A Note on the Lambert W Function: Bernstein and Stieltjes Properties for a Creep Model in Linear Viscoelasticity

The purpose of this note is to propose an application of the Lambert <i<W</i< function in linear viscoelasticity based on the Bernstein and Stieltjes properties of this function. In particular, we recognize the role of its main branch, <inline-formula<<math xmlns="http://ww...
Ausführliche Beschreibung

Gespeichert in:

Autor*in:	Francesco Mainardi [verfasserIn] Enrico Masina [verfasserIn] Juan Luis González-Santander [verfasserIn]

Format:	E-Artikel
Sprache:	Englisch

Erschienen:	2023

Schlagwörter:	Lambert function completely monotonic functions Bernstein functions Stieltjes functions Laplace transform Stieltjes transform

Übergeordnetes Werk:	In: Symmetry - MDPI AG, 2009, 15(2023), 1654, p 1654
Übergeordnetes Werk:	volume:15 ; year:2023 ; number:1654, p 1654

Links:	Link aufrufen Link aufrufen Link aufrufen Journal toc

DOI / URN:	10.3390/sym15091654

Katalog-ID:	DOAJ093261128

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allfields	10.3390/sym15091654 doi (DE-627)DOAJ093261128 (DE-599)DOAJ6b9fb82769b94de8a6866ae058c2c3c1 DE-627 ger DE-627 rakwb eng QA1-939 Francesco Mainardi verfasserin aut A Note on the Lambert W Function: Bernstein and Stieltjes Properties for a Creep Model in Linear Viscoelasticity 2023 Text txt rdacontent Computermedien c rdamedia Online-Ressource cr rdacarrier The purpose of this note is to propose an application of the Lambert <i<W</i< function in linear viscoelasticity based on the Bernstein and Stieltjes properties of this function. In particular, we recognize the role of its main branch, <inline-formula<<math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"<<semantics<<mrow<<msub<<mi<W</mi<<mn<0</mn<</msub<<mrow<<mo<(</mo<<mi<t</mi<<mo<)</mo<</mrow<</mrow<</semantics<</math<</inline-formula<, in a peculiar model of creep with two spectral functions in frequency that completely characterize the creep model. In order to calculate these spectral functions, it turns out that the conjugate symmetry property of the Lambert <i<W</i< function along its branch cut on the negative real axis is essential. We supplement our analysis by computing the corresponding relaxation function and providing the plots of all computed functions. Lambert function completely monotonic functions Bernstein functions Stieltjes functions Laplace transform Stieltjes transform Mathematics Enrico Masina verfasserin aut Juan Luis González-Santander verfasserin aut In Symmetry MDPI AG, 2009 15(2023), 1654, p 1654 (DE-627)610604112 (DE-600)2518382-5 20738994 nnns volume:15 year:2023 number:1654, p 1654 https://doi.org/10.3390/sym15091654 kostenfrei https://doaj.org/article/6b9fb82769b94de8a6866ae058c2c3c1 kostenfrei https://www.mdpi.com/2073-8994/15/9/1654 kostenfrei https://doaj.org/toc/2073-8994 Journal toc kostenfrei GBV_USEFLAG_A SYSFLAG_A GBV_DOAJ GBV_ILN_20 GBV_ILN_22 GBV_ILN_23 GBV_ILN_24 GBV_ILN_39 GBV_ILN_40 GBV_ILN_60 GBV_ILN_62 GBV_ILN_63 GBV_ILN_65 GBV_ILN_69 GBV_ILN_70 GBV_ILN_73 GBV_ILN_74 GBV_ILN_95 GBV_ILN_105 GBV_ILN_110 GBV_ILN_151 GBV_ILN_161 GBV_ILN_170 GBV_ILN_206 GBV_ILN_213 GBV_ILN_230 GBV_ILN_285 GBV_ILN_293 GBV_ILN_602 GBV_ILN_2005 GBV_ILN_2009 GBV_ILN_2011 GBV_ILN_2014 GBV_ILN_2055 GBV_ILN_2111 GBV_ILN_4012 GBV_ILN_4037 GBV_ILN_4112 GBV_ILN_4125 GBV_ILN_4126 GBV_ILN_4249 GBV_ILN_4305 GBV_ILN_4306 GBV_ILN_4307 GBV_ILN_4313 GBV_ILN_4322 GBV_ILN_4323 GBV_ILN_4324 GBV_ILN_4325 GBV_ILN_4326 GBV_ILN_4335 GBV_ILN_4338 GBV_ILN_4367 GBV_ILN_4700 AR 15 2023 1654, p 1654
