Fourier interpolation with zeros of zeta and LL-functions

We construct a large family of Fourier interpolation bases for functions analytic in a strip symmetric about the real line. Interesting examples involve the nontrivial zeros of the Riemann zeta function and other $L$-functions. We establish a duality principle for Fourier interpolation bases in terms of certain kernels of general Dirichlet series with variable coefficients. Such kernels admit meromorphic continuation, with poles at a sequence dual to the sequence of frequencies of the Dirichlet series, and they satisfy a functional equation. Our construction of concrete bases relies on a strengthening of Knopp's abundance principle for Dirichlet series with functional equations and a careful analysis of the associated Dirichlet series kernel, with coefficients arising from certain modular integrals for the theta group.Comment: We have made an update and addition in the bibliograph

Optimal asymptotic bounds for spherical designs

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On concentrators and related approximation constants

Pippenger [Pi77] showed the existence of (6m,4m,3m,6)-concentrator for each positive integer m using a probabilistic method. We generalize his approach and prove existence of (6m,4m,3m,5.05)-concentrator (which is no longer regular, but has fewer edges). We apply this result to improve the constant of approximation of almost additive set functions by additive set functions from 44.5 (established by Kalton and Roberts in [KaRo83] to 39. We show a more direct connection of the latter problem to the Whitney type estimate for approximation of continuous functions on a cube in &b&R&/b&&sup&d&/sup& by linear functions, and improve the estimate of this Whitney constant from 802 (proved by Brudnyi and Kalton in [BrKa00] to 73

Real Time Bridge Scour Monitoring with Magneto-Inductive Field Coupling

Scour was responsible for most of the U.S. bridges that collapsed during the past 40 years. The maximum scour depth is the most critical parameter in bridge design and maintenance. Due to scouring and refilling of river-bed deposits, existing technologies face a challenge in measuring the maximum scour depth during a strong flood. In this study, a new methodology is proposed for real time scour monitoring of bridges. Smart Rocks with embedded electronics are deployed around the foundation of a bridge as field agents. With wireless communications, these sensors can send their position change information to a nearby mobile station. This paper is focused on the design, characterization, and performance validation of active sensors. The active sensors use 3-axis accelerometers/magnetometers with a magneto-inductive communication system. In addition, each sensor includes an ID, a timer, and a battery level indicator. A Smart Rock system enables the monitoring of the most critical scour condition and time by logging and analyzing sliding, rolling, tilting, and heading of the spatially distributed sensors

Smart Rocks and Wireless Communication System for Real-Time Monitoring and Mitigation of Bridge Scour -- A Proof-of-Concept Study

This study aims to integrate commercial measurement and communication components into a scour monitoring system with magnets or electronics embedded in smart rocks, and evaluate and improve its performance in laboratory and field conditions for the movement of smart rocks. Properly-designed smart rocks were found to be automatically rolled into the very bottom of a scour hole and can give critical information about the maximum scour depth and effectiveness of rip-rap mitigation strategies. Four types of smart rock technologies were investigated in this proof-of-concept phase of study, including passive with embedded magnets, active with magneto-inductive communication, active with controllable magnet rotation, and active with acoustic communication. Their performances were evaluated against three criteria: 1) movement accuracy within 0.5 m, 2) transmission distance between 5 and 30 m, and 3) at least one measurement every 15 minutes. Test results demonstrated that the proposed smart rocks are cost-effective, viable technologies for bridge scour monitoring

On a family of strongly regular graphs with λ = 1

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