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  • Springer  (885,267)
  • 2005-2009  (225,194)
  • 2000-2004  (173,866)
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  • 1
    Keywords: Air ; Chlor ; GSM-Postponed Project ; Manual ; Oxide ; Water ; bacteria ; microorganism ; pollution ; production ; soil ; toxicity
    Description / Table of Contents: Environmental Chemistry: Fundamentals, by Jorge Ibanez et al., is an exceptionally useful and well organized book. After reviewing basic chemical concepts, Environmental Chemistry: Fundamentals quickly progresses to more advanced and contemporary applications including ozone depletion, physiochemical and biological treatment of pollutants, and green chemistry. The chemistry of processes of the atmosphere, lithosphere and hydrosphere are covered in detail and the effects of pollutants on each of these chemical processes are extensively considered, as are their effects on the biosphere. The book also has an experimental companion, Environmental Chemistry: Microscale Laboratory Experiments, which includes an array of environmental chemistry experiments that can be readily performed at the microscale level. Ideas for additional open-ended projects are provided for all experiments, and they impart a thorough introduction to environmental experimentation. I strongly recommend Environmental Chemistry: Fundamentals and its experimental accompaniment, Environmental Chemistry: Microscale Laboratory Experiments. Dr. Zvi Szafran Vice President for Academic Affairs and Professor of Chemistry Southern Polytechnic State University Our Earth is a remarkable reaction vessel. It is of paramount importance that students grow in their understanding and awareness of the astounding effects that chemistry and biochemistry have on our environment…and why they are so significant to our present and future hopes as a civilization. Environmental Chemistry: Microscale Laboratory Experiments, intended to complement lessons in the companion textbook Environmental Chemistry: Fundamentals, covers the chemical and biochemical processes that take place in air, water, soil, and living systems. The corresponding experiments range from the characterization of aqueous media to pollutant-treatment schemes. For increased safety, as well as for reduced costs, wastes, and environmental damage, the experiments are presented at the microscale level. Pre- and post-laboratory exercises and open-ended projects accompany each experiment, to develop problem-solving skills and initiative among students.
    Pages: Online-Ressource (XII, 238 pages)
    ISBN: 9780387494937
    Language: English
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  • 2
    Keywords: Atom ; Fulleren ; Fullerene ; Nanocar ; Nanomaterial ; Nanotube ; Transport ; carbon nanotubes ; electricity
    Description / Table of Contents: The 2007 ARW “Using Carbon Nanomaterials in Clean-Energy Hydrogen Systems” (UCNCEHS’2007) was held in September 22–28, 2007 in the remarkable town Sudak (Crimea, Ukraine) known for its heroic and unusual fate. In the tradition of the earlier conferences, UCNCEHS’2007 meeting served as an multidisciplinary forum for the presentation and discussion of the most recent research on transition to hydrogen-based energy systems, technologies for hydrogen production, storage, utilization, carbon nanomaterials processing and chemical behavior, energy and environmental problems. The aim of UCNCEHS’2007 was to provide the wide overview of the latest scientific results on basic research and technological applications of hydrogen interactions with carbon materials. The active representatives from research/academic organizations and governmental agencies could meet, discuss and present the most recent advances in hydrogen concepts, processes and systems, to evaluate current progress and to exchange academic information, to identify research needs and future development in this important area. This ARW should help further the progress of hydrogen-based science and promote the role of hydrogen and carbon nanomaterials in the energy field.
    ISBN: 9781402088988
    Language: English
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  • 3
    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
    Language: English
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  • 4
    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
    Language: English
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  • 5
    Keywords: Assessment ; Malaria ; Public Health ; Scale ; Weather ; climate change ; public health policy ; temperature
    Description / Table of Contents: Awareness that many key aspects of public health are strongly influenced by climate is growing dramatically, driven by new research and experience and fears of climate change and the research needed to underpin policy developments in area is growing rapidly . This awareness has yet to translate into a practical use of climate knowledge by health policy-makers. Evidence based policy and practice is the mantra of the health sector. If climate scientists are to contribute effectively to health policy at local and global scales then careful empirical studies must be undertaken – focused on the needs of the public health policy and decision-makers. Results presented at the Wengen conference make clear that the science and art of integrating climate knowledge into the control of climate sensitive diseases on a year to year time frame as well as careful assessments of the potential impacts of climate change on health outcomes over longer time frames is advancing rapidly on many fronts. This includes advances in the empirical understanding of mechanisms, methodologies for modeling future impacts, new partnership developments between the health and climate community along with access to relevant data resources, and education and training. In a rapidly evolving field this book provides a snapshot of these emerging themes.
