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  • Springer  (1,186,624)
  • Wiley  (309,854)
  • American Meteorological Society
  • 2000-2004  (272,791)
  • 1995-1999  (426,264)
  • 1990-1994  (390,827)
  • 1975-1979  (259,012)
  • 1965-1969  (174,254)
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  • 1
    Unknown
    Effects of Space Weather on Technology Infrastructure : Proceedings of the NATO ARW on Effects of Space Weather on Technology Infrastructure, Rhodes, Greece, from 25 to 29 March 2003. (2004)
    Springer
    Details
    Keywords: communication ; design ; dynamics ; environment ; network ; physics ; power transmission ; radio ; satellite ; simulation ; technology ; transmission
    Description / Table of Contents: The 17 chapters of this book grew out of the tutorial lectures given by leading world-class experts at the NATO Advanced Research Workshop “Effects of Space Weather on Technology Infrastructure” - ESPRIT, which was held in Rhodes on March 25-29, 2004. All manuscripts were refereed and subsequently meticulously edited by the editor to ensure the highest quality for this monograph. I owe particular thanks to the lecturers of the ESPRIT Advanced Research Workshop for producing these excellent tutorial reviews, which convey the essential knowledge and the latest advances in our field. Due to the breadth, extensive literature citations and quality of the reviews we expect this publication to serve extremely well as a reference book. Multimedia material referring to individual chapters of the book is accessible on the accompanying CD. The aim of ESPRIT was to assess existing knowledge and identify future actions regarding monitoring, forecasting and mitigation of space weather induced malfunction and damage of vital technological systems operating in space and on the ground.
    ISBN: 9781402027543
    URL: https://doi.org/10.1007/1-4020-2754-0
    Language: English
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  • 2
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    The Conversion of Liquid Rocket Fuels : Risk Assessment, Technology and Treatment Options for the Conversion of Abandoned Liquid Ballistic Missile Propellants (Fuels and Oxidizers) in Azerbaijan (2004)
    Springer
    Details
    Description / Table of Contents: Prof. Dr. -Ing. Wolfgang Spyra Brandenburg University of Technology in Cottbus, Germany The demilitarization and conversion of military properties wor- wide has been a topic of growing importance since the end of the Cold War. The slowing of the arms race brought on by weapons treaties and relaxed tensions between NATO and Warsaw Pact nations caused sto- piles of conventional weapons to become superfluous. The need to process and dispose of such weapons began more quickly in NATO countries. This demilitarization process began shortly after the reunification of Germany and was largely completed by the mid to late 1990’s. The remaining process, no small task in itself, of converting lands formerly used by the military into safe and environmentally acceptable landscapes may continue for decades to come. Due to a lack of resources and technology, the process of demilitarization in the former Warsaw Pact countries has launched more slowly. In 2002 both Georgia and Moldova finished projects which destroyed their stocks of liquid ballistic missile components. Both these projects were carried out through the cooperative support of trans-national organizations, private contractors, and research institutions. The Republic of Azerbaijan now finds itself at the beginning of its demilitarization process. Stored at the country’s military depots are over 2000 tons of missile fuels, oxidizer, and chemical additives. This hazardous waste is kept in tanks intended only for temporary transport and storage.
    Pages: Online-Ressource (X, 148 pages)
    ISBN: 9781402023811
    URL: https://doi.org/10.1007/1-4020-2381-2
    Language: English
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  • 3
    Unknown
    Strategic decision making : applying the analytic hierarchy process (2004)
    London ; New York : Springer
    Decision engineering  
    Details
    Keywords: Decision making, Mathematical models. ; Decision making, Methodology.
    Pages: ix, 172 p.
    ISBN: 1-85233-864-4
    URL: http://www.netLibrary.com/urlapi.asp?action=summary&v=1&bookid=108180
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  • 4
    Unknown
    Web services, E-Business, and the Semantic Web : second international workshop, WES 2003, Klagenfurt, Austria, June 16-17, 2003 ; WES 2003 (2004)
    Berlin ; New York : Springer
    Lecture notes in computer science  
    Details
    Keywords: Semantic Web, Congresses.
    Pages: x, 145 p.
    ISBN: 3-540-25982-1
    URL: http://www.netLibrary.com/urlapi.asp?action=summary&v=1&bookid=130186
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  • 5
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    Lattice-Gas Cellular Automata and Lattice Boltzmann Models - An Introduction (2000)
    Springer
    In:  EPIC3Springer, Berlinpp. (Lecture Notes in Mathematics ; 1725) Remark (September 2002): The original edition is now out of print. A slightly revised version (compare `Errata' and `Additions' under: {http://www.awi-bremerhaven.de/Modelling/LGCA+LBM/} is availab, Berlin, Springer, 308, 308 p., ISBN: 3-540-66973-6
    Details
    Publication Date: 2019-07-17
    Description: Lattice-gas cellular automata (LGCA) and lattice Boltzmann models (LBM) are relatively new andpromising methods for the numerical solution of nonlinear partial differential equations. The bookprovides an introduction for graduate students and researchers. Working knowledge of calculus isrequired and experience in PDEs and fluid dynamics is recommended. Some peculiarities of cellularautomata are outlined in Chapter 2. The properties of various LGCA and special coding techniquesare discussed in Chapter 3. Concepts from statistical mechanics (Chapter 4) provide the necessarytheoretical background for LGCA and LBM. The properties of lattice Boltzmann models and amethod for their construction are presented in Chapter 5.
    Repository Name: EPIC Alfred Wegener Institut
    Type: Book , peerRev
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  • 6
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    Climate change and Arctic ecosystems: 2. Modeling, paleodata‐model comparisons, and future projections (2003)
    Wiley
    In:  EPIC3Journal of Geophysical Research-Atmospheres, Wiley, 8171 p., ISSN: 0148-0227
    Details
    Publication Date: 2019-08-23
    Repository Name: EPIC Alfred Wegener Institut
    Type: Article , isiRev
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  • 7
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    Temperature histories in liquid and solid polar stratospheric cloud formation (1997)
    Wiley
    In:  EPIC3Journal of Geophysical Research: Atmospheres, Wiley, 102(D19), pp. 23505-23517, ISSN: 0148-0227
    Details
    Publication Date: 2019-07-17
    Repository Name: EPIC Alfred Wegener Institut
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  • 8
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    Polar stratospheric cloud threshold temperatures in the 1995–1996 arctic vortex (1997)
    Wiley
    In:  EPIC3Journal of Geophysical Research: Atmospheres, Wiley, 102(D23), pp. 28195-28202, ISSN: 0148-0227
    Details
    Publication Date: 2019-07-17
    Description: Balloon-borne backscattersondes have been used to study the relationship between particle scattering and ambient temperature near the vertical edge of arctic polar stratospheric clouds (PSCs) as well as to delineate the cloud type occurrence probability as a function of temperature. The observed typical threshold temperatures as a function of altitude are about1°K warmer than the temperature TSTS expected for rapid growth of supercooled ternary solution aerosols. A more descriptive analysis shows that the threshold temperatures occur over a definable range of temperatures and tend to cluster near, but somewhat warmer than, TSTS. Considering the experimental and theoretical uncertainties, this difference may not be significant. The probability of type Ib PSC occurrence shows a dramatic increase at TSTS±1°K, while for type Ia PSCs the probability is roughly constant at 10% for temperatures below the formation point of nitric acid trihydrate (TNAT).
    Repository Name: EPIC Alfred Wegener Institut
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  • 9
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    Palaeoclimate reconstruction on Big Lyakhovsky Island, north Siberia—hydrogen and oxygen isotopes in ice wedges (2002)
    Wiley
    In:  EPIC3Permafrost and Periglacial Processes, Wiley, 13(2), pp. 91-105, ISSN: 1045-6740
    Details
    Publication Date: 2023-07-06
    Description: Late Quaternary permafrost deposits on Big Lyakhovsky Island (New Siberian Islands, Russian Arctic) were studied with the aim of reconstructing the palaeoclimatic and palaeoenvironmental conditions of northern Siberia. Hydrogen and oxygen stable isotope analyses are presented for six different generations of ice wedges as well as for recent ice wedges and precipitation. An age of about 200 ka BP was determined for an autochtonous peat layer in ice-rich deposits by U/Th method, containing the oldest ice wedges ever analysed for hydrogen and oxygen isotopes. The palaeoclimatic reconstruction revealed a period of severe winter temperatures at that time. After a gap in the sedimentation history of several tens of thousands of years, ice-wedge growth was re-initiated around 50 ka BP by a short period of extremely cold winters and rapid sedimentation leading to ice-wedge burial and characteristic ice-soil wedges (‘polosatics’). This corresponds to the initial stage for the Late Weichselian Ice Complex, a peculiar cryolithogenic periglacial formation typical of the lowlands of northern Siberia. The Ice Complex ice wedges reflect cold winters and similar climatic conditions as around 200 ka BP. With a sharp rise in υ18O of 6‰ and υD of 40‰, the warming trend between Pleistocene and Holocene ice wedges is documented. Stable isotope data of recent ice wedges show that Big Lyakhovsky Island has never been as warm in winter as today.
