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### BCJ Numerators from Differential Operator of Multidimensional Residue [article]

Gang Chen, Tianheng Wang
<span title="2019-12-22">2019</span> <i > arXiv </i> &nbsp; <span class="release-stage" >pre-print</span>
We finally give a compact expression for the multidimensional residue for any CHY-like integral in terms of the reduction matrices.  ...  These BCJ numerators are efficiently computed by the improved method involving the reduction matrix.  ...  we briefly summarize our method for computing the multidimensional residue.  ...
<span class="external-identifiers"> <a target="_blank" rel="external noopener" href="https://arxiv.org/abs/1709.08503v3">arXiv:1709.08503v3</a> <a target="_blank" rel="external noopener" href="https://fatcat.wiki/release/a2hqae7b75fmpa5wjriyb32hku">fatcat:a2hqae7b75fmpa5wjriyb32hku</a> </span>
<a target="_blank" rel="noopener" href="https://web.archive.org/web/20200809051154/https://arxiv.org/pdf/1709.08503v3.pdf" title="fulltext PDF download" data-goatcounter-click="serp-fulltext" data-goatcounter-title="serp-fulltext"> <button class="ui simple right pointing dropdown compact black labeled icon button serp-button"> <i class="icon ia-icon"></i> Web Archive [PDF] <div class="menu fulltext-thumbnail"> <img src="https://blobs.fatcat.wiki/thumbnail/pdf/2f/c0/2fc070e66d595846908a5afee8d4b341104b83e7.180px.jpg" alt="fulltext thumbnail" loading="lazy"> </div> </button> </a> <a target="_blank" rel="external noopener" href="https://arxiv.org/abs/1709.08503v3" title="arxiv.org access"> <button class="ui compact blue labeled icon button serp-button"> <i class="file alternate outline icon"></i> arxiv.org </button> </a>

### Numerical Simulation of Residual Stresses in Welding and Ultrasonic Impact Treatment Process [chapter]

Lanqing Tang, Ayhan Ince, Jing Zheng
<span title="2018-05-16">2018</span> <i title="InTech"> Residual Stress Analysis on Welded Joints by Means of Numerical Simulation and Experiments </i> &nbsp;
The FE residual stress results in UIT-treated weld joint demonstrated that the UIT introduced compressive residual stress layer with various depth, which brought beneficial effect on fatigue strength of  ...  In this study, the effect of the UIT on residual stress distribution of 304L weld joints was particularly investigated.  ...  Residual Stress Analysis on Welded Joints by Means of Numerical Simulation and Experiments  ...
<span class="external-identifiers"> <a target="_blank" rel="external noopener noreferrer" href="https://doi.org/10.5772/intechopen.72394">doi:10.5772/intechopen.72394</a> <a target="_blank" rel="external noopener" href="https://fatcat.wiki/release/uya24yahizdshdpbl3wsqwyyn4">fatcat:uya24yahizdshdpbl3wsqwyyn4</a> </span>
<a target="_blank" rel="noopener" href="https://web.archive.org/web/20190501061033/https://cdn.intechopen.com/pdfs/58147.pdf" title="fulltext PDF download" data-goatcounter-click="serp-fulltext" data-goatcounter-title="serp-fulltext"> <button class="ui simple right pointing dropdown compact black labeled icon button serp-button"> <i class="icon ia-icon"></i> Web Archive [PDF] <div class="menu fulltext-thumbnail"> <img src="https://blobs.fatcat.wiki/thumbnail/pdf/26/10/2610e8f04b63784a6af057f581b00c3ad978166c.180px.jpg" alt="fulltext thumbnail" loading="lazy"> </div> </button> </a> <a target="_blank" rel="external noopener noreferrer" href="https://doi.org/10.5772/intechopen.72394"> <button class="ui left aligned compact blue labeled icon button serp-button"> <i class="external alternate icon"></i> Publisher / doi.org </button> </a>

