Issue 3, Volume 47, September 2022

2022

1. Mahler Coefficients of Some 3-adic Ergodic Functions Nacima Memić PDF

   ▸ Abstract

   We provide sufficient conditions for ergodicity of 3-adic compatible functions expressed by means of their Mahler coefficients.

   597-610
2. Regularity of the Donaldson Geometric Flow Robin S. Krom PDF

   ▸ Abstract

   We prove a regularity theorem for the solutions of the Donaldson geometric flow equation on the space of symplectic forms on a closed smooth four-manifold, representing a fixed cohomology class. The minimal initial conditions lay in the Besov space $B^{1,p}_{2}(M, {\varLambda }^{2}) $ for $p>4.$ The Donaldson geometric flow was introduced by Simon Donaldson in Donaldson (Asian J. Math. 3, 1–16 1999). For a detailed exposition see Krom and Salamon (J. Symplectic Geom. 17, 381–417 2019).

   611-633
3. Rates of Convergence in the Central Limit Theorem for Nonlinear Statistics Under Relaxed Moment Conditions Nguyen Tien Dung PDF

   ▸ Abstract

   This paper is concerned with normal approximation under relaxed moment conditions using Stein’s method. We obtain the explicit rates of convergence in the central limit theorem for (i) nonlinear statistics with finite absolute moment of order 2 + δ ∈ (2,3] and (ii) nonlinear statistics with vanishing third moment and finite absolute moment of order 3 + δ ∈ (3,4]. When applied to specific examples, these rates are of the optimal order $O\left (n^{-\frac {\delta }{2}}\right )$ and $O\left (n^{-\frac {1+\delta }{2}}\right ) $. Our proofs are based on the covariance identity formula and simple observations about the solution of Stein’s equation.

   635-660
4. Mixed Commuting Varieties over Nilpotent Matrices Jerry Magana , Nham V. Ngo PDF

   ▸ Abstract

   We give an explicit description of all irreducible components and their dimensions of mixed commuting varieties over nilpotent 3 × 3 matrices, hence describing the varieties of 3-dimensional modules for certain quotients of polynomial algebras over an algebraically closed field. Our results also provide insights on support varieties of simple modules over Frobenius kernels of $SL_3$.

   661-669
5. On Approximately σ -biflat Banach Algebras Sanaz Haddad Sabzevar , Amin Mahmoodi PDF

   ▸ Abstract

   We define and study approximate versions of σ-biflatness and σ-biprojectivity of a Banach algebra A where σ ∈Hom(A). We generalize the concepts pseudo amenability and pseudo contractibility via homomorphisms. We investigate their relations.

   671-681
6. Extensions of Valuation Domains and Going-up Shai Sarussi PDF

   ▸ Abstract

   Suppose F is a field with valuation v and valuation domain $O_v$, E/F is a finite-dimensional field extension, and R is an $O_v$-subalgebra of E such that F ⋅ R = E and R ∩ F =$O_v$. It is known that R satisfies LO, INC, GD and SGB over $O_v$; it is also known that under certain conditions R satisfies GU over $O_v$. In this paper, we present a necessary and sufficient condition for the existence of such R that does not satisfy GU over $O_v$. We also present an explicit example of such R that does not satisfy GU over $O_v$.

   683-687
7. The First Syzygy of Hibi Rings Associated with Planar Distributive Lattices Priya Das , Himadri Mukherjee PDF

   ▸ Abstract

   In this article, we give explicit minimal generators of the first syzygy of the Hibi ring for a planar distributive lattice in terms of sublattices. We also give a characterization when it is linearly related and derive an exact formula for the first Betti number of a planar distributive lattice.

   689-707
8. On the Cohen-Macaulayness of Bracket Powers of Generalized Mixed Product Ideals Roya Moghimipor PDF

   ▸ Abstract

   Let L be the generalized mixed product ideal induced by a monomial ideal I. For every integer k ≥ 1, we denote the k th bracket power of L by $L^{[k]}$. We study algebraic properties of $L^{[k]}$, and show that $L^{[k]}$ is Cohen-Macaulay if I is Cohen-Macaulay.

   709-718
9. On Hyperbolicity Modulo a Closed Subset of Singular Complex Spaces Pham Nguyen Thu Trang , Nguyen Van Trao PDF

   ▸ Abstract

   The purpose of this article is threefold. In 1971, H. L. Royden introduced the Kobayashi-Royden pseudometrics on (nonsingular) complex manifolds and gave a criterion for the Kobayashi hyperbolicity of (nonsingular) complex manifolds which plays an essentially important role in Hyperbolic Complex Geometry. Perhaps, since there are some unresolved technical problems, the above theorem of Royden is not yet completely cleared up for singular complex spaces. Thus, the first is to prove Royden’s theorem for singular complex spaces. The second is to give a criteria of the hyperbolicity modulo a closed subset of singular complex spaces from the viewpoint of comparing the Kobayashi k-differential pseudometrics on these spaces and the Landau property of the ones. The third is to investigate the hyperbolicity modulo a closed subset of domains in a singular complex space from the condition on localization at their boundary points.

   719-729