    Repository Name: EPIC Alfred Wegener Institut
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  • 10
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    Late Saalian and Eemian palaeoenvironmental history of the Bol'shoy Lyakhovsky Island (Laptev Sea region, Arctic Siberia) (2004)
    Wiley
    In:  EPIC3Boreas, Wiley, 33(4), pp. 319-348, ISSN: 0300-9483
    Details
    Publication Date: 2024-04-25
    Description: Palaeoenvironmental records from permafrost sequences complemented by infrared stimulated luminescence (IRSL) and 230Th/U dates from Bol'shoy Lyakhovsky Island (73°20′N, 141°30′E) document the environmental history in the region for at least the past 200 ka. Pollen spectra and insect fauna indicate that relatively wet grasssedge tundra habitats dominated during an interstadial c. 200-170 ka BP. Summers were rather warm and wet, while stable isotopes reflect severe winter conditions. The pollen spectra reflect sparser grass-sedge vegetation during a Taz (Late Saalian) stage, c. 170-130 ka BP, with environmental conditions much more severe compared with the previous interstadial. Open Poaceae and Artemisia plant associations dominated vegetation at the beginning of the Kazantsevo (Eemian) c. 130 ka BP. Some shrubs (Alnus fruticosa, Salix, Betula nana) grew in more protected and wetter places as well. The climate was relatively warm during this time, resulting in the melting of Saalian ice wedges. Later, during the interglacial optimum, shrub tundra with Alnus fruticosa and Betula nana s.l. dominated vegetation. Climate was relatively wet and warm. Quantitative pollen-based climate reconstruction suggests that mean July temperatures were 4-5°C higher than the present during the optimum of the Eemian, while late Eemian records indicate significant climate deterioration. © 2004 Taylor & Francis.
    Repository Name: EPIC Alfred Wegener Institut
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  • 11
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    Early warning systems for natural disaster reduction (2003)
    Springer
    Details
    Publication Date: 2020-02-12
    Keywords: 550 - Earth sciences
    Type: info:eu-repo/semantics/book
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  • 12
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    GPS : theory, algorithms and applications (2003)
    Springer
    Details
    Publication Date: 2020-02-12
    Keywords: 550 - Earth sciences
    Type: info:eu-repo/semantics/book
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  • 13
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    Gold metallogeny in the Sino-Korean Platform: examples from Hebei province, NE China. (1992)
    Springer
    Details
    Publication Date: 2020-02-12
    Keywords: 550 - Earth sciences
    Type: info:eu-repo/semantics/book
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  • 14
    Electronic Resource
    Electronic Resource
    Composting of explosives and propellant contaminated soils under thermophilic and mesophilic conditions (1992)
    Springer
    Journal of industrial microbiology and biotechnology 9 (1992), S. 137-144 
    Details
    ISSN: 1476-5535
    Keywords: Composting ; Explosives ; Propellants ; Thermophilic ; Mesophilic ; Bioremediation
    Source: Springer Online Journal Archives 1860-2000
    Topics: Biology , Process Engineering, Biotechnology, Nutrition Technology
    Notes: Summary Composting was investigated as a bioremediation technology for clean-up of sediments contaminated with explosives and propellants. Two field demonstrations were conducted, the first using 2,4,6-trinitrotoluene (TNT), octahydro-1,3,5,7-tetranitro-1,3,5,7-tetraazocine (HMX), hexahydro-1,3,5-trinitro-1,3,5-triazine (RDX), and N-methyl-N,2,4,6-tetranitroaniline (tetryl) contaminated sediment, and the second using nitrocellulose (NC) contaminated soil. Tests were conducted in thermophilic and mesophilic aerated static piles. Extractable TNT was reduced from 11840 mg/kg to 3 mg/kg, and NC from 13090 mg/kg to 16 mg/kg under thermophilic conditions. Under mesophilic conditions, TNT was reduced from 11 190 mg/kg to 50 mg/kg. The thermophilic and mesophilic half-lives were 11.9 and 21.9 days for TNT, 17.3 and 30.1 days for RDX, and 22.8 and 42.0 days for HMX, respectively. Known nitroaromatic transformation products increased in concentration over the first several weeks of the test period, but decreased to low concentrations thereafter.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF01569746
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  • 15
    Electronic Resource
    Electronic Resource
    Purification and properties of extracellularβ-fructofuranosidases fromAureobasidium sp. ATCC 20524 (1992)
    Springer
    Journal of industrial microbiology and biotechnology 9 (1992), S. 145-147 
    Details
    ISSN: 1476-5535
    Keywords: Fructo-oligosaccharide ; 1-Kestose ; Glycoprotein ; Fructosyl-transferring activity
    Source: Springer Online Journal Archives 1860-2000
    Topics: Biology , Process Engineering, Biotechnology, Nutrition Technology
    Notes: Summary Two extracellular β-fructofuranosidases (E-1 andE-2) fromAureobasidium sp. ATCC 20524, producing 1-kestose (1F-β-fructofuranosyl-sucrose) from sucrose, were purified to homogeneity. Molecular weights of the enzymes were estimated to be about 304000 (E-1) and 315000 (E-2) Da by gel filtration. The enzymes contained 33% (w/w) (E-1) and 27% (w/w) (E-2) carbohydrate. TheK m values for sucrose ofE-1 andE-2 andE-2 were 0.34 and 0.28 M, respectively. were 0.34 and 0.28 M, respectively. The enzymatic profiles of these enzymes were almost identical to intracellular enzymesP-1 andP-2 except for the differences in carbohydrate content andK m values ofE-2 andP-2.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF01569747
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  • 16
    Electronic Resource
    Electronic Resource
    Insect fungal symbionts: A promising source of detoxifying enzymes (1992)
    Springer
    Journal of industrial microbiology and biotechnology 9 (1992), S. 149-161 
    Details
    ISSN: 1476-5535
    Keywords: Toxin ; Secondary plant metabolite ; Allelochemical ; Insecticide ; Mycotoxin ; Endocytobiont
    Source: Springer Online Journal Archives 1860-2000
    Topics: Biology , Process Engineering, Biotechnology, Nutrition Technology
    Notes: Summary Many species of insects cultivate, inoculate, or contain symbiotic fungi. Insects feed on plant materials that contain plant-produced defensive toxins, or are exposed to insecticides or other pesticides when they become economically important pests. Therefore, it is likely that the symbiotic fungi are also exposed to these toxins and may actually contribute to detoxification of these compounds. Fungi associated with bark beetles, ambrosia beetles, termites, leaf-cutting ants, long-horned beetles, wood wasps, and drug store beetles can variously metabolize/detoxify tannins, lignins, terpenes, esters, chlorinated hydrocarbons, and other toxins. The fungi (Attamyces) cultivated by the ants and the yeast (Symbiotaphrina) contained in the cigarette beetle gut appear to have broad-spectrum detoxifying abilities. The present limiting factor for using many of these fungi for large scale detoxification of, for example, contaminated soils or agricultural commodities is their slow growth rate, but conventional strain selection techniques or biotechnological approaches should overcome this problem.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF01569619
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  • 17
    Electronic Resource
    Electronic Resource
    Biosensors for process monitoring (1992)
    Springer
    Journal of industrial microbiology and biotechnology 9 (1992), S. 163-172 
    Details
    ISSN: 1476-5535
    Keywords: Biosensors ; Process control ; Enzyme thermistor ; Immunoassay ; Bio-field effect transistor
    Source: Springer Online Journal Archives 1860-2000
    Topics: Biology , Process Engineering, Biotechnology, Nutrition Technology
    Notes: Summary A short review about the biosensor research activities for bioprocess monitoring in the F.R.G. after its reunification is given. The principles of biosensor applications are presented. In situ sensors and sensors based on the principles of flow injection analysis are studied. Some applications of a four-channel enzyme thermistor, bio-field effect transistors, and immunoanalysis systems for real process monitoring are presented.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF01569620
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  • 18
    Electronic Resource
    Electronic Resource
    Ecology ofVibrio vulnificus in Galveston Bay oysters, suspended particulate matter, sediment and seawater: Detection by monoclonal antibody — immunoassay — most probable number procedures (1992)
    Springer
    Journal of industrial microbiology and biotechnology 9 (1992), S. 219-223 
    Details
    ISSN: 1476-5535
    Keywords: Vibrio vulnificus ; Oyster ; Monoclonal antibody ; Most probable number ; Enzyme immunoassay
    Source: Springer Online Journal Archives 1860-2000
    Topics: Biology , Process Engineering, Biotechnology, Nutrition Technology
    Notes: Summary Oysters, suspended particulate matter (SPM), sediment and seawater samples were collected from West Galveston Bay, Texas over a 16-month period and analyzed for the presence ofVibrio vulnificus, a naturally-occurring human marine pathogen. Detection and enumeration ofV. vulnificus was performed using a species-specific monoclonal antibody (mAb FRBT37) in an enzyme immunoassay (EIA)-most probable number (MPN) procedure capable of detecting as few as 2000 target organisms.V. vulnificus was not detected in seawater, oyster or SPM samples during the cold weather months, but was detected at low levels in several sediment samples during this time period. Increased levels of the organism were first observed in early spring in the sediment, and then in SPM and oysters. The major increase inV. vulnificus occurred only after the seawater temperature had increased above 20°C and the winter-spring rainfall had lowered the salinity below 16‰. The highestV. vulnificus levels at each site were associated with suspended particulate matter. These results are consistent with the hypothesis that (1)V. vulnificus over-winters in a floc zone present at the sediment-water interface, (2) is resuspended into the water column in early spring following changes in climatic conditions, (3) colonizes the surfaces of zooplankton which are also blooming during early spring and (4) are ingested by oysters during their normal feeding process.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF01569626
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  • 19
    Electronic Resource
    Electronic Resource
    Conversion of sodium cyanide to carbon dioxide and ammonia by immobilized cells ofPseudomonas putida (1992)
    Springer
    Journal of industrial microbiology and biotechnology 9 (1992), S. 235-238 
    Details
    ISSN: 1476-5535
    Keywords: Biodegradation ; Pseudomonas putida ; Immobilization ; Sodium cyanide
    Source: Springer Online Journal Archives 1860-2000
    Topics: Biology , Process Engineering, Biotechnology, Nutrition Technology
    Notes: Summary Pseudomonas putida, isolated from contaminated industrial wastewaters and soil sites, was found to utilize sodium cyanide (NaCN) as a sole source of carbon and nitrogen. Cells, immobilized in calcium alginate beads (1–2 mm diameter) were aerated in air-uplift-type fluidized batch bioreactor containing 100–400 ppm of NaCN. Degradation of NaCN was monitored for 168 h by analyzing gaseous and dissolved ammonia (NH3), CO2, pH and optical density. The results indicated that the alginate-immobilized cells ofP. putida were able to degrade NaCN into NH3 and CO2 in a time-dependent manner.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF01569629
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  • 20
    Electronic Resource
    Electronic Resource
    Changes in protein composition ofSaccharomyces brewing strains in response to heat shock and ethanol stress (1992)
    Springer
    Journal of industrial microbiology and biotechnology 9 (1992), S. 229-234 
    Details
    ISSN: 1476-5535
    Keywords: Heat shock protein (HSP) ; Yeast ; Saccharomyces ; Viability ; Thermotolerance ; Ethanol tolerance
    Source: Springer Online Journal Archives 1860-2000
    Topics: Biology , Process Engineering, Biotechnology, Nutrition Technology
    Notes: Summary Heat shock and ethanol stress of brewing yeast strains resulted in the induction of a set of proteins referred to as heat shock proteins (HSPs). At least six strongly induced HSPs were identified in a lager brewing strain and four HSPs in an ale brewing strain. Four of these HSPs with molecular masses of approximately 70, 38, 26 and 23 kDa were also identified in two laboratory strains ofSaccharomyces cerevisiae. The appearance of HSPs correlated with increased survival of strains at elevated temperatures and high concentrations of ethanol. These results suggest that HSPs may play a role in the ethanol and thermotolerance of yeasts. The properties of these proteins and membrane fatty acids in relation to heat and ethanol shock are being investigated.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF01569628
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  • 21
    Electronic Resource
    Electronic Resource
    Isolation and characterization of a novel polysaccharide fromBacillus licheniformis NCIB 11634 (1992)
    Springer
    Journal of industrial microbiology and biotechnology 9 (1992), S. 239-245 
    Details
    ISSN: 1476-5535
    Keywords: Novel polysaccharide ; Bacillus licheniformis ; Raffia venifera ; d-Glucose ; d-Mannose ; d-Xylose
    Source: Springer Online Journal Archives 1860-2000
    Topics: Biology , Process Engineering, Biotechnology, Nutrition Technology
    Notes: Summary A polysaccharide producing strain ofBacillus licheniformis was isolated from exudate of raffia palm,Raffia vinifera. The optimum conditions for growth and polysaccharide production have been investigated and established. No appreciable polysaccharide was formed on glucose. It grew best in Czapek-Dox media with sucrose as the carbon source. The polysaccharide has been characterized as a heteropolymer containingd-glucose,d-mannose andd-xylose.