### Numerical Welding Simulation as a Basis for Structural Integrity Assessment of Structures: Microstructure and Residual Stresses [chapter]

Kimiya Hemmesi, Majid Farajian
<span title="2018-05-16">2018</span> <i title="InTech"> Residual Stress Analysis on Welded Joints by Means of Numerical Simulation and Experiments </i> &nbsp;
The numerical results are compared directly with the measured data.  ...  Residual stress measurements are carried out to determine the distribution of residual stresses in three orthogonal directions, on the surface and in the bulk of the material.  ...  behavior of welding residual stress field under multiaxial mechanical loading" and DFG FA992/2-2 "Numerical Incorporation of the Damaging Effects of Residual Stresses in the Multiaxial Fatigue Assessment  ...
<span class="external-identifiers"> <a target="_blank" rel="external noopener noreferrer" href="https://doi.org/10.5772/intechopen.74466">doi:10.5772/intechopen.74466</a> <a target="_blank" rel="external noopener" href="https://fatcat.wiki/release/vwiexsionnhi5pv6ujelqkq5mq">fatcat:vwiexsionnhi5pv6ujelqkq5mq</a> </span>
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### Matrix methods for Padé approximation: numerical calculation of poles, zeros and residues [article]

Luca Perotti, Michal Wojtylak
<span title="2018-01-17">2018</span> <i > arXiv </i> &nbsp; <span class="release-stage" >pre-print</span>
Several formulas for the poles, zeros and residues of the Padé approximation in terms of the matrix J are proposed. Their numerical stability is tested and compared.  ...  Acknowledgments We would like to thank Christian Schröder for many fruitful discussions and an essential help in implementing some of the numerical algorithms.  ...  In the present section we shall derive numerically stable algorithms for computing the poles, zeros and residues.  ...
<span class="external-identifiers"> <a target="_blank" rel="external noopener" href="https://arxiv.org/abs/1712.01155v2">arXiv:1712.01155v2</a> <a target="_blank" rel="external noopener" href="https://fatcat.wiki/release/5v2ysl4xgjghronc5ymjbjrcbq">fatcat:5v2ysl4xgjghronc5ymjbjrcbq</a> </span>
<a target="_blank" rel="noopener" href="https://web.archive.org/web/20200929162156/https://arxiv.org/pdf/1712.01155v2.pdf" title="fulltext PDF download" data-goatcounter-click="serp-fulltext" data-goatcounter-title="serp-fulltext"> <button class="ui simple right pointing dropdown compact black labeled icon button serp-button"> <i class="icon ia-icon"></i> Web Archive [PDF] <div class="menu fulltext-thumbnail"> <img src="https://blobs.fatcat.wiki/thumbnail/pdf/1f/30/1f30d480f4b5169c7613719df204aa36999db87f.180px.jpg" alt="fulltext thumbnail" loading="lazy"> </div> </button> </a> <a target="_blank" rel="external noopener" href="https://arxiv.org/abs/1712.01155v2" title="arxiv.org access"> <button class="ui compact blue labeled icon button serp-button"> <i class="file alternate outline icon"></i> arxiv.org </button> </a>

