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  • Springer  (487,036)
  • American Geophysical Union  (37,911)
  • 2020-2023  (428)
  • 2005-2009  (253,284)
  • 1975-1979  (220,344)
  • 1950-1954  (35,379)
  • 1940-1944  (15,512)
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  • 1
    Pages: Online-Ressource (XII, 543 Seiten)
    Edition: 3. Aufl.
    ISBN: 9783540345251
    Language: German
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  • 2
    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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  • 3
    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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  • 4
    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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  • 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
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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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  • 7
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    Publication Date: 2020-02-12
    Keywords: 550 - Earth sciences
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  • 8
    Publication Date: 2020-02-12
    Keywords: 550 - Earth sciences
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  • 9
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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.
    Language: English
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  • 10
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  • 11
    Publication Date: 2020-02-12
    Keywords: 550 - Earth sciences
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  • 12
    Publication Date: 2020-02-12
    Keywords: 550 - Earth sciences
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  • 13
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  • 14
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  • 15
    Publication Date: 2022-01-18
    Description: Gashydrate, auch „brennendes Eis“ genannt, sind faszinierende, eisähnliche Feststoffe, die aus Wasser- und Gasmolekülen aufgebaut sind und weltweit an allen aktiven und passiven Kontinentalhängen und in Permafrostgebieten vorkommen. Doch ihr unauffälliges Erscheinungsbild täuscht: Die Einschlussverbindungen können beachtliche Mengen Methangas enthalten. Daher besteht einerseits die Hoffnung auf einen möglichen neuen Energieträger und andererseits die Sorge um eine nicht zu unterschätzende Quelle an klimaschädlichem Methangas. Gashydrate, hat die neueste Forschung gezeigt, bieten zudem in vielen Bereichen industrieller Anwendung eine durchaus vielversprechende Alternative zu konventionellen Verfahren. Das vorliegende Buch gibt eine Einführung in die physikalisch-chemischen Grundlagen der Hydratbildung und die Strukturen der Gashydratphasen. Basierend auf diesem grundlegenden Verständnis erklärt es die natürlichen Gashydratvorkommen und zeichnet mögliche Methoden des Abbaus und der Gewinnung von Methangas auf. Es beleuchtet Risiken, die von den Gashydratvorkommen in der Natur ausgehen könnten, und führt in die Möglichkeiten der Nutzung dieser Einschlussverbindungen in verschiedenen industriellen Anwendungsbereichen wie z.B. der Aufbereitung von Abwässern oder der Speicherung von Gasen ein. Zielgruppe dieser kompakten Einführung in die verschiedenen Aspekte der Gashydratforschung sind Studierende der Chemie und Geowissenschaften, Ingenieure, Techniker oder auch Wissenschaftler.
    Language: German
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  • 16
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  • 17
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    Bulletin of mathematical biology 15 (1953), S. 311-338 
    ISSN: 1522-9602
    Source: Springer Online Journal Archives 1860-2000
    Topics: Biology , Mathematics
    Notes: Abstract The partial differential equation of the random walk problem with persistence of direction and external bias is derived. By persistence of direction or internal bias we mean that the probability a particle will travel in a given direction need not be the same for all directions, but depends solely upon the particle's previous direction of motion. The external bias arises from an anisotropy of the medium or an external force on the particle. The problem is treated by considering that the net displacement of a particle arises from two factors, namely, that neither the probability of the particle traveling in any direction after turning nor the distance the particle travels in a given direction need be the same for all directions. A modified Fokker-Planck equation is first obtained using the assumptions that the particles have a distribution of travel times and speeds and that the average time of travel between turns need not be zero. The fional equation incopporating the assumption of a persistence of direction and an external bias is then derived. Applications to the study of diffusion and to long-chain polymers are then made.
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  • 18
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    Bulletin of mathematical biology 15 (1953), S. 383-383 
    ISSN: 1522-9602
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  • 19
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    Bulletin of mathematical biology 15 (1953), S. 385-385 
    ISSN: 1522-9602
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  • 20
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    Bulletin of mathematical biology 15 (1953), S. 367-381 
    ISSN: 1522-9602
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    Topics: Biology , Mathematics
    Notes: Abstract The transmission of some information or behavior pattern is treated as a flow of “particles” which execute random motions over a population of individuals and which may multiply or disappear. Equations are derived for the number density of these “particles” and from this is calculated the number of individuals through which the “particles” have passed. The results are applied to a number of situations such as 1) uniform spatial distribution with multiplication factor decreasing with time because of loss of interest or confusion of the information, 2) multiplication factor constant but the rate of spreal decreasing with multiple hearings, 3) one-dimensional region with a small starting region with or without an absorbing barrier 4) two-dimensional region with absorbing barrier, 5) continous sources of information within a small region in one dimension, 6) uniform spatial distribution in which individuals do not respond to more than one hearing.