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    URL: http://dx.doi.org/10.1007/BF01569630
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  • 22
    Electronic Resource
    Electronic Resource
    Announcement from the publisher (1992)
    Springer
    Journal of industrial microbiology and biotechnology 9 (1992), S. 269-269 
    Details
    ISSN: 1476-5535
    Source: Springer Online Journal Archives 1860-2000
    Topics: Biology , Process Engineering, Biotechnology, Nutrition Technology
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF01569634
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  • 23
    Electronic Resource
    Electronic Resource
    Effect of deglycosylation on the properties of β-fructofuranosidaseP-1 fromAureobasidium sp. ATCC 20524 (1992)
    Springer
    Journal of industrial microbiology and biotechnology 9 (1992), S. 251-255 
    Details
    ISSN: 1476-5535
    Keywords: β-Fructofuranosidase ; Deglycosylation ; Aureobasidium ; Enzymatic stability
    Source: Springer Online Journal Archives 1860-2000
    Topics: Biology , Process Engineering, Biotechnology, Nutrition Technology
    Notes: Summary Most of the carbohydrate moiety of β-fructofuranosidaseP-1 fromAureobasidium sp. ATCC 20524 was removed by endo-β-N-acetylglucosaminidase F. A subunit of 94000 Da was observed in SDS-PAGE after deglycosylation. TheK m value for sucrose was not changed by deglycosylation but the stability at pH 4–5 and 50°C was decreased. The deglycosylated enzyme was more sensitive to proteases such as pronase E and subtilisin than the native enzyme. It is considered that the carbohydrate moiety of β-fructofuranosidaseP-1 contributes to the stability of the enzyme but is not essential in its catalytic function.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF01569632
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  • 24
    Electronic Resource
    Electronic Resource
    Modeling of biological tree structures (1979)
    Springer
    Bulletin of mathematical biology 41 (1979), S. 893-898 
    Details
    ISSN: 1522-9602
    Source: Springer Online Journal Archives 1860-2000
    Topics: Biology , Mathematics
    Notes: Abstract Biological tree-like structures, such as mammalian tracheobronchial airways, are complicated branching systems. One problem in modeling such systems is the reassignment of the number of segments at a given generation in the model being constructed. A hypothesis is proposed which has successfully been used in modeling mammalian lung airways.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF02462385
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  • 25
    Electronic Resource
    Electronic Resource
    A multidimensional birth process and its application to some problems in the dynamics of biological populations (1966)
    Springer
    Bulletin of mathematical biology 28 (1966), S. 333-345 
    Details
    ISSN: 1522-9602
    Source: Springer Online Journal Archives 1860-2000
    Topics: Biology , Mathematics
    Notes: Abstract This paper is a sequel to a paper by the author entitled “Restricted Transition Probabilities and Their Applications to Some Problems in the Dynamics of Biological Populations” (Bull. Math. Biophysics, 1966,28, 315–331). The paper is divided into two parts. In part one some aspects of the maximum size attained by the population during a finite time interval are studied for the case the stochastic process underlying the evolution of the population is a birth process. Two interesting by-products emerge from the study presented in part one; namely a combinatorial method of finding solutions to the Kolmogorov differential equations in special cases, and secondly, a set of criteria for the optimum allocation of genotypes in the host population of a host-pathogen system. The optimum allocation of genotypes in the host population is a problem of practical importance in controlling plant pathogens. In part two the theory of restricted transition probabilities developed in the companion paper is applied in finding the distribution of the time to the appearance of the first mutation for the case of a two dimensional birth process. The distribution of the time to the appearance of the first mutation is of importance in understanding the role mutation plays in the evolution of a population, particularly in the pathogen population of a host-pathogen system.
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    URL: http://dx.doi.org/10.1007/BF02476814
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  • 26
    Electronic Resource
    Electronic Resource
    The motion of the left ventricle. I (1966)
    Springer
    Bulletin of mathematical biology 28 (1966), S. 355-362 
    Details
    ISSN: 1522-9602
    Source: Springer Online Journal Archives 1860-2000
    Topics: Biology , Mathematics
    Notes: Abstract The complex arrangement of the muscle fibers in the ventricular wall and the nonsymmetric contraction and expansion of the ventricle preclude the writing of a differential equation of motion for the ventricle as a whole. We can, however, describe the motion of the ventricle by describing the motion of the dimensional parameters length and diameter; the radius, circumference, cross-sectional area, and volume following naturally from these. The ventricle is assumed to be an ellipsoid of revolution and the dimensional parameters to be periodic functions of time. Each of the parameters is expressed as a Fourier series.
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    Comparaison des modeles de neurone de Hodgkin-Huxley et de Nelson (1966)
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    Bulletin of mathematical biology 28 (1966), S. 347-354 
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    Notes: Abstract Le modèle de Nelson peut-être considéré comme une approximation du modèle de Hodgkin-Huxley. Moins précis, il est plus maniable. Le modèle de Nelson peut également être considéré comme une généralisation du modèle de Hodgkin-Huxley. En effet, il introduit des liaisons synaptiques localisées ou diffusantes, et un processus de facilitation. Le mécanisme des liaisons synaptiques ne se traduit pas facilement dans le langage de Hodgkin-Huxley. Par contre, le processus de facilitation s'interprète facilement. Nelson's model can be taken as an approximation of Hodgkin-Huxley's model. Its precision is lesser, but it is more usable. Nelson's model can also be taken as a generalization of Hodgkin-Huxley's one; for it introduces localized or diffusing synaptic connexions and a facilitating process. The mechanism of synaptic connexions cannot be easily translated into Hodgkin-Huxley's language. On the contrary, the facilitating process is easily interpreted.
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    The theory of the left ventricular aneurysm (1966)
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    Bulletin of mathematical biology 28 (1966), S. 363-370 
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    Notes: Abstract A spherical model for the human left ventricle with two different types of aneurysms, circular and rectangular-square, is proposed and meaningful relations are derived between the parameters of the aneurysms and ventricle. Such ventricular parameters as stroke volume, end-diastolic volume, and end-systolic volume are given normal human values to compute values for end-systolic radius and percentage shortening of muscle for various sized circular and rectangular-square aneurysms.
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    A note on crime control (1966)
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    Bulletin of mathematical biology 28 (1966), S. 375-378 
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    Notes: Abstract The Volterra theory of two competing populations is extended to the contemporary social problem of crime control. Domains of stability for the time dependence of the numbers in the criminal and enforcement groups are exposed by a numerical example. Both augmentation and reduction of enforcement can produce a stable system. Average values of the ratio of members in each group show great sensitivity to the control policies adopted by the remaining sector of the total population.