### Residual Stress Pattern Prediction in Spray Transfer Multipass Welding by Means of Numerical Simulation [chapter]

Jon Ander Esnaola, Ibai Ulacia, Arkaitz Lopez-Jauregi, Done Ugarte
<span title="2018-05-16">2018</span> <i title="InTech"> Residual Stress Analysis on Welded Joints by Means of Numerical Simulation and Experiments </i> &nbsp;
Nowadays, there are different numerical methods to predict the RS generated in GMAW process, being Goldak's method one of the most widely used model.  ...  One of the main problems of gas metal arc welding (GMAW) process is the generation of residual stresses (RS), which has a direct impact on the mechanical performance of welded components.  ...  Residual Stress Analysis on Welded Joints by Means of Numerical Simulation and Experiments  ...
<span class="external-identifiers"> <a target="_blank" rel="external noopener noreferrer" href="https://doi.org/10.5772/intechopen.72134">doi:10.5772/intechopen.72134</a> <a target="_blank" rel="external noopener" href="https://fatcat.wiki/release/dfis33yf3jhapdm6ugtsotsene">fatcat:dfis33yf3jhapdm6ugtsotsene</a> </span>
<a target="_blank" rel="noopener" href="https://web.archive.org/web/20190427105223/https://cdn.intechopen.com/pdfs/58182.pdf" title="fulltext PDF download" data-goatcounter-click="serp-fulltext" data-goatcounter-title="serp-fulltext"> <button class="ui simple right pointing dropdown compact black labeled icon button serp-button"> <i class="icon ia-icon"></i> Web Archive [PDF] <div class="menu fulltext-thumbnail"> <img src="https://blobs.fatcat.wiki/thumbnail/pdf/2c/22/2c22a491709766207380662773ebc2ca9b7fd5d5.180px.jpg" alt="fulltext thumbnail" loading="lazy"> </div> </button> </a> <a target="_blank" rel="external noopener noreferrer" href="https://doi.org/10.5772/intechopen.72134"> <button class="ui left aligned compact blue labeled icon button serp-button"> <i class="external alternate icon"></i> Publisher / doi.org </button> </a>

### Noise residuals for GW150914 using maximum likelihood and numerical relativity templates

Andrew D. Jackson, Hao Liu, Pavel Naselsky
<span title="2019-05-09">2019</span> <i title="IOP Publishing"> <a target="_blank" rel="noopener" href="https://fatcat.wiki/container/khdydolemfax3aa6z3uhleeviy" style="color: black;">Journal of Cosmology and Astroparticle Physics</a> </i> &nbsp;
., about 0.80) correlations between residual noise in the Hanford and Livingston detectors in the chirp domain as previously seen by us [2] when using a numerical relativity template given in [3].  ...  We reexamine the results presented in a recent work by Nielsen et al. [1], in which the properties of the noise residuals in the 40 ms chirp domain of GW150914 were investigated.  ...  This situation is particularly dangerous since the parameters all have names that invite the reader to attach physical significance to their numerical values.  ...
<span class="external-identifiers"> <a target="_blank" rel="external noopener noreferrer" href="https://doi.org/10.1088/1475-7516/2019/05/014">doi:10.1088/1475-7516/2019/05/014</a> <a target="_blank" rel="external noopener" href="https://fatcat.wiki/release/mgq4vc7k35aqbmqfyn37qhljfm">fatcat:mgq4vc7k35aqbmqfyn37qhljfm</a> </span>
<a target="_blank" rel="noopener" href="https://web.archive.org/web/20200826102027/https://arxiv.org/pdf/1903.02401v2.pdf" title="fulltext PDF download [not primary version]" data-goatcounter-click="serp-fulltext" data-goatcounter-title="serp-fulltext"> <button class="ui simple right pointing dropdown compact black labeled icon button serp-button"> <i class="icon ia-icon"></i> Web Archive [PDF] <span style="color: #f43e3e;">&#10033;</span> <div class="menu fulltext-thumbnail"> <img src="https://blobs.fatcat.wiki/thumbnail/pdf/16/4a/164a9b57aa1f34d7fa35129d8862edf4ea01049a.180px.jpg" alt="fulltext thumbnail" loading="lazy"> </div> </button> </a> <a target="_blank" rel="external noopener noreferrer" href="https://doi.org/10.1088/1475-7516/2019/05/014"> <button class="ui left aligned compact blue labeled icon button serp-button"> <i class="external alternate icon"></i> iop.org </button> </a>

### Residual Stress in Friction Stir Welding and Laser-Assisted Friction Stir Welding by Numerical Simulation and Experiments [chapter]