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  • 21
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    Bulletin of mathematical biology 15 (1953), S. 387-394 
    ISSN: 1522-9602
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    Topics: Biology , Mathematics
    Notes: Abstract A situation is considered in which a fluid containing a substance flows through a vessel at a constant rate, the substance being permeable to the vessel wall. In the region outside the vessel there is supposed to be rapid mixing in the direction perpendicular to the axis of the vessel but no mixing longitudinally. The solution for the spatial distribution at any time is given for the case of an arbitrary initial distribution along the vessel length in the absence of an input. The solution is also given for the case of a single impulsive input, the concentration being initially zero everywhere.
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  • 22
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    Bulletin of mathematical biology 15 (1953), S. 431-476 
    ISSN: 1522-9602
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    Topics: Biology , Mathematics
    Notes: Abstract Organisms orient themselves to a stimulus by two general methods. One method is by directed orientation (taxis); the other is by undirected locomotory reaction (kinesis). An equation, and the methods for finding the necessary parameters of this equation, is derived for the distribution of organisms within a container, with the following limitations: (1) the organisms have no accommodation, (2) they are always active, and (3) the stimulus changes slowly with position. Necessary modifications of the equation are then derived, so that the last two limitations may be eliminated. The equation cannot be solved excatly because of its complexity; hence an approximation method must be used. This method is discussed, an approximate solution is found, and a time constant for equilibrium to be established is derived. Applications tovarious experiments in the literature are then made with fairly satisfactory results. A new interpretation of the theory of klino-kinesis with accommodation is found upon application of the equations developed to experimental work. Further limitations and uses of these equations are then discussed.
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  • 23
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    Bulletin of mathematical biology 15 (1953), S. 501-507 
    ISSN: 1522-9602
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    Topics: Biology , Mathematics
    Notes: Abstract Certain parameters are defined which roughly characterize the internal structure of networks. A given network structure uniquely determines the values of the parameters, but the reverse is not true. The parameters therefore define certain classes of networks. One of the parameters, thedispersion D(S) gives an indication of the “compactness” of the internal structure. Addition theorems and inequalities are derived relating the dispersions of sub-systems to the dispersion of the complete structure.
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  • 24
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    Bulletin of mathematical biology 15 (1953), S. 489-500 
    ISSN: 1522-9602
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    Notes: Abstract A mathematical theory is developed which permits the determination of certain parameters of an inhomogenous tissue, such as a nerve trunk without its epineurium. The parameters are the permeability coefficients for entrance into an exit of a substance from the nerve fibers, and the diffusion coefficient of the interstitial material. The experimental data required are the dimensions of the cross-section, the average diameter of the fibers, and the ratio of the cross-sectional are of the fibers to the total cross-section, as well as the time course of the decrease of the fraction of the substance left in the nerve trunk, when the trunk is immersed in a bathing solution containing none of it.
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  • 25
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    Bulletin of mathematical biology 15 (1953), S. 509-522 
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    Notes: Abstract A model based on enzyme localization is developed which gives rise to an apparent active transport of a metabolite into or out of cells. The model is applied to three simple situations, using Fick's equation and the Rashevsky approximation. It is shown that the apparent efficiency can be made as large as desired if, for constant reaction, the outer cell region is made sufficiently small, or, for autocatalytic reaction, if the metabolite concentration in the outer region is sufficiently small. The physical limitations imposed by this mechanism are developed for all three situations.
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  • 26
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    Bulletin of mathematical biology 15 (1953), S. 523-533 
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    Notes: Abstract A previously derived iteration formula for a random net was applied to some data on the spread of information through a population. It was found that if the axon density (the only free parameter in the formula) is determined by the first pair of experimental values, the predicted spread is much more rapid than the observed one. If the successive values of the “apparent axon density” are calculated from the successive experimental values, it is noticed that this quantity at first suffers a sharp drop from an initial high value to its lowest value and then gradually “recovers”. An attempt is made to account for this behavior of the apparent axon density in terms of the “assumption of transitivity”, based on a certain socio-structural bias, namely, that the likely contacts of two individuals who themselves have been in contact are expected to be strongly overlapping. The assumption of transitivity leads to a drop in the apparent axon density from an arbitrary initial value to the vicinity of unity (if the actual axon density is not too small). However, the “recovery” is not accounted for, and thus the predicted spread turns out to beslower than the observed.
