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First Passage Density of Brownian Motion with Two-sided Piecewise Linear Boundaries Acta. Math. Sin. Engl. Ser. (IF 0.7) Pub Date : 2024-03-15 Zhen Yu, Mao Zai Tian
The first passage time has many applications in fields like finance, econometrics, statistics, and biology. However, explicit formulas for the first passage density have only been obtained for a few cases. This paper derives an explicit formula for the first passage density of Brownian motion with two-sided piecewise continuous boundaries which may have some points of discontinuity. Approximations
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On Stability Discrimination of Limit Cycles for Piecewise Smooth Systems Acta. Math. Sin. Engl. Ser. (IF 0.7) Pub Date : 2024-03-15 Mao An Han, Xia Yu Zhou
This paper is concerned with the problem of stability discrimination of limit cycles for piecewise smooth systems. We first establish the Poincaré map near a periodic orbit, and deduce the first order derivative of the map for general piecewise smooth systems on the plane. Then, we obtain a sufficient condition for determining the stability of limit cycles for these systems.
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Some Rotundities of Orlicz–Lorentz Spaces Acta. Math. Sin. Engl. Ser. (IF 0.7) Pub Date : 2024-03-15 Wan Zhong Gong, Peng Wang
Abstract K-UR, K-LUR and K-R are the generalizations of UR, LUR and R respectively, which are of great significance in Banach space theory. While in Orlicz–Lorentz function space \(\Lambda_{\varphi,\omega}^{\circ}[0,\gamma)\) equipped with the Orlicz norm, the research methods of K-UR, K-LUR and K-R are much more complicated than those of UR, LUR and R. In this paper we obtain some criteria of K-UR
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Solution of the Center Problem for a Class of Polynomial Differential Systems Acta. Math. Sin. Engl. Ser. (IF 0.7) Pub Date : 2024-03-15 Chang Jian Liu, Jaume Llibre, Rafael Ramírez, Valentín Ramírez
Consider the polynomial differential system of degree m of the form $$\eqalign{&\dot{x}=-y(1+\mu(a_{2}x-a_{1}y))+x(\nu(a_{1}x+a_{2}y)+\Omega_{m-1}(x,y)),\cr &\dot{y}=x(1+\mu(a_{2}x-a_{1}y))+y(\nu(a_{1}x+a_{2}y)+\Omega_{m-1}(x,y)),}$$ where μ and ν are real numbers such that \((\mu^{2}+\nu^{2})(\mu+\nu(m-2))(a_{1}^{2}+a_{2}^{2})\ne 0,m > 2\) and Ωm−1(x,y) is a homogenous polynomial of degree m − 1.
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Irreducible Representations of GLn(ℂ) of Minimal Gelfand–Kirillov Dimension Acta. Math. Sin. Engl. Ser. (IF 0.7) Pub Date : 2024-03-15 Zhan Qiang Bai, Yang Yang Chen, Dong Wen Liu, Bin Yong Sun
In this article, by studying the Bernstein degrees and Goldie rank polynomials, we establish a comparison between the irreducible representations of G = GLn(ℂ) possessing the minimal Gelfand–Kirillov dimension and those induced from finite-dimensional representations of the maximal parabolic subgroup of G of type (n − 1,1). We give the transition matrix between the two bases for the corresponding coherent
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Transfer of Highest Weight Modules and Small Unipotent Representations Acta. Math. Sin. Engl. Ser. (IF 0.7) Pub Date : 2024-03-15 Hai An He, Jing Song Huang, Kayue Daniel Wong
We study the transfer between small special unipotent representations for all equal rank real forms of type E6 and E7. As a consequence, one can verify these modules are unitarity using the results of Wallach and Zhu. Moreover, the K-spectra of these modules can be obtained explicitly.
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Special Unipotent Representations of Simple Linear Lie Groups of Type A Acta. Math. Sin. Engl. Ser. (IF 0.7) Pub Date : 2024-03-15 Dan Barbasch, Jia Jun Ma, Bin Yong Sun, Chen Bo Zhu
Let G be a special linear group over the real, the complex or the quaternion, or a special unitary group. In this note, we determine all special unipotent representations of G in the sense of Arthur and Barbasch–Vogan, and show in particular that all of them are unitarizable.
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Big Theta Equals Small Theta Generically Acta. Math. Sin. Engl. Ser. (IF 0.7) Pub Date : 2024-03-01 Rui Chen, Jia Liang Zou
Abstract In this paper we consider the theta correspondence over a non-Archimedean local field. Using the homological method and the theory of derivatives, we show that under a mild condition the big theta lift is irreducible.
