scholarly journals A simple algorithm to compute link polynomials defined by using skein relations

2020 ◽  
Vol 8 (1) ◽  
pp. 68-73
Author(s):  
Xuezhi Zhao

AbstractWe give a simple and practical algorithm to compute the link polynomials, which are defined according to the skein relations. Our method is based on a new total order on the set of all braid representatives. As by-product a new complete link invariant are obtained.

2018 ◽  
Author(s):  
Darren Whitaker ◽  
Kevin Hayes

Raman Spectroscopy is a widely used analytical technique, favoured when molecular specificity with minimal sample preparation is required.<br>The majority of Raman instruments use charge-coupled device (CCD) detectors, these are susceptible to cosmic rays and as such multiple spurious spikes can occur in the measurement. These spikes are problematic as they may hinder subsequent analysis, particularly if multivariate data analysis is required. In this work we present a new algorithm to remove these spikes from spectra after acquisition. Specifically we use calculation of modified <i>Z</i> scores to locate spikes followed by a simple moving average filter to remove them. The algorithm is very simple and its execution is essentially instantaneous, resulting in spike-free spectra with minimal distortion of actual Raman data. The presented algorithm represents an improvement on existing spike removal methods by utilising simple, easy to understand mathematical concepts, making it ideal for experts and non-experts alike. <br>


2018 ◽  
Author(s):  
Darren Whitaker ◽  
Kevin Hayes

Raman Spectroscopy is a widely used analytical technique, favoured when molecular specificity with minimal sample preparation is required.<br>The majority of Raman instruments use charge-coupled device (CCD) detectors, these are susceptible to cosmic rays and as such multiple spurious spikes can occur in the measurement. These spikes are problematic as they may hinder subsequent analysis, particularly if multivariate data analysis is required. In this work we present a new algorithm to remove these spikes from spectra after acquisition. Specifically we use calculation of modified <i>Z</i> scores to locate spikes followed by a simple moving average filter to remove them. The algorithm is very simple and its execution is essentially instantaneous, resulting in spike-free spectra with minimal distortion of actual Raman data. The presented algorithm represents an improvement on existing spike removal methods by utilising simple, easy to understand mathematical concepts, making it ideal for experts and non-experts alike. <br>


2018 ◽  
Author(s):  
Darren Whitaker ◽  
Kevin Hayes

Raman Spectroscopy is a widely used analytical technique, favoured when molecular specificity with minimal sample preparation is required.<br>The majority of Raman instruments use charge-coupled device (CCD) detectors, these are susceptible to cosmic rays and as such multiple spurious spikes can occur in the measurement. These spikes are problematic as they may hinder subsequent analysis, particularly if multivariate data analysis is required. In this work we present a new algorithm to remove these spikes from spectra after acquisition. Specifically we use calculation of modified <i>Z</i> scores to locate spikes followed by a simple moving average filter to remove them. The algorithm is very simple and its execution is essentially instantaneous, resulting in spike-free spectra with minimal distortion of actual Raman data. The presented algorithm represents an improvement on existing spike removal methods by utilising simple, easy to understand mathematical concepts, making it ideal for experts and non-experts alike. <br>


Author(s):  
Lexi Eikelboom

In contrast to the previous two chapters, which theologically engage rhythm in continental philosophy, this chapter examines Augustine’s explicitly theological approach to rhythm and its various receptions. The chapter uses Przywara’s scheme of intra-creaturely and theological analogies to frame Augustine’s treatment of rhythm in chapter six of De Musica. While Agamben represents an intra-creaturely perspective, Augustine represents a theological perspective. The degree to which this synchronic, theological view, which envisions rhythm as that which binds metaphysical layers of reality together allowing for communication between them, is problematic depends on the degree to which it is uncoupled from an intra-creaturely perspective like that of Agamben. Proponents of Radical Orthodoxy who propose an Augustinian musical ontology represent such an uncoupling, leading to a total order that betrays creatureliness. Erich Przywara’s interpretation, in contrast, retains the tension in Augustine between both the theological perspective on reality as harmonious and the intra-creaturely experience of interruption.


1999 ◽  
Vol 9 (3) ◽  
pp. 755-778 ◽  
Author(s):  
Paul T. Boggs ◽  
Anthony J. Kearsley ◽  
Jon W. Tolle

Author(s):  
Zhengyan Chang ◽  
Zhengwei Zhang ◽  
Qiang Deng ◽  
Zheren Li

The artificial potential field method is usually applied to the path planning problem of driverless cars or mobile robots. For example, it has been applied for the obstacle avoidance problem of intelligent cars and the autonomous navigation system of storage robots. However, there have been few studies on its application to intelligent bridge cranes. The artificial potential field method has the advantages of being a simple algorithm with short operation times. However, it is also prone to problems of unreachable targets and local minima. Based on the analysis of the operating characteristics of bridge cranes, a two-dimensional intelligent running environment model of a bridge crane was constructed in MATLAB. According to the basic theory of the artificial potential field method, the double-layer artificial potential field method was deduced, and the path and track fuzzy processing method was proposed. These two methods were implemented in MATLAB simulations. The results showed that the improved artificial potential field method could avoid static obstacles efficiently.


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