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  • 27
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    Bulletin of mathematical biology 15 (1953), S. 535-546 
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    Notes: Abstract The assumption of transitivity treated in part I is modified in various ways to describe an information-diffusion process, in which a certain amount of randomness of contact does occur. In one model a parameter is introduced which is indicative of a tendency to go beyond one's immediate vicinity to spread the information as the vicinity becomes saturated with knowers. In another model the randomness appears in the assumption that new knowers are uniformly distributed among the knowers. Two of the equations thus derived, each with two free parameters are in good agreement with experimental results.
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  • 28
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    Bulletin of mathematical biology 41 (1979), S. 893-898 
    ISSN: 1522-9602
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    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.
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  • 29
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    Bulletin of mathematical biology 37 (1975), S. 37-49 
    ISSN: 1522-9602
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    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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    Bulletin of mathematical biology 37 (1975), S. 59-69 
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    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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    ISSN: 1522-9602
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    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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    Bulletin of mathematical biology 37 (1975), S. 71-78 
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    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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    Bulletin of mathematical biology 37 (1975), S. 127-138 
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    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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    Bulletin of mathematical biology 37 (1975), S. 565-572 
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    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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    Bulletin of mathematical biology 37 (1975), S. 555-564 
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    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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    Bulletin of mathematical biology 37 (1975), S. 573-588 
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    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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    Bulletin of mathematical biology 37 (1975), S. 219-219 
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    Bulletin of mathematical biology 37 (1975), S. 291-299 
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    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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    Bulletin of mathematical biology 37 (1975), S. 367-387 
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    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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    Bulletin of mathematical biology 37 (1975), S. 419-425 
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    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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    Bulletin of mathematical biology 37 (1975), S. 459-470 
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    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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    Bulletin of mathematical biology 37 (1975), S. 489-504 
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    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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    Bulletin of mathematical biology 37 (1975), S. 521-553 
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    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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    Bulletin of mathematical biology 37 (1975), S. 659-673 
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    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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    Bulletin of mathematical biology 38 (1976), S. 205-207 
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    Bulletin of mathematical biology 38 (1976), S. 161-192 
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    Notes: Abstract In order to evaluate the effect of anatomic asymmetries on the gas concentration distribution in the pulmonary airways, a Monte Carlo simulation of combined bulk flow and molecular diffusion was carried out in a realistic distal airway model (Parkeret al., 1971). This airway model, composed of branches distal to the 0.5-ram diameter airways, contained an upper symmetric segment consisting of four generations of conducting airways and a lower asymmetric segment of alveolar ducts and sacs arranged in five transport paths of varying lengths. In accounting for the volume increases of these ducts and sacs occurring during normal respiration, uniform alveolar filling rates and a fixed length-to-diameter ratio of all airways were assumed. For a pulse injection of inert tracer gas, the simulation was employed to determine the longitudinal concentration profiles in the conducting airways. In the alveolated airways, not only were the longitudinal profiles determined along each path, but radial transport from the core to the periphery of the airways was considered. The results of the simulations indicate that geometric asymmetries alone contribute substantially to regional concentration variations in the distal airways. For example, when a gas bolus is injected at mid*inspiration, there are concentration differences as great as 40% between two points along different transport paths located equi-distant from the proximal end of the model. As viewed from the terminal end of the model (acinus), average concentration differences as large as 6-to-1 exist between the longest and shortest transport paths respectively for gas boli introduced near the end of inspiration. The results further indicate because of large radial diffusion rates, no significant concentration differences exist between the periphery a-ld the central core of alveolated airways. Simulation of the expired concentration profiles indicate that boll injected very late during inspiration exhibit a sloping tail, unlike the earlier injected boll whose tails are virtually horizontal. Through the use of superposition teehniqnes, it was found that these sloping tails correspond to an alveolar slope of 1.5 vol% between 750 and 1250 ml expired for a continuous washing of tracer. This result is in disagreement with other transport analyses which did not directly account for the effect of geometric asymmetries.