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Gelfand–Kirillov Dimension and Reducibility of Scalar Generalized Verma Modules for Classical Lie Algebras Acta. Math. Sin. Engl. Ser. (IF 0.7) Pub Date : 2024-03-15 Zhan Qiang Bai, Jing Jiang
Let \(\mathfrak{g}\) be a classical complex simple Lie algebra and \(\mathfrak{q}\) be a parabolic subalgebra. Let M be a generalized Verma module induced from a one dimensional representation of \(\mathfrak{q}\). Such M is called a scalar generalized Verma module. In this paper, we will determine the reducibility of scalar generalized Verma modules associated to maximal parabolic subalgebras by computing
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The Wave Front Set Correspondence for Dual Pairs with One Member Compact Acta. Math. Sin. Engl. Ser. (IF 0.7) Pub Date : 2024-03-15 Mark McKee, Angela Pasquale, Tomasz Przebinda
Let W be a real symplectic space and (G, G′) an irreducible dual pair in Sp(W), in the sense of Howe, with G compact. Let \(\widetilde {\rm{G}}\) be the preimage of G in the metaplectic group \(\widetilde {{\rm{Sp}}}({\rm{W}})\). Given an irreducible unitary representation Π of \(\widetilde {\rm{G}}\) that occurs in the restriction of the Weil representation to \(\widetilde {\rm{G}}\), let ΘΠ denote
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Quaternionic Monge–Ampère Measure on Pluripolar Set Acta. Math. Sin. Engl. Ser. (IF 0.7) Pub Date : 2024-02-02 Hichame Amal, Saïd Asserda, Fadoua Boukhari
In this paper, we prove that in a hyperconvex domain Ω in ℍn, if a non-negative Borel measure is dominated by a quaternionic Monge–Ampère measure, then it is a quaternionic Monge–Ampère measure of a function in the class \({\cal E}(\Omega )\).
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Quasi-shadowing for ℤd-actions Acta. Math. Sin. Engl. Ser. (IF 0.7) Pub Date : 2023-12-29 Juan Pan, Xian Kun Ren, Yun Hua Zhou
A diffeomorphism is non-uniformly partially hyperbolic if it preserves an ergodic measure with at least one zero Lyapunov exponent. We prove that a C1-smooth ℤd-action has the quasi-shadowing property if one of the generators is C1+α (α > 0) non-uniformly partially hyperbolic.
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Continuous Orbit Equivalence of Semigroup Actions Acta. Math. Sin. Engl. Ser. (IF 0.7) Pub Date : 2023-12-29 Xiang Qi Qiang, Cheng Jun Hou
We introduce notions of continuous orbit equivalence and its one-sided version for countable left Ore semigroup actions on compact spaces by surjective local homeomorphisms, and characterize them in terms of the corresponding transformation groupoids and their operator algebras. In particular, we show that two essentially free semigroup actions on totally disconnected compact spaces are continuously
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On the Proper Holomorphic Mappings between Equidimensional Hartogs Domains over Hermitian Symmetric Manifolds Acta. Math. Sin. Engl. Ser. (IF 0.7) Pub Date : 2023-12-08 En Chao Bi
In this paper, we study a family of Hartogs domains fibred over Hermitian symmetric manifolds being a unit ball in ℂm. The aim of the present study is to establish the rigidity results about proper holomorphic mappings between two equidimensional Hartogs domains over Hermitian symmetric manifolds. In particular, we can fully determine its biholomorphic equivalence and automorphism group.
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Homoclinic Solutions for a Class of Perturbed Fractional Hamiltonian Systems with Subquadratic Conditions Acta. Math. Sin. Engl. Ser. (IF 0.7) Pub Date : 2023-12-08 Ying Luo, Fei Guo, Yan Liu
In this paper, we consider the following perturbed fractional Hamiltonian systems $$\left\{ {\matrix{{_tD_\infty ^\alpha {(_{ - \infty }}D_t^\alpha u(t)) + L(t)u(t) = {\nabla _u}W(t,u(t)) + {\nabla _u}G(t,u(t)),} \hfill & {t \in \mathbb{R},} \hfill \cr {u \in {H^\alpha }(\mathbb{R},{\mathbb{R}^N}),} \hfill & {} \hfill \cr } } \right.$$ where \(\alpha \in (1/2,1],\,\,L \in C(\mathbb{R},{\mathbb{R}^{N
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New Identities for Moore–Penrose Inverses of Some Operator Products and Their Reverse-order Laws Acta. Math. Sin. Engl. Ser. (IF 0.7) Pub Date : 2023-12-07 Mehdi Mohammadzadeh Karizaki, Javad Farokhi-Ostad
We establish new identities for Moore–Penrose inverses of some operator products, and prove their associated reverse-order laws. Moreover, our results concerning the Moore–Penrose inverse of a product of two operators lead in finding a relation between the operators in the case where Greville’s inclusions are made into equalities.
