Analysis of tracer experiments V: Integral equations of perturbation-tracer analysis
Abstract An integral equation approach to perturbation-tracer analysis in steady-state multicompartment systems is formulated. The theory is developed for δ function perturbation and tracer inputs and extended to the case of continuous small perturbations and continuous tracer inputs. It is shown th...
Ausführliche Beschreibung
Gespeichert in:
| Autor*in: |
Hart, H. E. [verfasserIn] |
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| Format: |
Artikel |
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| Sprache: |
Englisch |
| Erschienen: |
1965 |
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| Schlagwörter: |
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| Anmerkung: |
© N. Rashevsky 1965 |
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| Übergeordnetes Werk: |
Enthalten in: Bulletin of mathematical biology - Springer-Verlag, 1973, 27(1965), 4 vom: Dez., Seite 417-429 |
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| Übergeordnetes Werk: |
volume:27 ; year:1965 ; number:4 ; month:12 ; pages:417-429 |
| Links: |
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| DOI / URN: |
10.1007/BF02476846 |
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| Katalog-ID: |
OLC2087050554 |
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| 520 | |a Abstract An integral equation approach to perturbation-tracer analysis in steady-state multicompartment systems is formulated. The theory is developed for δ function perturbation and tracer inputs and extended to the case of continuous small perturbations and continuous tracer inputs. It is shown that the first order dependence of the initial entry function can then be expressed by means of an integral equation:$$B_1 (t) = \int_{t_2 = - \infty }^\infty {\int_{t_1 = - \infty }^\infty {P(t_1 )T(t_2 )B_1 (t - t_2 ,t_1 - t_2 )dt_1 dt_2 } } $$ whereB1(t) is the first order initial entry function for the tracer material,P($ t_{1} $) the perturbation function.T(t2) is the tracer input function, andB1(t−t2,t1−t2) is a continuous function of two variables characterizing the first order perturbation-tracer response of the system. | ||
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| 650 | 4 | |a Tracer Experiment | |
| 650 | 4 | |a Initial Entry | |
| 650 | 4 | |a Tracer Material | |
| 650 | 4 | |a Tracer Input | |
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10.1007/BF02476846 doi (DE-627)OLC2087050554 (DE-He213)BF02476846-p DE-627 ger DE-627 rakwb eng 570 510 VZ 12 ssgn BIODIV DE-30 fid 42.00 bkl Hart, H. E. verfasserin aut Analysis of tracer experiments V: Integral equations of perturbation-tracer analysis 1965 Text txt rdacontent ohne Hilfsmittel zu benutzen n rdamedia Band nc rdacarrier © N. Rashevsky 1965 Abstract An integral equation approach to perturbation-tracer analysis in steady-state multicompartment systems is formulated. The theory is developed for δ function perturbation and tracer inputs and extended to the case of continuous small perturbations and continuous tracer inputs. It is shown that the first order dependence of the initial entry function can then be expressed by means of an integral equation:$$B_1 (t) = \int_{t_2 = - \infty }^\infty {\int_{t_1 = - \infty }^\infty {P(t_1 )T(t_2 )B_1 (t - t_2 ,t_1 - t_2 )dt_1 dt_2 } } $$ whereB1(t) is the first order initial entry function for the tracer material,P($ t_{1} $) the perturbation function.T(t2) is the tracer input function, andB1(t−t2,t1−t2) is a continuous function of two variables characterizing the first order perturbation-tracer response of the system. Tracer Injection Tracer Experiment Initial Entry Tracer Material Tracer Input Enthalten in Bulletin of mathematical biology Springer-Verlag, 1973 27(1965), 4 vom: Dez., Seite 417-429 (DE-627)129391719 (DE-600)184905-0 (DE-576)014776863 0092-8240 nnns volume:27 year:1965 number:4 month:12 pages:417-429 https://doi.org/10.1007/BF02476846 lizenzpflichtig Volltext GBV_USEFLAG_A SYSFLAG_A GBV_OLC FID-BIODIV SSG-OLC-MAT SSG-OPC-MAT 42.00 VZ AR 27 1965 4 12 417-429 |
