Acta Mathematica Vietnamica最新文献

The Schmidt subspace theorem has been studied extensively for both cases of fixed and moving targets in projective spaces over number fields and the case of fixed targets in projective spaces over function fields. This paper studies the case of function fields with moving targets; in particular, we extend the result of Min Ru and Paul Vojta in the Inventiones Mathematicae (1997) to the case of moving hyperplane targets in projective spaces over function fields.

We study the question of which rings, and which families of ideals, have uniform symbolic topologies. In particular, we show that the uniform symbolic topology property holds for all dimension one primes in any normal complete local domain, provided dimension one primes in hypersurfaces have the uniform symbolic topology property. We also discuss bootstrapping techniques and provide a strong bootstrapping statement in positive characteristic. We apply these techniques to give families of primes in hypersurfaces of positive characteristic which have uniform symbolic topologies.

The notion of a nilpotent-invariant module was introduced and thoroughly investigated in Koşan and Quynh (Comm. Algebra 45, 2775–2782 2017) as a proper extension of an automorphism-invariant module. In this paper a ring is called a right (mathfrak {n})-ring if every right ideal is nilpotent-invariant. We show that a right (mathfrak {n})-ring is the direct sum of a square full semisimple artinian ring and a right square-free ring. Moreover, right (mathfrak {n})-rings are shown to be stably finite, and if the ring is also an exchange ring then it satisfies the substitution property, has stable range 1. These results are non-trivial extensions of similar ones on rings every right ideal is automorphism-invariant.

In this paper, we prove that the Watanabe-Yoshida conjecture holds up to dimension 7. Our primary new tool is a function, (varphi _J(R;z^t),) that interpolates between the Hilbert-Kunz multiplicities of a base ring, R, and various radical extensions, (R_n). We prove that this function is concave and show that its rate of growth is related to the size of (e_{textrm{HK}}(R)). We combine techniques from Celikbas et al. (Nagoya Math. J. 205, 149–165, 2012) and Aberbach and Enescu (Nagoya Math. J. 212, 59–85, 2013) to get effective lower bounds for (varphi ,) which translate to improved bounds on the size of Hilbert-Kunz multiplicities of singular rings. The improved inequalities are powerful enough to show that the conjecture of Watanabe and Yoshida holds in dimension 7.

We extend the asymptotic Samuel function of an ideal to a filtration and show that many of the good properties of this function for an ideal are true for filtrations. There are, however, interesting differences, which we explore. We study the notion of projective equivalence of filtrations and the relation between the asymptotic Samuel function and the multiplicity of a filtration. We further consider the case of discrete valued filtrations and show that they have particularly nice properties.

Let G be a finite simple connected graph on the vertex set (V(G)=[d]={1,dots ,d}) with edge set (E(G)={e_{1},dots , e_{n}}). Let (mathbb {K}[textbf{t}]=mathbb {K}[t_{1},dots ,t_{d}]) be the polynomial ring in d variables over a field (mathbb {K}). The edge ring of G is the affine semigroup ring (mathbb {K}[G]) generated by monomials (textbf{t}^{e}:=t_{i}t_{j}), for (e={i,j} in E(G)). In this paper, we will prove that, given integers d and n, where (dge 7) and (d+1le nle frac{d^{2}-7d+24}{2}), there exists a finite simple connected graph G with (|V(G)|=d) and (|E(G)|=n), such that (mathbb {K}[G]) is non-normal and satisfies ((S_{2}))-condition.

In this paper, we introduce a new inertial Tseng’s extragradient method with self-adaptive step sizes for approximating a common solution of split equalities of equilibrium problem (EP), non-Lipschitz pseudomonotone variational inequality problem (VIP) and fixed point problem (FPP) of nonexpansive semigroups in real Hilbert spaces. We prove that the sequence generated by our proposed method converges strongly to a common solution of the EP, pseudomonotone VIP and FPP of nonexpansive semigroups without any linesearch procedure nor the sequential weak continuity condition often assumed by authors when solving non-Lipschitz VIPs. Finally, we provide some numerical experiments for the proposed method in comparison with related methods in the literature. Our result improves, extends and generalizes several of the existing results in this direction.

This paper studies the first-order behavior of the weak optimal value mapping in a parametric multi-objective discrete optimal control problem under linear state equations, where the solution set may be empty. By establishing an abstract result on the (varepsilon )-weak subdifferential of the weak optimal value mapping in a parametric multi-objective mathematical programming problem with an inclusion constraint, we derive a formula for computing the (varepsilon )-weak subdifferential of the weak optimal value mapping in a parametric multi-objective discrete optimal control problem. The obtained results are proved directly without using scalarization techniques.

In this paper, we extend the concept of s-convexity from the case where the functions are with real variables to the case where the functions are with operator arguments. Afterwards, we investigate some related properties and operator inequalities. As an application, some inequalities of Hermite-Hadamard and Jensen types involving some operator means are established.

In this paper, we construct Carathéodory type and exponential Carathéodory type schemes for Caputo stochastic fractional differential equations (CSFDEs) of order (alpha in (frac{1}{2},1)) in (L^p) spaces with (p ge 2) whose coefficients satisfy a standard Lipschitz and a linear growth bound conditions. The strong convergence and the convergence rate of these schemes are also established.