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Boundary Regularity for k-Hessian Equations Acta. Math. Sin. Engl. Ser. (IF 0.7) Pub Date : 2023-12-07 You Li, Meng Ni Li, Yan Nan Liu
In this paper we focus on the boundary regularity for a class of k-Hessian equations which can be degenerate and (or) singular on the boundary of the domain. Motivated by the case of Monge–Ampère equations, we first construct sub-solutions, then apply the characteristic of the global Hölder continuity for convex functions, and finally use the maximum principle to obtain the boundary Hölder continuity
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A New Inertial Self-adaptive Gradient Algorithm for the Split Feasibility Problem and an Application to the Sparse Recovery Problem Acta. Math. Sin. Engl. Ser. (IF 0.7) Pub Date : 2023-12-15 Nguyen The Vinh, Pham Thi Hoai, Le Anh Dung, Yeol Je Cho
In this paper, by combining the inertial technique and the gradient descent method with Polyak’s stepsizes, we propose a novel inertial self-adaptive gradient algorithm to solve the split feasibility problem in Hilbert spaces and prove some strong and weak convergence theorems of our method under standard assumptions. We examine the performance of our method on the sparse recovery problem beside an
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Homological Transfer between Additive Categories and Higher Differential Additive Categories Acta. Math. Sin. Engl. Ser. (IF 0.7) Pub Date : 2023-11-15 Xi Tang, Zhao Yong Huang
Given an additive category \({\cal C}\) and an integer n ≥ 2. The higher differential additive category consists of objects X in \({\cal C}\) equipped with an endomorphism ϵX satisfying \(\epsilon_X^n = 0\). Let R be a finite-dimensional basic algebra over an algebraically closed field and T the augmenting functor from the category of finitely generated left R-modules to that of finitely generated
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Derivatives of Intersection Local Time for Two Independent Symmetric α-stable Processes Acta. Math. Sin. Engl. Ser. (IF 0.7) Pub Date : 2023-11-15 Huan Zhou, Guang Jun Shen, Qian Yu
In this paper, we consider the derivatives of intersection local time for two independent d-dimensional symmetric α-stable processes Xα and \({\widetilde X^{\widetilde \alpha }}\) with respective indices α and \(\widetilde \alpha \). We first study the sufficient condition for the existence of the derivatives, which makes us obtain the exponential integrability and Hölder continuity. Then we show that
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Nuclearity and Finite-Representability in the System of Completely Integral Mapping Spaces Acta. Math. Sin. Engl. Ser. (IF 0.7) Pub Date : 2023-11-15 Zhe Dong, Ji Cheng Tao, Ya Fei Zhao
In this paper, we investigate local properties in the system of completely integral mapping spaces. We introduce notions of injectivity, local reflexivity, exactness, nuclearity, finite-representability and WEP in the system of completely integral mapping spaces. First we obtain that any finite-dimensional operator space is injective in the system of completely integral mapping spaces. Furthermore
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Fully Nonlinear Equations of Krylov Type on Riemannian Manifolds with Totally Geodesic Boundary Acta. Math. Sin. Engl. Ser. (IF 0.7) Pub Date : 2023-11-15 Li Chen, Yan He
In this paper, we study fully nonlinear equations of Krylov type in conformal geometry on compact smooth Riemannian manifolds with totally geodesic boundary. We prove the a priori estimates for solutions to these equations and establish an existence result.
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Lower Bounds for Moments of Quadratic Twisted Self-dual GL(3) Central L-values Acta. Math. Sin. Engl. Ser. (IF 0.7) Pub Date : 2023-11-15 Sheng Hao Hua, Bing Rong Huang
In this paper, we prove the conjectured order lower bound for the k-th moment of central values of quadratic twisted self-dual GL(3) L-functions for all k ≥ 1, based on our recent work on the twisted first moment of central values in this family of L-functions.