    Pages: Online-Ressource (X, 232 pages)
    ISBN: 9781402068775
    Language: English
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  • 6
    Keywords: Biomass conversion ; Biotechnology ; Chemical Engineering ; Chemistry industry ; Industrial Chemistry ; Kent ; Riegel ; biochemical engineering
    Description / Table of Contents: Substantially revising and updating the classic reference in the field, this handbook offers a valuable overview and myriad details on current chemical processes, products, and practices. No other source offers as much data on the chemistry, engineering, economics, and infrastructure of the industry. The Handbook serves a spectrum of individuals, from those who are directly involved in the chemical industry to others in related industries and activities. It provides not only the underlying science and technology for important industry sectors, but also broad coverage of critical supporting topics. Industrial processes and products can be much enhanced through observing the tenets and applying the methodologies found in chapters on Green Engineering and Chemistry (specifically, biomass conversion), Practical Catalysis, and Environmental Measurements; as well as expanded treatment of Safety, chemistry plant security, and Emergency Preparedness. Understanding these factors allows them to be part of the total process and helps achieve optimum results in, for example, process development, review, and modification. Important topics in the energy field, namely nuclear, coal, natural gas, and petroleum, are covered in individual chapters. Other new chapters include energy conversion, energy storage, emerging nanoscience and technology. Updated sections include more material on biomass conversion, as well as three chapters covering biotechnology topics, namely, Industrial Biotechnology, Industrial Enzymes, and Industrial Production of Therapeutic Proteins.
    Pages: Online-Ressource (XIV, 1562 pages)
    ISBN: 9780387278438
    Language: English
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  • 7
    Pages: Online-Ressource (XII, 543 Seiten)
    Edition: 3. Aufl.
    ISBN: 9783540345251
    Language: German
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  • 8
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    Decision engineering  
    Keywords: Decision making, Mathematical models. ; Decision making, Methodology.
    Pages: ix, 172 p.
    ISBN: 1-85233-864-4
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  • 9
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    Keywords: Computer engineering. ; Computer security. ; Electronic data processing, Distributed processing.
    Pages: xx, 239 p.
    ISBN: 0-387-23917-0
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  • 10
    Keywords: Semantic Web, Congresses.
    Pages: x, 145 p.
    ISBN: 3-540-25982-1
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  • 11
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    Publication Date: 2020-02-12
    Keywords: 550 - Earth sciences
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    Publication Date: 2020-02-12
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    In:  International Association of Geodesy Symposia
    Publication Date: 2020-02-12
    Description: The lAG International Symposium on Gravity, Geoid, and Space Missions 2004 (GGSM2004) was lield in the beautiful city of Porto, Portugal, from 30 August to 3 September 2004. This symposium encompassed the themes of Commission 2 (Gravity Field) of the newly structured lAG, as well as interdisciplinary topics related to geoid and gravity modeling, with special attention given to the current and planned gravi- dedicated satellite missions. The symposium also followed in the tradition of mid-term meetings that were held between the quadrennial joint meetings of the International Geoid and Gravity Commissions. The previous mid-term meetings were the International Symposia on Gravity, Geoid, and Marine Geodesy (Tokyo, 1996), and Gravity, Geoid, and Geodynamics (Banff, 2000). GGSM2004 aimed to bring together scientists from different areas in the geosciences, working with gravity and geoid related problems, both from the theoretical and practical points of view. Topics of interest included the integration of heterogeneous data and contributions from satellite and airborne techniques to the study of the spatial and temporal variations of the gravity field. In addition to the special focus on the CHAMP, GRACE, and GOCE satellite missions, attention was also directed toward projects addressing topographic and ice field mapping using SAR, LIDAR, and laser altimetry, as well as missions and studies related to planetary geodesy.
