative dualizing sheaves on families of stable curves over a smooth projective curve. 

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5. Small Gröbner fans of ideals of points

   https://doi.org/10.1142/S0219498820500875  

   Dimitrova, Elena; He, Qijun; Robbiano, Lorenzo; Stigler, Brandilyn (May 2020, Journal of Algebra and Its Applications)

   In the context of modeling biological systems, it is of interest to generate ideals of points with a unique reduced Gröbner basis, and the first main goal of this paper is to identify classes of ideals in polynomial rings which share this property. Moreover, we provide methodologies for constructing such ideals. We then relax the condition of uniqueness. The second and most relevant topic discussed here is to consider and identify pairs of ideals with the same number of reduced Gröbner bases, that is, with the same cardinality of their associated Gröbner fan. 

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