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On the Structure of Quantum Toroidal Superalgebra $${{\cal E}_{m|n}}$$ Acta. Math. Sin. Engl. Ser. (IF 0.7) Pub Date : 2023-11-15 Xiang Hua Wu, Hong Da Lin, Hong Lian Zhang
Recently the quantum toroidal superalgebra \({{\cal E}_{m|n}}\) associated with \({\mathfrak{g}\mathfrak{l}_{m|n}}\) was introduced by L. Bezerra and E. Mukhin, which is not a quantum Kac–Moody algebra. The quantum toroidal superalgebra \({{\cal E}_{m|n}}\) exploits infinite sequences of generators and relations of the form, which are called Drinfeld realization. In this paper, we use only finite set
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Group LASSO for Change-points in Functional Time Series Acta. Math. Sin. Engl. Ser. (IF 0.7) Pub Date : 2023-11-15 Chang Xiong Chi, Rong Mao Zhang
Multiple change-points estimation for functional time series is studied in this paper. The change-point problem is first transformed into a high-dimensional sparse estimation problem via basis functions. Group least absolute shrinkage and selection operator (LASSO) is then applied to estimate the number and the locations of possible change points. However, the group LASSO (GLASSO) always overestimate
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Improved Hardy–Littlewood–Sobolev Inequality on $${\mathbb{S}^n}$$ under Constraints Acta. Math. Sin. Engl. Ser. (IF 0.7) Pub Date : 2023-11-15 Yun Yun Hu, Jing Bo Dou
In this paper, we establish an improved Hardy–Littlewood–Sobolev inequality on \({\mathbb{S}^n}\) under higher-order moments constraint. Moreover, by constructing precise test functions, using improved Hardy–Littlewood–Sobolev inequality on \({\mathbb{S}^n}\), we show such inequality is almost optimal in critical case. As an application, we give a simpler proof of the existence of the maximizer for
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Resonant-Superlinear Nonhomogeneous Dirichlet Problems Acta. Math. Sin. Engl. Ser. (IF 0.7) Pub Date : 2023-11-15 Zhen Hai Liu, Nikolaos S. Papageorgiou
We consider a Dirichlet nonlinear equation driven by the (p, 2)-Laplacian and with a reaction having the competing effects of a parametric asymmetric superlinear term and a resonant perturbation. We show that for all small values of the parameter the problem has at least five nontrivial smooth solutions all with sign information.
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The Brezis–Nirenberg Problem for the Fractional p-Laplacian in Unbounded Domains Acta. Math. Sin. Engl. Ser. (IF 0.7) Pub Date : 2023-11-15 Yan Sheng Shen
In this paper we study the existence of nontrivial solutions to the well-known Brezis–Nirenberg problem involving the fractional p-Laplace operator in unbounded cylinder type domains. By means of the fractional Poincaré inequality in unbounded cylindrical domains, we first study the asymptotic property of the first eigenvalue \({\lambda _{p,s}}(\widehat {{\omega _\delta }})\) with respect to the domain
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Single Peak Solutions for a Schrödinger Equation with Variable Exponent Acta. Math. Sin. Engl. Ser. (IF 0.7) Pub Date : 2023-11-15 Zhong Yuan Liu, Peng Luo, Hua Fei Xie
We study the following Schrödinger equation with variable exponent $$ - \Delta u + u = {u^{p + \epsilon a(x)}},\,\,\,u > 0\,\,{\rm{in}}\,\,{\mathbb{R}^N},$$ where \(\epsilon > 0,\,\,1 < p < {{N + 2} \over {N - 2}},\,\,a(x) \in {C^1}({\mathbb{R}^N}) \cap {L^\infty }({\mathbb{R}^N}),\,\,N \ge 3\) Under certain assumptions on a vector field related to a(x), we use the Lyapunov–Schmidt reduction to show
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Spectrum and Spectral Singularities of a Quadratic Pencil of a Schrödinger Operator with Boundary Conditions Dependent on the Eigenparameter Acta. Math. Sin. Engl. Ser. (IF 0.7) Pub Date : 2023-11-15 Xiang Zhu, Zhao Wen Zheng, Kun Li
In this paper, we consider the following quadratic pencil of Schrödinger operators L(λ) generated in \({L^2}({\mathbb{R}^ + })\) by the equation $$ - {y^{\prime \prime }} + [p(x) + 2\lambda q(x)]y = {\lambda ^2}y,\,\,\,\,\,x \in {\mathbb{R}^ + } = [0, + \infty )$$ with the boundary condition $${{{y^\prime }(0)} \over {y(0)}} = {{{\beta _1}\lambda + {\beta _0}} \over {{\alpha _1}\lambda + {\alpha _0}}}
