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Iterative imputation, in which variables are imputed one at a time each given a model predicting from all the others, is a popular technique that can be convenient and flexible, as it replaces a potentially difficult multivariate modeling…

Statistics Theory · Mathematics 2012-04-04 Jingchen Liu , Andrew Gelman , Jennifer Hill , Yu-Sung Su

We derive an upper bound for the efficiency of estimating entries in the inverse covariance matrix of a high dimensional distribution. We show that in order to approximate an off-diagonal entry of the density matrix of a $d$-dimensional…

Statistics Theory · Mathematics 2015-05-06 Ronen Eldan

In this note we apply a spectral method to the graph of alternating bilinear forms. In this way, we obtain upper bounds on the size of an alternating rank-metric code for given values of the minimum rank distance. We computationally compare…

Combinatorics · Mathematics 2024-05-16 Aida Abiad , Gianira N. Alfarano , Alberto Ravagnani

How to establish some specific quantitative weighted estimates for the generalized commutator of multilinear fractional singular integral operator $\mathcal{T}_{\eta}^{{\bf b}}$ is the focus of this paper, which is defined by…

Classical Analysis and ODEs · Mathematics 2025-01-24 Xi Cen , Zichen Song

We prove the following conjecture due to Bryant Mathews (2008). Let Q be the orthogonal grassmannian of totally isotropic i-planes of a non-degenerate quadratic form q over an arbitrary field (where i is an integer in the interval [1, (\dim…

Algebraic Geometry · Mathematics 2011-10-12 Nikita A. Karpenko

In their celebrated paper "On Siegel's Lemma", Bombieri and Vaaler found an upper bound on the height of integer solutions of systems of linear Diophantine equations. Calculating the bound directly, however, requires exponential time. In…

Number Theory · Mathematics 2017-07-20 Jun Zhang , Qi Cheng

For a bilinear form obtained by adding a Dirac mass to a positive definite moment functional in several variables, explicit formulas of orthogonal polynomials are derived from the orthogonal polynomials associated with the moment…

Classical Analysis and ODEs · Mathematics 2008-01-03 Lidia Fernandez , Teresa E. Perez , Miguel A. Pinar , Yuan Xu

We prove new bounds on bilinear forms with Kloosterman sums, complementing and improving a series of results by \'E. Fouvry, E. Kowalski and Ph. Michel (2014), V. Blomer, \'E. Fouvry, E. Kowalski, Ph. Michel and D. Mili\'cevi\'c (2017), E.…

Number Theory · Mathematics 2023-04-18 Bryce Kerr , Igor E. Shparlinski , Xiaosheng Wu , Ping Xi

We prove the well-posedness and regularity of solutions in mixed-norm weighted Sobolev spaces for a class of second-order parabolic and elliptic systems in divergence form in the half-space $\mathbb{R}^d_+ = \{x_d > 0\}$ subject to the…

Analysis of PDEs · Mathematics 2026-05-22 Bekarys Bekmaganbetov , Hongjie Dong

We establish an $L^\infty\times L^2 \to L^2$ norm estimate for a bilinear oscillatory integral along parabolas incorporating oscillatory factors $e^{i|t|^{-\beta}}$.

Classical Analysis and ODEs · Mathematics 2008-07-10 Dashan Fan , Xiaochun Li

We prove bounds in the local $ L^2 $ range for exotic paraproducts motivated by bilinear multipliers associated with convex sets. One result assumes an exponential boundary curve. Another one assumes a higher order lacunarity condition.

Classical Analysis and ODEs · Mathematics 2024-02-28 Olli Saari , Christoph Thiele

We consider two types of multilinear pseudodifferential operators. First, we prove the boundedness of multilinear pseudodifferential operators with symbols which are only measurable in the spatial variables in weighted Lebesgue spaces.…

Classical Analysis and ODEs · Mathematics 2012-06-22 Nicholas Michalowski , David J. Rule , Wolfgang Staubach

We give an overview of the generalized Calder\'on-Zygmund theory for "non-integral" singular operators, that is, operators without kernels bounds but appropriate off-diagonal estimates. This theory is powerful enough to obtain weighted…

Classical Analysis and ODEs · Mathematics 2018-10-10 Pascal Auscher , José Maria Martell

A sufficient condition for the two-weight boundedness of higher order commutators was recently obtained by Holmes and Wick in terms of an intersection of two BMO spaces. We provide an alternative proof, showing that the higher order case…

Classical Analysis and ODEs · Mathematics 2016-04-11 Tuomas P. Hytönen

The motivation of this work stems from the numerical approximation of bounded functions by polynomials satisfying the same bounds. The present contribution makes use of the recent algebraic characterization found in [B. Despr\'es, Numer.…

Numerical Analysis · Mathematics 2020-06-30 Martin Campos Pinto , Frédérique Charles , Bruno Després , Maxime Herda

We prove a double-exponential upper bound on the degree and on the complexity of constructing a Janet basis of a $D$-module. This generalizes a well known bound on the complexity of a Gr\"obner basis of a module over the algebra of…

Analysis of PDEs · Mathematics 2007-05-23 Alexander Chistov , Dima Grigoriev

We study the nonparametric estimators of the infinitesimal coefficients of the second-order jump-diffusion models. Under the mild conditions, we obtain the weak consistency and the asymptotic normalities of the estimators.

Statistics Theory · Mathematics 2017-07-07 Zheng-Yan Lin , Yu-Ping Song , Han-Chao Wang

We establish various upper bounds on Type-I and Type-II shifted bilinear sums with Sali\'e sums modulo a large prime $q$. We use these bounds to study, for fixed integers $a,b\not \equiv 0 \bmod q$, the distribution ofsolutions to the…

Number Theory · Mathematics 2026-01-16 Igor E. Shparlinski , Yixiu Xiao

We prove a determinantal formula for quantities related to the problem of enumeration of (semi-) meanders, namely the topologically inequivalent planar configurations of non-self-intersecting loops crossing a given (half-) line through a…

High Energy Physics - Theory · Physics 2008-02-03 P. Di Francesco

We obtain several estimates for bilinear form with Kloosterman sums. Such results can be interpreted as a measure of cancellations amongst with parameters from short intervals. In particular, for certain ranges of parameters we improve some…

Number Theory · Mathematics 2016-08-23 Igor E. Shparlinski