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    Notes: Abstract Assuming a spherical geometry for the left ventricle, passive elastic stiffness-stress relations have been obtained on the basis of linear elasticity theory and large deformation theory. Employing pressure-volume aata taken from rat hearts of various age groups, it is shown that young rat heart muscle (1 month) is stiffer than either adult (7 months) or old rat heart muscle (17 months). Although the qualitative results are similar for both elasticity theories, the large deformation theory gave results in closer agreement with those obtained from papillary muscle studies. These results imply that stiffness of muscleper se can be assessed from left ventricular pressure-volume data.
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    Bulletin of mathematical biology 38 (1976), S. 277-293 
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    Notes: Abstract Deliberate evaluation of the quantum theory of nerve excitation is made by comparing it with Hill's theory in fitting the experimental data on threshold-frequency relation, optimum frequency (v0) for nerve excitation and strength-duration relation. Decrease of v0 and increase of all the time constants (Hill's λ andk, Wei'sT 2 and spike durationw) with decreasing temperature are interpreted on the basis of the dipole relaxation timeT 2 but inexplicable from Hill's theory or any other existing theory. The closeness ofk,T 2 andw values is explained. A variety of experimental results obtained by others is discussed. Finally, a comparison is made between the Hodgkin-Huxley equations and the quantum theory. Most of the facts (electrical and non-electrical) tend to support the thesis that nerve excitation is a macroscopic expression of quantum transitions of dipoles between energy states.
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    Bulletin of mathematical biology 38 (1976), S. 317-319 
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    Notes: Abstract In the periodic Leslie model the asymptotic period of total population is a divisor of the asymptotic period of the population vector. Under reasonable circumstances these periods are identical.
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    Bulletin of mathematical biology 38 (1976), S. 305-315 
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    Notes: Abstract A number of biological branching systems, such as the bronchial and pulmonary arterial trees, are being investigated in an ongoing study in order to define their physiological properties. The technique involves the description of branching trees by the use of hierarchical systems of ordering, especially those described by Horsfield and by Strahler. During this work some mathematical properties of branching trees were demonstrated and these are described in this paper.
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    Bulletin of mathematical biology 38 (1976), S. 323-324 
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    Bulletin of mathematical biology 38 (1976), S. 209-217 
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    Bulletin of mathematical biology 38 (1976), S. 387-400 
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    Notes: Abstract Luteinizing hormone (LH) is secreted continuously from the anterior pituitary gland. The concentration in the blood of this gonadotropic hormone plays a regulatory role in the development of puberty in both sexes, in the induction of ovulation in females, and in the production of testosterone in males. The secretion of LH is in turn controlled by luteinizing hormone releasing hormone (LHRH) secreted by the hypothalamus. LH and LHRH are removed from the blood by degradation and excretion. This hormonal system is modelled by a system of ordinary differential equations based upon specific physiological and biochemical assumptions current among experimentalists in this field. The one exception is the assumption that LHRH may bind reversibly to a serum protein; an analysis of the data shows that this or a similar mechanism is a crucial specification. Data on the serum levels of LH and LHRH in two human subjects were fitted using the model. The data consist of the transients and subsequent decays created by a bolus intravenous injection of LHRH.
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    Bulletin of mathematical biology 38 (1976), S. 401-413 
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    Notes: Abstract A thick-wall incompressible, elastic sphere was used as a model for the diastolic rat left ventricle. A model for myocardial nonhomogeneity was derived assuming that fiber (circumferential) stress was independent of position in the ventricular wall. The theoretical implications of the resulting constitutive relations together with the spherical model were analyzed in the context of large deformation elasticity theory. It was found that muscle stiffness at a given level of uniaxial stress increased monotonically from the endocardium to the epicardium. In addition, fiber stress was found to be essentially a linear function of transmural pressure above a pressure of 6 g/cm2. It was also shown theoretically that neglecting the nonhomogeneity of the myocardium resulted in a state of stress which differed significantly from that predicted by the nonhomogeneous model. For example, at a transmural pressure of 14 g/cm2, fiber stress in the nonhomogenous model was equal to 17 g/cm2 while fiber stress in the homogeneous model varied between 100 g/cm2 at the endocardial surface and 2 g/cm2 at the epicardial surface. The change in muscle stiffness with position which characterized the nonhomogeneous model also tended to linearize the highly curvilinear radial stress distribution predicted by the homogeneous model at a given transmural pressure.