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Classification of Proper Holomorphic Mappings between Hartogs Domains over Homogeneous Siegel Domains Acta. Math. Sin. Engl. Ser. (IF 0.7) Pub Date : 2023-11-15 Lei Wang
The Hartogs domain over homogeneous Siegel domain DN,s (s > 0) is defined by the inequality ∥ζ∥2 < KD(z, z)−s, where D is a homogeneous Siegel domain of type II, (z, ζ) ∈ D × ℂN and KD(z, z) is the Bergman kernel of D. Recently, Seo obtained the rigidity result that proper holomorphic mappings between two equidimensional domains DN,s and D′N′,s′ are biholomorphisms for N ≥ 2. In this article, we find
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Every Graph Embedded on the Surface with Euler Characteristic Number ε = −1 is Acyclically 11-choosable Acta. Math. Sin. Engl. Ser. (IF 0.7) Pub Date : 2023-11-15 Lin Sun, Guang Long Yu, Xin Li
A proper vertex coloring of a graph G is acyclic if there is no bicolored cycles in G. A graph G is acyclically k-choosable if for any list assignment L = {L(v): v ∈ V(G)} with ∣L(v)∣ ≥ k for each vertex v ∈ V(G), there exists an acyclic proper vertex coloring ϕ of G such that ϕ(v) ∈ L(v) for each vertex v ∈ V(G). In this paper, we prove that every graph G embedded on the surface with Euler characteristic
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Partial Regularity of Suitable Weak Solutions of the Model Arising in Amorphous Molecular Beam Epitaxy Acta. Math. Sin. Engl. Ser. (IF 0.7) Pub Date : 2023-11-15 Yan Qing Wang, Yi Ke Huang, Gang Wu, Dao Guo Zhou
In this paper, we are concerned with the precise relationship between the Hausdorff dimension of possible singular point set \({\cal S}\) of suitable weak solutions and the parameter α in the nonlinear term in the following parabolic equation $${h_t} + {h_{xxxx}} + {\partial _{xx}}|{h_x}{|^\alpha } = f.$$ It is shown that when \(5/3 \le \alpha < 7/3\), the \({{3\alpha - 5} \over {\alpha - 1}}\) dimensional
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Centroid Hom-associative Algebras and Centroid Hom-Lie Algebras Acta. Math. Sin. Engl. Ser. (IF 0.7) Pub Date : 2023-10-17 Yu Xiu Bai, Leonid A. Bokut, Yu Qun Chen, Ze Rui Zhang
In this article, we construct free centroid hom-associative algebras and free centroid hom-Lie algebras. We also construct some other relatively free centroid hom-associative algebras by applying the Gröbner–Shirshov basis theory for (unital) centroid hom-associative algebras. Finally, we prove that the “Poincaré–Birkhoff–Witt theorem” holds for certain type of centroid hom-Lie algebras over a field
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The Enhanced Period Map and Equivariant Deformation Quantizations of Nilpotent Orbits Acta. Math. Sin. Engl. Ser. (IF 0.7) Pub Date : 2023-10-17 Shi Lin Yu
In a previous paper, the author and his collaborator studied the problem of lifting Hamiltonian group actions on symplectic varieties and Lagrangian subvarieties to their graded deformation quantizations and apply the general results to coadjoint orbit method for semisimple Lie groups. Only even quantizations were considered there. In this paper, these results are generalized to the case of general
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Character Sheaves for Classical Graded Lie Algebras Acta. Math. Sin. Engl. Ser. (IF 0.7) Pub Date : 2023-10-17 Ting Xue
In this note we study character sheaves for graded Lie algebras arising from inner automorphisms of special linear groups and Vinberg’s type II classical graded Lie algebras.
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Remarks on Some Compact Symplectic Solvmanifolds Acta. Math. Sin. Engl. Ser. (IF 0.7) Pub Date : 2023-10-15 Qiang Tan, Adriano Tomassini
We study the hard Lefschetz property on compact symplectic solvmanifolds, i.e., compact quotients M = ΓG of a simply-connected solvable Lie group G by a lattice Γ, admitting a symplectic structure.
