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This paper compares two models of the equivariant homotopy type of the smash powers of a spectrum, namely the "Bökstedt smash product" and the Hill-Hopkins-Ravenel norm. [ABSTRACT FROM AUTHOR]

This is a corrigendum to the paper "On iterated function systems with place-dependent probabilities" published in Proc. Amer. Math. Soc. 143 (2015), 419–432. [ABSTRACT FROM AUTHOR]

This paper is concerned with a diffusive logistic model in population ecology. As observed by Y. Lou, in a spatially heterogeneous environment, this model can always support a total population at equilibrium greater than the total carrying capacity. In other words, the ratio of the total population at equilibrium to the total carrying capacity is always larger than 1. Our goal is to find the supremum of this ratio taken over all possible choices of spatial distributions of resources and the species' dispersal rate. A conjecture proposed by W.-M. Ni is that, in the one-dimensional case, the supremum is 3. We settle this conjecture and then apply our result to study the global dynamics of a heterogeneous Lotka-Volterra competition-diffusion system. [ABSTRACT FROM AUTHOR]

By a classical result of Kadec and Pełczyński (1962), every normalized weakly null sequence in Lp, p > 2, contains a subsequence equivalent to the unit vector basis of ℓ² or to the unit vector basis of ℓp. In this paper we investigate the case 1 ≤ p < 2 and show that a necessary and sufficient condition for the first alternative in the Kadec-Pełczyński theorem is that the limit random measure μ of the sequence satisfies ∫∨x²dμ(x) ∈ Lp/2. [ABSTRACT FROM AUTHOR]

In this paper we compute the restricted 0, 1-, and 2-dimensional cohomology groups with trivial coefficients of the modular Witt algebras W for any prime p > 3, and give explicit description of all one-dimensional restricted central extensions of W. [ABSTRACT FROM AUTHOR]

In this paper we consider extremal and almost extremal bounds on the normal Hilbert coefficients of m-primary ideals of an analytically unramified Cohen-Macaulay ring R of dimension d > 0 and infinite residue field. In these circumstances we show that the associated graded ring of the normal filtration of the ideal is either Cohen-Macaulay or almost Cohen-Macaulay. [ABSTRACT FROM AUTHOR]

In this paper, we prove the Lazer-McKenna conjecture for the suspension bridge model in higher dimension. We also discuss some properties of the limiting problem related to the Swift-Hohenberg equation. [ABSTRACT FROM AUTHOR]

In this paper, we extend the holomorphic L² torsion introduced by Carey, Farber and Mathai to the case without the determinant class condition. We compute the metric variation formula for the holomorphic L² torsion in our case. We also study the asymptotics of the holomorphic L² torsion associated with a power of a positive line bundle. [ABSTRACT FROM AUTHOR]

In this paper, it is demonstrated that derived equivalence between smooth, projective varieties that are either surfaces or abelian implies equality of zeta functions. [ABSTRACT FROM AUTHOR]

We correct an error in the statement of a theorem in our paper ''Incompleteness and jump hierarchies'' [Proc. Amer. Math. Soc. 148 (2020), pp. 4997-5006]. [ABSTRACT FROM AUTHOR]

We make an observation that may clarify the main definition from our paper [Proc. Amer. Math. Soc. 144 (2016), pp. 5275-5290]. [ABSTRACT FROM AUTHOR]

In our paper "On solvable compact Clifford-Klein forms" [Proc. Amer. Math. Soc. 145 (2017), pp. 1819-1832] we have found a small gap in the proof of the main theorem. In this note we show that the result is correct and that the proof goes through after a slight modification. [ABSTRACT FROM AUTHOR]