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  • 22
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    Bulletin of mathematical biology 22 (1960), S. 323-349 
    ISSN: 1522-9602
    Source: Springer Online Journal Archives 1860-2000
    Topics: Biology , Mathematics
    Notes: Abstract Equations were derived showing the relationship between the membrane potential and the quantities which influence it under steady state conditions. Essentially, the membrane potential is caused by the valence and concentration of the non-permeating ions. The permeating ions can modify the membrane potential by altering the relative concentration of the non-permeating ions with respect to the concentration of the permeating ions. For muscle, the sodium cations act as the non-permeating ions in the extracellular environment by the maintenance of some type of active metabolic process and large anions act as the non-permeating ions in the intracellular environment. Both of these non-permeating ions contribute about equally to the maintenance of the resting membrane potential. When the active metabolic process for sodium extrusion breaks down or when acids are added, the membrane potential should decrease. Water should enter the cell when the sodium metabolic process is diminished; water should leave the cell when acids are added. When acid is added, it is expected that the cations potassium and sodium will leave the cell with little or no shift of the chloride ions.
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  • 23
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    Bulletin of mathematical biology 22 (1960), S. 351-364 
    ISSN: 1522-9602
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    Topics: Biology , Mathematics
    Notes: Abstract A purely information-theoretical approach to the problem of self-replication of elementary living units implies that pure chance is the determining factor in the formation of the first living unit. The probability of such a spontaneous formation can be calculated from the minimum amount of information which an organism must possess in order to replicate itself. An estimation of this amount of information is made here by two different methods. First by a “paper and pencil experiment” which indicates the minimum amount of information needed on a printed page in order that with given tools the page could be reproduced. Second—by an analytical consideration of some hypothetical molecular mechanisms. A general method for handling such problems is suggested. On the basis of estimated information contents it is shown that under most favorable conditions the probability of a spontaneous generation by pure chance during the lifetime of the earth is vanishingly small. It is concluded that dynamic factors, which may reduce tremendously the information content, must play a role in the genesis of life on earth.
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  • 24
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    Bulletin of mathematical biology 22 (1960), S. 365-370 
    ISSN: 1522-9602
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    Topics: Biology , Mathematics
    Notes: Abstract The binding energy of a very long molecular chain, composed of different classes of molecules, depends in general on the order of the molecules. It is shown that under very general conditions there exists for a givenbrutto chemical composition of a chain, a class of chains which is characterized by a total binding energy which is equal to the total binding energy of any other prescribed chain of different composition within the limits of unsharpness of the energy level. This establishes a criterion formapping of a class of configurations of long chain molecules on another class. To the extent that a mapping constitutes a generalized code those results contribute to the theory of molecular codes. Applying to our results the results of a previous paper (1959,Bull. Math. Biophysics,21, 309–326), we arrive at the conclusion that the self-replication of a living molecule may be the property not of a particular structure but of classes of structures.
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  • 25
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    Bulletin of mathematical biology 22 (1960), S. 371-389 
    ISSN: 1522-9602
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    Topics: Biology , Mathematics
    Notes: Abstract Making some plausible assumptions about the over-all mechanism of food catching and consumption by fishes and evaluating in the light of those assumptions some available experimental data, it is possible to calculate from those data the variation of several important factors with the concentration of food. The factors considered are: total rate of metabolism, total diurnal energy expenditure in the process of feeding, average number of hours per day during which the fish feeds, average length of path traveled by a fish per day, and the so-called “energetic coefficient of growth.” A possible relation with the work of N. Rashevsky (Bull. Math. Biophysics,20, 299–308, 1959) is discussed.