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Oracle Inequality for Sparse Trace Regression Models with Exponential β-mixing Errors Acta. Math. Sin. Engl. Ser. (IF 0.7) Pub Date : 2023-10-15 Ling Peng, Xiang Yong Tan, Pei Wen Xiao, Zeinab Rizk, Xiao Hui Liu
In applications involving, e.g., panel data, images, genomics microarrays, etc., trace regression models are useful tools. To address the high-dimensional issue of these applications, it is common to assume some sparsity property. For the case of the parameter matrix being simultaneously low rank and elements-wise sparse, we estimate the parameter matrix through the least-squares approach with the
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Response Solutions for Degenerate Reversible Harmonic Oscillators with Zero-average Perturbation Acta. Math. Sin. Engl. Ser. (IF 0.7) Pub Date : 2023-10-15 Xin Yu Guan, Jian Guo Si, Wen Si
In this paper, we consider a class of normally degenerate quasi-periodically forced reversible systems, obtained as perturbations of a set of harmonic oscillators, $$\left\{ {\matrix{{\dot x = y + {f_1}(\omega t,x,y),} \hfill \cr {\dot y = \lambda {x^l} + {f_2}(\omega t,x,y),} \hfill \cr } } \right.$$ where 0 ≠ λ ∈ ℝ, l > 1 is an integer and the corresponding involution G is (−θ, x, −y) → (θ, x, y)
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Several Dynamics of Dynamical Systems with the Eventual Shadowing Property Acta. Math. Sin. Engl. Ser. (IF 0.7) Pub Date : 2023-10-15 Xue Rong Xie, Jian Dong Yin
In this article, we provide some sufficient conditions for the dynamical systems with the eventual shadowing property to have positive topological entropy and several equivalent conditions for the dynamical systems with the eventual shadowing property to be mixing.
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Turán Number of the Family Consisting of a Blow-up of a Cycle and a Blow-up of a Star Acta. Math. Sin. Engl. Ser. (IF 0.7) Pub Date : 2023-10-15 Zhi Wei Wu, Li Ying Kang
Let \({\cal F} = \{ {H_1}, \ldots ,{H_k}\} \,\,(k \ge 1)\) be a family of graphs. The Turán number of the family \({\cal F}\) is the maximum number of edges in an n-vertex {H1, …, Hk}-free graph, denoted by ex(n, \({\cal F}\)) or ex(n, {H1,H2, … Hk}). The blow-up of a graph H is the graph obtained from H by replacing each edge in H by a clique of the same size where the new vertices of the cliques
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A No Shrinking Breather Theorem for Noncompact Harmonic Ricci Flows Acta. Math. Sin. Engl. Ser. (IF 0.7) Pub Date : 2023-10-15 Jia Rui Chen, Qun Chen
In this paper, we construct an ancient solution by using a given shrinking breather and prove a no shrinking breather theorem for noncompact harmonic Ricci flow under the condition that \({\rm{Sic}}: = {\rm{Ric}} - \alpha \nabla \phi \otimes \nabla \phi \) is bounded from below.
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Global Existence of Smooth Solutions for the Diffusion Approximation Model of General Gas in Radiation Hydrodynamics Acta. Math. Sin. Engl. Ser. (IF 0.7) Pub Date : 2023-10-15 Hyejong Kim, Hakho Hong, Jongsung Kim
In this paper, we consider the 3-D Cauchy problem for the diffusion approximation model in radiation hydrodynamics. The existence and uniqueness of global solutions is proved in perturbation framework, for more general gases including ideal polytropic gas. Moreover, the optimal time decay rates are obtained for higher-order spatial derivatives of density, velocity, temperature, and radiation field
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On the Prescribed Boundary Mean Curvature Problem via Local Pohozaev Identities Acta. Math. Sin. Engl. Ser. (IF 0.7) Pub Date : 2023-10-15 Qiu Xiang Bian, Jing Chen, Jing Yang
This paper deals with the following prescribed boundary mean curvature problem in \({\mathbb{B}^N}\)$$\left\{ {\matrix{{ - \Delta u = 0,\,u > 0,} \hfill & {y \in {\mathbb{B}^N},} \hfill \cr {{{\partial u} \over {\partial \nu }} + {{N - 2} \over 2}u = {{N - 2} \over 2}\tilde K(y){u^{{2^\sharp } - 1}},} \hfill & {y \in {\mathbb{S}^{N - 1}},} \hfill \cr } } \right.$$ where \(\tilde K(y) = \tilde K(|{y^\prime
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On Hom-groups and Hom-group Actions Acta. Math. Sin. Engl. Ser. (IF 0.7) Pub Date : 2023-10-15 Liang Yun Chen, Tian Qi Feng, Yao Ma, Ripan Saha, Hong Yi Zhang
A Hom-group is the non-associative generalization of a group whose associativity and unitality are twisted by a compatible bijective map. In this paper, we give some new examples of Hom-groups, and show the first, second and third isomorphism theorems of Hom-groups. We also introduce the notion of Hom-group action, and as an application, we prove the first Sylow theorem for Hom-groups along the line
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Commuting Toeplitz Operators on Fock–Sobolev Spaces of Negative Orders Acta. Math. Sin. Engl. Ser. (IF 0.7) Pub Date : 2023-10-15 Hong Rae Cho, Han-Wool Lee
In the setting of Fock–Sobolev spaces of positive orders over the complex plane, Choe and Yang showed that if the one of the symbols of two commuting Toeplitz operators with bounded symbols is non-trivially radial, then the other must also be radial. In this paper, we extend this result to the Fock–Sobolev space of negative order using the Fock-type space with a confluent hypergeometric function.
