Search Results - "Berger, Arno"

More Grade School Triangles by Berger, Arno

“…Planar triangles with each side having a positive integer length are among the simplest geometrical objects imaginable. What can be said about the angles of…”
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On Planar Curves with Position-Dependent Curvature by Berger, Arno

“…Motivated by homothetic solutions in curvature-driven flows of planar curves, as well as their many physical applications, this article carries out a…”
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Circling the uniform distribution by Berger, Arno, Rahmatidehkordi, Ardalan

“…Distributions modulo one of slowly varying sequences are of wide interest in analysis and number theory. For every real sequence (xn) for which…”
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One-dimensional dynamical systems and Benford's law by Berger, Arno, Bunimovich, Leonid A., Hill, Theodore P.

“…Near a stable fixed point at 0 or \infty, many real-valued dynamical systems follow Benford's law: under iteration of a map T the proportion of values in \{x,…”
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Most linear flows on R d are Benford by Berger, Arno

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Most linear flows on Rd are Benford by Berger, Arno

“…A necessary and sufficient condition (“exponential nonresonance”) is established for every signal obtained from a linear flow on Rd by means of a linear…”
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On linear independence of trigonometric numbers by Berger, Arno

“…A necessary and sufficient condition is established for 1, cos(πr₁), and cos(r₂) to be rationally independent, where r₁, r₂ are rational numbers. The…”
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On the Classification of Finite-Dimensional Linear Flows by Berger, Arno, Wynne, Anthony

“…New elementary, self-contained proofs are presented for the topological and the smooth classification theorems of linear flows on finite-dimensional normed…”
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On the significands of uniform random variables by Berger, Arno, Twelves, Isaac

“…For all α > 0 and real random variables X, we establish sharp bounds for the smallest and the largest deviation of αX from the logarithmic distribution also…”
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The mathematics of Benford’s law: a primer by Berger, Arno, Hill, Theodore P.

“…This article provides a concise overview of the main mathematical theory of Benford’s law in a form accessible to scientists and students who have had first…”
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Intermittent Synchronization in Finite-State Random Networks Under Markov Perturbations by Berger, Arno, Qian, Hong, Wang, Shirou, Yi, Yingfei

“…By introducing extrinsic noise as well as intrinsic uncertainty into a network with stochastic events, this paper studies the dynamics of the resulting Markov…”
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A Characterization of Benford’s Law in Discrete-Time Linear Systems by Berger, Arno, Eshun, Gideon

“…A necessary and sufficient condition (“nonresonance”) is established for every solution of an autonomous linear difference equation, or more generally for…”
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Asymptotics of One-Dimensional Lévy Approximations by Berger, Arno, Xu, Chuang

“…For arbitrary Borel probability measures on the real line, necessary and sufficient conditions are presented that characterize best purely atomic…”
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Best Finite Approximations of Benford’s Law by Berger, Arno, Xu, Chuang

“…For arbitrary Borel probability measures with compact support on the real line, characterizations are established of the best finitely supported…”
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A basic theory of Benford’s Law by Berger, Arno, Hill, Theodore P.

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Some dynamical properties of Benford sequences by Berger, Arno

“…Numerical data generated by dynamical processes often obey Benford's law of logarithmic mantissa distributions. For non-autonomous difference equations this…”
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Benford’s Law Strikes Back: No Simple Explanation in Sight for Mathematical Gem by Berger, Arno, Hill, Theodore P.

“…The widely known phenomenon called Benford's Law continues to defy attempts at an easy derivation. Here, Berger and Hill briefly review recurring flaws in…”
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An Improved Maximum Allowable Transfer Interval for L p-Stability of Networked Control Systems by Jentzen, Arnulf, Leber, Frank, Schneisgen, Daniela, Berger, Arno, Siegmund, Stefan

“…An elementary self-contained proof is given for an improved bound on the maximum allowable transfer interval that guarantees L p-stability in networked control…”
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On planar curves with position-dependent curvature by Berger, Arno

“…Motivated by homothetic solutions to curvature-driven flows of planar curves, as well as their many physical applications, this work carries out a systematic…”
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More on finite-time hyperbolicity by Berger, Arno

“…A solution of a nonautonomous ordinary differential equation is finite-time hyperbolic, i.e. hyperbolic on a compact interval of time, if the linearisation…”
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