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10.1007/BF02476846 doi (DE-627)OLC2087050554 (DE-He213)BF02476846-p DE-627 ger DE-627 rakwb eng 570 510 VZ 12 ssgn BIODIV DE-30 fid 42.00 bkl Hart, H. E. verfasserin aut Analysis of tracer experiments V: Integral equations of perturbation-tracer analysis 1965 Text txt rdacontent ohne Hilfsmittel zu benutzen n rdamedia Band nc rdacarrier © N. Rashevsky 1965 Abstract An integral equation approach to perturbation-tracer analysis in steady-state multicompartment systems is formulated. The theory is developed for δ function perturbation and tracer inputs and extended to the case of continuous small perturbations and continuous tracer inputs. It is shown that the first order dependence of the initial entry function can then be expressed by means of an integral equation:$$B_1 (t) = \int_{t_2 = - \infty }^\infty {\int_{t_1 = - \infty }^\infty {P(t_1 )T(t_2 )B_1 (t - t_2 ,t_1 - t_2 )dt_1 dt_2 } } $$ whereB1(t) is the first order initial entry function for the tracer material,P($ t_{1} $) the perturbation function.T(t2) is the tracer input function, andB1(t−t2,t1−t2) is a continuous function of two variables characterizing the first order perturbation-tracer response of the system. Tracer Injection Tracer Experiment Initial Entry Tracer Material Tracer Input Enthalten in Bulletin of mathematical biology Springer-Verlag, 1973 27(1965), 4 vom: Dez., Seite 417-429 (DE-627)129391719 (DE-600)184905-0 (DE-576)014776863 0092-8240 nnns volume:27 year:1965 number:4 month:12 pages:417-429 https://doi.org/10.1007/BF02476846 lizenzpflichtig Volltext GBV_USEFLAG_A SYSFLAG_A GBV_OLC FID-BIODIV SSG-OLC-MAT SSG-OPC-MAT 42.00 VZ AR 27 1965 4 12 417-429 |
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10.1007/BF02476846 doi (DE-627)OLC2087050554 (DE-He213)BF02476846-p DE-627 ger DE-627 rakwb eng 570 510 VZ 12 ssgn BIODIV DE-30 fid 42.00 bkl Hart, H. E. verfasserin aut Analysis of tracer experiments V: Integral equations of perturbation-tracer analysis 1965 Text txt rdacontent ohne Hilfsmittel zu benutzen n rdamedia Band nc rdacarrier © N. Rashevsky 1965 Abstract An integral equation approach to perturbation-tracer analysis in steady-state multicompartment systems is formulated. The theory is developed for δ function perturbation and tracer inputs and extended to the case of continuous small perturbations and continuous tracer inputs. It is shown that the first order dependence of the initial entry function can then be expressed by means of an integral equation:$$B_1 (t) = \int_{t_2 = - \infty }^\infty {\int_{t_1 = - \infty }^\infty {P(t_1 )T(t_2 )B_1 (t - t_2 ,t_1 - t_2 )dt_1 dt_2 } } $$ whereB1(t) is the first order initial entry function for the tracer material,P($ t_{1} $) the perturbation function.T(t2) is the tracer input function, andB1(t−t2,t1−t2) is a continuous function of two variables characterizing the first order perturbation-tracer response of the system. Tracer Injection Tracer Experiment Initial Entry Tracer Material Tracer Input Enthalten in Bulletin of mathematical biology Springer-Verlag, 1973 27(1965), 4 vom: Dez., Seite 417-429 (DE-627)129391719 (DE-600)184905-0 (DE-576)014776863 0092-8240 nnns volume:27 year:1965 number:4 month:12 pages:417-429 https://doi.org/10.1007/BF02476846 lizenzpflichtig Volltext GBV_USEFLAG_A SYSFLAG_A GBV_OLC FID-BIODIV SSG-OLC-MAT SSG-OPC-MAT 42.00 VZ AR 27 1965 4 12 417-429 |
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10.1007/BF02476846 doi (DE-627)OLC2087050554 (DE-He213)BF02476846-p DE-627 ger DE-627 rakwb eng 570 510 VZ 12 ssgn BIODIV DE-30 fid 42.00 bkl Hart, H. E. verfasserin aut Analysis of tracer experiments V: Integral equations of perturbation-tracer analysis 1965 Text txt rdacontent ohne Hilfsmittel zu benutzen n rdamedia Band nc rdacarrier © N. Rashevsky 1965 Abstract An integral equation approach to perturbation-tracer analysis in steady-state multicompartment systems is formulated. The theory is developed for δ function perturbation and tracer inputs and extended to the case of continuous small perturbations and continuous tracer inputs. It is shown that the first order dependence of the initial entry function can then be expressed by means of an integral equation:$$B_1 (t) = \int_{t_2 = - \infty }^\infty {\int_{t_1 = - \infty }^\infty {P(t_1 )T(t_2 )B_1 (t - t_2 ,t_1 - t_2 )dt_1 dt_2 } } $$ whereB1(t) is the first order initial entry function for the tracer material,P($ t_{1} $) the perturbation function.T(t2) is the tracer input function, andB1(t−t2,t1−t2) is a continuous function of two variables characterizing the first order perturbation-tracer response of the system. Tracer Injection Tracer Experiment Initial Entry Tracer Material Tracer Input Enthalten in Bulletin of mathematical biology Springer-Verlag, 1973 27(1965), 4 vom: Dez., Seite 417-429 (DE-627)129391719 (DE-600)184905-0 (DE-576)014776863 0092-8240 nnns volume:27 year:1965 number:4 month:12 pages:417-429 https://doi.org/10.1007/BF02476846 lizenzpflichtig Volltext GBV_USEFLAG_A SYSFLAG_A GBV_OLC FID-BIODIV SSG-OLC-MAT SSG-OPC-MAT 42.00 VZ AR 27 1965 4 12 417-429 |