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Integration Operators on Spaces of Dirichlet Series Acta. Math. Sin. Engl. Ser. (IF 0.7) Pub Date : 2023-10-15 Jia Le Chen, Mao Fa Wang
We first study the Volterra operator V acting on spaces of Dirichlet series. We prove that V is bounded on the Hardy space \({\cal H}_0^p\) for any 0 < p ≤ ∞, and is compact on \({\cal H}_0^p\) for 1
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The Extension Dimension of Subcategories and Recollements of Abelian Categories Acta. Math. Sin. Engl. Ser. (IF 0.7) Pub Date : 2023-09-15 Xin Ma, Ye Yang Peng, Zhao Yong Huang
We investigate the behavior of the extension dimension of subcategories of abelian categories under recollements. Let Λ′, Λ, Λ″ be artin algebras such that (mod Λ′, mod Λ, mod Λ′) is a recollement, and let \(\cal{D}^{\prime}\) and \(\cal{D}^{\prime\prime}\) be subcategories of mod Λ′ and mod Λ″ respectively. For any n, m ≥ 0, under some conditions, we get \(\text{dim}\Omega^{k}(\cal{D})\leq \text{
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Composition Operators with Universal Translates on $${S^2}(\mathbb{D})$$ Acta. Math. Sin. Engl. Ser. (IF 0.7) Pub Date : 2023-09-15 Kai Kai Han, Yan Yan Tang
It is known that the Invariant Subspace Problem for Hilbert spaces is equivalent to the statement that all minimal non-trivial invariant subspaces for a universal operator are one dimensional. In this paper, we characterize all linear fractional composition operators and their adjoints that have universal translates on the space \({S^2}(\mathbb{D})\). Moreover, we characterize all adjoints of linear
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Weyl Type Theorem for Bounded Linear Operator and Its Functional Calculus Acta. Math. Sin. Engl. Ser. (IF 0.7) Pub Date : 2023-09-15 Gao Hui Zi Feng, Peng Tong Li
Let \(\cal{H}\) be a complex infinite dimensional Hilbert space and \(\cal{B}(\cal{H})\) be the algebra of all bounded linear operators on \(\cal{H}\). In this paper, we mainly study the operators that satisfy both a-Weyl’s theorem and property (R). Also, the operators whose functional calculus satisfies the two properties are also explored. We give the features for the operator or its functional calculus
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Scattering for the Radial Schrödinger Equation with Combined Power-type and Choquard-type Nonlinearities Acta. Math. Sin. Engl. Ser. (IF 0.7) Pub Date : 2023-09-15 Ying Wang, Cheng Bin Xu
In this paper, we show the scattering of the radial solution for the nonlinear Schrödinger equation with combined power-type and Choquard-type nonlinearities $$\rm{i}u_{t}+\Delta u=\lambda_{1}\vert u\vert^{p_{1}-1}u+\lambda_{2}(I_{\alpha}\ast\vert u\vert^{p_{2}})\vert u\vert^{p_{2}-2}u.$$ in the energy space H1(ℝN) for λ1λ2 = −1. We establish a scattering criterion for radial solution together with
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Characterization of Lipschitz Functions via Commutators of Multilinear Singular Integral Operators in Variable Lebesgue Spaces Acta. Math. Sin. Engl. Ser. (IF 0.7) Pub Date : 2023-09-15 Jiang Long Wu, Pu Zhang
Let \(\overrightarrow{b}=(b_{1},b_{2},\ldots,b_{m})\) be a collection of locally integrable functions and \(T_{\Sigma\overrightarrow{b}}\) the commutator of multilinear singular integral operator T. Denote by \(\mathbb{L}(\delta)\) and \(\mathbb{L}(\delta(\cdot))\) the Lipschitz spaces and the variable Lipschitz spaces, respectively. The main purpose of this paper is to establish some new characterizations
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Ergodicity of 3D Stochastic Burgers Equation Acta. Math. Sin. Engl. Ser. (IF 0.7) Pub Date : 2023-09-15 Zhao Dong, Jiang Lun Wu, Guo Li Zhou
3D Burgers equation is an important model for turbulence. It is natural to expect the long-time behaviour for this hydrodynamics equation. However, there is no result about the long-time behaviour for this deterministic model. Surprisingly, if the system is perturbed by stochastic noise, we establish the existence and uniqueness of invariant measure for 3D stochastic Burgers equation.
