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<正>Aims and Scope:Communications in Mathematical Research (CMR) was established in1985 by Jilin University,with the title Northeastern Mathematical Journal.Recently the journal was renamed to the current one and publishes articles written in English.In early 2020,a new editorial board is formed aiming to enhance the quality of the journal.CMR publishes original research and survey papers in major areas of mathematics,including pure mathematics,applied mathematics,computational mathematics,and statistics.
2021年02期 v.37 138页 [查看摘要][在线阅读][下载 1055K] - Pierre Chau Huu-Tai;Bernard Ducomet;
We study spectral properties of a quantum Hamiltonian with a complex-valued energy-dependent potential related to a model introduced in physics of nuclear reactions [30] and we prove that the principle of limiting absorption holds at any point of a large subset of the essential spectrum. When an additional dissipative or smallness hypothesis is assumed on the potential,we show that the principle of limiting absorption holds at any point of the essential spectrum.
2021年02期 v.37 141-179页 [查看摘要][在线阅读][下载 299K] - Lingfeng Li;Shousheng Luo;Xue-Cheng Tai;Jiang Yang;
In this work, we present a new method for convex shape representation, which is regardless of the dimension of the concerned objects, using level-set approaches. To the best of our knowledge, the proposed prior is the first one which can work for high dimensional objects. Convexity prior is very useful for object completion in computer vision. It is a very challenging task to represent high dimensional convex objects. In this paper, we first prove that the convexity of the considered object is equivalent to the convexity of the associated signed distance function. Then, the second order condition of convex functions is used to characterize the shape convexity equivalently. We apply this new method to two applications: object segmentation with convexity prior and convex hull problem(especially with outliers). For both applications, the involved problems can be written as a general optimization problem with three constraints. An algorithm based on the alternating direction method of multipliers is presented for the optimization problem. Numerical experiments are conducted to verify the effectiveness of the proposed representation method and algorithm.
2021年02期 v.37 180-208页 [查看摘要][在线阅读][下载 2690K] - Junichi Aramaki;
In this paper, we consider the equivalent conditions with L~p-version(1 < p < ∞) of the J.L. Lions lemma. As applications, we first derive the existence of a weak solution to the Maxwell-Stokes type problem and then we consider the Korn inequality. Furthermore, we consider the relation to other fundamental results.
2021年02期 v.37 209-235页 [查看摘要][在线阅读][下载 252K] - Wenting Liang;Chunyuan Deng;
In this paper, we study the existence of the reflexive, reflexive selfadjoint and reflexive positive solutions to some operator equations with respect to the generalized reflection operator dual(P, Q). We derive necessary and sufficient conditions for the solvability of these equations and provide a detailed description of the solutions in the solvable case by using the Moore-Penrose inverses.
2021年02期 v.37 236-254页 [查看摘要][在线阅读][下载 175K] - Wei-Xi Li;Juan Zeng;
We consider a Fokker-Planck operator with electric potential and electromagnetic fields. We establish the sharp weighted and subelliptic estimates, involving the control of the derivatives of electric potential and electromagnetic fields. Our proof relies on a localization argument as well as a careful calculation on commutators.
2021年02期 v.37 255-270页 [查看摘要][在线阅读][下载 161K] 下载本期数据