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Weighted and restricted sum formulas of Euler sums
Research in Number TheoryOne of the most interesting formulas for multiple zeta values is the sum formula proved by Granville and Zagier independently in 1990s. Many variations and generalizations of it have been found since then. In this paper, we will provide a uniform approach to proving these results using the regularized double shuffle relations of Euler sums.
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How Should We Use Colour in Euler Diagrams? [PDF]
, 2014 This paper addresses the problem of how best to use colour in Euler diagrams. The choice of using coloured curves, rather than black curves, possibly with coloured fill is often made in tools that automatically draw Euler diagrams for information ...
Howse, John +8 more
core +1 more source
Advanced Intelligent Systems, Volume 7, Issue 3, March 2025.Magnetic soft robots offer promise in biomedicine due to their wireless actuation and rapid response, but current fabrication methods are complex and have limited cellular compatibility. A new, contactless bioassembly strategy using hydrodynamic instabilities is introduced, enabling customizable, centimeter‐scale robots.
Wei Gao +5 more
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Zagier–Hoffman’s Conjectures in Positive Characteristic
Forum of Mathematics, PiMultiples zeta values and alternating multiple zeta values in positive characteristic were introduced by Thakur and Harada as analogues of classical multiple zeta values of Euler and Euler sums.
Bo-Hae Im +4 more
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Combinatorial relations for Euler–Zagier sums [PDF]
Acta Arithmetica, 2004 From the text: Let \(k_ 1,\dots,k_ n\) be positive integers with \(k_ n\geq 2\). The Euler-Zagier sum of weight \(k=k_ 1+\dots+k_ n\) and depth \(n\) is the sum \[ \zeta(k_ 1,\dots,k_ n) :=\sum_ {1\leq m_ ...
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Dynamic Euler Diagram Drawing [PDF]
, 2004 In this paper we describe a method to lay out a graph enhanced Euler diagram so that it looks similar to a previously drawn graph enhanced Euler diagram. This task is non-trivial when the underlying structures of the diagrams differ.
Rodgers, Peter +2 more
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Advanced Intelligent Systems, Volume 7, Issue 3, March 2025.Herein, a patient‐mounted neuro optical coherence tomography system that integrates a 5 degrees‐of‐freedom skull‐mounted robot (Skullbot) with a 0.6 mm neuroendoscope for targeted, minimally invasive deep brain imaging, is developed. The system offers high‐resolution imaging with precise deployment, demonstrated through successful tumor imaging in a ...
Chao Xu +7 more
wiley +1 more source
Advanced Intelligent Systems, EarlyView.A quadrupedal integrated leg‐arm robot with an underactuated reconfigurable body is developed. By using a Sarrus mechanism as the body, the robot enables reconfiguration through its supporting limbs, achieving mode switching without additional actuators.
Xinghan Zhuang +8 more
wiley +1 more source
Advanced Intelligent Systems, EarlyView.TwinX shows how a single interbody wire connecting two robots can support both integrated morphological reconfiguration and distributed wire‐mediated cooperation. When the robots dock, they reconfigure into different forms for locomotion and manipulation.
Shintaro Inoue +5 more
wiley +1 more source
Bronchoscope Tip Localization With Learned Airway Constraints and an Open Source Simulator
Advanced Intelligent Systems, EarlyView.BronchoLoc addresses feature‐poor bronchoscopic imaging by combining monocular video with a preoperative CT graph to estimate 3D camera location. A local tracker identifies candidate branches, while a sequence‐aware global module refines the trajectory. Demonstrating sub‐centimeter accuracy across synthetic and phantom datasets, this framework advances
Emanuele Nicotra +7 more
wiley +1 more source