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  • 26
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    Bulletin of mathematical biology 22 (1960), S. 425-425 
    ISSN: 1522-9602
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  • 27
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    Bulletin of mathematical biology 22 (1960), S. 417-424 
    ISSN: 1522-9602
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    Topics: Biology , Mathematics
    Notes: Abstract The theory of measurement of flow and volume by indicator dilution techniques is given in conditions of time-variable flow rates. It is shown that the usual Hamilton (1932,Am. J. Physiol.,99, 534–551) methods can be misleading if the flow changes at a rate of close to that of the transport function.
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  • 28
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    Bulletin of mathematical biology 23 (1961), S. 305-318 
    ISSN: 1522-9602
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    Topics: Biology , Mathematics
    Notes: Abstract Freese’s Hypothesis states that a single specific alteration in the sequence of nucleotides of an information-bearing DNA molecule results in a specific mutational effect. Within the framework of the DNA-protein coding problem developed elsewhere, and assuming the quasi-ergodicity of the general coding process, it is shown that Freese’s Hypothesis allows us to derive expressions for the length of the smallest mutable DNA molecule and to obtain a bound for the maximal number of allelic molecules of fixed length. To illustrate these ideas, calculations are carried out on appropriate data from bacternophage and man, and the results are shown to differ by a factor of 10 (modulo the rather crude approximations used). It is further shown that, if ρ(N) and ϱ(N) are respectively the number of information-bearing words of lengthN in a given code and the number of words of lengthN, then the number lim ρ(N)/ϱ(N) depends sensitively on the parameter ∈ which specifiesN→∞ the given code. The implications of this result for the spontaneous aggregation of a sufficient number of information-bearing words to characterize an organism are discussed.
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  • 29
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    Bulletin of mathematical biology 23 (1961), S. 319-319 
    ISSN: 1522-9602
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  • 30
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    Bulletin of mathematical biology 23 (1961), S. 321-335 
    ISSN: 1522-9602
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    Topics: Biology , Mathematics
    Notes: Abstract As a “base line” of memorization performance, the behavior of a “perfect learner” is considered. He is characterized by a perfect memory and by the ability to choose the best search procedure in problems where the correct response from a given repertoire is to be found to each of several stimuli under the condition of “right” and “wroing” promptings by the experimenter. Expected learning curves are derived for the case of disjoint response repertoires associated with the stimuli under cyclic and random presentation of the stimuli and for the case of a single response repertoire (a one-to-one matching problem) under cyclic presentation.
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  • 31
    ISSN: 1522-9602
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    Notes: Abstract Detailed equations are given for the computation of aortic distensibility in the intact living human patient from measurements of systolic and diastolic arterial pressures, heart rate and cardiac output. From these equations, the aortic characteristics of a large series of normal men of different ages were computed. Comparing these results with measurements on excised aortas, a more pronounced trend toward increasing aortic stiffness with increasing age is evident in living than in dead aortas. Nor-epinephrine and exercise apparently cause the living aortas to constrict but to become more distensible. The same change occurs after 30 minutes of high spinal anesthesia. The ganglionic blocking agents hexamethonium, pentamethonium, and tetraethylammonium usually cause the living aorta to become stiffer, presumably due to dilatation. The aortas of patients with pulmonary disease usually react in different fashion to exercise or tetraethylammonium. The increased aortic distensibility that occurs with the hypertension induced by nor-epinephrine or exercise acts as a compensatory mechanism by decreasing systolic pressure.
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  • 32
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    Bulletin of mathematical biology 23 (1961), S. 355-376 
    ISSN: 1522-9602
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    Notes: Abstract Dimensional analysis is discussed from the viewpoint of its basic group properties and shown to be an algebraic Abelian group that is useful for analysis of physical measurements. The application of the method to various types of equations and the formulation of previously unclassified dimensions are discussed. Functional dimensional analysis is applied to the problems of cell size and biomass proliferation; future applications are also noted. A number of dimensionless terms have been formulated for cellular physiochemical phenomena. They apparently represent the first systematic study of biological dimensionless numbers recorded in the literature. A dimensionless proliferation law is suggested. A brief analysis of the physical dimensionality associated with information measures is carried out. Entropy and “information” are shown to be completely different in their dimensional meaning; other informational measures of possible interest in biology are proposed. The dimensional coding and computor analysis of biomathematical equations is suggested.