Caterina Casavola, Alberto Cazzato, Vincenzo Moramarco
<span title="2018-05-16">2018</span> <i title="InTech"> Residual Stress Analysis on Welded Joints by Means of Numerical Simulation and Experiments </i> &nbsp;
In this chapter, two numerical models that predict temperatures and residual stresses in friction stir welding and laser-assisted friction stir welding will be described.  ...  As the presence of high residual stress values influences the post-weld mechanical properties, e.g. fatigue properties, it is important to investigate the residual stress distribution in the FSW welds.  ...  Numerical prediction of residual stresses in FSW Numerical model description An uncoupled FE model has been carried out to calculate residual stress field.  ...
<span class="external-identifiers"> <a target="_blank" rel="external noopener noreferrer" href="https://doi.org/10.5772/intechopen.72271">doi:10.5772/intechopen.72271</a> <a target="_blank" rel="external noopener" href="https://fatcat.wiki/release/uz56e2nw4jcmxanx3kpfczfgsm">fatcat:uz56e2nw4jcmxanx3kpfczfgsm</a> </span>
<a target="_blank" rel="noopener" href="https://web.archive.org/web/20190501212315/https://cdn.intechopen.com/pdfs/58083.pdf" title="fulltext PDF download" data-goatcounter-click="serp-fulltext" data-goatcounter-title="serp-fulltext"> <button class="ui simple right pointing dropdown compact black labeled icon button serp-button"> <i class="icon ia-icon"></i> Web Archive [PDF] <div class="menu fulltext-thumbnail"> <img src="https://blobs.fatcat.wiki/thumbnail/pdf/01/2f/012ff0854899ff79e8164ea2be9394d2646c9484.180px.jpg" alt="fulltext thumbnail" loading="lazy"> </div> </button> </a> <a target="_blank" rel="external noopener noreferrer" href="https://doi.org/10.5772/intechopen.72271"> <button class="ui left aligned compact blue labeled icon button serp-button"> <i class="external alternate icon"></i> Publisher / doi.org </button> </a>

### Numerical Study of Residual Thermal Stresses in MMC

Tayeb Nehari
<span title="2020-09-02">2020</span> <i title="Walter de Gruyter GmbH"> <a target="_blank" rel="noopener" href="https://fatcat.wiki/container/fjpcpdh3m5gjdeocd3ww3kianu" style="color: black;">Mechanics and Mechanical Engineering</a> </i> &nbsp;
AbstractIn this paper, numerical study analysis of residual thermal stresses in aluminum matrix reinforced with silicon carbide particles with double-crack has been carried out. is studied in order to  ...  The lower the inter-distance, the higher the internal stresses of normal residual stresses of σzz.  ...  The numerical analysis revealed that residual stresses within the matrix increases when the particulate volume fraction is enhanced.  ...
<span class="external-identifiers"> <a target="_blank" rel="external noopener noreferrer" href="https://doi.org/10.2478/mme-2018-0086">doi:10.2478/mme-2018-0086</a> <a target="_blank" rel="external noopener" href="https://fatcat.wiki/release/zdpk2mqobbbyho5tsg3ivfae3e">fatcat:zdpk2mqobbbyho5tsg3ivfae3e</a> </span>
<a target="_blank" rel="noopener" href="https://web.archive.org/web/20200918014149/https://content.sciendo.com/downloadpdf/journals/mme/22/4/article-p1099.pdf" title="fulltext PDF download" data-goatcounter-click="serp-fulltext" data-goatcounter-title="serp-fulltext"> <button class="ui simple right pointing dropdown compact black labeled icon button serp-button"> <i class="icon ia-icon"></i> Web Archive [PDF] <div class="menu fulltext-thumbnail"> <img src="https://blobs.fatcat.wiki/thumbnail/pdf/e7/ca/e7ca2b1aeb3a676af84e3b68bf0d3ec0d9723759.180px.jpg" alt="fulltext thumbnail" loading="lazy"> </div> </button> </a> <a target="_blank" rel="external noopener noreferrer" href="https://doi.org/10.2478/mme-2018-0086"> <button class="ui left aligned compact blue labeled icon button serp-button"> <i class="unlock alternate icon" style="background-color: #fb971f;"></i> Publisher / doi.org </button> </a>

