Acta Mathematica Sinica-English Series最新文献

In this article, we study deformations of conjugate self-dual Galois representations. The study is twofold. First, we prove an R=T type theorem for a conjugate self-dual Galois representation with coefficients in a finite field, satisfying a certain property called rigid. Second, we study the rigidity property for the family of residue Galois representations attached to a symmetric power of an elliptic curve, as well as to a regular algebraic conjugate self-dual cuspidal representation.

Let G be a symplectic or orthogonal group defined over a finite field with odd characteristic and let D ≤ G be a Sylow 2-subgroup. In this paper, we classify the essential 2-subgroups and determine the essential 2-rank of the Frobenius category ℱ_D(G). Together with the results of An-Dietrich and Cao–An–Zeng, this completes the work of essential subgroups and essential ranks of classical groups.

In this paper, with (Σ, g) being a closed Riemann surface, we analyze the possible concentration behavior of a heat flow related to the Trudinger-Moser energy. We obtain a long time existence for the flow. And along some sequence of times t_k → + ∞, we can deduce the convergence of the flow in H²(Σ). Furthermore, the limit function is a critical point of the Trudinger-Moser functional under certain constraint.

This paper mainly investigates the approximation of a global maximizer of the Monge-Kantorovich mass transfer problem in higher dimensions through the approach of nonlinear partial differential equations with Dirichlet boundary. Using an approximation mechanism, the primal maximization problem can be transformed into a sequence of minimization problems. By applying the systematic canonical duality theory, one is able to derive a sequence of analytic solutions for the minimization problems. In the final analysis, the convergence of the sequence to an analytical global maximizer of the primal Monge-Kantorovich problem will be demonstrated.

Let A_n ∈ M₂ (ℤ) be integral matrices such that the infinite convolution of Dirac measures with equal weights

is a probability measure with compact support, where (cal{D}={(0,0)^{t},(1,0)^{t},(0,1)^{t}}) is the Sierpinski digit. We prove that there exists a set Λ ⊂ ℝ² such that the family {e^{2πi〈λ,x〉}: λ ∈ Λ} is an orthonormal basis of (L^{2}(mu_{{A_{n},ngeq1}})) if and only if ({1over{3}}(1,-1)A_{n}inmathbb{Z}^{2}) for n ≥ 2 under some metric conditions on A_n.

In this article, we mainly study the products of commutator ideals of Lie-admissible algebras such as Novikov algebras, bicommutative algebras, and assosymmetric algebras. More precisely, we first study the properties of the lower central chains for Novikov algebras and bicommutative algebras. Then we show that for every Lie nilpotent Novikov algebra or Lie nilpotent bicommutative algebra (cal{A}),the ideal of (cal{A}) generated by the set ({ab-ba vert a,bincal{A}}) is nilpotent. Finally, we study properties of the lower central chains for assosymmetric algebras, study the products of commutator ideals of assosymmetric algebras and show that the products of commutator ideals have a similar property as that for associative algebras.

In this paper we define the delocalized L²-analytic torsion form and the delocalized L²-combinatorial torsion form. By using the method of Bismut-Goette, under the conditions of positive Novikov-Shubin invariants, nontrivial finite conjugacy class and the existence of a family of fiberwise Morse functions whose gradient fields satisfy the Thom-Smale transversality condition in every fiber, we prove the Cheeger-Müller type relation between the delocalized L²-analytic torsion form and the delocalized L²-combinatorial torsion form.

We present an example of a potential such that the corresponding discrete Schrödinger operator has singular continuous spectrum embedded in the absolutely continuous spectrum.

Let (Z_n) be a supercritical branching process with immigration in an independent and identically distributed random environment. Under necessary moment conditions, we show the exact convergence rate in the central limit theorem on log Z_n and establish the corresponding local limit theorem by using the moments of the natural submartingale and the convergence rates of its logarithm. By similar approach and with the help of a change of measure, we also present the so-called integrolocal theorem and integral large deviation theorem to characterize the precise asymptotics of the upper large deviations.

This is a continuation of our previous work (Ann. Sc. Norm. Super. Pisa Cl. Sci., 20, 1295–1324, 2020). Let (Σ, g) be a closed Riemann surface, where the metric g has conical singularities at finite points. Suppose G is a group whose elements are isometries acting on (Σ, g). Trudinger–Moser inequalities involving G are established via the method of blow-up analysis, and the corresponding extremals are also obtained. This extends previous results of Chen (Proc. Amer. Math. Soc., 1990), Iula–Manicini (Nonlinear Anal., 2017), and the authors (2020).