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    Interactions in enzymatic reactions (1966)
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    Bulletin of mathematical biology 28 (1966), S. 379-390 
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    Notes: Abstract The paper deals with interactions of substances via an enzymatic reaction (Bull. Math. Biophysics,25, 141–154, 1963). The substances are the activators, inhibitors and/or substrates of the reaction. Due to the bimolecularity of the processes in the reaction, the quantitative relation between the steady state amount of complexes and the amounts of the substances assumes a typical form. In multiple enzymatic reactions this form is more complicated, though basically similar. Because the substances may influence the steady state amounts of the complexes in opposite directions, the compensation and blocking effects are the properties of enzymatic reactions. The substances with the same direction of influence may potentiate each other. In the enzymatic reaction here considered, the potentiation is always non-negative.
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    Decay of cell synchronization: Solutions of the cell-growth equation (1966)
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    Bulletin of mathematical biology 28 (1966), S. 391-409 
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    Notes: Abstract Growth-rate functions in analytic form have been obtained for cell cultures in which the doubling times follow the Gaussian and Poisson distributions. The growth-rate functions are calculated by using Laplace transforms to solve an integral equation previously presented. Oscillatory solutions result if a substantial fraction of the cells in a culture are synchronized to divide at some particular time. The synchrony and, hence, the oscillatory character of the growth-rate function eventually disappear because of the non-zero variance of the doubling-time distribution. If their variances are sufficiently small, the Gaussian and Poisson doubling-time distributions lead to growth-rate functions that become identical in the limit of large time.
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    On the derivation of a mean growth equation for cell cultures (1966)
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    Bulletin of mathematical biology 28 (1966), S. 411-416 
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    Notes: Abstract IfN(t) is the expected number of cells in a culture at timet, $$\dot N(t)$$ the corresponding time derivative, andf(t−τ)dt the probability that a cell of aget−τ at timet will divide in the succeeding time intervaldt, then according to Hirsch and Engelberg (this issue) there obtains the integral equation $$\dot N(t) = 2\int_{ - \infty }^t {f(t - \tau )\dot N(\tau )d\tau }$$ for describing the dynamics of the cell population. It is the purpose of this note to give two alternative derivations of this equation, one based on the age density equation of Von Foerster, and the other based on a generalized form of the Harris-Bellman equation describing the first moment of an age dependent, branching process. In addition, a probability model is posed from which the Von Foerster equation and, hence, the Hirsch-Engelberg equation readily follows.
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    A mathematical theory of enamel solubility and the onset of dental caries: I. The kinetics of dissolution of powdered enamel in acid buffer (1966)
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    Bulletin of mathematical biology 28 (1966), S. 417-432 
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    Notes: Abstract A model of the dissolution kinetics of powdered enamel is developed based on the kinetic rate termq, $$q = K'H - k'C \cdot P_1$$ , whereH=[H +],C=[Ca ++] andP 1=[HPO 4 = ]. The differential equations describing the rate of mineral dissolution (and the linearly related rate of appearance of calcium and phosphate in solution) have been derived and solved for three basic cases: (1) when thepH of the solution and surface area of the enamel are considered constant, (2) when thepH is assumed constant, but the reduction in surface area during dissolution is considered, and (3) when the rise ofpH resulting from the buffering effect of the dissolved enamel is considered along with the change in surface area. Analytical solutions have been obtained for cases (1) and (2), while a numerical solution has been found for case (3). Data from a study on enamel dissolution are presented that agree with the theory of case (3), and it is noted that apH rise as large as 0.5 can occur, as has been shown elsewhere in the literature.
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    Reward and punishment in learning with possible reference to punishment for crime (1966)
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    Bulletin of mathematical biology 28 (1966), S. 477-481 
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    Notes: Abstract On the basis of Landahl's theory of two-choice learning it is shown that application of punishment for wrong responses, without giving award for correct ones, does not lead to complete learning, no matter how many trials are used. If initially a “wrong response” was learned, then an attempt to inhibit it by punishment alone will in a class of cases lead only to a 50% suppression of that wrong response. Possible connection with the problem of effectiveness of punishment as a deterrent for crime is mentioned.
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    The use of two radiotracers for transfer-rate determinations in closed two compartment systems (1966)
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    Bulletin of mathematical biology 28 (1966), S. 483-483 
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    Cooperative specific adsorption of iona at charged sites in an electric field (1966)
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    Bulletin of mathematical biology 28 (1966), S. 483-483 
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    Operations research around the world meetings (1966)
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    Bulletin of mathematical biology 28 (1966), S. 485-485 
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    Dimensional anlaysis and the equations of electrophoresis (1966)
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    Bulletin of mathematical biology 28 (1966), S. 501-510 
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    Notes: Abstract A set of characteristic parameters is given for electrophoresis accompanied by diffusion, followed by a method of simplification of the transport equation. The concept of electrophoretic similarity is introduced in connection with the presentation of solutions and the final section contains some dimensional considerations of the potential equation.
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    Categories of (ℓ, ℛ)-systems (1966)
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    Bulletin of mathematical biology 28 (1966), S. 511-517 
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    Notes: Abstract We show that when we represent (ℓ, ℛ)-systems with fixed genome as automata (sequential machines), we get automata with output-dependent states. This yields a short proof that ((ℓ, ℛ)-systems from a subcategory of automata—and with more homomorphisms than previously exhibited. We show how ((ℓ, ℛ)-systems with variable genetic structure may be represented as automata and use this embedding to set up a larger subcategory of the category of automata. An analogy with dynamical systems is briefly discussed. This paper presents a formal exploration and extension of some of the ideas presented by Rosen (Bull. Math. Biophyss,26, 103–111, 1964;28, 141–148;28 149–151). We refer the reader to these papers, and references cited therein, for a discussion of the relevance of this material to relational biology.
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    The origin of lift forces in fluttering flight (1966)
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    Bulletin of mathematical biology 28 (1966), S. 487-500 
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    Notes: Abstract A two-dimensional nonlinear integro-differential equation with time-varying coefficients describing the behavior of the fluttering wing-body systems typical of natural flight mechanisms has been deduced from the Navier-Stokes equation which generalizes local pressure and velocity distributions in the externally oscillating air field. The resulting equation for the wing forces is combined with an analogous expression for the forces of gravitation and acceleration associated with the body. The air acceleration force, not previously considered in bio-physical models of insect and bird flight, is shown to arise from a formal analysis of unsteady or time-varying contributions to the velocity field, while the square form of the conventional steady state aerodynamic forces is derived from the intertial terms in the Navier-Stokes equation with the aid of the approximations of Newtonian impact theory. Previous calculations (Houghton, 1964) have indicated that the contribution to gravitational stability of air acceleration and aerodynamic life are roughly in the ratio of 3:1.
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    Evoked potentials arising from neural population elements excited at different times on a warped surface (1966)
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    Bulletin of mathematical biology 28 (1966), S. 519-536 
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    Notes: Abstract Certain types of cortical electrical events are non-propagated so that the associated electric fields must have standing wave characteristics. However, cortical electric events typically are generated by neurone populations which cannot be activated simultaneously on impulse driving. Hence the sum of the standing wave fields due to asynchronous activation of adjoining regions of cortical neurones must give the appearance of a traveling wave. Analysis of cortical waveforms is further complicated by curvature in cortical surfaces. A model is presented that shows the effects of curvature and time lag in activation on the form of the potential at points in space around a laminar array of elements simulating a population of cortical neurones. The results are compared with waveforms evoked by single-shock stimulation of the prepyriform cortex in cats.
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    A continuity equation for cell populations (1966)
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    Bulletin of mathematical biology 28 (1966), S. 545-554 
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    Notes: Abstract A continuity equation for cell-number density in a population of cells is derived, and a system of equations for eliminating parameters between the general solution and the initial distribution obtained.
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    The behavior of the weakening and failing myocardium (1966)
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    Bulletin of mathematical biology 28 (1966), S. 537-544 
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    Notes: Abstract Use of an electrical model of the left ventricle of the heart and the arterial system permits analysis of the changes which take place as the capacity of the myocardium for generation of force decreases. The model is simple in structure, and its construction and practical testing would not be difficult. It demonstrates that, as the heart muscle weakens, the peak of intracardiac force occurs later in systole, and the difference between the intracardiac pressure and the aortic pressure in the second half of systole is much greater than for the normal heart. The feedback mechanisms which are proposed to affect myocardial contractility would affect this compensation for cardiac weakening. Indices to categorize the behavior of the normal, compensated though weakened, and decompensated myocardium are proposed.
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    The frequency distribution of chromosome constituents in cells with chromosome-number dispersion (1966)
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    Bulletin of mathematical biology 28 (1966), S. 555-566 
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    Notes: Abstract The frequency distribution in a population of cells of the quantityCD (defined as the amount of some chromosomal substance in a cell which containsC chromosomes) is calculated using the distribution in the population of the amount per chromosome,D, and the distribution of chromosome number,C.
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    Calculation of rate of synthesis of chromosomal DNA in cells with chromosome-number dispersion (1966)
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    Bulletin of mathematical biology 28 (1966), S. 567-574 
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    Notes: Abstract The rate of chromosomal DNA synthesis in an exponentially growing population of cells having chromosome-number dispersion is calculated using DNA histogram data, chromosome-number distribution data, and the assumptions that the synthesis rate is constant and DNA double exactly.
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    Estimation of rate of synthesis of chromosomal DNA in ehrlich ascites tumor cells (1966)
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    Bulletin of mathematical biology 28 (1966), S. 575-584 
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    Notes: Abstract An estimate is made of the rate coefficient for linear DNA synthesis with exact doubling in an exponentially growing population of Ehrlich ascites tumor cells having chromosome-number dispersion. Comparison of calculated and experimental results suggest that the assumptions used in the calculation are tenable, but further experimental evidence is needed to prove this.