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The Sufficient and Necessary Conditions of the Strong Law of Large Numbers under Sub-linear Expectations Acta. Math. Sin. Engl. Ser. (IF 0.7) Pub Date : 2023-09-15 Li Xin Zhang
In this paper, by establishing a Borel–Cantelli lemma for a capacity which is not necessarily continuous, and a link between a sequence of independent random variables under the sub-linear expectation and a sequence of independent random variables on \({\mathbb{R}^\infty}\) under a probability, we give the sufficient and necessary conditions of the strong law of large numbers for independent and identically
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Spacelike Framed Curves with Lightlike Components and Singularities of Their Evolutes and Focal Surfaces in Minkowski 3-space Acta. Math. Sin. Engl. Ser. (IF 0.7) Pub Date : 2023-09-15 Peng Cheng Li, Dong He Pei, Xin Zhao
In this paper, we define the evolute and focal surface of a spacelike framed curve with lightlike components in Minkowski 3-space. It is a generalization of the previous results of regular spacelike curves, since singularities are allowed in the original spacelike curves studied by spacelike framed curves with lightlike components. Meanwhile, we show a new geometric invariant to characterise singularities
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Uniqueness on Difference Operators of Meromorphic Functions of Infinite Order Acta. Math. Sin. Engl. Ser. (IF 0.7) Pub Date : 2023-09-15 Hui Li, Ming Liang Fang, Xiao Yao
We investigate the uniqueness problems of meromorphic functions and their difference operators by using a new method. It is proved that if a non-constant meromorphic function f shares a non-zero constant and ∞ counting multiplicities with its difference operators Δcf(z) and \(\Delta_{c}^{2}f(z)\), then \(\Delta_{c}f(z)\equiv\Delta_{c}^{2}f(z)\). In particular, we give a difference analogue of a result
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A Simple Proof of ACC for Minimal Log Discrepancies for Surfaces Acta. Math. Sin. Engl. Ser. (IF 0.7) Pub Date : 2023-09-15 Jing Jun Han, Yu Jie Luo
Following Shokurov’s idea, we give a simple proof of the ACC conjecture for minimal log discrepancies for surfaces.
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A Semiparametric Additive-multiplicative Rates Model for the Weighted Composite Endpoint of Recurrent and Terminal Events Acta. Math. Sin. Engl. Ser. (IF 0.7) Pub Date : 2023-09-15 Yi Deng, Qiang Xiong, Shu Wei Li
Recurrent event data are commonly encountered in many scientific fields, including biomedical studies, clinical trials and epidemiological surveys, and many statistical methods have been proposed for their analysis. In this paper, we consider to use a weighted composite endpoint of recurrent and terminal events, which is weighted by the severity of each event, to assess the overall effects of covariates
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Topological Stability and Entropy for Certain Set-valued Maps Acta. Math. Sin. Engl. Ser. (IF 0.7) Pub Date : 2023-09-15 Yu Zhang, Yu Jun Zhu
In this paper, the dynamics (including shadowing property, expansiveness, topological stability and entropy) of several types of upper semi-continuous set-valued maps are mainly considered from differentiable dynamical systems points of view. It is shown that (1) if f is a hyperbolic endomor-phism then for each ε> 0 there exists a C1-neighborhood \({\cal U}\) of f such that the induced set-valued map
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Toeplitz Operators and Carleson Measures for Weighted Bergman Spaces Induced by Regular Weights Acta. Math. Sin. Engl. Ser. (IF 0.7) Pub Date : 2023-09-15 Jun Tao Du, Song Xiao Li, Hasi Wulan
In this paper, we give a universal description of the boundedness and compactness of Toeplitz operator \({\cal T}_\mu ^\omega \) between Bergman spaces \(A_\eta ^p\) and \(A_\nu^q\) when μ is a positive Borel measure, 1 < p,q < ∞ and ω, η, ν are regular weights. By using Khinchin’s inequality and Kahane’s inequality, we get a new characterization of the Carleson measure for Bergman spaces induced by