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    Bulletin of mathematical biology 23 (1961), S. 377-391 
    ISSN: 1522-9602
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    Notes: Abstract Expenditure of energy under several simultaneous forms (mechanical, chemical, etc.) is associated with all muscular activity. The energy is directly related to what is commonly called exertion or effort. This paper defines “muscular effort” quantitatively in terms of some of the elements of the dynamics of the human (and animal) body. It postulates that in all likelihood the individual will, consciously or otherwise, determine his motion (or his posture, if at rest) in such a manner as to reduce his total muscular effort to a minimum consistent with imposed conditions, or “constraints”. The principle, formulated in mathematical terms, is sufficient to ascribe to the moments at all body joints—a matter generally of free choice on the part of the individual—their most likely magnitudes. It therefore renders the equations of human (and animal) motion determinate within this context. The paper also describes briefly an iteration method for the solution of these equations, once they have been made determinate. A simple illustrative application of the principle is included.
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    Bulletin of mathematical biology 23 (1961), S. 393-403 
    ISSN: 1522-9602
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    Notes: Abstract It is pointed out that two fundamentally different views of primary genetic processes occur in the literature which are frequently confused. The first is a true communication-theoretic view, which regards the genetic apparatus as containing a real information-source and a transducer which converts that information to useful form. The second view is generally expressed as a template scheme based on the Watson-Crick model; it is shown that in this model there is actually no such thing as genetic information in a communication-theoretic sense. Both views are then discussed on the basis of microphysical principles developed in previous work of the author (Bull. Math. Biophysics,22, 227–255, 1960) in an attempt to find which approach is in closer accord with the biological facts. It is shown that, if the communication-theoretic view is correct, then the information-bearing object must act as a “catalyst,” but it is pointed out that the type of catalysis involved must be of a fundamentally different nature than that occurring in familiar enzyme-catalyzed reactions. On the basis of general considerations of irreversible changes in microphysical measuring systems, it is shown that any type of template must suffer a gradual and irreversible denaturation, which seems to make it unlikely that a template could play a primary role in fundamental genetic processes.
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    Bulletin of mathematical biology 23 (1961), S. 405-411 
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    Notes: Abstract The theory developed in previous papers and based on distribution curves of definite form is generalized to any form of unimodel distributions. The time course of the change from one behavior to another is discussed and a general theorem about the time course is established.
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    Bulletin of mathematical biology 23 (1961), S. 417-417 
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    Bulletin of mathematical biology 25 (1963), S. 471-471 
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    Bulletin of mathematical biology 25 (1963), S. 421-469 
    ISSN: 1522-9602
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    Notes: Résumé Nous appliquons le modèle de neurone introduit dans un article antérieur à l’étude d’une microstructure isotrope. La stabilité de cette microstructure implique l’existence d’une régulation d’activité que le principe de construction adéquate permet de définir entièrement. Nous aboutissons à une conception stratifiée du cerveau. Un réseau de neurones spécialisés exercerait, grâce à certains médiateurs chimiques, une action diffuse qui modulerait les propriétés du réseau localisé classique. Les lois de Pavlov peuvent être retrouvées à partir des propriétés de la microstructure et de celles de la régulation. La microstructure isotrope peut également fonctionner comme analyseur. Un certain nombre de temps caractéristiques apparaissent alors, qui semblent jouer un grand rôle en psychologie.
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    Bulletin of mathematical biology 26 (1964), S. 1-7 
    ISSN: 1522-9602
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    Notes: Abstract In the arteries, blood flow and blood pressure are pulsatile in nature (Roston, 1962a; Roston 1962b). The patterns of blood movement and mural distension in the arteries are important because they may be associated with life-threatening degenerative changes in the arterial walls. As the vascular channels narrow, the pulsation decreases. At the level of the capillaries, almost no pulsation exists (Best and Taylor, 1961). The tissues are affected by the direct flow in the capillaries and not by the pulsation in the arteries. Thus, such quantities as pulse pressure, systolic pressure, and diastolic pressure which characterize blood movement in the arteries are not important as far as the tissues are concerned. Rather, the average pressure and flow in the capillaries are the quantities significant for tissue blood flow. The present study analyzes the local blood circulation in a typical tissue. Logical extension of this analysis results in insights into the physiological behavior of the circulation which integrate a considerable body of experimental data.
