Acta Mathematica Vietnamica最新文献

In 1980, White conjectured that the toric ideal of a matroid is generated by quadratic binomials corresponding to a symmetric exchange. In this paper, we compute Gröbner bases of toric ideals associated with matroids and show that, for every matroid on ground sets of size at most seven except for two matroids, Gröbner bases of toric ideals consist of quadratic binomials corresponding to a symmetric exchange.

The purpose of this paper is to introduce a new kind of q −Stancu-Kantorovich type operators and study its various approximation properties. We establish some local direct theorems, e.g., Voronovskaja type asymptotic theorem, global approximation and an estimate of error by means of the Lipschitz type maximal function and the Peetre K-functional. We also consider a n th-order generalization of these operators and study its approximation properties. Next, we define a bivariate case of these operators and investigate the order of convergence by means of moduli of continuity and the elements of Lipschitz class. Furthermore, we consider the associated Generalized Boolean Sum (GBS) operators and examine the approximation degree for functions in a Bögel space. Some numerical examples to illustrate the convergence of these operators to certain functions are also given.

Let R be a prime ring of char(R)≠ 2, U its Utumi ring of quotients and center C = Z(U) its extended centroid, I a both sided ideal of R, f(x₁,…,x_n) a multilinear polynomial over C, that is noncentral-valued on R, F, G be two generalized derivations of R and d be a derivation of R. Let f(I) be the set of all evaluations of the multilinear polynomial f(x₁,…,x_n) in I. If @@@ for all u ∈ f(I), then all possible forms of the maps are determined. As an application of this result, we also study the commutator identity [F²(u)u,G²(v)v] = 0 for all u,v ∈ f(I), where F and G are two generalized derivations of R.

The degree excess function 𝜖(I; n) is the difference between the maximal generating degree d(Iⁿ) of the n-th power of a homogeneous ideal I of a polynomial ring and p(I)n, where p(I) is the leading coefficient of the asymptotically linear function d(Iⁿ). It is shown that any non-increasing numerical function can be realized as a degree excess function, and there is a monomial ideal I whose 𝜖(I; n) has exactly a given number of local maxima. In the case of monomial ideals, an upper bound on 𝜖(I; n) is provided. As an application, it is shown that in the worst case, the so-called stability index of the Castelnuovo-Mumford regularity of a monomial ideal I must be at least an exponential function of the number of variables.

The aim of this paper is to introduce the notion of Lelong number and the log canonical thresholds of plurisubharmonic functions on analytic subsets A in an open subset Ω of (mathbb {C}^{n}). Next, we establish some results about the relationship between these quantities in the relation with the analyticity of A.

The aim of the paper is to investigate all transcendental entire solutions of the following general nonlinear equation of the form (f^{n}+P_{d}(z,f)=p_{1}e^{alpha _{1}z}+p_{2}e^{alpha _{2}z}), where P_d(z,f) is a differential-difference polynomial in f of degree d. Our result is a generalization and complement of known results obtained by Liu-Mao, L({ddot {mathrm {u}}}) et al. and the references therein.

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.

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.

For given integers m,n ≥ 2 there are examples of ideals I of complete determinantal local rings ((R,mathfrak {m}), dim R = m+n-1, text {grade}~I = n-1,) with the canonical module ω_R and the property that the socle dimensions of (H^{m+n-2}_{I}(omega _{R})) and (H^{m}_{mathfrak {m}}left (H^{n-1}_{I}(omega _{R})right )) are not finite. In the case of m = n, i.e., a Gorenstein ring, the socle dimensions provide further information about the τ-numbers as studied in Mahmood and Schenzel (J. Algebra372, 56–67, 10). Moreover, the endomorphism ring of (H^{n-1}_{I}(omega _{R})) is studied and shown to be an R-algebra of finite type but not finitely generated as R-module generalizing an example of Schenzel (J. Algebra 344, 229–245, 15).