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    Bulletin of mathematical biology 38 (1976), S. 435-444 
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    Notes: Abstract The phenomenon of axonal transport has been well documented (Ochs, 971; Lasek, 1970; and Grafstein, 1967). In a previous paper, we showed how diffusion alone could not account for this process. In this report we show that convection or convection with diffusion can account for the observed build-up of material. By including a first-order catabolic sequestration term, we are able to offer an understanding of the several apparent rates of transport with the same underlying velocity and variable sequestration.
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    Bulletin of mathematical biology 38 (1976), S. 459-465 
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    Notes: Abstract It is known that the Lotka-Volterra coupled nonlinear differential equations for a two-species prey-predator ecosystem possess a periodic solution, although its exact form is not yet obtained analytically. The conventional linearization approximation for solving these nonlinear equations leads to a harmonic oscillator whose frequency depends only on the intraspecific coefficients. We propose here a prescription for obtaining nonlinear correction to the linear frequency by using the Hamilton-Jacobi canonical formalism of classical mechanics. It is found that the first-order correction, which also involves interspecific parameters, exhibits the basic qualitative features of the nonlinearity.
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    Bulletin of mathematical biology 38 (1976), S. 467-478 
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    Notes: Abstract Environmental safety testing typically requires procedures for extrapolating from the relatively high experimental to the very low use doses of potentially harmful substances. In the present paper, a stochastic mammillary compartmental model for environmental safety testing is proposed and extrapolation procedures based on its dose-response relationship are developed. The proposed model is a direct generalization of one of the basic safety models, the one-hit model, in that a harmful reaction is assumed to occur if at any time any of the peripheral compartments attains a specified threshold of particles. Consideration of a closed model yields an upper bound on the probability of attaining a certain threshold level, thus providing a conservative procedure for extrapolating to a low dose, while a lower bound obtained from a related open model provides a useful monitoring device as to the sharpness of the upper, bound. The extrapolation procedure is illustrated with simulated data and approximations for initial values are developed.
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    Bulletin of mathematical biology 38 (1976), S. 505-516 
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    Notes: Abstract By using chromosome images as a framework, algorithms for finding most dissimilar images are presented and illustrated by examples. In terms of angles, a chromosome image consists of two exterior biangles and two interior biangles. Biangles are defined and classified into 180° biangles, 〉180° biangles and 〈180° biangles. The dissimilarity of biangles and its geometric interpretation together with various properties of biangles are also presented. The results may have useful applications in pattern recognition, scene analysis, information storage and retrieval, artificial intelligence and fuzzy set theory.
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    Bulletin of mathematical biology 38 (1976), S. 517-526 
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    Notes: Abstract The Volterra equations which represent competitions between two species are utilized to examine the phenomenon of boundary formation between two species of plants. The set of stable stationary points for these equations is determined and is illustrated in a product space of parameters and dynamical variables. The stages of boundary appearance and succession are visualized by considering slow changes of the parameters as functions of time and space.
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    Bulletin of mathematical biology 40 (1978), S. 45-58 
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    Notes: Abstract For certain environments, the Darwinian model allows unique prediction of a function that any surviving system adapted to such an environment has to perform. This is the case for those environments that determine a “survival functional” of position in space-time of known shape. Purely temporal survival functionals can be distinguished from spatial and mixed ones. In each case, there exists an optimum path in combined physical and (reduced) metabolic space. Dependent on the admissible error, approximate solutions of different complexity are sufficient. All solutions possess an afferent, a central, and an efferent part. Within this general frame, specific, “probably simplest”, solutions are proposed for adaptive chemotaxis, insect locomotion, lower vertebrates locomotion, higher vertebrates locomotion, chronobiological systems, and immune systems, respectively—or rather, for the underlying functionals.
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    Bulletin of mathematical biology 40 (1978), S. 59-77 
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    Notes: Abstract Mathematical models afford a procedure of unifying concepts and hypotheses by expressing quantitative relationships between observables. The model presented indicates the roles of both insulin and glucagon as regulators of blood glucose, albeit in different ranges of the blood glucose concentrations. Insulin secretion is induced during hyperglycemia, while glucagon secretion results during hypoglycemia. These are demonstrated by simulations of a mathematical model conformed to data from the oral glucose tolerance test and the insulin infusion test in normal control subjects and stable and unstable diabetic patients. The model studies suggest the parameters could prove of value in quantifying the diabetic condition by indicating the degree of instability.
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    Bulletin of mathematical biology 40 (1978), S. 123-131 
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    Notes: Abstract A model for the dynamics of a single-species population whose birth rate depends on densities of previous generations is introduced. A difference equation formulation is proposed and the solutions classified for the various parameter values. Data from an experimental population of mice growing in limited space is cited and compared with the model predictions.