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    Bulletin of mathematical biology 46 (1984), S. 967-969 
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    Notes: Abstract It is observed that a dynamical continuity equation for biomass distribution yields the asymptotic steady-state exponential dependencen=A exp( $$ - m/\bar m$$ ) exhibited by certain fishery data, wherem is the biomass of an individual,n is the number of individuals per unit biomass interval, andA, $$\bar m$$ are positive constants. This dynamical approach to biomass distribution is an alternative to the global maximization principle proposed recently by Lurié and Wagensberg.
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    Bulletin of mathematical biology 46 (1984), S. 971-972 
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    Bulletin of mathematical biology 46 (1984), S. 973-974 
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    Bulletin of mathematical biology 28 (1966), S. 333-345 
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    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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    Bulletin of mathematical biology 28 (1966), S. 355-362 
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    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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    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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    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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    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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    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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    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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    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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    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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    Bulletin of mathematical biology 42 (1980), S. 131-135 
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    Notes: Abstract The theory of complementary variational principles is used to obtain maximum and minimum principles for diffusion problems with Michaelis-Menten kinetics. In an illustrative calculation we obtain an extremely accurate variational solution in good agreement with the numerical solution of McElwain (1978).
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    Bulletin of mathematical biology 42 (1980), S. 137-141 
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    Bulletin of mathematical biology 42 (1980), S. 181-189 
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    Notes: Abstract Necessary and sufficient conditions for primitivity of a product of two Leslie matrices are given. Such a product could be used in modeling the growth of a population governed alternately by two different sets of fertility and survival parameters.
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    Bulletin of mathematical biology 42 (1980), S. 173-180 
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    Notes: Abstract Zadeh's transfer function method for linear time-variable systems is used to apply frequency-domain analysis to a periodically time-varying elastance model of the left ventricle. Left ventricular pressure computed from the system function of the time-varying elastance and the phasors of aortic flow shows a typical waveform of the measured ventricular pressure.
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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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    Bulletin of mathematical biology 28 (1966), S. 483-483 
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    Bulletin of mathematical biology 28 (1966), S. 483-483 
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    Bulletin of mathematical biology 28 (1966), S. 485-485 
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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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    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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    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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    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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    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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    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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    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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    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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    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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    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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    Bulletin of mathematical biology 28 (1966), S. 663-663 
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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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    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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    Bulletin of mathematical biology 28 (1966), S. 663-663 
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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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    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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    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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    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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    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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    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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    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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    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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    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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    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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    Bulletin of mathematical biology 29 (1967), S. 403-404 
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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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    Bulletin of mathematical biology 42 (1980), S. 901-901 
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    Bulletin of mathematical biology 29 (1967), S. 407-407 
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    Bulletin of mathematical biology 29 (1967), S. 409-409 
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    Bulletin of mathematical biology 43 (1981), S. 1-19 
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    Notes: Abstract By studying the behavior of various tracer species in the lungs, one can assess many important characteristics which distinguish normal and abnormal function. Quantitative evaluation of function depends on the use of an appropriate model in conjunction with experimental data. A multi-compartment model is derived from mass balances to describe dynamic as well as (breath-averaged) steady-state transport processes between the environment and pulmonary capillary blood. The breathing cycle is divided into three time periods (inspiration, expiration, and pause) so that the model equations are discrete in time. No other model of tracer species transport in the lungs deals simultaneously with species dynamics, variable breathing pattern, distribution inhomogeneities, and non-equilibrium between alveolar gas and capillary blood. Models currently in the literature are shown to be special cases of the model presented here.
