Acta Mathematica Sinica-English Series最新文献

In this paper, we study the long-time behavior of global solutions to the Schrödinger–Choquard equation

Inspired by Murphy who gave a simple proof of scattering for the non-radial INLS, we find that the inhomogeneous term ∣x∣^b can replace the radial Sobolev embedding theorem, which allows us to prove scattering theory below the ground state for the intercritical case in energy space without radial assumption.

On the classical Bergman space, Toeplitz operators with radial symbols are diagonal and those operators commute. However, on the n-analytic Bergman space (A_{n}^{2}(mathbb D)) when n ≥ 2, the case is different. In this paper, our focus is on the problem of commuting Toeplitz operators with quasiho-mogeneous symbols, specifically in the context of the function space (A_{2}^{2}(mathbb D)). We show a kind of block matrice expression of Toeplitz operators on (A_{2}^{2}(mathbb D)). Based on the block expression, we give several important properties. Our results indicate that in some cases, two Toeplitz operators are commutative if and only if both operators are analytic or differ by a constant multiple.

In this paper, we discuss the concept of HN-semipositive (HN-positive) vector bundle and also introduce strongly HN-semipositive vector bundle over compact complex manifold. Let M be a projective manifold with HN-semipositive tangent bundle. If M is rationally connected, we show that T^1,0M is strongly HN-positive. We give a characterization of rationally connected compact Kähler manifolds with strongly HN-semipositive tangent bundle. In the second part, we show that a uniformly RC k-positivity implies mean curvature positivity.

In the article we study the solution u(x, t) of the Cauchy problem of linear damped fractional wave equation. We prove that u(x, t) has some sharp boundedness estimates on the Triebel–Lizorkin space. The proof of the necessity part is based on obtaining the precise asymptotic forms of the kernels of operators ({rm e}^{-t} cosh(t{sqrt L})) and ({rm e}^{-t} {{sinh(t{sqrt L})} over {sqrt L}}) with L = 1 − ∣Δ∣^α, where Δ is the Laplacian, as well as the method of stationary phase. Additionally, we study the Riesz mean of the solution and show its convergence in the Triebel–Lizorkin space norm.

We study inhomogeneous oscillator representations of the strange Lie superalgebras P(n) on supersymmetric polynomial algebras and on spaces of supersymmetric exponential-polynomial functions. We obtain the composition series for these representations. The obtained irreducible modules are infinite dimensional. Some of them are not of highest-weight type and even not weight modules.

An operator T on a complex separable infinite dimensional Hilbert space is hypercyclic if there is a vector (y in cal{H}) such that the orbit Orb(T, y) = {y, Ty, T²y, T³y, …} is dense in (cal{H}). Hypercyclic property and supercyclic proeprty are liable to fail for 2 × 2 upper triangular operator matrices. In this paper, we aim to explore and characterize the hypercyclicity and the supercyclicity for 2 × 2 upper triangular operator matrices. We obtain a spectral characterization of the norm-closure of the class of all hypercyclic (supercyclic) operators for 2 × 2 upper triangular operator matrices.

In this paper, we consider λ-translating solitons in ℝ³. These surfaces are critical points of the weighted area when the density is a coordinate function. If λ = 0, these surfaces evolve by translations along the mean curvature flow. We give a full classification of λ-translating solitons that satisfy a linear Weingarten relation between their curvatures. These surfaces are planes, circular cylinders, grim reapers and certain types of cylindrical surfaces. We also prove that planes and circular cylinders are the only λ-translating soliton with constant squared norm of the second fundamental form.

Cyclotomic multiple zeta values are generalizations of multiple zeta values. In this paper, we establish sum formulas for various kinds of cyclotomic multiple zeta values. As an interesting application, we show that the ℚ-algebra generated by Riemann zeta values are contained in the ℚ-algebra generated by unit cyclotomic multiple zeta values of level N for any N ≥ 2.

The main purpose of this article is to study the lattice structure of quantum logics by using the theory of partially order sets. The goal is achieved by constructing a natural embedding map from the quantum logic posets into the complete lattices. The embedding map needs to be dense (in the order sense) and such complete lattices are so-called extended logics which preserve all essential features of the quantum logic. We obtain that the extended logic is unique up to a lattice isomorphism.

In many practical applications, we need to recover block sparse signals. In this paper, we encounter the system model where joint sparse signals exhibit block structure. To reconstruct this category of signals, we propose a new algorithm called block signal subspace matching pursuit (BSSMP) for the block joint sparse recovery problem in compressed sensing, which simultaneously reconstructs the support of block jointly sparse signals from a common sensing matrix. To begin with, we consider the case where block joint sparse matrix X has full column rank and any r nonzero row-blocks are linearly independent. Based on these assumptions, our theoretical analysis indicates that the BSSMP algorithm could reconstruct the support of X through at most (k - r + leftlceil {{r over L}} rightrceil) iterations if sensing matrix A satisfies the block restricted isometry property of order L(K − r) + r + 1 with ({delta _{{B_{L( {K - r}) + r + 1}}}}< max {{{{sqrt r} over {sqrt {K + {r over 4}} + sqrt {{r over 4}} }},{{sqrt L} over {sqrt {Kd} + sqrt L}}}}). This condition improves the existing result.