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The manuscripts published below have been examined by the peer-review process and have been accepted for publication. A “Just Accepted” manuscript is published online shortly after its acceptance, which is prior to technical editing and formatting and author proofing. Higher Education Press (HEP) provides “Just Accepted” as an optional and free service which allows authors to make their results available to the research community as soon as possible after acceptance. After a manuscript has been technically edited and formatted, it will be removed from the “Just Accepted” Web site and published as an Online First article. Please note that technical editing may introduce minor changes to the manuscript text and/or graphics which may affect the content, and all legal disclaimers that apply to the journal pertain. In no event shall HEP be held responsible for errors or consequences arising from the use of any information contained in these “Just Accepted” manuscripts. To cite this manuscript please use its Digital Object Identifier (DOI(r)), which is identical for all formats of publication.
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  • Qiu-Ya Wang, Fu-Rong Lin
    Communications on Applied Mathematics and Computation, https://doi.org/10.1007/s42967-024-00430-w

    In this paper, we consider numerical methods for two-sided space variable-order fractional diffusion equations (VOFDEs) with a nonlinear source term. The implicit Euler (IE) method and a shifted Grünwald (SG) scheme are used to approximate the temporal derivative and the space variable-order (VO) fractional derivatives, respectively, which leads to an IE-SG scheme. Since the order of the VO derivatives depends on the space and the time variables, the corresponding coefficient matrices arising from the discretization of VOFDEs are dense and without the Toeplitz-like structure. In light of the off-diagonal decay property of the coefficient matrices, we consider applying the preconditioned generalized minimum residual methods with banded preconditioners to solve the discretization systems. The eigenvalue distribution and the condition number of the preconditioned matrices are studied. Numerical results show that the proposed banded preconditioners are efficient.

  • Boujamaa Janati Idrissi, Yahya Sahmoudi, Omar El Ogri, Jaouad El-Mekkaoui
    Communications on Applied Mathematics and Computation, https://doi.org/10.1007/s42967-024-00412-y

    Recent advances have been made in a wide range of imaging and pattern recognition applications, including picture categorization and object identification systems. These systems necessitate a robust feature extraction method. This study proposes a new class of orthogonal functions known as orthogonal mountain functions (OMFs). Using these functions, a novel set of orthogonal moments and associated scaling, rotation, and translation (SRT) invariants are presented for building a color image’s feature vector components. These orthogonal moments are presented as quaternion orthogonal mountain Fourier moments (QOMFMs). To demonstrate the validity of our theoretically recommended technique, we conduct a number of image analysis and pattern recognition experiments, including a comparison of the performance of the feature vectors proposed above to preexisting orthogonal invariant moments. The result of this study experimentally proves the effectiveness and quality of our QOMFMs.