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    Bulletin of mathematical biology 40 (1978), S. 161-182 
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    Notes: Abstract All soft tissues are modeled as either one-dimensionalstrings, two-dimensionalmembranes, or three-dimensionalsolids. Attention is restricted to tissues in which one of the principal stress components is large and positive in comparison with the other negligible components. Results indicate the following: (1) If a deformed string isconstrained to lie on a surface and is free of tangential pressure, the tension is carried by rays which are geodesics of the surface. If a string or membrane isfree to deform in space without normal pressure, the tension rays are straight lines. If a membrane deforms without tangential surface loads, the tension rays are always geodesics on the deformed surface. If a solid deforms without body forces, the tension rays are straight lines. (2) The stress in a string is a constant if the string is free of tangential pressure and has constant cross-sectional area. The stress in flat tension fields free of tangential surface loads decays inversely with distance along a tension ray from the edge of regression. The stress in a spherically symmetric tension field free of body forces decays inversely with the square of the distance from the center of the sphere. (3) Stress singularities can occur in soft tissues, such as at the corners of a closed rectangular hole in a flat membrane strip. (4) The tension rays in the torsion of soft annular membranes are more steeply inclined from the radial direction than the tension rays for hard metals equally displaced.
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    The Geneva risk and insurance review 10 (1978), S. 50-66 
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    Topics: Economics
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    The Geneva risk and insurance review 10 (1978), S. 44-49 
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    Notes: Conclusion For all these reasons, the rediscovery of the equivalence theorem, first stated by David Ricardo in 1817, must be rejected as an adequate basis for policy, just as Ricardo had denied its applicability to the real world. Correspondingly, the concern with the adverse consequences of unfunded social insurance wealth for the supply of national saving, capital intensity, and living standards remains well founded. p ]If, as a practical matter, public pension and social security programs will never be funded actuarially in the United States and most other postindustrial countries, then government-supervised substitution of private for public retirement plans is the only way to achieve at least partial funding. If such substitution follows the British model of allowing employers to contract out of the earnings-related part of the state scheme if equivalent pensions are provided by the company plan, payroll taxes and social security wealth decline so as to reduce their adverse impact on capital formation.
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    The Geneva risk and insurance review 10 (1978), S. 73-84 
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    The Geneva risk and insurance review 10 (1978), S. 85-95 
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    The Geneva risk and insurance review 10 (1978), S. 96-98 
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    The Geneva risk and insurance review 11 (1979), S. 5-13 
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    The Geneva risk and insurance review 10 (1978), S. 67-72 
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    Notes: Summary: Social Policy in the Italian Economy Favourable social and economic conditions constitute the essential framework for a stable development of savings. Saving in the form of insurance becomes advantageous for the individual, and private insurance can thus extend its activity, when social attitudes and the economic situation favour the propensity to save. If conditions change, the State can take over the coverage of risks through social insurance. By means of this institutions, an anti-cyclical policy can be pursued: the amount of social security contributions, for instance, can be increased during the expansion of the cycle and the amounts thus accumulated can be used to grant benefits during the recession period, when contributions can be fixed at a lower percentage of wages. Another type of policy can be pursued by government authorities: that of adjusting social security contributions to industrial profits, thereby directing the subsequent effects on economic growth. Inflation cab cause instability in decisional policies taken by private insurance companies. A solution to the unbalanced increase of costs can be found in index-linking. Life policies of this kind, for instance, cab be closely related to investments in houses, to be bought by the insured themselves in price-linked instalments. After a reference to present developments regarding risk instability and to possibilities of new forms of insurance, this paper considers the competition resulting from the opening of the EEC insurance markets as an opportunity for the Italian market to strengthen its structures.
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    Bulletin of mathematical biology 39 (1977), S. 663-678 
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    Notes: Abstract A number of apparently different lines of inquiry into fundamental biological processes point to the central role played by the notion of observation in the theory of biological systems. Not only do we use the results of our own observations to obtain the system descriptions which are the starting-points for an understanding of biological processes, but it is a basic postulate of physics that the interactions between biological systems themselves can be regarded as observations. On this basis, it is clear that we cannot properly understand biological interactions unless the observables we employ for system description are the same as those involved in the interactions we are describing. To do this requires a general theory of observables and system description, establishing the relationship between different modes of description. A sketch of such a theory is developed in the present paper, using only two postulates: (a) that all interactions are determined by the values of observables of a system evaluated on specific states, and (b) that real-valued observables suffice. As an application, a specific test is proposed whereby it can be determined whether the observables employed to describe interacting systems are sufficient to specify the observables involved in the interaction itself.