spelling	10.3390/sym15091654 doi (DE-627)DOAJ093261128 (DE-599)DOAJ6b9fb82769b94de8a6866ae058c2c3c1 DE-627 ger DE-627 rakwb eng QA1-939 Francesco Mainardi verfasserin aut A Note on the Lambert W Function: Bernstein and Stieltjes Properties for a Creep Model in Linear Viscoelasticity 2023 Text txt rdacontent Computermedien c rdamedia Online-Ressource cr rdacarrier The purpose of this note is to propose an application of the Lambert <i<W</i< function in linear viscoelasticity based on the Bernstein and Stieltjes properties of this function. In particular, we recognize the role of its main branch, <inline-formula<<math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"<<semantics<<mrow<<msub<<mi<W</mi<<mn<0</mn<</msub<<mrow<<mo<(</mo<<mi<t</mi<<mo<)</mo<</mrow<</mrow<</semantics<</math<</inline-formula<, in a peculiar model of creep with two spectral functions in frequency that completely characterize the creep model. In order to calculate these spectral functions, it turns out that the conjugate symmetry property of the Lambert <i<W</i< function along its branch cut on the negative real axis is essential. We supplement our analysis by computing the corresponding relaxation function and providing the plots of all computed functions. Lambert function completely monotonic functions Bernstein functions Stieltjes functions Laplace transform Stieltjes transform Mathematics Enrico Masina verfasserin aut Juan Luis González-Santander verfasserin aut In Symmetry MDPI AG, 2009 15(2023), 1654, p 1654 (DE-627)610604112 (DE-600)2518382-5 20738994 nnns volume:15 year:2023 number:1654, p 1654 https://doi.org/10.3390/sym15091654 kostenfrei https://doaj.org/article/6b9fb82769b94de8a6866ae058c2c3c1 kostenfrei https://www.mdpi.com/2073-8994/15/9/1654 kostenfrei https://doaj.org/toc/2073-8994 Journal toc kostenfrei GBV_USEFLAG_A SYSFLAG_A GBV_DOAJ GBV_ILN_20 GBV_ILN_22 GBV_ILN_23 GBV_ILN_24 GBV_ILN_39 GBV_ILN_40 GBV_ILN_60 GBV_ILN_62 GBV_ILN_63 GBV_ILN_65 GBV_ILN_69 GBV_ILN_70 GBV_ILN_73 GBV_ILN_74 GBV_ILN_95 GBV_ILN_105 GBV_ILN_110 GBV_ILN_151 GBV_ILN_161 GBV_ILN_170 GBV_ILN_206 GBV_ILN_213 GBV_ILN_230 GBV_ILN_285 GBV_ILN_293 GBV_ILN_602 GBV_ILN_2005 GBV_ILN_2009 GBV_ILN_2011 GBV_ILN_2014 GBV_ILN_2055 GBV_ILN_2111 GBV_ILN_4012 GBV_ILN_4037 GBV_ILN_4112 GBV_ILN_4125 GBV_ILN_4126 GBV_ILN_4249 GBV_ILN_4305 GBV_ILN_4306 GBV_ILN_4307 GBV_ILN_4313 GBV_ILN_4322 GBV_ILN_4323 GBV_ILN_4324 GBV_ILN_4325 GBV_ILN_4326 GBV_ILN_4335 GBV_ILN_4338 GBV_ILN_4367 GBV_ILN_4700 AR 15 2023 1654, p 1654
allfields_unstemmed	10.3390/sym15091654 doi (DE-627)DOAJ093261128 (DE-599)DOAJ6b9fb82769b94de8a6866ae058c2c3c1 DE-627 ger DE-627 rakwb eng QA1-939 Francesco Mainardi verfasserin aut A Note on the Lambert W Function: Bernstein and Stieltjes Properties for a Creep Model in Linear Viscoelasticity 2023 Text txt rdacontent Computermedien c rdamedia Online-Ressource cr rdacarrier The purpose of this note is to propose an application of the Lambert <i<W</i< function in linear viscoelasticity based on the Bernstein and Stieltjes properties of this function. In particular, we recognize the role of its main branch, <inline-formula<<math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"<<semantics<<mrow<<msub<<mi<W</mi<<mn<0</mn<</msub<<mrow<<mo<(</mo<<mi<t</mi<<mo<)</mo<</mrow<</mrow<</semantics<</math<</inline-formula<, in a peculiar model of creep with two spectral functions in frequency that completely characterize the creep model. In order to calculate these spectral functions, it turns out that the conjugate symmetry property of the Lambert <i<W</i< function along its branch cut on the negative real axis is essential. We supplement our analysis by computing the corresponding relaxation function and providing the plots of all computed functions. Lambert function completely monotonic functions Bernstein functions Stieltjes functions Laplace transform Stieltjes transform Mathematics Enrico Masina verfasserin aut Juan Luis González-Santander verfasserin aut In Symmetry MDPI AG, 2009 15(2023), 1654, p 1654 (DE-627)610604112 (DE-600)2518382-5 20738994 nnns volume:15 