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10.1007/BF02476846 doi (DE-627)OLC2087050554 (DE-He213)BF02476846-p DE-627 ger DE-627 rakwb eng 570 510 VZ 12 ssgn BIODIV DE-30 fid 42.00 bkl Hart, H. E. verfasserin aut Analysis of tracer experiments V: Integral equations of perturbation-tracer analysis 1965 Text txt rdacontent ohne Hilfsmittel zu benutzen n rdamedia Band nc rdacarrier © N. Rashevsky 1965 Abstract An integral equation approach to perturbation-tracer analysis in steady-state multicompartment systems is formulated. The theory is developed for δ function perturbation and tracer inputs and extended to the case of continuous small perturbations and continuous tracer inputs. It is shown that the first order dependence of the initial entry function can then be expressed by means of an integral equation:$$B_1 (t) = \int_{t_2 = - \infty }^\infty {\int_{t_1 = - \infty }^\infty {P(t_1 )T(t_2 )B_1 (t - t_2 ,t_1 - t_2 )dt_1 dt_2 } } $$ whereB1(t) is the first order initial entry function for the tracer material,P($ t_{1} $) the perturbation function.T(t2) is the tracer input function, andB1(t−t2,t1−t2) is a continuous function of two variables characterizing the first order perturbation-tracer response of the system. Tracer Injection Tracer Experiment Initial Entry Tracer Material Tracer Input Enthalten in Bulletin of mathematical biology Springer-Verlag, 1973 27(1965), 4 vom: Dez., Seite 417-429 (DE-627)129391719 (DE-600)184905-0 (DE-576)014776863 0092-8240 nnns volume:27 year:1965 number:4 month:12 pages:417-429 https://doi.org/10.1007/BF02476846 lizenzpflichtig Volltext GBV_USEFLAG_A SYSFLAG_A GBV_OLC FID-BIODIV SSG-OLC-MAT SSG-OPC-MAT 42.00 VZ AR 27 1965 4 12 417-429 |
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Analysis of tracer experiments V: Integral equations of perturbation-tracer analysis |
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Abstract An integral equation approach to perturbation-tracer analysis in steady-state multicompartment systems is formulated. The theory is developed for δ function perturbation and tracer inputs and extended to the case of continuous small perturbations and continuous tracer inputs. It is shown that the first order dependence of the initial entry function can then be expressed by means of an integral equation:$$B_1 (t) = \int_{t_2 = - \infty }^\infty {\int_{t_1 = - \infty }^\infty {P(t_1 )T(t_2 )B_1 (t - t_2 ,t_1 - t_2 )dt_1 dt_2 } } $$ whereB1(t) is the first order initial entry function for the tracer material,P($ t_{1} $) the perturbation function.T(t2) is the tracer input function, andB1(t−t2,t1−t2) is a continuous function of two variables characterizing the first order perturbation-tracer response of the system. © N. Rashevsky 1965 |
| abstractGer |
Abstract An integral equation approach to perturbation-tracer analysis in steady-state multicompartment systems is formulated. The theory is developed for δ function perturbation and tracer inputs and extended to the case of continuous small perturbations and continuous tracer inputs. It is shown that the first order dependence of the initial entry function can then be expressed by means of an integral equation:$$B_1 (t) = \int_{t_2 = - \infty }^\infty {\int_{t_1 = - \infty }^\infty {P(t_1 )T(t_2 )B_1 (t - t_2 ,t_1 - t_2 )dt_1 dt_2 } } $$ whereB1(t) is the first order initial entry function for the tracer material,P($ t_{1} $) the perturbation function.T(t2) is the tracer input function, andB1(t−t2,t1−t2) is a continuous function of two variables characterizing the first order perturbation-tracer response of the system. © N. Rashevsky 1965 |
| abstract_unstemmed |
Abstract An integral equation approach to perturbation-tracer analysis in steady-state multicompartment systems is formulated. The theory is developed for δ function perturbation and tracer inputs and extended to the case of continuous small perturbations and continuous tracer inputs. It is shown that the first order dependence of the initial entry function can then be expressed by means of an integral equation:$$B_1 (t) = \int_{t_2 = - \infty }^\infty {\int_{t_1 = - \infty }^\infty {P(t_1 )T(t_2 )B_1 (t - t_2 ,t_1 - t_2 )dt_1 dt_2 } } $$ whereB1(t) is the first order initial entry function for the tracer material,P($ t_{1} $) the perturbation function.T(t2) is the tracer input function, andB1(t−t2,t1−t2) is a continuous function of two variables characterizing the first order perturbation-tracer response of the system. © N. Rashevsky 1965 |
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Analysis of tracer experiments V: Integral equations of perturbation-tracer analysis |
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https://doi.org/10.1007/BF02476846 |
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10.1007/BF02476846 |
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2024-07-03T13:25:20.339Z |
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