### Extraction of Numerical Residues in Families of Levelings

Wonder Alexandre Luz Alves, Alexandre Morimitsu, Joel Sanchez Castro, Ronaldo Fumio Hashimoto
<span title="">2013</span> <i title="IEEE"> <a target="_blank" rel="noopener" href="https://fatcat.wiki/container/hplpd6af5zbedpxqbmdj3kyssm" style="color: black;">2013 XXVI Conference on Graphics, Patterns and Images</a> </i> &nbsp;
This work introduces a residual operator called ultimate attribute leveling.  ...  Keywords -residual morphological operator; ultimate attribute opening; ultimate attribute closing; ultimate attribute leveling.  ...  The extraction of numerical residues based on connected operators has been combined with a specific priori shape [8] , [18] .  ...
<span class="external-identifiers"> <a target="_blank" rel="external noopener noreferrer" href="https://doi.org/10.1109/sibgrapi.2013.55">doi:10.1109/sibgrapi.2013.55</a> <a target="_blank" rel="external noopener" href="https://dblp.org/rec/conf/sibgrapi/AlvesMCH13.html">dblp:conf/sibgrapi/AlvesMCH13</a> <a target="_blank" rel="external noopener" href="https://fatcat.wiki/release/2kvw6wj2bbchrkzezj3gehffiq">fatcat:2kvw6wj2bbchrkzezj3gehffiq</a> </span>
<a target="_blank" rel="noopener" href="https://web.archive.org/web/20170829104735/http://www.ucsp.edu.pe/sibgrapi2013/eproceedings/technical/114903_2.pdf" title="fulltext PDF download" data-goatcounter-click="serp-fulltext" data-goatcounter-title="serp-fulltext"> <button class="ui simple right pointing dropdown compact black labeled icon button serp-button"> <i class="icon ia-icon"></i> Web Archive [PDF] <div class="menu fulltext-thumbnail"> <img src="https://blobs.fatcat.wiki/thumbnail/pdf/c2/10/c210e086488e790372fdcc83fe31df79bac357fe.180px.jpg" alt="fulltext thumbnail" loading="lazy"> </div> </button> </a> <a target="_blank" rel="external noopener noreferrer" href="https://doi.org/10.1109/sibgrapi.2013.55"> <button class="ui left aligned compact blue labeled icon button serp-button"> <i class="external alternate icon"></i> ieee.com </button> </a>

