Acta Mathematica Vietnamica最新文献

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 (Oleft (n^{-frac {delta }{2}}right )) and (Oleft (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.

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.

Let (R = oplus _{nin mathbb {N}_{0}}R_{n}) be a Noetherian homogeneous ring with irrelevant ideal (R_{+} = oplus _{nin mathbb {N}} R_{n}) and with local base ring ((R_{0},mathfrak {m}_{0})). Let M, N be two finitely generated (mathbb {Z})-graded R-modules. We show that the lengths of the graded components of various graded submodules and quotients of the i-th generalized local cohomology (H^{i}_{R_{+}}(M, N)) are anti-polynomial. Under some mild assumptions, the Artinianness of (H^{i}_{R_{+}}(M, N)) and the asymptotic behavior of the R₀-modules (H^{i}_{R_{+}}(M, N)_{n}) for (nrightarrow -infty ) in the range (ileq inf {iin mathbb {N}_{0} vert sharp {nvert ell _{R_{0}}) ((H^{i}_{ R_{+}}(M , N)_{n}) = infty }=infty }) will be studied. Moreover, it has been proved that, if u is the least integer i for which (H^{i}_{R_{+}}(M,N)) is not Artinian and (mathfrak {q}_{0}) is an (mathfrak {m}_{0})-primary ideal of R₀, then (H^{u}_{R_{+}}(M,N)/mathfrak q_{0}H^{u}_{R_{+}}(M,) N) is Artinian with Hilbert-Kirby polynomial of degree less than u. In particular, with M = R, we deduce the correspondent result for ordinary local cohomology module (H^{i}_{R_{+}}(N)).

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.

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).

We prove upper bounds for the graded Betti numbers of Stanley-Reisner rings of balanced simplicial complexes. Along the way we show bounds for Cohen-Macaulay graded rings S/I, where S is a polynomial ring and (Isubseteq S) is a homogeneous ideal containing a certain number of generators in degree 2, including the squares of the variables. Using similar techniques we provide upper bounds for the number of linear syzygies for Stanley-Reisner rings of balanced normal pseudomanifolds. Moreover, we compute explicitly the graded Betti numbers of cross-polytopal stacked spheres, and show that they only depend on the dimension and the number of vertices, rather than also the combinatorial type.

Let R be a commutative ring with the unit element. It is shown that an ideal I in R is pure if and only if Ann(f) + I = R for all f ∈ I. If J is the trace of a projective R-module M, we prove that J is generated by the “coordinates” of M and JM = M. These lead to a few new results and alternative proofs for some known results.

Our goal is to give Schmidt’s subspace theorem for moving hypersurface targets in subgeneral position in projective varieties.

In this paper, we investigate maximal subgroups of an almost subnormal subgroup G in a division ring D whose center is infinite. Among results, we prove that if M is such a maximal subgroup, then M is abelian provided M is either locally finite or FC-group, and D is weakly locally finite. Also, we prove a theorem on the existence of non-cyclic free subgroups of a maximal subgroup M in such a G.

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 SL₃.