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    Bulletin of mathematical biology 39 (1977), S. 679-691 
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    Notes: Abstract Differential equations are derived whose solution gives the cross-sectional shape of a flexible tube as a function of the transmural pressure. These equations are solved digitally to produce a series of closed curves, each curve representing the shape of a cross section for a particular set of conditions. These are then applied to the case of systemic arteries, pulmonary arteries, and large veins. The results predict that systemic arteries must always be circular, even when the internal and external pressures are equal. In veins, a small positive internal pressure causes them to become circular, regardless of their initial state, with negligible stretching. Further increases in internal pressure cause the area of the cross section to increase due only to stretching, the shape remaining essentially circular. With pulmonary arteries, known to be noncircular, changes in the cross-sectional area result from a combination of stretching and changes of shape.
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    Bulletin of mathematical biology 39 (1977), S. 693-704 
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    Notes: Abstract Stochastic models of human reproduction are beginning to play significant roles in the evaluation of family planning programs. A class of stochastic processes called absorbing, agedependent, semi-Markov processes frequently arises in the construction of such models. The paper begins with a discussion of some technicalities regarding absorbing, age-dependent, semi-Markov processes. Then, an algorithm due to Littman, which makes possible the computerization of this class of stochastic processes, is presented. Briefly, Littman’s algorithm provides an efficient method for numerically solving systems of renewal type integral equations, provided the system does not contain a large number of equations. After setting down a concrete model for a large clinical trial of intrauterine devices conducted in Taiwan, the paper concludes with a discussion of a method for validating the model based on the data collected in the clinical trial.
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    Bulletin of mathematical biology 39 (1977), S. 743-743 
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    Bulletin of mathematical biology 39 (1977), S. 705-719 
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    Notes: Abstract Some theoretical requirements for the valid use of hemolytic plaque inhibition as a method for studying cellular selection and recognition in an immune response are reviewed. Aside from providing a rational basis for the use of this technique, the theory resolves a growing body of apparently conflicting results on the affinity regulation of IgM secreting cells and can also be used to deduce structural (in particular, morphological) features of the IgM molecule. The diverse predictions of the theory are examined in light of experimental results and find support in a wide data base. Additional specific experiments are proposed which can be used in conjunction with the theory to help clarify the relation between cellular proliferation and maturation.
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    Bulletin of mathematical biology 39 (1977), S. 721-741 
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    Notes: Abstract A theory of the cell volume is presented with emphasis on the swelling effect of high concentrations of KCl and other chloride salts. In this theory a particular cell volume represents a state of balance between the tendency of the cell water to build deeper layers of polarized water and the restraining forces exerted by the salt linkages and H-bonds. Taking into account also the different structure-breaking effects of different salts, theoretical curves can be constructed which describe the complex multiple peak-plateau of swelling curve observed in frog muscle in response to increasing concentrations of different chloride salts.
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    Bulletin of mathematical biology 15 (1953), S. 1-13 
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    Notes: Abstract The impressed field, “Window Field” (WF), due to a half-wave action potential on a muscle fiber, has been calculated on the basis of potential theory. It has been shown that in spite of the small intensity of the field, its integrated action can transfer the energy needed to induce, contraction from the membrane to the interior of the fiber. The energy of polarization has been found to be sufficient to exceed the energy of, thermal agitation on that length of fiber, which can be identified as the length of a sarcomere. The changes of ion concentration, caused by the WF, if calculated on the assumption of the semipermeability of theZ membranes, was found to be equal to the changes necessary to induce contraction of actomyosinin vitro.
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    Bulletin of mathematical biology 15 (1953), S. 15-21 
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    Notes: Abstract Some general properties of the solution of the diffusion equation are deduced for the steady-state, spherically symmetric system. On the basis of these developments some results of N. Rashevsky (Bull. Math. Biophysics,11, 15, 1949) are discussed and the results of a previous investigation (Hearon,Bull. Math. Biophysics,12, 135, 1950b) are extended to more general conditions. In particular these extensions apply to the flow of a soluteagainst its concentration gradient, the nonzero gradient of an inert metabolite, and theaccumulation or exclusion of an inert metabolite in a metabolic system.
