A nonlinear integral equation for visual impedance

Abstract The Hartline-Ratliff equation is a linear integral equation of the second kind and is employed in modeling inhibitory networks. Saturation of the inhibiting elements is commonly modeled as a function whose form is sigmoid; however, the resulting integral equation is nonlinear. Whenever the...
Ausführliche Beschreibung

Gespeichert in:

Autor*in:	Berman, Simeon M. [verfasserIn] Stewart, Alan L.

Format:	Artikel
Sprache:	Englisch

Erschienen:	1979

Schlagwörter:	Integral Equation Unknown Function Nonlinear Function Uniqueness Theorem Nonlinear Integral Equation

Anmerkung:	© Springer-Verlag 1979

Übergeordnetes Werk:	Enthalten in: Biological cybernetics - Springer-Verlag, 1975, 33(1979), 3 vom: Aug., Seite 137-141
Übergeordnetes Werk:	volume:33 ; year:1979 ; number:3 ; month:08 ; pages:137-141

Links:	Volltext

DOI / URN:	10.1007/BF00337291

Katalog-ID:	OLC2052680403

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520			\|a Abstract The Hartline-Ratliff equation is a linear integral equation of the second kind and is employed in modeling inhibitory networks. Saturation of the inhibiting elements is commonly modeled as a function whose form is sigmoid; however, the resulting integral equation is nonlinear. Whenever the unknown function within the integral is hypothesized to be a nondecreasing nonlinear function, the Hartline-Ratliff equation becomes a nonlinear integral equation of the Hammerstein type. We present existence and uniqueness theorems for a Hammerstein equation which represents a further generalization of the Hartline-Ratliff equation.
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650		4	\|a Uniqueness Theorem
650		4	\|a Nonlinear Integral Equation
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allfields	10.1007/BF00337291 doi (DE-627)OLC2052680403 (DE-He213)BF00337291-p DE-627 ger DE-627 rakwb eng 570 VZ 570 000 VZ 12 ssgn BIODIV DE-30 fid Berman, Simeon M. verfasserin aut A nonlinear integral equation for visual impedance 1979 Text txt rdacontent ohne Hilfsmittel zu benutzen n rdamedia Band nc rdacarrier © Springer-Verlag 1979 Abstract The Hartline-Ratliff equation is a linear integral equation of the second kind and is employed in modeling inhibitory networks. Saturation of the inhibiting elements is commonly modeled as a function whose form is sigmoid; however, the resulting integral equation is nonlinear. Whenever the unknown function within the integral is hypothesized to be a nondecreasing nonlinear function, the Hartline-Ratliff equation becomes a nonlinear integral equation of the Hammerstein type. We present existence and uniqueness theorems for a Hammerstein equation which represents a further generalization of the Hartline-Ratliff equation. Integral Equation Unknown Function Nonlinear Function Uniqueness Theorem Nonlinear Integral Equation Stewart, Alan L. aut Enthalten in Biological cybernetics Springer-Verlag, 1975 33(1979), 3 vom: Aug., Seite 137-141 (DE-627)129556351 (DE-600)220699-7 (DE-576)015013545 0340-1200 nnns volume:33 year:1979 number:3 month:08 pages:137-141 https://doi.org/10.1007/BF00337291 lizenzpflichtig Volltext GBV_USEFLAG_A SYSFLAG_A GBV_OLC FID-BIODIV SSG-OLC-MAT SSG-OLC-PHA SSG-OLC-DE-84 SSG-OPC-BBI SSG-OPC-MAT GBV_ILN_11 GBV_ILN_21 GBV_ILN_22 GBV_ILN_23 GBV_ILN_24 