Acta Mathematica Sinica-English Series最新文献

In this paper, we characterize the boundedness and compactness of the block dual Toeplitz operators acting on the orthogonal complement of the Fock spaces, and the compactness of the finite sum of two dual Toeplitz operators products. The commutator and semi-commutator induced by the block dual Toeplitz operators are considered.

In this paper, the notion of C-semigroup of continuous module homomorphisms on a complete random normal (RN) module is introduced and investigated. The existence and uniqueness of solution to the Cauchy problem with respect to exponentially bounded C-semigroups of continuous module homomorphisms in a complete RN module are established.

This research paper deals with an extension of the non-central Wishart introduced in 1944 by Anderson and Girshick, that is the non-central Riesz distribution when the scale parameter is derived from a discrete vector. It is related to the matrix of normal samples with monotonous missing data. We characterize this distribution by means of its Laplace transform and we give an algorithm for generating it. Then we investigate, based on the method of the moment, the estimation of the parameters of the proposed model. The performance of the proposed estimators is evaluated by a numerical study.

Let {X_υ: υ ∈ ℤ^d} be i.i.d. random variables. Let (S(pi) = sumnolimits_{upsilonin pi} {{X_upsilon}}) be the weight of a self-avoiding lattice path π. Let

We are interested in the asymptotics of M_n as n → ∞. This model is closely related to the first passage percolation when the weights {X_υ: υ ∈ ℤ^d} are non-positive and it is closely related to the last passage percolation when the weights {X_υ, υ ∈ ℤ^d} are non-negative. For general weights, this model could be viewed as an interpolation between first passage models and last passage models. Besides, this model is also closely related to a variant of the position of right-most particles of branching random walks. Under the two assumptions that (exists alpha > 0,,E{(X_0^ + )^d}{({log ^ + }X_0^ + )^{d + alpha }} < + ,infty) and that (E[X_0^ - ] < + ,infty), we prove that there exists a finite real number M such that M_n/n converges to a deterministic constant M in L¹ as n tends to infinity. And under the stronger assumptions that (exists alpha > 0,,,E{(X_0^ + )^d}{({log ^ + },X_0^ + )^{d + alpha }} < , + ,infty) and that (E[{(X_0^ - )^4}] < , + ,infty), we prove that M_n/n converges to the same constant M almost surely as n tends to infinity.

In this paper, we give a locally parabolic version of Tb theorem for a class of vector-valued operators with off-diagonal decay in L² and certain quasi-orthogonality on a subspace of L², in which the testing functions themselves are also vector-valued. As an application, we establish the boundedness of layer potentials related to parabolic operators in divergence form, defined in the upper half-space ℝ ⁿ⁺²₊ ≔ {(x, t, λ) ∈ ℝⁿ⁺¹ × (0, ∞)}, with uniformly complex elliptic, L^∞, t, λ-independent coefficients, and satisfying the De Giorgi/Nash estimates.

Let M = Sⁿ /Γ and h be a nontrivial element of finite order p in π₁(Μ), where the integers n, p ≥ 2, Γ is a finite abelian group which acts freely and isometrically on the n-sphere and therefore M is diffeomorphic to a compact space form. In this paper, we prove that there are infinitely many non-contractible closed geodesics of class [h] on the compact space form with C^r-generic Finsler metrics, where 4 ≤ r ≤ ∞. The conclusion also holds for C^r-generic Riemannian metrics for 2 ≤ r ≤ ∞. The proof is based on the resonance identity of non-contractible closed geodesics on compact space forms.

For a quasi-split Satake diagram, we define a modified q-Weyl algebra, and show that there is an algebra homomorphism between it and the corresponding ıquantum group. In other words, we provide a differential operator approach to ıquantum groups. Meanwhile, the oscillator representations of ıquantum groups are obtained. The crystal basis of the irreducible subrepresentations of these oscillator representations are constructed.

For a character χ of a finite group G, the number cod(χ)≔ ∣G: ker(χ)∣/χ(1) is called the codegree of χ. In this paper, we give a solvability criterion for a finite group G depending on the minimum of the ratio χ(1)²/cod(χ), when χ varies among the irreducible characters of G.

Let G be a semi-simple simply connected algebraic group over the field ℂ of complex numbers. Let T be a maximal torus of G, and let W be the Weyl group of G with respect to T. Let Z(w, i) be the Bott-Samelson-Demazure-Hansen variety corresponding to a tuple i associated to a reduced expression of an element w ∈ W. We prove that for the tuple i associated to any reduced expression of a minuscule Weyl group element w, the anti-canonical line bundle on Z(w, i) is globally generated. As consequence, we prove that Z(w, i) is weak Fano.

Assume that G is a simple algebraic group whose type is different from A₂. Let S = {α₁, …, α_n} be the set of simple roots. Let w be such that support of w is equal to S. We prove that Z(w, i) is Fano for the tuple i associated to any reduced expression of w if and only if w is a Coxeter element and ({w^{ - 1}}(sumnolimits_{t = 1}^n {{alpha _t}) in - S} ).

In this article, we consider a modified version of minimal L² integrals on sublevel sets of plurisubharmonic functions related to modules at boundary points, and obtain a concavity property of the modified version. As applications, we give characterizations for the concavity degenerating to linearity on open Riemann surfaces and on fibrations over open Riemann surfaces.