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The Golden Ratio and Fibonacci Numbers

TLDR
The first 100 Fibonacci and Lucas numbers relationships involving the Lucas numbers were shown in this article, and the first 100 relationships involving Lucas numbers involving the Fiboni numbers were also shown in this paper.
Abstract
Basic properties of the golden ratio geometric problems in two dimensions geometric problems in three dimensions Fibonacci numbers Lucas numbers and generalized Fibonacci numbers continued fractions and rational approximants generalized Fibonacci representation theorems optimal spacing and search algorithms commensurate and incommensurate projections Penrose tilings quasicrystallography biological applications construction of the regular pentagon the first 100 Fibonacci and Lucas numbers relationships involving Fibonacci and Lucas numbers.

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Journal ArticleDOI

The effect of gradient sampling schemes on measures derived from diffusion tensor MRI: A Monte Carlo study

TL;DR: The results challenge the recently proposed notion that a set of six icosahedrally‐arranged orientations is optimal for DT‐MRI and show that at least 20 unique samplingorientations are necessary for a robust estimation of anisotropy, whereas at least 30 unique sampling orientations are required for a strong estimation of tensor‐orientation and mean diffusivity.
Journal ArticleDOI

Comparison of gradient encoding schemes for diffusion-tensor MRI

TL;DR: It is indicated that there is no significant advantage to using more than six encoding directions as long as an optimum encoding is used for six directions, and a previously described heuristic encoding scheme was found to be optimum.
Journal ArticleDOI

Stochastic and empirical models of the absolute asymmetric synthesis by the Soai-autocatalysis

TL;DR: The results show that in this highly interesting autocatalysis two or even perhaps three catalytic cycles are cooperating, and that the initial steps of the reaction might be controlled by simple normal distribution (“coin tossing”) formalism.
Journal ArticleDOI

Sunflower Array Antenna with Adjustable Density Taper

TL;DR: In this paper, a deterministic procedure to design a nonperiodic planar array radiating a rotationally symmetric pencil beam pattern with an adjustable sidelobe level is proposed.
Proceedings ArticleDOI

Bringing a Blurry Frame Alive at High Frame-Rate With an Event Camera

TL;DR: In this article, a simple and effective approach, the Event-based Double Integral (EDI) model, was proposed to reconstruct a high frame-rate, sharp video from a single blurry frame and its event data.