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  1. Content type: Research

    Given a tensor f in a Euclidean tensor space, we are interested in the critical points of the distance function from f to the set of tensors of rank at most k, which we call the critical rank-at-most-k tensors fo...

    Authors: Jan Draisma, Giorgio Ottaviani and Alicia Tocino

    Citation: Research in the Mathematical Sciences 2018 5:27

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  2. Content type: Research

    This introductory paper studies a class of real analytic functions on the upper half plane satisfying a certain modular transformation property. They are not eigenfunctions of the Laplacian and are quite disti...

    Authors: Francis Brown

    Citation: Research in the Mathematical Sciences 2018 5:7

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  3. Content type: Research

    This is a slightly expanded version of my lecture at the conference Modular forms are everywhere at Bonn, May 2017, taking into account remarks by Don Zagier and Shaul Zemel, and suggestions of the referees.

    Authors: Roelof Bruggeman

    Citation: Research in the Mathematical Sciences 2018 5:5

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  4. Content type: Research

    We prove that certain degenerate abelian varieties that include compactified Jacobians, namely stable semiabelic varieties, satisfy autoduality. We establish this result by proving a comparison theorem that re...

    Authors: Jesse Leo Kass

    Citation: Research in the Mathematical Sciences 2017 4:27

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  5. Content type: Research

    A fourientation of a graph is a choice for each edge of the graph whether to orient that edge in either direction, leave it unoriented, or biorient it. Fixing a total order on the edges and a reference orienta...

    Authors: Spencer Backman and Sam Hopkins

    Citation: Research in the Mathematical Sciences 2017 4:18

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  6. Content type: Research

    In this paper we study the stochastic Galerkin approximation for the linear transport equation with random inputs and diffusive scaling. We first establish uniform (in the Knudsen number) stability results in ...

    Authors: Shi Jin, Jian-Guo Liu and Zheng Ma

    Citation: Research in the Mathematical Sciences 2017 4:15

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  7. Content type: Research

    A polynomial with integer coefficients yields a family of dynamical systems indexed by primes as follows: For any prime p, reduce its coefficients mod p and consider its action on the field ...

    Authors: Andrew Bridy and Derek Garton

    Citation: Research in the Mathematical Sciences 2017 4:13

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  8. Content type: Research

    What is the probability that the smallest part of a random integer partition of N is odd? What is the expected value of the smallest part of a random integer partition of N? It is straightforward to see that the ...

    Authors: Hieu T. Ngo and Robert C. Rhoades

    Citation: Research in the Mathematical Sciences 2017 4:17

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  9. Content type: Research

    The hierarchical interpolative factorization (HIF) offers an efficient way for solving or preconditioning elliptic partial differential equations. By exploiting locality and low-rank properties of the operator...

    Authors: Yingzhou Li and Lexing Ying

    Citation: Research in the Mathematical Sciences 2017 4:12

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  10. Content type: Research

    We implement new techniques involving Artin fans to study the realizability of tropical stable maps in superabundant combinatorial types. Our approach is to understand the skeleton of a fundamental object in l...

    Authors: Dhruv Ranganathan

    Citation: Research in the Mathematical Sciences 2017 4:11

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  11. Content type: Research

    We present a ray-based finite element method for the high-frequency Helmholtz equation in smooth media, whose basis is learned adaptively from the medium and source. The method requires a fixed number of grid ...

    Authors: Jun Fang, Jianliang Qian, Leonardo Zepeda-Núñez and Hongkai Zhao

    Citation: Research in the Mathematical Sciences 2017 4:9

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