GBV_ILN_31 GBV_ILN_32 GBV_ILN_40 GBV_ILN_55 GBV_ILN_62 GBV_ILN_65 GBV_ILN_69 GBV_ILN_70 GBV_ILN_72 GBV_ILN_74 GBV_ILN_101 GBV_ILN_105 GBV_ILN_130 GBV_ILN_259 GBV_ILN_267 GBV_ILN_2002 GBV_ILN_2005 GBV_ILN_2006 GBV_ILN_2009 GBV_ILN_2010 GBV_ILN_2015 GBV_ILN_2018 GBV_ILN_2020 GBV_ILN_2021 GBV_ILN_2027 GBV_ILN_2045 GBV_ILN_2088 GBV_ILN_2219 GBV_ILN_2237 GBV_ILN_2409 GBV_ILN_2410 GBV_ILN_4012 GBV_ILN_4028 GBV_ILN_4035 GBV_ILN_4037 GBV_ILN_4046 GBV_ILN_4082 GBV_ILN_4103 GBV_ILN_4193 GBV_ILN_4219 GBV_ILN_4277 GBV_ILN_4302 GBV_ILN_4305 GBV_ILN_4306 GBV_ILN_4307 GBV_ILN_4310 GBV_ILN_4317 GBV_ILN_4318 GBV_ILN_4319 GBV_ILN_4320 GBV_ILN_4323 GBV_ILN_4324 GBV_ILN_4700 AR 33 1979 3 08 137-141
spelling	10.1007/BF00337291 doi (DE-627)OLC2052680403 (DE-He213)BF00337291-p DE-627 ger DE-627 rakwb eng 570 VZ 570 000 VZ 12 ssgn BIODIV DE-30 fid Berman, Simeon M. verfasserin aut A nonlinear integral equation for visual impedance 1979 Text txt rdacontent ohne Hilfsmittel zu benutzen n rdamedia Band nc rdacarrier © Springer-Verlag 1979 Abstract The Hartline-Ratliff equation is a linear integral equation of the second kind and is employed in modeling inhibitory networks. Saturation of the inhibiting elements is commonly modeled as a function whose form is sigmoid; however, the resulting integral equation is nonlinear. Whenever the unknown function within the integral is hypothesized to be a nondecreasing nonlinear function, the Hartline-Ratliff equation becomes a nonlinear integral equation of the Hammerstein type. We present existence and uniqueness theorems for a Hammerstein equation which represents a further generalization of the Hartline-Ratliff equation. Integral Equation Unknown Function Nonlinear Function Uniqueness Theorem Nonlinear Integral Equation Stewart, Alan L. aut Enthalten in Biological cybernetics Springer-Verlag, 1975 33(1979), 3 vom: Aug., Seite 137-141 (DE-627)129556351 (DE-600)220699-7 (DE-576)015013545 0340-1200 nnns volume:33 year:1979 number:3 month:08 pages:137-141 https://doi.org/10.1007/BF00337291 lizenzpflichtig Volltext GBV_USEFLAG_A SYSFLAG_A GBV_OLC FID-BIODIV SSG-OLC-MAT SSG-OLC-PHA SSG-OLC-DE-84 SSG-OPC-BBI SSG-OPC-MAT GBV_ILN_11 GBV_ILN_21 GBV_ILN_22 GBV_ILN_23 GBV_ILN_24 GBV_ILN_31 GBV_ILN_32 GBV_ILN_40 GBV_ILN_55 GBV_ILN_62 GBV_ILN_65 GBV_ILN_69 GBV_ILN_70 GBV_ILN_72 GBV_ILN_74 GBV_ILN_101 GBV_ILN_105 GBV_ILN_130 GBV_ILN_259 GBV_ILN_267 GBV_ILN_2002 GBV_ILN_2005 GBV_ILN_2006 GBV_ILN_2009 GBV_ILN_2010 GBV_ILN_2015 GBV_ILN_2018 GBV_ILN_2020 GBV_ILN_2021 GBV_ILN_2027 GBV_ILN_2045 GBV_ILN_2088 GBV_ILN_2219 GBV_ILN_2237 GBV_ILN_2409 GBV_ILN_2410 GBV_ILN_4012 GBV_ILN_4028 GBV_ILN_4035 GBV_ILN_4037 GBV_ILN_4046 GBV_ILN_4082 GBV_ILN_4103 GBV_ILN_4193 GBV_ILN_4219 GBV_ILN_4277 GBV_ILN_4302 GBV_ILN_4305 GBV_ILN_4306 GBV_ILN_4307 GBV_ILN_4310 GBV_ILN_4317 GBV_ILN_4318 GBV_ILN_4319 GBV_ILN_4320 GBV_ILN_4323 GBV_ILN_4324 GBV_ILN_4700 AR 33 1979 3 08 137-141