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    A sociological approach to biology (1966)
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    Bulletin of mathematical biology 28 (1966), S. 655-661 
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    Notes: Abstract The paper develops further some suggestions made previously (Bulletin of Mathematical Biophysics,28, 283–308, 1966) that certain biological phenomena may be more easily interpreted from a “sociological” point of view by considering the organism as a social aggregate of cells and a cell as a social aggregate of genes. In this light the problems of origin of life on earth, of aging, and of parasitism and symbiosis are discussed. The notion of social aggregates of different orders is introduced.
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    Theorems on random evolution (1966)
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    Bulletin of mathematical biology 28 (1966), S. 663-663 
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    A theoretical and experimental study of the mechanical behavior of the cornea with application to the measurement of intraocular pressure (1966)
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    Bulletin of mathematical biology 28 (1966), S. 585-643 
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    Notes: Abstract A theoretical and experimental study was made of the mechanical behavior of the cornea. The theoretical analysis included an analytical solution for the symmetrical constraint of a thin, shallow, spherical shell by a rigid indenter. The experimental study investigated the rheology of the cornea with particular emphasis on its compliance with the requirements of the Boltzmann Superposition Principle. Representative results of tests on twenty enucleated hog eyes and two human eyes have been reported. The corneas of the human and hog eyes behaved as linear viscoelastic solids; the human eyes differed from the hog eyes in having a long term creep component. Several eyes were tested at the site of procurement, six to seven minutes after the animal's death, and it was established that creep is not an artifact due to aging or enucleation. The analytical and experimental results were combined to study some instruments used to detect the level of pressure in the eye. The theoretical analysis predicted that a type of elastic instability occurs during the process of flattening a small portion of the cornea; this is discussed with reference to the Goldmann and Mackay-Marg tonometers. The role of corneal creep was considered with reference to the response of the Schiøtz indentation tonometer during the time dependent process known as tonography.
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    Further studies on the shape of the tracking curve of an automobile and its dependence on biological parameters of the driver (1966)
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    Bulletin of mathematical biology 28 (1966), S. 645-654 
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    Notes: Abstract Following previous studies, differential equations are established which determine the variation of the stimulus towards a corrective turn of the steering wheel and its effect on the excitation of the centers in the brain which results in the production of the corrective turn. The equations are derived under the highly oversimplified assumption that all excitation thresholds are so small that they can be neglected. Under these assumptions it is found that the tracking curve of a car is a sinusoid with negative damping, that is, with an ever increasing amplitude. Driving under these assumptions is imposible since the car will always eventually jump off the road. The possible effects of the threshold as well as stimuli towards corrective turns other than the distance from the edge of the lane are very briefly discussed. In spite of the negative results of the paper, its interest lies in the circumstance that with the complication of the model, we find that driving depends not only on the reaction times as the only “purely biological” parameter, but on three other neurobiophysical constants. In a subsequent paper (Rashevsky, 1967) it is shown how the introduction of one or more purely biological parameters of the driver makes a stable driving regime possible.
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    The motion of thhe left ventriele: I (1966)
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    Bulletin of mathematical biology 28 (1966), S. 663-663 
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    Bimolecular systems: I. Linear systems of complexes (1967)
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    Bulletin of mathematical biology 29 (1967), S. 1-16 
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    Notes: Abstract A vast number of biologically important processes are based upon bimolecular systems. In these systems intermediate complexes are formed. Bimolecular systems in which no complex-complex interactions occur are called linear systems of complexes. A definition and some characteristic properties of these systems are given here. There may exist a contradiction of Onsager's principle of detailed balancing in these systems; however, no principal differences are found between the steady state behavior of an open system and that of a closed system. It is shown that the steady state behavior of a linear system of complexes of arbitrary complexity has some similarities with the steady state behavior of a simple bimolecular system, e.g., Michaelis-Menten enzymatic reaction. Multiplicity of action of the substances participating in biomolecular processes may produce some qualitative differences in the steady state behavior of the system.
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    DNA histograms of irradiated cells: The case of prophase-trapping (1967)
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    Bulletin of mathematical biology 29 (1967), S. 17-32 
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    Notes: Abstract A time-dependent DNA histogram is calculated for an irradiated population of cells under the limiting assumption that the cells cannot pass through prophase due to the effects of the radiation. The population is assumed to increase exponentially prior to irradiation, but after irradiation to neither gain nor lose cells. Chromosome-number dispersion is taken into account in the calculation. The qualitative behavior of the calculated and experimental histograms are in reasonable agreement. The quantitative agreement between the two is relatively good at short post-irradiation times but is poor at long post-irradiation times (say, greater than half the doubling time). This suggests that recovery phenomena cannot be neglected at long post-irradiation times.
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    A note on the mathematical biology of automobile driving (1967)
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    Bulletin of mathematical biology 29 (1967), S. 187-188 
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    Notes: Abstract It is pointed out that the three different stimuli for a corrective turn, namely the distance from the edge of the lane, the rate of approach to the edge, and the angle between the direction of the car and the direction of the lane (Bull. Math. Biophysics,28, 645–654, 1966,29, 181–186, 1967) may act all three simultaneously. It is found that in that case the tracking curve of the car is stable below a critical speed and becomes unstable above it.
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    Mathematical biology of automobile driving (1967)
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    Bulletin of mathematical biology 29 (1967), S. 181-186 
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    Notes: Abstract Continuing a previous study (Bull. Math. Biophysics, 28, 645–654, 1966), the biophysical mechanism of a corrective turn is investigated for the case where the stimulus for the corrective turn is produced not only by the perception of the nearness of an edge of the lane, but also by the rate of approach of the car towards the edge. In that case it is found that the tracking curve of the car may consist of a series of damped sinusoids and safe driving would be possible at any speed if it were not for the endogenous fluctuation in the driver's central nervous system. If the effect of the rate of approach increases sufficiently rapidly as the distance to the edge of the lane decreases, then a stable undamped oscillating tracking curve is possible. The case is also studied where the driver makes a corrective turn in response to a direct perception of the angle between the direction of the lane and the longitudinal axis of the car.
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    Angles of branching and diameters of branches in the human bronchial tree (1967)
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    Bulletin of mathematical biology 29 (1967), S. 245-259 
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    Notes: Abstract The principle of minimal work requires that the conducting airways of the human lung should have a maximum radius for minimal resistance to gas flow. At the same time there is a requirement that the airways should have a minimal volume for economy of space. These two opposing requirements have been investigated mathematically, and a method for calculating the angle of branching which produces minimal volume has been derived. The relationship of the radii of the parent and daughter branches to produce minimal resistance has been similarly defined. By measurement of a bronchial cast from a human lung the extent to which the predicted optimum structure is realized in practice has been shown. The change in structure associated with change of function at the transition from conducting airway to diffusion zone has been demonstrated.
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    Finite linnaean structures (1967)
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    Bulletin of mathematical biology 29 (1967), S. 191-206 
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    Notes: Abstract This paper considers a class of set-theoretical entities, calledn-rank Linnaean structures, which are intended as abstract models of the taxonomic classificatory systems of biology. In the first part, devoted to formalism, finite Linnaean structures are discussed in complete generality; but, in addition, eight distinct subclasses are noted and some of the properties of their elements are explored. In the second part, concerned with applications, it is shown that taxonomic systems may be recast in the form of finite Linnaean structures, and an effort is made to show that some undesirable features of earlier models are avoided without artificiality and without abandoning extensional mathematics.
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    Abstract power structures (APS) and related bumping orders (1967)
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    Bulletin of mathematical biology 29 (1967), S. 207-216 
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    Notes: Abstract Generalizing an idea of M. Richardson (Fundamentals of Mathematics, New York: Macmillan Co., 1958), an APS on a given populationP is a non-empty collection of non-empty subsets ofP such that ifA is in the collection andA⊆B, thenB is in the collection. From a structure of this kind a partial ordering ofP, called therelated bumping order, is derived. The question is raised as to what kinds of partial orderings can be so obtained. For structures determined by voting weights of the members of the population, a complete characterization of all possible bumping orders is obtained.
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    Stability analysis of a mathematical neuron model (1967)
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    Bulletin of mathematical biology 29 (1967), S. 217-226 
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    Notes: Abstract The “second method” of Liapunov is used to perform a stability analysis of a mathematical model of the neuron. This analysis is based on the hypothesis that the firing of the neuron coincides with a temporary state of instability of the system, and that the initiation of all-or-none process depends on the magnitude of membrane depolarization and its first time derivative. It is found that the stability (and hence the possibility of a second firing) is restored approximately when the rate of membrane repolarization is at a maximum. This result predicts that the duration of the period of absolute refractoriness in neurons would be about 75 per cent of the spike duration, and thus shorter than the value usually obtained from experimental measurements.
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    A neural net model for masking phenomena (1967)
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    Bulletin of mathematical biology 29 (1967), S. 227-232 
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    Notes: Abstract Some aspects of masking phenomena are considered in terms of the simplest possible model of two-factor neural elements. The effect of a number of variables can be accounted for, but the introduction of an internuncial element results in a masking function which need not be symmetric about zero delay interval. As an illustration, the results for a special case are compared with available data. In general, such a model results in a masking function which depends on the intensity, area, and duration of the stimuli, as well as on the temporal and spatial separation between them.
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    The struggle for life: I. Two species (1967)
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    Bulletin of mathematical biology 29 (1967), S. 377-388 
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    Notes: Abstract The general equations are discussed describing two species in competition or in symbiosis or feeding one on the other.
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    A note on Rashevsky’s postulate of relational forces (1967)
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    Bulletin of mathematical biology 29 (1967), S. 403-404 
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    Organismic sets and biological epimorphism (1967)
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    Bulletin of mathematical biology 29 (1967), S. 389-393 
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    Notes: Abstract It is shown that the principle of biological epimorphism (Rashevsky,Mathematical Principles in Biology and Their Applications, Springfield, Ill.: Charles Thomas, 1960) is contained in the theory of organismic sets (Bull. Math. Biophysics,29, 139–152, 1967) if an additional postulate not directly connected to mappings is made.