year:2023 number:1654, p 1654 https://doi.org/10.3390/sym15091654 kostenfrei https://doaj.org/article/6b9fb82769b94de8a6866ae058c2c3c1 kostenfrei https://www.mdpi.com/2073-8994/15/9/1654 kostenfrei https://doaj.org/toc/2073-8994 Journal toc kostenfrei GBV_USEFLAG_A SYSFLAG_A GBV_DOAJ GBV_ILN_20 GBV_ILN_22 GBV_ILN_23 GBV_ILN_24 GBV_ILN_39 GBV_ILN_40 GBV_ILN_60 GBV_ILN_62 GBV_ILN_63 GBV_ILN_65 GBV_ILN_69 GBV_ILN_70 GBV_ILN_73 GBV_ILN_74 GBV_ILN_95 GBV_ILN_105 GBV_ILN_110 GBV_ILN_151 GBV_ILN_161 GBV_ILN_170 GBV_ILN_206 GBV_ILN_213 GBV_ILN_230 GBV_ILN_285 GBV_ILN_293 GBV_ILN_602 GBV_ILN_2005 GBV_ILN_2009 GBV_ILN_2011 GBV_ILN_2014 GBV_ILN_2055 GBV_ILN_2111 GBV_ILN_4012 GBV_ILN_4037 GBV_ILN_4112 GBV_ILN_4125 GBV_ILN_4126 GBV_ILN_4249 GBV_ILN_4305 GBV_ILN_4306 GBV_ILN_4307 GBV_ILN_4313 GBV_ILN_4322 GBV_ILN_4323 GBV_ILN_4324 GBV_ILN_4325 GBV_ILN_4326 GBV_ILN_4335 GBV_ILN_4338 GBV_ILN_4367 GBV_ILN_4700 AR 15 2023 1654, p 1654
allfieldsGer	10.3390/sym15091654 doi (DE-627)DOAJ093261128 (DE-599)DOAJ6b9fb82769b94de8a6866ae058c2c3c1 DE-627 ger DE-627 rakwb eng QA1-939 Francesco Mainardi verfasserin aut A Note on the Lambert W Function: Bernstein and Stieltjes Properties for a Creep Model in Linear Viscoelasticity 2023 Text txt rdacontent Computermedien c rdamedia Online-Ressource cr rdacarrier The purpose of this note is to propose an application of the Lambert <i<W</i< function in linear viscoelasticity based on the Bernstein and Stieltjes properties of this function. In particular, we recognize the role of its main branch, <inline-formula<<math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"<<semantics<<mrow<<msub<<mi<W</mi<<mn<0</mn<</msub<<mrow<<mo<(</mo<<mi<t</mi<<mo<)</mo<</mrow<</mrow<</semantics<</math<</inline-formula<, in a peculiar model of creep with two spectral functions in frequency that completely characterize the creep model. In order to calculate these spectral functions, it turns out that the conjugate symmetry property of the Lambert <i<W</i< function along its branch cut on the negative real axis is essential. We supplement our analysis by computing the corresponding relaxation function and providing the plots of all computed functions. Lambert function completely monotonic functions Bernstein functions Stieltjes functions Laplace transform Stieltjes transform Mathematics Enrico Masina verfasserin aut Juan Luis González-Santander verfasserin aut In Symmetry MDPI AG, 2009 15(2023), 1654, p 1654 (DE-627)610604112 (DE-600)2518382-5 20738994 nnns volume:15 year:2023 number:1654, p 1654 https://doi.org/10.3390/sym15091654 kostenfrei https://doaj.org/article/6b9fb82769b94de8a6866ae058c2c3c1 kostenfrei https://www.mdpi.com/2073-8994/15/9/1654 kostenfrei https://doaj.org/toc/2073-8994 Journal toc kostenfrei GBV_USEFLAG_A SYSFLAG_A GBV_DOAJ GBV_ILN_20 GBV_ILN_22 GBV_ILN_23 GBV_ILN_24 GBV_ILN_39 GBV_ILN_40 GBV_ILN_60 GBV_ILN_62 GBV_ILN_63 GBV_ILN_65 GBV_ILN_69 GBV_ILN_70 GBV_ILN_73 GBV_ILN_74 GBV_ILN_95 GBV_ILN_105 GBV_ILN_110 GBV_ILN_151 GBV_ILN_161 GBV_ILN_170 GBV_ILN_206 GBV_ILN_213 GBV_ILN_230 GBV_ILN_285 GBV_ILN_293 GBV_ILN_602 GBV_ILN_2005 GBV_ILN_2009 GBV_ILN_2011 GBV_ILN_2014 GBV_ILN_2055 GBV_ILN_2111 GBV_ILN_4012 GBV_ILN_4037 GBV_ILN_4112 GBV_ILN_4125 GBV_ILN_4126 GBV_ILN_4249 GBV_ILN_4305 GBV_ILN_4306 GBV_ILN_4307 GBV_ILN_4313 GBV_ILN_4322 GBV_ILN_4323 GBV_ILN_4324 GBV_ILN_4325 GBV_ILN_4326 GBV_ILN_4335 GBV_ILN_4338 GBV_ILN_4367 GBV_ILN_4700 AR 15 2023 1654, p 1654