### BCJ numerators from differential operator of multidimensional residue

Gang Chen, Tianheng Wang
<span title="">2020</span> <i title="Springer Science and Business Media LLC"> <a target="_blank" rel="noopener" href="https://fatcat.wiki/container/pkristlbcjejngw5nuiceaedmu" style="color: black;">European Physical Journal C: Particles and Fields</a> </i> &nbsp;
We finally give a compact expression for the multidimensional residue for any CHY-like integral in terms of the reduction matrices.  ...  These BCJ numerators are efficiently computed by the improved method involving the reduction matrix. Eur. Phys. J. C (2020) 80:37  ...  One method for computing multidimensional residues involving the Groebner basis or the H-basis is discussed in [20, 21] . A useful Mathematica package for computing such residues is given in [22] .  ...
<span class="external-identifiers"> <a target="_blank" rel="external noopener noreferrer" href="https://doi.org/10.1140/epjc/s10052-019-7604-8">doi:10.1140/epjc/s10052-019-7604-8</a> <a target="_blank" rel="external noopener" href="https://fatcat.wiki/release/qb7tmyzsdjaihmlfx3xgmvyxna">fatcat:qb7tmyzsdjaihmlfx3xgmvyxna</a> </span>
<a target="_blank" rel="noopener" href="https://web.archive.org/web/20200214140540/https://link.springer.com/content/pdf/10.1140%2Fepjc%2Fs10052-019-7604-8.pdf" title="fulltext PDF download" data-goatcounter-click="serp-fulltext" data-goatcounter-title="serp-fulltext"> <button class="ui simple right pointing dropdown compact black labeled icon button serp-button"> <i class="icon ia-icon"></i> Web Archive [PDF] <div class="menu fulltext-thumbnail"> <img src="https://blobs.fatcat.wiki/thumbnail/pdf/35/19/3519942418461127eba3df8f9f7f3b1c7150b4c7.180px.jpg" alt="fulltext thumbnail" loading="lazy"> </div> </button> </a> <a target="_blank" rel="external noopener noreferrer" href="https://doi.org/10.1140/epjc/s10052-019-7604-8"> <button class="ui left aligned compact blue labeled icon button serp-button"> <i class="unlock alternate icon" style="background-color: #fb971f;"></i> Publisher / doi.org </button> </a>

### Numerical Modelling of Turning to Find Residual Stresses

N. Stenberg, J. Proudian
<span title="">2013</span> <i title="Elsevier BV"> <a target="_blank" rel="noopener" href="https://fatcat.wiki/container/pg7ahjk7dvd2tinhv7p6przfy4" style="color: black;">Procedia CIRP</a> </i> &nbsp;
In this study a thermo-mechanical numerical simulation of the machining operation is presented. The purpose of the simulations is to obtain the residual stresses.  ...  The FE-simulations has proved to predict the residual stresses in principle.  ...  The results of the numerical simulations are validated by the experimental results that took place at both SWEREA IVF labs and at the SCANIA production line.  ...
<span class="external-identifiers"> <a target="_blank" rel="external noopener noreferrer" href="https://doi.org/10.1016/j.procir.2013.06.099">doi:10.1016/j.procir.2013.06.099</a> <a target="_blank" rel="external noopener" href="https://fatcat.wiki/release/kdjkv3olsjdjdpuctpoduxlm4e">fatcat:kdjkv3olsjdjdpuctpoduxlm4e</a> </span>
<a target="_blank" rel="noopener" href="https://web.archive.org/web/20190320124645/https://core.ac.uk/download/pdf/82764158.pdf" title="fulltext PDF download" data-goatcounter-click="serp-fulltext" data-goatcounter-title="serp-fulltext"> <button class="ui simple right pointing dropdown compact black labeled icon button serp-button"> <i class="icon ia-icon"></i> Web Archive [PDF] <div class="menu fulltext-thumbnail"> <img src="https://blobs.fatcat.wiki/thumbnail/pdf/65/34/65344ed367a8bef1f26f7a67fc0e3bd2d6d07281.180px.jpg" alt="fulltext thumbnail" loading="lazy"> </div> </button> </a> <a target="_blank" rel="external noopener noreferrer" href="https://doi.org/10.1016/j.procir.2013.06.099"> <button class="ui left aligned compact blue labeled icon button serp-button"> <i class="unlock alternate icon" style="background-color: #fb971f;"></i> elsevier.com </button> </a>