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    Out-of-print volumes and back issues of the Bulletin of Mathematical Biophysics (1967)
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    Bulletin of mathematical biology 29 (1967), S. 407-407 
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    Model of urethra under uniform circumferential tension (1967)
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    Bulletin of mathematical biology 29 (1967), S. 409-409 
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    Bimolecular systems: II. Nonlinear systems of complexes (1967)
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    Bulletin of mathematical biology 29 (1967), S. 605-613 
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    Notes: Abstract This paper deals with bimolecular systems in which also complex-complex interactions occur. Because of the complexity of the problem, an approximation in a form of coupled linear systems of complexes (Bull. Math. Biophysics,29, 1–16, 1967) is considered. Two types of couplings, serial and parallel, are studied. In the serial coupling the nonlinear system of complexes has the same behavior as its subsystems. An entity, initial sensitivity, has interesting properties: in serial coupling it is at most equal to the product and in parallel coupling, at most equal to the sum of partial initial sensitivities.
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    Bimolecular systems: III. Catalytic systems (1967)
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    Bulletin of mathematical biology 29 (1967), S. 615-623 
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    Notes: Abstract Amplification effect in the catalytic bimolecular systems is a consequence of the kinetic characteristic of the catalyst. Two types of the coefficient of amplification are defined. The applicability of these definitions is given by the type of the bimolecular system. In a simple example it is shown that the concept of amplification is meaningful in these systems. Furthermore, two rules, analogous to those for a coupling of amplifiers, are derived for the two basic modes of coupling of catalytic systems. Thus, in biological systems the catalytic reactions may be regarded as biologically effective amplifiers.
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    A theory of cell hydration governed by adsorption of water on cell proteins rather than by osmotic pressure (1967)
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    Bulletin of mathematical biology 29 (1967), S. 583-596 
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    Notes: Abstract It is postulated that cell hydration is governed by adsorption of water on cell proteins in accord with the Bradley adsorption isotherm, and that the action of a solute in the surrounding solution is to lower the vapor pressure of the solution so that cell water adsorption is decreased by moving down the Bradley isotherm. From these concepts, it is derived that cell volume (V) should be related to solute concentration (x) by the equationV=−E log10 x+F whereE andF are constants which are independent of type of solute. For a non-adsorbed solute this agrees well with experimental data. For solutes which are adsorbed by cell proteins, a correction in the above equation may be necessary at higher solute concentrations, which is shown to be compatible with various experimental data. The types of experiments which are generally used to support the osmotic pressure theory of cell hydration agree equally well with the adsorption theory. The virtue of the adsorption theory is that, unlike the osmotic pressure theory of cell swelling, it is compatible with permeability of the cell membrane to solutes, which has been experimentally observed for various solutes.
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    Considerations of quasi-stationarity in electrophysiological systems (1967)
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    Bulletin of mathematical biology 29 (1967), S. 657-664 
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    Notes: Abstract Conditions under which a time varying electromagnetic field problem (such as arises in electrophysiology, electrocardiography, etc.) can be reduced to the conventional quasistatic problem are summarized. These conditions are discussed for typical physiological parameters.
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    The dead space in a compartmental lung model (1967)
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    Bulletin of mathematical biology 29 (1967), S. 711-718 
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    Notes: Abstract A compartmental lung model with any number of synchronously filling and emptying functional chambers and a common dead space or conducting region is considered. It is shown that the model gives rise to an output, in an open circuit washout determination, which is a weighted sum of exponentials. From estimates of these weights and exponential components, estimates of the model parameters can be recovered. Relations giving the unique correspondence between the output parameters and the model parameters are derived and the existence and uniqueness of solutions established.
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    A charge transfer process in the visual pigments (1967)
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    Bulletin of mathematical biology 29 (1967), S. 677-690 
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    Notes: Abstract A physical model that incorporates all the experimental information on the formation of the visual pigment rhodopsin is presented. The visual pigments consist of a chromophore bound to an appropriate protein. Thus rhodopsin (λm 505 mμ) is formed by a Schiff’s base linkage C19H27CH=NH+-opsin (λm 440 mμ) between 11-cis retinal (λm 380 mμ) and the protein opsin (λm 280 mμ). It is found that there exists a red shift in the spectrum of rhodopsin from the Schiff’s base. The model brings an explanation for this red shift. It is shown that such a shift may be due to a charge transfer process (R. S. Mulliken,J. Am. Chem. Soc.,74, 811–824, 1952) between an electron at the double bond of carbons C11−C12 and an atomic orbital of the sulphur present in cysteine. This provides an explanation of the presence of SH-groups in the protein after the absorption of light. A one-electron approximation is used and the dipole momentμ NV ; hence, the oscillator strengthf of the transitionNV is estimated and compared with the experimentally determined extinction coefficient ∈m by mixing 3.5×10−3 M of 11-cis retinal with 8.3×10−5 M of cysteine at pH ranges 6 through 8. Reasonable agreement is found. Solvent, concentration and temperature dependence are shown also.
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    Optimal models for social change (1967)
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    Bulletin of mathematical biology 29 (1967), S. 841-862 
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    Notes: Abstract By assigning coordinates to the environmental function space comprising all physical and mental stimuli, mathematical interpretations can be based on such terms as adaptability, and reactivity which relate to individuals interacting with their environment within a society. These psychometric concepts are incorporated into a framework of functional analysis, which permits the optimization of social change by maximizing the satisfaction integral through the use of variational or dynamic programming methods in conjunction with some optimal social policy. The approach provides a mathematical connection between psychology and sociology, and further demonstrates that existing forms of government are simulated by differential equations belonging to the same general class. The synthesis of new classes of functional equations describing social progress is visualized as a legitimate objective for abstract mathematical sociology.
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    Note from the editor (1968)
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    Bulletin of mathematical biology 30 (1968), S. 1-1 
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    A suggestion for a new approach to the mathematical theory of imitative behavior (1967)
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    Bulletin of mathematical biology 29 (1967), S. 863-877 
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    Notes: Abstract The theory of imitative behavior as developed hitherto by the author was based on the assumption that each individual has a natural preference for one of the two mutually exclusive behaviors. The endogenous fluctuations in the central nervous system then result in the individual’s exhibiting the two behaviors alternately with a relative frequency determined by the natural preference. Imitation shifts the natural preference towards one or the other of the two mutually exclusive behaviors. In the present approach it is suggested that the relative frequency of the two mutually exclusive behaviors exhibited alternately is determined by maximizing the “satisfaction function” of the individual, that is by hedonistic factors rather than by purely random fluctuations. Corresponding equations are developed. It is shown that in certain cases, even when the imitation effect is absent, a sort of “pseudoimitation” may occur. Another situation leads, in the case of two individuals only, to a complete “division of labor” between them, with respect to the two behaviors. Each one exhibits only one behavior. After that imitation is introduced explicitly by assuming that imitation by one individual or another increases the satisfaction function of the imitating individual. Results thus obtained show similarities to the results of the old theory.
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    Erythrocyte distribution in arterial blood flow: IV. Simplification of the proposed equations (1968)
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    Bulletin of mathematical biology 30 (1968), S. 27-32 
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    Notes: Abstract In a previous paper (Bull. Math. Biophysics,29, 565–574, 1967) the author developed equations to represent velocity and hematocrit profiles in quasi-Poiseuille flow of blood. It was assumed that energy dissipation was minimized and that the viscosity depended on hematocrit and shear rate according to the Casson formula. These equations are simplified considerably, placed in a form more suitable for numerical solution and shown to depend on a single dimensionless parameter. Typicalin vivo values for this parameter are calculated.
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    Éléments d’une théorie générale de la croissance d’une population (1968)
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    Bulletin of mathematical biology 30 (1968), S. 33-46 
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    Notes: Abstract In this paper, discrete models of reproduction are studied. In part one, definitions are given, particularly on order of the reproduction; part two concerns the growth of the population; part three, the phenomena of delay or acceleration; and part four, the consequences of mortality.
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    Neuroendocrine control of thyroid secretion in living systems: A feedback control system model (1968)
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    Bulletin of mathematical biology 30 (1968), S. 3-26 
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    Notes: Abstract A model of the regulation of thyroid hormone in the bloodstream of living systems is formulated and analyzed. The portion of this model defined as theregulator includes components representing the thyroid, anterior pituitary and hypothalamic organs and their intercommunicating channels, that is, the peripheral plasma and hypophysial portal circulations and certain neuro-secretory connections. The loss of hormones from the plasma in the living system associated with physiological mechanisms within the peripheral tissue space and the excretory pathways is represented in the model by a lumpedload on the regulator. The model is reduced to a system of differential equations involving eleven parameters and variables, all of which are identified with certain physiological structures and states. Five of these are currently observable by available laboratory techniques and two others are computable explicity from the equations of the model; the remaining four can be computed in the same way to within a multiplicative constant. Procedires for carrying out ten of these measurements and calculations are suggested. On the basis of the equations and parameters of the model, a discussion of the normal behavior and the response of this system to certain types of disturbances is presented. A systematic effort has been made in the development of this model to include all relevant physiological data and relationships reported in the biological literature. A summary of this literature, reflecting the views and interpretations made by the authors of this paper, is included for completeness and ease of reference.
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    Linear bulk diffusion into heterogeneous tissue (1968)
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    Bulletin of mathematical biology 30 (1968), S. 47-59 
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    Notes: Abstract In this paper an expression is derived which describes the transient overall uptake of an inert solute by a section of tissue excised with parallel faces and placed upon an impermeable base. The approach diverges from the conventional analyses for perfused tissue (Morales and Smith,Bull. Math. Biophysics,6, 125–141, 1944;7, 47–99, 1945) because the extravascular zone is regarded as a heterogeneous diffusion medium. Account for this is taken by regarding tissue as effectively composed of two phases—a continuous (extracellular) phase similar to water, and a dispersed phase comprising cells of irregular profile. In both phases the relevant mode of uptake is taken as bulk diffusion rather than surface permeation, thus emphasizing the influence of the internal geometry of the tissue upon its overall exchange response.