allfieldsSound	10.3390/sym15091654 doi (DE-627)DOAJ093261128 (DE-599)DOAJ6b9fb82769b94de8a6866ae058c2c3c1 DE-627 ger DE-627 rakwb eng QA1-939 Francesco Mainardi verfasserin aut A Note on the Lambert W Function: Bernstein and Stieltjes Properties for a Creep Model in Linear Viscoelasticity 2023 Text txt rdacontent Computermedien c rdamedia Online-Ressource cr rdacarrier The purpose of this note is to propose an application of the Lambert <i<W</i< function in linear viscoelasticity based on the Bernstein and Stieltjes properties of this function. In particular, we recognize the role of its main branch, <inline-formula<<math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"<<semantics<<mrow<<msub<<mi<W</mi<<mn<0</mn<</msub<<mrow<<mo<(</mo<<mi<t</mi<<mo<)</mo<</mrow<</mrow<</semantics<</math<</inline-formula<, in a peculiar model of creep with two spectral functions in frequency that completely characterize the creep model. In order to calculate these spectral functions, it turns out that the conjugate symmetry property of the Lambert <i<W</i< function along its branch cut on the negative real axis is essential. We supplement our analysis by computing the corresponding relaxation function and providing the plots of all computed functions. Lambert function completely monotonic functions Bernstein functions Stieltjes functions Laplace transform Stieltjes transform Mathematics Enrico Masina verfasserin aut Juan Luis González-Santander verfasserin aut In Symmetry MDPI AG, 2009 15(2023), 1654, p 1654 (DE-627)610604112 (DE-600)2518382-5 20738994 nnns volume:15 year:2023 number:1654, p 1654 https://doi.org/10.3390/sym15091654 kostenfrei https://doaj.org/article/6b9fb82769b94de8a6866ae058c2c3c1 kostenfrei https://www.mdpi.com/2073-8994/15/9/1654 kostenfrei https://doaj.org/toc/2073-8994 Journal toc kostenfrei GBV_USEFLAG_A SYSFLAG_A GBV_DOAJ GBV_ILN_20 GBV_ILN_22 GBV_ILN_23 GBV_ILN_24 GBV_ILN_39 GBV_ILN_40 GBV_ILN_60 GBV_ILN_62 GBV_ILN_63 GBV_ILN_65 GBV_ILN_69 GBV_ILN_70 GBV_ILN_73 GBV_ILN_74 GBV_ILN_95 GBV_ILN_105 GBV_ILN_110 GBV_ILN_151 GBV_ILN_161 GBV_ILN_170 GBV_ILN_206 GBV_ILN_213 GBV_ILN_230 GBV_ILN_285 GBV_ILN_293 GBV_ILN_602 GBV_ILN_2005 GBV_ILN_2009 GBV_ILN_2011 GBV_ILN_2014 GBV_ILN_2055 GBV_ILN_2111 GBV_ILN_4012 GBV_ILN_4037 GBV_ILN_4112 GBV_ILN_4125 GBV_ILN_4126 GBV_ILN_4249 GBV_ILN_4305 GBV_ILN_4306 GBV_ILN_4307 GBV_ILN_4313 GBV_ILN_4322 GBV_ILN_4323 GBV_ILN_4324 GBV_ILN_4325 GBV_ILN_4326 GBV_ILN_4335 GBV_ILN_4338 GBV_ILN_4367 GBV_ILN_4700 AR 15 2023 1654, p 1654
language	English
source	In Symmetry 15(2023), 1654, p 1654 volume:15 year:2023 number:1654, p 1654
sourceStr	In Symmetry 15(2023), 1654, p 1654 volume:15 year:2023 number:1654, p 1654
format_phy_str_mv	Article
institution	findex.gbv.de
topic_facet	Lambert function completely monotonic functions Bernstein functions Stieltjes functions Laplace transform Stieltjes transform Mathematics
isfreeaccess_bool	true
container_title	Symmetry
authorswithroles_txt_mv	Francesco Mainardi @@aut@@ Enrico Masina @@aut@@ Juan Luis González-Santander @@aut@@
publishDateDaySort_date	2023-01-01T00:00:00Z
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callnumber-first	Q - Science
author	Francesco Mainardi
spellingShingle	Francesco Mainardi misc QA1-939 misc Lambert function misc completely monotonic functions misc Bernstein functions misc Stieltjes functions misc Laplace transform misc Stieltjes transform misc Mathematics A Note on the Lambert W Function: Bernstein and Stieltjes Properties for a Creep Model in Linear Viscoelasticity
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topic_title	QA1-939 A Note on the Lambert W Function: Bernstein and Stieltjes Properties for a Creep Model in Linear Viscoelasticity Lambert function completely monotonic functions Bernstein functions Stieltjes functions Laplace transform Stieltjes transform
topic	misc QA1-939 misc Lambert function misc completely monotonic functions misc Bernstein functions misc Stieltjes functions misc Laplace transform misc Stieltjes transform misc Mathematics
topic_unstemmed	misc QA1-939 misc Lambert function misc completely monotonic functions misc Bernstein functions misc Stieltjes functions misc Laplace transform misc Stieltjes transform misc Mathematics
