In 2000, Héthelyi and Külshammer [Bull. London Math. Soc. 32 (2000), pp. 668–672] proposed that if
In 2000, Héthelyi and Külshammer [Bull. London Math. Soc. 32 (2000), pp. 668–672] proposed that if
In this paper, we investigate the monotonicity of the functions
We prove that quotients of the Fulton-MacPherson compactification of configuration spaces of smooth projective varieties of dimension
This manuscript studies a no-flux initial-boundary value problem for a four-component chemotaxis system that has been proposed as a model for the response of cytotoxic T-lymphocytes to a solid tumor. In contrast to classical Keller-Segel type situations focusing on two-component interplay of chemotaxing populations with a signal directly secreted by themselves, the presently considered system accounts for a certain indirect mechanism of attractant evolution. Despite the presence of a zero-order exciting nonlinearity of quadratic type that forms a core mathematical feature of the model, the manuscript asserts the global existence of classical solutions for initial data of arbitrary size in three-dimensional domains.
We prove the strong Lefschetz property for Artinian Gorenstein algebras generated by the relative invariants of prehomogeneous vector spaces of commutative parabolic type.
Let
We continue our study on the global dynamics of a non- local reaction-diffusion-advection system modeling the population dynamics of two competing phytoplankton species in a eutrophic environment, where the species depend solely on light for their metabolism. In our previous works, we proved that system (1.1) is a strongly monotone dynamical system with respect to a non-standard cone, and some competitive exclusion results were obtained. In this paper, we aim to demonstrate the existence of coexistence steady state as well as competitive exclusion. Our results highlight that advection in dispersal strategy can lead to transitions between various competitive outcomes.
We consider periodic Jacobi operators and obtain upper and lower estimates on the sizes of the spectral bands. Our proofs are based on estimates on the logarithmic capacities and connections between the Chebyshev polynomials and logarithmic capacity of compact subsets of the real line.
We describe all possible coactions of finite groups (equivalently, all group gradings) on two-dimensional Artin-Schelter regular algebras. We give necessary and sufficient conditions for the associated Auslander map to be an isomorphism, and determine precisely when the invariant ring for the coaction is Artin-Schelter regular. The proofs of our results are combinatorial and exploit the structure of the McKay quiver associated to the coaction.
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