allfields_unstemmed	10.1007/BF00337291 doi (DE-627)OLC2052680403 (DE-He213)BF00337291-p DE-627 ger DE-627 rakwb eng 570 VZ 570 000 VZ 12 ssgn BIODIV DE-30 fid Berman, Simeon M. verfasserin aut A nonlinear integral equation for visual impedance 1979 Text txt rdacontent ohne Hilfsmittel zu benutzen n rdamedia Band nc rdacarrier © Springer-Verlag 1979 Abstract The Hartline-Ratliff equation is a linear integral equation of the second kind and is employed in modeling inhibitory networks. Saturation of the inhibiting elements is commonly modeled as a function whose form is sigmoid; however, the resulting integral equation is nonlinear. Whenever the unknown function within the integral is hypothesized to be a nondecreasing nonlinear function, the Hartline-Ratliff equation becomes a nonlinear integral equation of the Hammerstein type. We present existence and uniqueness theorems for a Hammerstein equation which represents a further generalization of the Hartline-Ratliff equation. Integral Equation Unknown Function Nonlinear Function Uniqueness Theorem Nonlinear Integral Equation Stewart, Alan L. aut Enthalten in Biological cybernetics Springer-Verlag, 1975 33(1979), 3 vom: Aug., Seite 137-141 (DE-627)129556351 (DE-600)220699-7 (DE-576)015013545 0340-1200 nnns volume:33 year:1979 number:3 month:08 pages:137-141 https://doi.org/10.1007/BF00337291 lizenzpflichtig Volltext GBV_USEFLAG_A SYSFLAG_A GBV_OLC FID-BIODIV SSG-OLC-MAT SSG-OLC-PHA SSG-OLC-DE-84 SSG-OPC-BBI SSG-OPC-MAT GBV_ILN_11 GBV_ILN_21 GBV_ILN_22 GBV_ILN_23 GBV_ILN_24 GBV_ILN_31 GBV_ILN_32 GBV_ILN_40 GBV_ILN_55 GBV_ILN_62 GBV_ILN_65 GBV_ILN_69 GBV_ILN_70 GBV_ILN_72 GBV_ILN_74 GBV_ILN_101 GBV_ILN_105 GBV_ILN_130 GBV_ILN_259 GBV_ILN_267 GBV_ILN_2002 GBV_ILN_2005 GBV_ILN_2006 GBV_ILN_2009 GBV_ILN_2010 GBV_ILN_2015 GBV_ILN_2018 GBV_ILN_2020 GBV_ILN_2021 GBV_ILN_2027 GBV_ILN_2045 GBV_ILN_2088 GBV_ILN_2219 GBV_ILN_2237 GBV_ILN_2409 GBV_ILN_2410 GBV_ILN_4012 GBV_ILN_4028 GBV_ILN_4035 GBV_ILN_4037 GBV_ILN_4046 GBV_ILN_4082 GBV_ILN_4103 GBV_ILN_4193 GBV_ILN_4219 GBV_ILN_4277 GBV_ILN_4302 GBV_ILN_4305 GBV_ILN_4306 GBV_ILN_4307 GBV_ILN_4310 GBV_ILN_4317 GBV_ILN_4318 GBV_ILN_4319 GBV_ILN_4320 GBV_ILN_4323 GBV_ILN_4324 GBV_ILN_4700 AR 33 1979 3 08 137-141
allfieldsGer	10.1007/BF00337291 doi (DE-627)OLC2052680403 (DE-He213)BF00337291-p DE-627 ger DE-627 rakwb eng 570 VZ 570 000 VZ 12 ssgn BIODIV DE-30 fid Berman, Simeon M. verfasserin aut A nonlinear integral equation for visual impedance 1979 Text txt rdacontent ohne Hilfsmittel zu benutzen n rdamedia Band nc rdacarrier © Springer-Verlag 1979 Abstract The Hartline-Ratliff equation is a linear integral equation of the second kind and is employed in modeling inhibitory networks. Saturation of the inhibiting elements is commonly modeled as a function whose form is sigmoid; however, the resulting integral equation is nonlinear. Whenever the unknown function within the integral is hypothesized to be a nondecreasing nonlinear function, the Hartline-Ratliff equation becomes a nonlinear integral equation of the Hammerstein type. We present existence and uniqueness theorems for a Hammerstein equation which represents a further generalization of the Hartline-Ratliff equation. Integral Equation Unknown Function Nonlinear Function Uniqueness Theorem Nonlinear Integral Equation Stewart, Alan L. aut Enthalten in Biological cybernetics Springer-Verlag, 1975 33(1979), 3 vom: Aug., Seite 137-141 (DE-627)129556351 (DE-600)220699-7 (DE-576)015013545 0340-1200 nnns volume:33 year:1979 number:3 month:08 pages:137-141 https://doi.org/10.1007/BF00337291 lizenzpflichtig Volltext GBV_USEFLAG_A SYSFLAG_A GBV_OLC FID-BIODIV SSG-OLC-MAT SSG-OLC-PHA SSG-OLC-DE-84 SSG-OPC-BBI SSG-OPC-MAT GBV_ILN_11 GBV_ILN_21 GBV_ILN_22 GBV_ILN_23 GBV_ILN_24 GBV_ILN_31 GBV_ILN_32 GBV_ILN_40 