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    Bulletin of mathematical biology 43 (1981), S. 47-58 
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    Notes: Abstract Local stability seems to imply global stability for population models. To investigate this claim, we formally define apopulation model. This definition seems to include the one-dimensional discrete models now in use. We derive a necessary and sufficient condition for the global stability of our defined class of models. We derive an easily testable sufficient condition for local stability to imply global stability. We also show that if a discrete model is majorized by one of these stable population models, then the discrete model is globally stable. We demonstrate the utility of these theorems by using them to prove that the regions of local and global stability coincide for six models from the literature. We close by arguing that these theorems give a method for demonstrating global stability that is simpler and easier to apply than the usual method of Liapunov functions.
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    Bulletin of mathematical biology 43 (1981), S. 125-140 
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    Notes: Abstract The asymptotic behaviour of a logistic equation with diffusion on a bounded region and a diffusionally coupled delay is investigated. An equivelent parabolic system is derived for certain types of delays. Using a Layapunov functional, sufficient conditions for the global asymptotic stability of the constant steady state are obtained. When the global stability is lost, using Hopf's bifurcation theory, existence of travelling waves is shown for ring-like and periodic one dimensional habitats.
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    Bulletin of mathematical biology 43 (1981), S. 141-149 
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    Notes: Abstract It was hypothesized in an earlier work that sensory perception can occur only when the perceiving system is uncertain about the nature of the event being perceived. In the absence of any uncertainty, perception will not take place. The response of the sensory afferent neuron (impulse transmission rate) was calculated using Shannon's measure of uncertainty or entropy. It will now be shown that when the event being perceived is the position and momentum of a particle, Shannon's measure of uncertainty leads to the Heisenberg Uncertainty relationship.
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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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    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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    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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    Bulletin of mathematical biology 43 (1981), S. 239-244 
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    Notes: Abstract It is not unusual for several classifications to be given for the same collection of objects. We present a method, called majority rule, which can be used to define a consensus of these classifications. We also discuss some mathematical properties of this consensus tree.
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    Bulletin of mathematical biology 43 (1981), S. 259-270 
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    Notes: Abstract The dependence of the spatial concentration profiles of morphogens on a characteristic dimension is obtained by continuation techniques for Gierer and Meinhardt's activator-inhibitor model of morphogenesis. The study of the behaviour of the system during growth, where the linear and exponential increase of the characteristic dimension is considered, revealed that more complex patterns of morphogen spatial concentrations appear regularly in a reproducible way.
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    Bulletin of mathematical biology 43 (1981), S. 271-278 
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    Notes: Abstract Computer models have been used by various authors to simulate both the growth of normal cellular tissue and the development of cancerous cells within normal tissue. As these models were the result of considerable idealization, the purpose of the present paper is to propose a model in which the degree of simplification is relaxed: the features of simultaneous growth, and cell growth whose rate depends on the free absorbing periphery of the cell are introduced. Simulation experiments have been conducted using the model, and the results are presented.
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    Bulletin of mathematical biology 43 (1981), S. 341-346 
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    Notes: Abstract The theory of complementary variational principles is used to obtain maximum and minimum principles for a nonlinear model of heat conduction in the human head. Accurate variational solutions are obtained in illustrative calculations. The effect of nonlinearity is seen to be significant from a comparison with the linearized model.
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    Bulletin of mathematical biology 43 (1981), S. 279-325 
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    Notes: Abstract A model for the nerve impulse due to Zeeman (1972) and based on catastrophe theory is compared with alternative models and criticisms of Zeeman's model by Sussmann and Zahler (1977, 1978) are assessed. The criticisms of Zeeman's motivation for his model are found to carry some weight. Sussmann and Zahler (1977, 1978) list numerous features of Zeeman's model which, they state, are not in agreement with experiment. These statements as they stand are largely erroneous, and the model still remains to be tested by a critical series of experiments. However, a detailed analysis reveals defects in Zeeman's model, not among those claimed by Sussmann and Zahler, showing that the explicit equations of the model cannot be correct. The possibility of a modified approach along similar lines and its ultimate adoption remains open.
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