scholarly journals The Spherical Harmonic Spectrum of a Function with Algebraic Singularities

2012 ◽  
Vol 18 (6) ◽  
pp. 1146-1166 ◽  
Author(s):  
Philip W. Livermore
Energies ◽  
2021 ◽  
Vol 14 (10) ◽  
pp. 2929
Author(s):  
Abraham Marquez Alcaide ◽  
Vito Giuseppe Monopoli ◽  
Xuchen Wang ◽  
Jose I. Leon ◽  
Giampaolo Buticchi ◽  
...  

Electric variable speed drives (VSD) have been replacing mechanic and hydraulic systems in many sectors of industry and transportation because of their better performance and reduced cost. However, the electric systems still face the issue of being considered less reliable than the mechanical ones. For this reason, researchers have been actively investigating effective ways to increase the reliability of such systems. This paper is focused on the analysis of the common-mode voltage (CMV) generated by the operation of the VSDs which directly affects to the lifetime and reliability of the complete system. The method is based on the mathematical description of the harmonic spectrum of the CMV depending on the PWM method implementation. A generalized PWM method where the carriers present a variable phase-displacement is developed. As a result of the presented analysis, the CMV reduction is achieved by applying the PWM method with optimal carrier phase-displacement angles without any external component and/or passive filtering technique. The optimal values of the carrier phase-displacement angles are obtained considering the minimization of the CMV total harmonic distortion. The resulting method is easily implementable on mostly off-the-shelf mid-range micro-controller control platforms. The strategy has been evaluated in a scaled-down experimental setup proving its good performance.


2021 ◽  
Vol 216 ◽  
pp. 105590
Author(s):  
Tao Zhao ◽  
Shuguo Pan ◽  
Wang Gao ◽  
Zhao Qing ◽  
Xing Yang ◽  
...  

2021 ◽  
Vol 2021 (4) ◽  
Author(s):  
James Drummond ◽  
Jack Foster ◽  
Ömer Gürdoğan ◽  
Chrysostomos Kalousios

Abstract We address the appearance of algebraic singularities in the symbol alphabet of scattering amplitudes in the context of planar $$ \mathcal{N} $$ N = 4 super Yang-Mills theory. We argue that connections between cluster algebras and tropical geometry provide a natural language for postulating a finite alphabet for scattering amplitudes beyond six and seven points where the corresponding Grassmannian cluster algebras are finite. As well as generating natural finite sets of letters, the tropical fans we discuss provide letters containing square roots. Remarkably, the minimal fan we consider provides all the square root letters recently discovered in an explicit two-loop eight-point NMHV calculation.


2021 ◽  
Vol 12 (1) ◽  
Author(s):  
Swetlana G. Meshcheryagina ◽  
Alexey Opaev

Abstract Background In the last decade, enigmatic male-like cuckoo calls have been reported several times in East Asia. These calls exhibited a combination of vocal traits of both Oriental Cuckoo (Cuculus optatus) and Common Cuckoo (Cuculus canorus) advertising calls, and some authors therefore suggested that the enigmatic calls were produced by either Common × Oriental Cuckoo male hybrids or Common Cuckoo males having a gene mutation. However, the exact identity of calling birds are still unknown. Methods We recorded previously unknown male-like calls from three captive Oriental Cuckoo females, and compared these calls with enigmatic vocalizations recorded in the wild as well as with advertising vocalizations of Common and Oriental Cuckoo males. To achieve this, we measured calls automatically. Besides, we video-recorded captive female emitting male-like calls, and compared these recordings with the YouTube recordings of calling males of both Common and Oriental Cuckoos to get insight into the mechanism of call production. Results The analysis showed that female male-like calls recorded in captivity were similar to enigmatic calls recorded in the wild. Therefore, Oriental Cuckoo females might produce the latter calls. Two features of these female calls appeared to be unusual among birds. First, females produced male-like calls at the time of spring and autumn migratory activity and on migration in the wild. Because of this, functional significance of this call remained puzzling. Secondly, the male-like female call unexpectedly combined features of both closed-mouth (closed beak and simultaneous inflation of the ‘throat sac’) and open-mouth (prominent harmonic spectrum and the maximum neck extension observed at the beginning of a sound) vocal behaviors. Conclusions The Cuculus vocalizations outside the reproductive season remain poorly understood. Here, we found for the first time that Oriental Cuckoo females can produce male-like calls in that time. Because of its rarity, this call might be an atavism. Indeed, female male-like vocalizations are still known in non-parasitic tropical and apparently more basal cuckoos only. Therefore, our findings may shed light on the evolution of vocal communication in avian brood parasites.


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