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Related papers: Tighter and Stable Bounds for Marcum Q-Function

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In this article, we propose a finite volume limiter function for a reconstruction on the three-point stencil. Compared to classical limiter functions in the MUSCL framework, which yield $2^{\text{nd}}$-order accuracy, the new limiter is…

Numerical Analysis · Mathematics 2016-06-28 Birte Schmidtmann , Rémi Abgrall , Manuel Torrilhon

Let $A(s) = \sum_n a_n n^{-s}$ be a Dirichlet series with meromorphic continuation. Say we are given information on the poles of $A(s)$ with $|\Im s| \leq T$ for some large constant $T$. What is the best way to use such finite spectral data…

Number Theory · Mathematics 2025-11-19 Andrés Chirre , Harald Andrés Helfgott

We review recent results on analytical properties (monotonicity and bounds) for ratios of contiguous functions of hypergeometric type. The cases of parabolic cylinder functions and modified Bessel functions have been discussed with…

Classical Analysis and ODEs · Mathematics 2024-08-13 Javier Segura

Constraint tightening to non-conservatively guarantee recursive feasibility and stability in Stochastic Model Predictive Control is addressed. Stability and feasibility requirements are considered separately, highlighting the difference…

Systems and Control · Computer Science 2016-05-13 Matthias Lorenzen , Fabrizio Dabbene , Roberto Tempo , Frank Allgöwer

Due to their importance in both data analysis and numerical algorithms, low rank approximations have recently been widely studied. They enable the handling of very large matrices. Tight error bounds for the computationally efficient…

Numerical Analysis · Mathematics 2023-04-06 Frank de Hoog , Markus Hegland

The central purpose of the present paper is to study boundary behavior of squeezing functions on bounded domains. We prove that the squeezing function of a strongly pseudoconvex domain tends to 1 near the boundary. In fact, such an estimate…

Complex Variables · Mathematics 2013-02-22 Fusheng Deng , Qi'an Guan , Liyou Zhang

It is shown that, if nu >= 1/2 then the generalized Marcum Q function Q_nu(a, b) is log-concave in 0<=b <infty. This proves a conjecture of Sun, Baricz and Zhou (2010). We also point out relevant results in the statistics literature.

Statistics Theory · Mathematics 2011-05-31 Yaming Yu

The inverse tangent function can be bounded by different inequalities, for example by Shafer's inequality. In this publication, we propose a new sharp double inequality, consisting of a lower and an upper bound, for the inverse tangent…

Information Theory · Computer Science 2013-07-19 Gholamreza Alirezaei

Simple inequalities for some integrals involving the modified Bessel functions $I_{\nu}(x)$ and $K_{\nu}(x)$ are established. We also obtain a monotonicity result for $K_{\nu}(x)$ and a new lower bound, that involves gamma functions, for…

Classical Analysis and ODEs · Mathematics 2017-03-21 Robert E. Gaunt

We present decay bounds for a broad class of Hermitian matrix functions where the matrix argument is banded or a Kronecker sum of banded matrices. Besides being significantly tighter than previous estimates, the new bounds closely capture…

Numerical Analysis · Mathematics 2015-01-30 Michele Benzi , Valeria Simoncini

We formulate a criterion for the existence of an invariant measure for a Feller semigroup defined on a metric space with the e-property for bounded continuous functions and use it to prove the asymptotic stability of a semigroup satisfying…

Probability · Mathematics 2018-09-25 Stanisław Wȩdrychowicz , Andrzej Wiśnicki

In this paper we established a new Simpson type conformable fractional integral equality for convex functions. Based on this identity, some results related to Simpson-like type inequalities are obtained. These results are then applied to…

Classical Analysis and ODEs · Mathematics 2024-09-05 Zeynep Şanlı

An apparently ideal way to generate continuous bounded stochastic processes is to consider the stochastically perturbed motion of a point of small mass in an infinite potential well, under overdamped approximation. Here, however, we show…

Mathematical Physics · Physics 2017-09-26 Dario Domingo , Alberto d Onofrio , Franco Flandoli

By $BMO_o(R)$ we denote the space consisting of all those odd and bounded mean oscillation functions on R. In this paper we characterize the functions in $BMO_o(R)$ with bounded support as those ones that can be written as a sum of a…

Classical Analysis and ODEs · Mathematics 2023-10-26 Víctor Almeida , Jorge J. Betancor , Alejandro J. Castro , Juan C. Fariña , Lourdes Rodríguez-Mesa

Partition functions arise in statistical physics and probability theory as the normalizing constant of Gibbs measures and in combinatorics and graph theory as graph polynomials. For instance the partition functions of the hard-core model…

Combinatorics · Mathematics 2021-03-05 Ewan Davies , Matthew Jenssen , Will Perkins , Barnaby Roberts

We present new tight bounds for averaging differential inclusions, which we apply to multi-frequency inclusions consisting of a sum of time periodic set-valued mappings. For this family of inclusions we establish an a tight estimate of…

Optimization and Control · Mathematics 2014-03-11 Ido Bright

Unlike well-established parameter estimation, function estimation faces conceptual and mathematical difficulties despite its enormous potential utility. We establish the fundamental error bounds on function estimation in quantum metrology…

Quantum Physics · Physics 2020-01-29 Naoto Kura , Masahito Ueda

The minimax theory for estimating linear functionals is extended to the case of a finite union of convex parameter spaces. Upper and lower bounds for the minimax risk can still be described in terms of a modulus of continuity. However in…

Statistics Theory · Mathematics 2007-06-13 T. Tony Cai , Mark G. Low

This work is devoted to the derivation of novel analytic results for special functions which are particularly useful in wireless communication theory. Capitalizing on recently reported series representations for the Nuttall $Q{-}$function…

Information Theory · Computer Science 2015-05-14 Paschalis C. Sofotasios , Khuong Ho- Van , Tuan Dang Anh , Hung Dinh Quoc

Upper bounds are obtained for the $p$-capacity of compact sets in $\R^d$, with $d \ge 2$ and $1<p<d$. Upper and lower bounds are obtained for the product of $p$-capacity and powers of the $q$-torsional rigidity over the collection of all…

Analysis of PDEs · Mathematics 2025-07-25 Michiel van den Berg , Nunzia Gavitone