GBV_ILN_55 GBV_ILN_62 GBV_ILN_65 GBV_ILN_69 GBV_ILN_70 GBV_ILN_72 GBV_ILN_74 GBV_ILN_101 GBV_ILN_105 GBV_ILN_130 GBV_ILN_259 GBV_ILN_267 GBV_ILN_2002 GBV_ILN_2005 GBV_ILN_2006 GBV_ILN_2009 GBV_ILN_2010 GBV_ILN_2015 GBV_ILN_2018 GBV_ILN_2020 GBV_ILN_2021 GBV_ILN_2027 GBV_ILN_2045 GBV_ILN_2088 GBV_ILN_2219 GBV_ILN_2237 GBV_ILN_2409 GBV_ILN_2410 GBV_ILN_4012 GBV_ILN_4028 GBV_ILN_4035 GBV_ILN_4037 GBV_ILN_4046 GBV_ILN_4082 GBV_ILN_4103 GBV_ILN_4193 GBV_ILN_4219 GBV_ILN_4277 GBV_ILN_4302 GBV_ILN_4305 GBV_ILN_4306 GBV_ILN_4307 GBV_ILN_4310 GBV_ILN_4317 GBV_ILN_4318 GBV_ILN_4319 GBV_ILN_4320 GBV_ILN_4323 GBV_ILN_4324 GBV_ILN_4700 AR 33 1979 3 08 137-141
allfieldsSound	10.1007/BF00337291 doi (DE-627)OLC2052680403 (DE-He213)BF00337291-p DE-627 ger DE-627 rakwb eng 570 VZ 570 000 VZ 12 ssgn BIODIV DE-30 fid Berman, Simeon M. verfasserin aut A nonlinear integral equation for visual impedance 1979 Text txt rdacontent ohne Hilfsmittel zu benutzen n rdamedia Band nc rdacarrier © Springer-Verlag 1979 Abstract The Hartline-Ratliff equation is a linear integral equation of the second kind and is employed in modeling inhibitory networks. Saturation of the inhibiting elements is commonly modeled as a function whose form is sigmoid; however, the resulting integral equation is nonlinear. Whenever the unknown function within the integral is hypothesized to be a nondecreasing nonlinear function, the Hartline-Ratliff equation becomes a nonlinear integral equation of the Hammerstein type. We present existence and uniqueness theorems for a Hammerstein equation which represents a further generalization of the Hartline-Ratliff equation. Integral Equation Unknown Function Nonlinear Function Uniqueness Theorem Nonlinear Integral Equation Stewart, Alan L. aut Enthalten in Biological cybernetics Springer-Verlag, 1975 33(1979), 3 vom: Aug., Seite 137-141 (DE-627)129556351 (DE-600)220699-7 (DE-576)015013545 0340-1200 nnns volume:33 year:1979 number:3 month:08 pages:137-141 https://doi.org/10.1007/BF00337291 lizenzpflichtig Volltext GBV_USEFLAG_A SYSFLAG_A GBV_OLC FID-BIODIV SSG-OLC-MAT SSG-OLC-PHA SSG-OLC-DE-84 SSG-OPC-BBI SSG-OPC-MAT GBV_ILN_11 GBV_ILN_21 GBV_ILN_22 GBV_ILN_23 GBV_ILN_24 GBV_ILN_31 GBV_ILN_32 GBV_ILN_40 GBV_ILN_55 GBV_ILN_62 GBV_ILN_65 GBV_ILN_69 GBV_ILN_70 GBV_ILN_72 GBV_ILN_74 GBV_ILN_101 GBV_ILN_105 GBV_ILN_130 GBV_ILN_259 GBV_ILN_267 GBV_ILN_2002 GBV_ILN_2005 GBV_ILN_2006 GBV_ILN_2009 GBV_ILN_2010 GBV_ILN_2015 GBV_ILN_2018 GBV_ILN_2020 GBV_ILN_2021 GBV_ILN_2027 GBV_ILN_2045 GBV_ILN_2088 GBV_ILN_2219 GBV_ILN_2237 GBV_ILN_2409 GBV_ILN_2410 GBV_ILN_4012 GBV_ILN_4028 GBV_ILN_4035 GBV_ILN_4037 GBV_ILN_4046 GBV_ILN_4082 GBV_ILN_4103 GBV_ILN_4193 GBV_ILN_4219 GBV_ILN_4277 GBV_ILN_4302 GBV_ILN_4305 GBV_ILN_4306 GBV_ILN_4307 GBV_ILN_4310 GBV_ILN_4317 GBV_ILN_4318 GBV_ILN_4319 GBV_ILN_4320 GBV_ILN_4323 GBV_ILN_4324 GBV_ILN_4700 AR 33 1979 3 08 137-141
language	English
source	Enthalten in Biological cybernetics 33(1979), 3 vom: Aug., Seite 137-141 volume:33 year:1979 number:3 month:08 pages:137-141
sourceStr	Enthalten in Biological cybernetics 33(1979), 3 vom: Aug., Seite 137-141 volume:33 year:1979 number:3 month:08 pages:137-141
format_phy_str_mv	Article
institution	findex.gbv.de
topic_facet	Integral Equation Unknown Function Nonlinear Function Uniqueness Theorem Nonlinear Integral Equation
