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1. The dipolar field of rotating bodies in two dimensions

   https://doi.org/10.1017/S0022112008001857  

   SMITH, STEFAN G.; MICHELIN, SÉBASTIEN; CROWDY, D. G. (July 2008, Journal of Fluid Mechanics)

   null (Ed.)

   The fluid velocity far from a translating body in two-dimensional irrotational flow is generally dipolar. This is a classical result. Here we ask when the dipolar component vanishes. Lamb (1945, § 126) provides symmetry conditions on the virtual mass tensor for this to be the case. We show that these conditions are not necessary and obtain the sufficient and necessary condition in terms of the shape of the body using conformal maps. Some explicit examples are constructed based on this condition. 

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2. Linear instability of Z-pinch in plasma: Inviscid case

   https://doi.org/10.1142/S0218202521500093  

   Bian, Dongfen; Guo, Yan; Tice, Ian (February 2021, Mathematical Models and Methods in Applied Sciences)

   null (Ed.)

   The [Formula: see text]-pinch is a classical steady state for the MHD model, where a confined plasma fluid is separated by vacuum, in the presence of a magnetic field which is generated by a prescribed current along the [Formula: see text] direction. We develop a variational framework to study its stability in the absence of viscosity effect, and demonstrate for the first time that such a [Formula: see text]-pinch is always unstable. Moreover, we discover a sufficient condition such that the eigenvalues can be unbounded, which leads to ill-posedness of the linearized MHD system. 

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3. Stability of characters and filters for weighted semilattices

   https://doi.org/10.1007/s00233-020-10147-w  

   Choi, Yemon; Ghandehari, Mahya; Pham, Hung Le (February 2021, Semigroup Forum)

   null (Ed.)

   Abstract We continue the study of the AMNM property for weighted semilattices that was initiated in Choi (J Aust Math Soc 95(1):36–67, 2013. 10.1017/S1446788713000189 ). We reformulate this in terms of stability of filters with respect to a given weight function, and then provide a combinatorial condition which is necessary and sufficient for this “filter stability” property to hold. Examples are given to show that this new condition allows for easier and unified proofs of some results in loc. cit., and furthermore allows us to verify the AMNM property in situations not covered by the results of that paper. As a final application, we show that for a large class of semilattices, arising naturally as union-closed set systems, one can always construct weights for which the AMNM property fails. 

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4. Randomized Asynchronous Recursions with a Sinusoidal Input

   https://doi.org/10.1109/IEEECONF44664.2019.9048998  

   Teke, Oguzhan; Vaidyanathan, P. P. (November 2019, Proc. Asil. Conf. Sig., Sys., and Comp.)

   This study considers a randomized asynchronous form of the discrete time-invariant state-space models, in which only a random subset of the state variables is updated in each iteration. When the system has a single input in the form of a complex exponential, it is shown that the output signal still behaves like an exponential in a statistical sense. The study presents the necessary and sufficient condition that ensures the stability of a randomized asynchronous system, which does not necessarily require the stability of the state transition matrix. 

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5. Essentially finite generation of valuation rings in terms of classical invariants

   https://doi.org/10.1002/mana.201900287  

   Cutkosky, Steven Dale; Novacoski, Josnei (October 2020, Mathematische Nachrichten)

   Abstract The main goal of this paper is to study some properties of an extension of valuations from classical invariants. More specifically, we consider a valued field and an extension ω of ν to a finite extensionLofK. Then we study when the valuation ring of ω is essentially finitely generated over the valuation ring of ν. We present a necessary condition in terms of classic invariants of the extension by Hagen Knaf and show that in some particular cases, this condition is also sufficient. We also study when the corresponding extension of graded algebras is finitely generated. For this problem we present an equivalent condition (which is weaker than the one for the finite generation of the valuation rings). 

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