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  1. Research

    Uniform spectral convergence of the stochastic Galerkin method for the linear transport equations with random inputs in diffusive regime and a micro–macro decomposition-based asymptotic-preserving method

    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 ...

    Shi Jin, Jian-Guo Liu and Zheng Ma

    Research in the Mathematical Sciences 2017 4:15

    Published on: 7 August 2017

  2. Research

    Dynamically distinguishing polynomials

    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 ...

    Andrew Bridy and Derek Garton

    Research in the Mathematical Sciences 2017 4:13

    Published on: 10 July 2017

  3. Research

    Distributed-memory hierarchical interpolative factorization

    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...

    Yingzhou Li and Lexing Ying

    Research in the Mathematical Sciences 2017 4:12

    Published on: 5 June 2017

  4. Research

    Skeletons of stable maps II: superabundant geometries

    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...

    Dhruv Ranganathan

    Research in the Mathematical Sciences 2017 4:11

    Published on: 1 June 2017

  5. Research

    Formulas for monodromy

    Given a family X of complex varieties degenerating over a punctured disk, one is interested in computing related invariants called the motivic nearby fiber and the refined limit mixed Hodge numbers, both of which...

    Alan Stapledon

    Research in the Mathematical Sciences 2017 4:8

    Published on: 10 April 2017

  6. Research

    A geometric perspective on p-adic properties of mock modular forms

    Bringmann et al. (Trans Am Math Soc 364(5):2393–2410, 2012) showed how to ‘regularize’ mock modular forms by a certain linear combination of the Eichler integral of their shadows in order to obtain p-adic modular...

    Luca Candelori and Francesc Castella

    Research in the Mathematical Sciences 2017 4:5

    Published on: 3 March 2017

  7. Research

    Fast Ewald summation for free-space Stokes potentials

    We present a spectrally accurate method for the rapid evaluation of free-space Stokes potentials, i.e., sums involving a large number of free space Green’s functions. We consider sums involving stokeslets, str...

    Ludvig af Klinteberg, Davoud Saffar Shamshirgar and Anna-Karin Tornberg

    Research in the Mathematical Sciences 2017 4:1

    Published on: 1 February 2017

  8. Research

    Stochastic regularity of a quadratic observable of high-frequency waves

    We consider high-frequency waves satisfying the scalar wave equation with highly oscillatory initial data. The wave speed, and the phase and amplitude of the initial data are assumed to be uncertain, described...

    G. Malenová, M. Motamed and O. Runborg

    Research in the Mathematical Sciences 2017 4:3

    Published on: 24 January 2017

  9. Research

    A proof of the Thompson moonshine conjecture

    In this paper, we prove the existence of an infinite-dimensional graded supermodule for the finite sporadic Thompson group Th whose McKay–Thompson series are weakly holomorphic modular forms of weight

    Michael J. Griffin and Michael H. Mertens

    Research in the Mathematical Sciences 2016 3:36

    Published on: 14 December 2016

  10. Research

    The Lerch zeta function IV. Hecke operators

    This paper studies algebraic and analytic structures associated with the Lerch zeta function. It defines a family of two-variable Hecke operators http://static-content.springer.com/image/art%3A10.1186%2Fs40687-016-0082-9/40687_2016_82_Article_IEq1.gif

    Jeffrey C. Lagarias and Wen-Ching Winnie Li

    Research in the Mathematical Sciences 2016 3:33

    Published on: 12 December 2016

  11. Research

    A problem of Petersson about weight 0 meromorphic modular forms

    In this paper, we provide an explicit construction of weight 0 meromorphic modular forms. Following work of Petersson, we build these via Poincaré series. There are two main aspects of our investigation which ...

    Kathrin Bringmann and Ben Kane

    Research in the Mathematical Sciences 2016 3:24

    Published on: 1 December 2016

  12. Research

    Vanishing theorems for coherent automorphic cohomology

    We consider the coherent cohomology of toroidal compactifications of locally symmetric varieties (such as Shimura varieties) with coefficients in the canonical and subcanonical extensions of automorphic vector...

    Kai-Wen Lan

    Research in the Mathematical Sciences 2016 3:39

    Published on: 10 November 2016

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