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container_title	Biological cybernetics
authorswithroles_txt_mv	Berman, Simeon M. @@aut@@ Stewart, Alan L. @@aut@@
publishDateDaySort_date	1979-08-01T00:00:00Z
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author	Berman, Simeon M.
spellingShingle	Berman, Simeon M. ddc 570 ssgn 12 fid BIODIV misc Integral Equation misc Unknown Function misc Nonlinear Function misc Uniqueness Theorem misc Nonlinear Integral Equation A nonlinear integral equation for visual impedance
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topic_title	570 VZ 570 000 VZ 12 ssgn BIODIV DE-30 fid A nonlinear integral equation for visual impedance Integral Equation Unknown Function Nonlinear Function Uniqueness Theorem Nonlinear Integral Equation
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title	A nonlinear integral equation for visual impedance
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title_sort	a nonlinear integral equation for visual impedance
title_auth	A nonlinear integral equation for visual impedance
abstract	Abstract The Hartline-Ratliff equation is a linear integral equation of the second kind and is employed in modeling inhibitory networks. Saturation of the inhibiting elements is commonly modeled as a function whose form is sigmoid; however, the resulting integral equation is nonlinear. Whenever the unknown function within the integral is hypothesized to be a nondecreasing nonlinear function, the Hartline-Ratliff equation becomes a nonlinear integral equation of the Hammerstein type. We present existence and uniqueness theorems for a Hammerstein equation which represents a further generalization of the Hartline-Ratliff equation. © Springer-Verlag 1979
abstractGer	Abstract The Hartline-Ratliff equation is a linear integral equation of the second kind and is employed in modeling inhibitory networks. Saturation of the inhibiting elements is commonly modeled as a function whose form is sigmoid; however, the resulting integral equation is nonlinear. Whenever the unknown function within the integral is hypothesized to be a nondecreasing nonlinear function, the Hartline-Ratliff equation becomes a nonlinear integral equation of the Hammerstein type. We present existence and uniqueness theorems for a Hammerstein equation which represents a further generalization of the Hartline-Ratliff equation. © Springer-Verlag 1979
abstract_unstemmed	Abstract The Hartline-Ratliff equation is a linear integral equation of the second kind and is employed in modeling inhibitory networks. Saturation of the inhibiting elements is commonly modeled as a function whose form is sigmoid; however, the resulting integral equation is nonlinear. Whenever the unknown function within the integral is hypothesized to be a nondecreasing nonlinear function, the Hartline-Ratliff equation becomes a nonlinear integral equation of the Hammerstein type. We present existence and uniqueness theorems for a Hammerstein equation which represents a further generalization of the Hartline-Ratliff equation. © Springer-Verlag 1979
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title_short	A nonlinear integral equation for visual impedance
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A nonlinear integral equation for visual impedance

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