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    The identification of recirculating systems in the frequency domain (1968)
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    Bulletin of mathematical biology 30 (1968), S. 87-104 
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    Notes: Abstract A method for the identification of flow systems by frequency domain analysis has been extended to include systems with recirculation and truncated data curves. Application of the technique to clinical indicator-dilution curves indicates that the method may be useful in the quantitation of intracardiac shunts. A number of numerical examples which demonstrate the accuracy of the method are included.
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    A systems-mathematical interpretation of psychoanalytic theory (1968)
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    Bulletin of mathematical biology 30 (1968), S. 61-86 
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    Notes: Abstract By assigning time-varying coordinates to all environmental stimuli, it has been possible to axiomatize psychoanalytic theory on the five principles of multiple causation, growth-aging influence, genetic influence, historic influence and conscious-unconscious activity. The theorems of summation of response and the inevitability of conscious-unconscious conflict with their corollaries follow directly from the axiomatic foundations, as does the existence of an adaptation-defense mechanism. The interpretation of the defense mechanism in terms of an ego-id feedback system provides the basis for the structural existence of conscious-conscious and unconscious-unconscious conflict.
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    Cellular systems as sequential machines: Stability properties (1968)
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    Bulletin of mathematical biology 30 (1968), S. 117-122 
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    Notes: Abstract In previous studies of (M,R) (Rosen, 1961; Demetrius, 1966), it was assumed that changes in the structure of (M,R) which were induced by environmental alternations occurred without error. Here, the effect of both “genetic” and “metabolic” malfunctions on the behavior of (M,R) is examined and a subclass of these systems whose behavior is invulnerable to such errors is specified.
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    Cellular systems as graphs (1968)
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    Bulletin of mathematical biology 30 (1968), S. 105-116 
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    Notes: Abstract The definition of an (M,R) is formulated in a way that emphasizes its mathematical properties. Neglecting interactions between the components, it is shown that: (1) An (M,R) contains only one non-reestablishable component. (2) If an (M,R) contains only one non-reestablishable component, then that component is central. Examples are given to illustrate the biological significance of these two results. The notion of “lag-independence” is introduced, and it is shown that if a system possesses only one non-reestablishable component which is “lag-independent” then all components are lag-independent. The concepts of reestablishability, centrality and lag-independence are applied in order to suggest various criteria for optimal organization of (M,R).
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    A theoretical model for the control mechanisms in biochemical reactions (1968)
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    Bulletin of mathematical biology 30 (1968), S. 123-133 
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    Notes: Abstract A mathematical representation for the analysis of control mechanisms in biochemical reactions is presented. First, the theoretical concept of concentration in biological systems is developed. Then a system consisting of two functions λ and τ is constructed as a network of single output automata. The range of λ is taken to be formed by a set of twostates qualitatively different from the “repair function” Φ f of a mappingf: A→B in the stimulated Φ1 and unstimulated state Φ0. Likewise, the range of τ is formed by the set δ={f o ,f 1} wheref 1 means the mappingf in its stimulated state andf o in the unstimulated one. It is demonstrated that the mathematical structure described acts as a control mechanism over thef and Φ f , so that two biochemical components,A→B, are transformed at a controlled rate. Some of the biological applications of this model are briefly examined. The Jacob-Monod model, the enzymatic adaptation phenomenon, and the “rheon unit” hypothesis are discussed within our framework. Eventually, a concrete model for the RNA-polymerase mechanism, based on the above discussion, is presented.
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    A contribution to Rashevsky’s mathematical theory of development (1968)
    Springer
    Bulletin of mathematical biology 30 (1968), S. 135-151 
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    ISSN: 1522-9602
    Source: Springer Online Journal Archives 1860-2000
    Topics: Biology , Mathematics
    Notes: Abstract The application of Rashevsky’s transformationT to a primordial graph yields a set of graphs corresponding to different stages in the development of the organism. However, sinceT is multiple-valued the graphs obtained are not ordered. To obtain an ordering, it is first shown that the set of graphs under consideration is equivalent to a well defined setO (for “organism”) ofn-tuples. A metric is then introduced which is based on a biological consideration discussed by Rashevsky (Bull. Math. Biophysics,16, 317–348, 1954). Since a metric implies an ordering of the setO, with a knowledge of the structure of the primordial, one can obtain the developmental sequence. Unfortunately, at present, the structure of the primordial graph is unknown which makes the direct application of the above principle impossible. Consequently, an indirect approach which makes use of more accessible biological phenomena is discussed as well. The hypothesis thatrate of development decreases exponentially and the implications this has with regard to the metric onO are discussed. It is shown that if the hypothesis is accepted the search for the developmental sequence is narrowed.
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    URL: http://dx.doi.org/10.1007/BF02476945
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    Comparaison des croisements au hasard, prère-sœur et demi frère-sœur par le coefficient de dépression (1975)
    Springer
    Bulletin of mathematical biology 37 (1975), S. 37-49 
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    ISSN: 1522-9602
    Source: Springer Online Journal Archives 1860-2000
    Topics: Biology , Mathematics
    Notes: Abstract The chromosomal theory of inbreeding based on a gametic interaction system lead us to define a depression coefficientD. Comparison of random, sib and half-sib matings (with inbreeding coefficientF=0, 1/4 and 1/8) shows thatD depends on the structure of the starting population and on values of the model parameters. This result accounts for responses of lines whose depression does not depend directly on the inbreeding coefficient and which theories of inbreeding based on increasing homozygosity fail to explain.
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    URL: http://dx.doi.org/10.1007/BF02463490
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    Self-assembly and differentiation as models of computability (1975)
    Springer
    Bulletin of mathematical biology 37 (1975), S. 59-69 
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    ISSN: 1522-9602
    Source: Springer Online Journal Archives 1860-2000
    Topics: Biology , Mathematics
    Notes: Abstract An idealization of chemical combination is formulated as a model of computability, and it is shown that this model has universal computational power just in case assembly has at least two-dimensional space in which to occur. It is also shown that this model, under reinterpretation, corresponds to a cellular automaton in which growth occurs by differentiation only (i.e., the state into which any cell is born is thereadfter fixed). Hence this latter model of growth is also computationally universal.
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    URL: http://dx.doi.org/10.1007/BF02463492
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  • 87
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    Kinetics of light emission by photosynthetic systems: Second order light decay kinetics means elovich kinetics in a solid state reaction; 1.5 order light decay kinetics means second order reaction kinetics (1975)
    Springer
    Bulletin of mathematical biology 37 (1975), S. 79-83 
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    ISSN: 1522-9602
    Source: Springer Online Journal Archives 1860-2000
    Topics: Biology , Mathematics
    Notes: Abstract Kinetics of biological light emission processes do not mean what they seem to mean, because measured light intensity is not proportional to reactant concentration but to reaction rate. Therefore, the differential equation for light decay is usually different from that of concentration decay, so that mass action interpretations cannot be applied directly to light intensity decay. An observed second order light decay for Chlorella at 6.5°C, implies Elovich solid state reaction kinetics, which agrees with other evidence for solid state processes in photosynthesis. An observed 1.5 order light decay for Cholorella at 28°C implies second order liquid or solid state reaction kinetics. First ordere light decay implies first order reaction kinetics.
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    URL: http://dx.doi.org/10.1007/BF02463494
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  • 88
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    Bounds on the total population for species governed by reaction-diffusion equations in arbitrary two-dimensional regions (1975)
    Springer
    Bulletin of mathematical biology 37 (1975), S. 71-78 
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    ISSN: 1522-9602
    Source: Springer Online Journal Archives 1860-2000
    Topics: Biology , Mathematics
    Notes: Abstract Analysis based on the integration of differential inequalities is employed to derive upper and lower bounds on the total populationN(t) = ∫ R θ(x 1,x 2,t) dx 1 dx 2 of a biological species with an area-density distribution function θ=θ(x 1,x 2,t) (≥0) governed by a reaction-diffusion equation of the form ∂θ/∂t =D∇2θ +fθ −gθ n+1 whereD (〉0),n (〉0),f andg are constant parameters, θ=0 at all points on the boundary ∂R of an (arbitrary) two-dimensional regionR, and the initial distribution (θ(x 1,x 2, 0) is such thatN(0) is finite. Forg≥0 withR the entire two-dimensional Euclidean space, a lower bound onN(t) is obtained, showing in particular thatN(∞) is bounded below by a finite positive quantity forf≥0 andn〉1. An upper bound onN(t) is obtained for arbitrary bounded or unbounded)R withn=1,f andg negative, and ∫ R θ(x 1,x 2, 0)2 dx 1 dx 2 sufficiently small in magnitude, implying that the population goes to extinction with increasing values of the time,N(∞)=0. Forg≥0 andR of finite area, the analysis yields upper bounds onN(t), predicting eventual extinction of the population if eitherf≤0 or if the area ofR is less than a certain grouping of the parameters in cases for whichf is positive. These results are directly applicable to biological species with distributions satisfying the Fisher equation in two spatial dimensions and to species governed by certain specialized population models.
