Acta Mathematica Sinica-English Series最新文献

An extension of slant Hankel operator, namely, the k-th-order λ-slant Hankel operator on the Lebesgue space (L^{2}(mathbb{T}^{n})), where (mathbb{T}) is the unit circle and n ≥ 1, a natural number, is described in terms of the solution of a system of operator equations, which is subsequently expressed in terms of the product of a slant Hankel operator and a unitary operator. The study is further lifted in Calkin algebra in terms of essentially k-th-order λ-slant Hankel operators on (L^{2}(mathbb{T}^{n})).

In this paper, we study the concept of split monotone variational inclusion problem with multiple output sets. We propose a new relaxed inertial iterative method with self-adaptive step sizes for approximating the solution of the problem in the framework of Hilbert spaces. Our proposed algorithm does not require the co-coerciveness nor the Lipschitz continuity of the associated single-valued operators. Moreover, some parameters are relaxed to accommodate a larger range of values for the step sizes. Under some mild conditions on the control parameters and without prior knowledge of the operator norms, we obtain strong convergence result for the proposed method. Finally, we apply our result to study certain classes of optimization problems and we present several numerical experiments to demonstrate the implementability of the proposed method. Several of the existing results in the literature could be viewed as special cases of our result in this paper.

In this paper, we consider the global spherically symmetric solutions for the initial boundary value problem of a coupled compressible Navier–Stokes/Allen–Cahn system which describes the motion of two-phase viscous compressible fluids. We prove the existence and uniqueness of global classical solution, weak solution and strong solution under the assumption of spherically symmetry condition for initial data ρ₀ without vacuum state.

The eccentricity matrix of a graph is obtained from the distance matrix by keeping the entries that are largest in their row or column, and replacing the remaining entries by zero. This matrix can be interpreted as an opposite to the adjacency matrix, which is on the contrary obtained from the distance matrix by keeping only the entries equal to 1. In the paper, we determine graphs having the second largest eigenvalue of eccentricity matrix less than 1.

Pseudo-differential operators (PDO) (Q(x,{{cal L}_{a,x}})) and ({cal Q}(x,{{cal L}_{a,x}})) involving the index Whittaker transform are defined. Estimates for these operators in Hilbert space L^a₂(ℝ₊;m_a(x)dx) are obtained. A symbol class Ω is introduced. Later product and commutators for the PDO are investigated and their boundedness results are discussed.

In this paper, pseudo-differential operators with homogeneous symbol classes associated with the Weinstein transform are introduced. The boundedness of pseudo-differential operators and commutator between two pseudo-differential operators on ℌ^r_α,2 are proven with the help of the Weinstein transform technique.

In this paper, we prove that for each positive k ≡ 1 mod m there exists a P-symmetric kmτ-periodic solution x_k for asymptotically linear mτ-periodic Hamiltonian systems, which are nonautonomous and endowed with a P-symmetry. If the P-symmetric Hamiltonian function is semi-positive, one can prove, under a new iteration inequality of the Maslov-type P-index, that ({x_{{k_1}}}) and ({x_{{k_2}}}) are geometrically distinct for k₁/k₂ ≥ (2n + 1)m + 1; and ({x_{{k_1}}}), ({x_{{k_2}}}) are geometrically distinct for k₁/k₂ ≥ m + 1 provided ({x_{{k_1}}}) is non-degenerate.

In this paper, we describe the minimal reducing subspaces of Toeplitz operators induced by non-analytic monomials on the weighted Bergman spaces and Dirichlet spaces over the unit ball ({mathbb{B}_2}). It is proved that each minimal reducing subspace M is finite dimensional, and if dim M ≥ 3, then M is induced by a monomial. Furthermore, the structure of commutant algebra (nu ({T_{overline w {N_z}N}}): = {{ M_{{w^N}}^ * {M_{{z^N}}},M_{{z^N}}^ * {M_{{w^N}}}} ^prime }) is determined by N and the two dimensional minimal reducing subspaces of ({T_{overline w {N_z}N}}). We also give some interesting examples.

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.

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.