### Numerical Analysis of a Tunnel in Residual Soils

Roberto F. Azevedo, Alexandre B. Parreira, Jorge G. Zornberg
<span title="">2002</span> <i title="American Society of Civil Engineers (ASCE)"> <a target="_blank" rel="noopener" href="https://fatcat.wiki/container/34atekmf5vc3biacymg62qvksq" style="color: black;">Journal of Geotechnical and Geoenvironmental Engineering</a> </i> &nbsp;
Good agreement is achieved between the displacements obtained from field instrumentation data and the empirical and numerical results.  ...  This paper presents results of an elastoplastic finite element back analysis of a shallow tunnel through residual soils.  ...  The best agreement between field and numerical results was obtained for a K 0 value of 0.40 for the residual red clay layers.  ...
<span class="external-identifiers"> <a target="_blank" rel="external noopener noreferrer" href="https://doi.org/10.1061/(asce)1090-0241(2002)128:3(227)">doi:10.1061/(asce)1090-0241(2002)128:3(227)</a> <a target="_blank" rel="external noopener" href="https://fatcat.wiki/release/reokq3zda5dp5jtf24fu2ekqde">fatcat:reokq3zda5dp5jtf24fu2ekqde</a> </span>
<a target="_blank" rel="noopener" href="https://web.archive.org/web/20170908200907/https://www.researchgate.net/profile/Roberto_Azevedo/publication/242462712_Numerical_Analysis_of_a_Tunnel_in_Residual_Soils/links/53ff1fa30cf21edafd15bb6e.pdf" title="fulltext PDF download" data-goatcounter-click="serp-fulltext" data-goatcounter-title="serp-fulltext"> <button class="ui simple right pointing dropdown compact black labeled icon button serp-button"> <i class="icon ia-icon"></i> Web Archive [PDF] <div class="menu fulltext-thumbnail"> <img src="https://blobs.fatcat.wiki/thumbnail/pdf/fa/86/fa86707046e92d3e53e53b54752f08772f023e76.180px.jpg" alt="fulltext thumbnail" loading="lazy"> </div> </button> </a> <a target="_blank" rel="external noopener noreferrer" href="https://doi.org/10.1061/(asce)1090-0241(2002)128:3(227)"> <button class="ui left aligned compact blue labeled icon button serp-button"> <i class="external alternate icon"></i> Publisher / doi.org </button> </a>

### Kinematic numerators and a double-copy formula forN=4super-Yang-Mills residues

Sean Litsey, James Stankowicz
<span title="2014-07-09">2014</span> <i title="American Physical Society (APS)"> <a target="_blank" rel="noopener" href="https://fatcat.wiki/container/chloqzh6grayjgjxdzjq5ktthu" style="color: black;">Physical Review D</a> </i> &nbsp;
Here we offer a new way of interpreting this result via objects that we call residue numerators.  ...  These objects behave like the kinematic numerators introduced by BCJ except that they are associated with individual residues.  ...  of RSVW residues into residue numerators.  ...
<span class="external-identifiers"> <a target="_blank" rel="external noopener noreferrer" href="https://doi.org/10.1103/physrevd.90.025013">doi:10.1103/physrevd.90.025013</a> <a target="_blank" rel="external noopener" href="https://fatcat.wiki/release/e3ox5e6r6nft3ldj24aezvvo3y">fatcat:e3ox5e6r6nft3ldj24aezvvo3y</a> </span>
<a target="_blank" rel="noopener" href="https://web.archive.org/web/20200904123136/https://arxiv.org/pdf/1309.7681v1.pdf" title="fulltext PDF download [not primary version]" data-goatcounter-click="serp-fulltext" data-goatcounter-title="serp-fulltext"> <button class="ui simple right pointing dropdown compact black labeled icon button serp-button"> <i class="icon ia-icon"></i> Web Archive [PDF] <span style="color: #f43e3e;">&#10033;</span> <div class="menu fulltext-thumbnail"> <img src="https://blobs.fatcat.wiki/thumbnail/pdf/aa/96/aa96adac2e4694102097ba672eff2ff5e45597ee.180px.jpg" alt="fulltext thumbnail" loading="lazy"> </div> </button> </a> <a target="_blank" rel="external noopener noreferrer" href="https://doi.org/10.1103/physrevd.90.025013"> <button class="ui left aligned compact blue labeled icon button serp-button"> <i class="external alternate icon"></i> aps.org </button> </a>