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title	A Note on the Lambert W Function: Bernstein and Stieltjes Properties for a Creep Model in Linear Viscoelasticity
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title_full	A Note on the Lambert W Function: Bernstein and Stieltjes Properties for a Creep Model in Linear Viscoelasticity
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title_sort	note on the lambert w function: bernstein and stieltjes properties for a creep model in linear viscoelasticity
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title_auth	A Note on the Lambert W Function: Bernstein and Stieltjes Properties for a Creep Model in Linear Viscoelasticity
abstract	The purpose of this note is to propose an application of the Lambert <i<W</i< function in linear viscoelasticity based on the Bernstein and Stieltjes properties of this function. In particular, we recognize the role of its main branch, <inline-formula<<math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"<<semantics<<mrow<<msub<<mi<W</mi<<mn<0</mn<</msub<<mrow<<mo<(</mo<<mi<t</mi<<mo<)</mo<</mrow<</mrow<</semantics<</math<</inline-formula<, in a peculiar model of creep with two spectral functions in frequency that completely characterize the creep model. In order to calculate these spectral functions, it turns out that the conjugate symmetry property of the Lambert <i<W</i< function along its branch cut on the negative real axis is essential. We supplement our analysis by computing the corresponding relaxation function and providing the plots of all computed functions.
abstractGer	The purpose of this note is to propose an application of the Lambert <i<W</i< function in linear viscoelasticity based on the Bernstein and Stieltjes properties of this function. In particular, we recognize the role of its main branch, <inline-formula<<math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"<<semantics<<mrow<<msub<<mi<W</mi<<mn<0</mn<</msub<<mrow<<mo<(</mo<<mi<t</mi<<mo<)</mo<</mrow<</mrow<</semantics<</math<</inline-formula<, in a peculiar model of creep with two spectral functions in frequency that completely characterize the creep model. In order to calculate these spectral functions, it turns out that the conjugate symmetry property of the Lambert <i<W</i< function along its branch cut on the negative real axis is essential. We supplement our analysis by computing the corresponding relaxation function and providing the plots of all computed functions.
abstract_unstemmed	The purpose of this note is to propose an application of the Lambert <i<W</i< function in linear viscoelasticity based on the Bernstein and Stieltjes properties of this function. In particular, we recognize the role of its main branch, <inline-formula<<math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"<<semantics<<mrow<<msub<<mi<W</mi<<mn<0</mn<</msub<<mrow<<mo<(</mo<<mi<t</mi<<mo<)</mo<</mrow<</mrow<</semantics<</math<</inline-formula<, in a peculiar model of creep with two spectral functions in frequency that completely characterize the creep model. In order to calculate these spectral functions, it turns out that the conjugate symmetry property of the Lambert <i<W</i< function along its branch cut on the negative real axis is essential. We supplement our analysis by computing the corresponding relaxation function and providing the plots of all computed functions.
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title_short	A Note on the Lambert W Function: Bernstein and Stieltjes Properties for a Creep Model in Linear Viscoelasticity
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A Note on the Lambert W Function: Bernstein and Stieltjes Properties for a Creep Model in Linear Viscoelasticity

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