Several new product identities in relation to Rogers–Ramanujan type sums and mock theta functions
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In the past decade, deep learning as a branch of machine learning has influenced scientific computing in a fundamental way. This computational breakthrough presents tremendous opportunities and needs for new perspectives on computational mathematics and related emerging fields, such as approximation theory, operator estimation, numerical PDEs, inverse problems, data-driven modeling of dynamical systems, unsupervised and semi-supervised learnings. This special issue will feature high-quality original research, including (but not limited to) the theoretical and computational developments in these topics.
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This special issue will feature recent developments in the theory and applications of transmission eigenvalues and related spectral problems in direct and inverse scattering theory. The transmission eigenvalue problem is at the heart of inverse scattering theory for inhomogeneous media. It has a deceptively simple formulation but presents a perplexing mathematical structure; in particular it is a non-self-adjoint eigenvalue problem. This subject is rich, active and in the past decade has taken a multitude of directions, including developments in the spectral theory for various operators related to scattering, as well as many applications in inverse scattering problems and imaging. We solicit high quality original research papers targeting results on the theory, computations and applications of these topics.
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