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    URL: http://dx.doi.org/10.1007/BF02463493
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    Stochastic kinetic models for small reversible systes; The equilibrium distribution (1975)
    Springer
    Bulletin of mathematical biology 37 (1975), S. 127-138 
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    ISSN: 1522-9602
    Source: Springer Online Journal Archives 1860-2000
    Topics: Biology , Mathematics
    Notes: Abstract The equilibrium probability distribution of the process level is studied for a general class of reversible stochastic reactions. A calculationally convenient approximation for equilibrium probabilities is derived and its accuracy is investigated over a range of values of the equilibrium constant. A method of approximating the equilibrium means and variance is developed and illustrated forQ th-order processes.
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    URL: http://dx.doi.org/10.1007/BF02470619
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    Concept of energy in biological systems (1975)
    Springer
    Bulletin of mathematical biology 37 (1975), S. 565-572 
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    ISSN: 1522-9602
    Source: Springer Online Journal Archives 1860-2000
    Topics: Biology , Mathematics
    Notes: Abstract Beside the concept of material inputs and outputs of components of the representation of biological systems given to us by Rosen, the concept of energy is incorporated. The interaction of material and energy is represented by a cartesian product; and separate material and energetical mappings are considered as the new representation of components. These developments generate aMα category, and it is shown thatMα is isomorphic to theM category of previous developments.
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    URL: http://dx.doi.org/10.1007/BF02459525
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  • 91
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    On the time-dependent reversible stochastic compartmental model—II. A class ofn-compartment systems (1975)
    Springer
    Bulletin of mathematical biology 37 (1975), S. 555-564 
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    ISSN: 1522-9602
    Source: Springer Online Journal Archives 1860-2000
    Topics: Biology , Mathematics
    Notes: Abstract This paper discusses the solution of a generaln-compartment system with time dependent transition probabilities utilizing the technique described by Cardenas and Matis (1975) (hereafter abbreviated (CM)). In addition, the cumulant generating function is derived for a special class of reversiblen-compartment systems where the time-dependent intensity coefficients corresponding to the migration and death rates are some multiple of each other. The immigration rates can be any integrable function of time. The moments are also obtained and the solution to the two-compartment system is presented explicitly. The solution is illustrated with a linear and a periodic function which forms have been widely reported in the literature.
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    URL: http://dx.doi.org/10.1007/BF02459524
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  • 92
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    Matrix proof of flow, volume and mean transit time theorems for regional and compartmental systems (1975)
    Springer
    Bulletin of mathematical biology 37 (1975), S. 573-588 
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    ISSN: 1522-9602
    Source: Springer Online Journal Archives 1860-2000
    Topics: Biology , Mathematics
    Notes: Abstract The relations (inflow) = (dose)/(area under indicator curve), and (volume of distribution) = (throughflow) × (mean transit time) are derived by a matrix method for a system of interconnected subsystems, within which spatial indicator activity gradients may exist, and for compartments, within which the indicator activity is spatially uniform. The inflow theorem, is different from the outflow theorem. Equivalent labeling of multi-input systems reduces them formally to single input systems. Foreign indicator flow-volume kinetics are more general than, and include as a special case, tracer flux-mass (metabolic) kinetics. Volume of distribution in the indicator steady state may be different from the equilibrium volume of distribution.
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    URL: http://dx.doi.org/10.1007/BF02459526
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    The Society for Mathematical Biology announces Central Regional Meeting (1975)
    Springer
    Bulletin of mathematical biology 37 (1975), S. 219-219 
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    ISSN: 1522-9602
    Source: Springer Online Journal Archives 1860-2000
    Topics: Biology , Mathematics
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    URL: http://dx.doi.org/10.1007/BF02470626
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    Estimates of predator-prey limit cycles (1975)
    Springer
    Bulletin of mathematical biology 37 (1975), S. 291-299 
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    ISSN: 1522-9602
    Source: Springer Online Journal Archives 1860-2000
    Topics: Biology , Mathematics
    Notes: Abstract Perturbation methods are applied to a differential equation predator-prey model to find the approximate amplitudes and period of limit cycle solutions. In the model the feeding rate per unit predator per unit prey decreases as the prey become scare. The rigorous applicability of the perturbation technique depends on the assumptions that the limit cycle amplitude is relatively small and that near the equilibrium point the growth rate of each species is most sensitive to changes in the density of the other species. The second assumption is usually roughly satisfied in practice and examples are considered which suggest that the first assumption can be greatly relaxed.
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    URL: http://dx.doi.org/10.1007/BF02461447
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    Batesian mimicry and signal detection theory (1975)
    Springer
    Bulletin of mathematical biology 37 (1975), S. 367-387 
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    ISSN: 1522-9602
    Source: Springer Online Journal Archives 1860-2000
    Topics: Biology , Mathematics
    Notes: Abstract Signal Detection Theory can be used to provide a mathematical model describing the choice of a predator trying to distinguish between a model and a Batesian mimic. The mathematical model yields a number of a deductions, in particular that it may or may not assist the mimic population if mimics more closely resemble their models. The assumptions underlying the analysis are discussed in some detail.
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    On a possible biological spectroscopy (1975)
    Springer
    Bulletin of mathematical biology 37 (1975), S. 419-425 
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    ISSN: 1522-9602
    Source: Springer Online Journal Archives 1860-2000
    Topics: Biology , Mathematics
    Notes: Abstract A new type of physical transition, denotedS→S *, has been detected in irradiated organic molecules (λ=546 nm) through their interaction with specific biological macromolecules. In a specific enzyme-substrate interaction, a clear enhancement of the reaction rate is observed, when the substrate is irradiated with sharply well defined times. These “efficient irradiation times” are always of the 5k sec type (k=1, 2, 3, …). They have been consistently revealed in a great number of specific biological interactions. The present note demonstrates an important property, i.e. that forevery irradiation time aS→S * transition is induced in organic molecules. It is shown that for any irradiation times different from the 5k sec type (k=1, 2, 3, …) states of theS * type may occur, but the biological macromolecules may “detect” only theS * states induced by irradiations of the 5k sec type.
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    URL: http://dx.doi.org/10.1007/BF02459523
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    A semi-empirical model for flow of blood and other particulate suspensions through narrow tubes (1975)
    Springer
    Bulletin of mathematical biology 37 (1975), S. 459-470 
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    ISSN: 1522-9602
    Source: Springer Online Journal Archives 1860-2000
    Topics: Biology , Mathematics
    Notes: Abstract A semi-empirical model applicable to the flow of blood and other particulate suspensions through narrow tubes has been developed. It envisages a central core of blood surrounded by a wall layer of reduced hematocrit. With the help of this model the wall layer thickness and extent of plug flow may be calculated using pressure drop, flow rate and hematocrit reduction data. It has been found from the available data in the literature that for a given sample of blood the extent of plug flow increases with decreasing tube diameter. Also for a flow through a given tube it increases with hematocrit. The wall layer thickness is found to decrease with increase in blood hematocrit. A comparison between the results of rigid particulate suspensions and blood reveals that the thicker wall layer and smaller plug flow radius in the case of blood may be attributed to the deformability of the erythrocytes.
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    URL: http://dx.doi.org/10.1007/BF02459514
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    Three dimensional laminar flow in distorting, axisymmetric, axially varying vessels (1975)
    Springer
    Bulletin of mathematical biology 37 (1975), S. 489-504 
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    ISSN: 1522-9602
    Source: Springer Online Journal Archives 1860-2000
    Topics: Biology , Mathematics
    Notes: Abstract Three dimensional laminar, viscid flow is developed for Newtonian fluids which provides absolute values for axial, radial and tangential velocity fields everywhere if the dimensions of the vessel are known and two simultaneous axial velocities e.g. on and off the central axis in the same plane, and the central axis axial velocity gradient are measured. In addition, normal and shear stresses are determinable. The equation set satisfies geometric and other known flow limiting conditions such as no slip at surfaces etc. and are amenable for inclusion in general, dynamic flow expressions. Alternatively they may be used alone for certain problems involving gradients and secondary flows. A range of illustrations are shown for a distorting vessel with elliptic cross-section and small axial taper (analogous to the pulmonary trunk during ejection).
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    URL: http://dx.doi.org/10.1007/BF02459516
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    Construction, simulation, clinical application and sensitivity analyses of a human left ventricular control system model (1975)
    Springer
    Bulletin of mathematical biology 37 (1975), S. 521-553 
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    ISSN: 1522-9602
    Source: Springer Online Journal Archives 1860-2000
    Topics: Biology , Mathematics
    Notes: Abstract A regulated left ventricular dynamics model is presented which involves interaction of the dynamics of the left ventricular and circulatory systems and their regulation by the central nervous system. On-line human parametric simulation (parameter estimation) and consequential prognostic implications (based on parametric values) are demonstrated. Model responses to simulated physiologic stresses help delineate tolerances of subjects. In order to have an estimate of the reliability of the model, the sensitivity of the model's responses to changes in the values of its intrinsic parameters is assessed. Also determined is the extent to which errors in measuring the pressure affect the calculated values of the model's simulation parameters and subsequently influence the values of other diagnostically useful variables (such as contractility, oxygen consumption rate, heart rate), when the model is used to determine the limiting physiological stress sustainable by the subject. A comparison of the model's composition with those of other similar cardio-circulatory models is included.
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    URL: http://dx.doi.org/10.1007/BF02459518
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    Some strategies for harvesting a single species (1975)
    Springer
    Bulletin of mathematical biology 37 (1975), S. 659-673 
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    ISSN: 1522-9602
    Source: Springer Online Journal Archives 1860-2000
    Topics: Biology , Mathematics
    Notes: Abstract Then-stage harvesting strategy of Elizarov and Svirezhev is examined. As a result, some important new features appear. A discussion is presented on whether or not one should harvest a species at one time stage or wait until a later time. The paper is concerned with contributions which are primarily mathematical formulations and results for continuous, as well as discrete time, logistic growth of a single species being harvested. Age class structure is ignored.
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    URL: http://dx.doi.org/10.1007/BF02459529
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