### Canonical trace ideal and residue for numerical semigroup rings [article]

Jürgen Herzog, Takayuki Hibi, Dumitru I. Stamate
<span title="2020-08-04">2020</span> <i > arXiv </i> &nbsp; <span class="release-stage" >pre-print</span>
For 3-generated numerical semigroups we give explicit formulas for the canonical trace ideal and the residue of H.  ...  For a numerical semigroup ring K[H] we study the trace of its canonical ideal. The colength of this ideal is called the residue of H. This invariant measures how far is H from being symmetric, i.e.  ...  The residue in shifted families of semigroups Remark 2.6 indicates that the residue of a 3-generated numerical semigroup H may be as large as possible.  ...
<span class="external-identifiers"> <a target="_blank" rel="external noopener" href="https://arxiv.org/abs/2008.01428v1">arXiv:2008.01428v1</a> <a target="_blank" rel="external noopener" href="https://fatcat.wiki/release/rysbyuy3dnfyfa4czxr6o4gihq">fatcat:rysbyuy3dnfyfa4czxr6o4gihq</a> </span>
<a target="_blank" rel="noopener" href="https://web.archive.org/web/20200811115133/https://arxiv.org/pdf/2008.01428v1.pdf" title="fulltext PDF download" data-goatcounter-click="serp-fulltext" data-goatcounter-title="serp-fulltext"> <button class="ui simple right pointing dropdown compact black labeled icon button serp-button"> <i class="icon ia-icon"></i> Web Archive [PDF] </button> </a> <a target="_blank" rel="external noopener" href="https://arxiv.org/abs/2008.01428v1" title="arxiv.org access"> <button class="ui compact blue labeled icon button serp-button"> <i class="file alternate outline icon"></i> arxiv.org </button> </a>

### Numerical recovery of location and residue of poles of meromorphic functions

Enrico De Micheli, Giovanni A. Viano
<span title="2010-11-03">2010</span> <i title="Springer Nature"> <a target="_blank" rel="noopener" href="https://fatcat.wiki/container/efryqrcvkzhfxdvy4uymtgkbfm" style="color: black;">Numerische Mathematik</a> </i> &nbsp;
We show that this method is numerically stable by proving that the algorithm is convergent as the number of data points tends to infinity and the noise on the input data goes to zero.  ...  We present a method able to recover location and residue of poles of functions meromorphic in a half--plane from samples of the function on the real positive semi-axis.  ...  Introduction A classical problem of numerical complex analysis consists in recovering location and residue of poles of meromorphic functions.  ...
<span class="external-identifiers"> <a target="_blank" rel="external noopener noreferrer" href="https://doi.org/10.1007/s00211-010-0345-0">doi:10.1007/s00211-010-0345-0</a> <a target="_blank" rel="external noopener" href="https://fatcat.wiki/release/v3tofvsmr5c2dnt6s27nowc74q">fatcat:v3tofvsmr5c2dnt6s27nowc74q</a> </span>
<a target="_blank" rel="noopener" href="https://web.archive.org/web/20200831074946/https://arxiv.org/pdf/1409.1145v1.pdf" title="fulltext PDF download [not primary version]" data-goatcounter-click="serp-fulltext" data-goatcounter-title="serp-fulltext"> <button class="ui simple right pointing dropdown compact black labeled icon button serp-button"> <i class="icon ia-icon"></i> Web Archive [PDF] <span style="color: #f43e3e;">&#10033;</span> <div class="menu fulltext-thumbnail"> <img src="https://blobs.fatcat.wiki/thumbnail/pdf/d4/6e/d46ed4387919f0b568d419dca1a02e7d566f67f2.180px.jpg" alt="fulltext thumbnail" loading="lazy"> </div> </button> </a> <a target="_blank" rel="external noopener noreferrer" href="https://doi.org/10.1007/s00211-010-0345-0"> <button class="ui left aligned compact blue labeled icon button serp-button"> <i class="external alternate icon"></i> springer.com </button> </a>
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