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    Bulletin of mathematical biology 15 (1953), S. 23-31 
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    Notes: Abstract The approximation method of N. Rashevsky is discussed and reviewed. It is shown that in addition to theexplicit assumptions and approximations there is involved the assumption that the rate of metabolism is the same at every point in the cell and that theaverage rate of metabolism is different from zero. An expression is given for the error in the approximate method when the rate of metabolism is any function of the concentration. It is also shown that a solution in theform of that obtained by the approximate method is not possible if the generalized laws of diffusion are assumed to apply.
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    Bulletin of mathematical biology 15 (1953), S. 33-42 
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    Notes: Abstract Rate equations for the enzymatic oxidation of succinic acid are derived on the assumption that when a single molecule of substrate combines with an enzyme molecule, it can do so with either one or two sites on the enzyme, and that oxidation occurs only in the second case. In addition it is assumed that the product of the reaction, fumaric acid, combines reversibly with the enzyme. With certain enzyme preparations the data fitted such an equation satisfactorily. In others the rate was that of a first-order reaction, but addition of cytochrome changed it to the former type. It was concluded that the transfer of hydrogen to oxygen was a first-order reaction and dominated the whole rate when enzyme preparations were used which had been washed relatively free of cytochrome. When the limiting factor was succino-dehydrogenase the rates followed the new equation. Criteria for recognizing noncompetitive inhibition are given, and inhibition by di-tertiary butyl peroxide was shown to be of this type.
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    Bulletin of mathematical biology 15 (1953), S. 43-47 
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    Notes: Abstract This paper deals with the following question: Which distributions of radiosensitivity in a population can lead to an exponential survival curve? The problem is solved exactly, with statistical fluctuations in dose fully accounted for. It is shown that only an exponential distribution of sensitivities can give rise to an exponential survival curve.
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    Bulletin of mathematical biology 15 (1953), S. 49-61 
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    Notes: Abstract An approximation method is introduced which enables a number of diffusion-type problems to be solved in an approximate but simple manner. Many cases require only the solution of a simple first-order differential equation. The method is applied to a number of cases in which the exact solutions are available. A comparison shows that the method is quite satisfactory in these cases. The method is applied to diffusion problems with rate of consumption proportional to concentration or to the square of the concentration. In the latter case, the result obtained is essentially the same as that found by H. G. Landau (1950) after elaborate calculations.
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    Bulletin of mathematical biology 15 (1953), S. 83-91 
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    Notes: Abstract It is shown that a slight modification of a model of excitatory phenomena in irritable tissues, which has been treated before, exhibits spontaneous oscillations. The frequency of these oscillations and the time-course of the potential across the model membrane have been determined, together with the dependence of some of their characteristics on some important parameters, particularly (Ca++).
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    Bulletin of mathematical biology 15 (1953), S. 73-81 
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    Notes: Abstract It is demonstrated that, if the variations of viscosity throughout a cell are considered, swelling stresses may produce elongation and division. To do this it is necessary to generalize Betti's theorem to cover systems containing viscosity gradients and such a generalization is presented. On the basis of two special assumptions it is shown that most of the results of the diffusion drag theory of cell division may be duplicated by the present theory.
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    Bulletin of mathematical biology 15 (1953), S. 63-71 
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    Notes: Abstract The theory of imitative behavior, developed previously, is applied to the case of two social groups which are separated spatially. If the information of each group as to the behavior of the other is complete, the case reduces to that of a single group. When any information is lacking at all, the two groups are independent. If we have two mutually exclusive behaviorsA andB, all four combinationsAA, AB, BA, andBB are possible. If the mutual information gradually increases from zero, then for a certain value of it, the group which is more informed about the behavior of the other will change to that behavior if it did not already exhibit it. If for constant information the size of the group increases, then above a certain threshold value, the larger group imposes its behavior on the smaller.
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    Bulletin of mathematical biology 15 (1953), S. 103-104 
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    Bulletin of mathematical biology 15 (1953), S. 107-107 
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    Bulletin of mathematical biology 15 (1953), S. 105-106 
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    Bulletin of mathematical biology 15 (1953), S. 93-101 
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    Notes: Abstract Local regulation of blood flow as determined by capillary diameter and the number of open capillaries in a region is considered. The local changes in capillary diameter and in the number of open capillaries are assumed to be due to concentration changes of a diffusible, nonspecified metabolite. This metabolite is produced in the tissue and carried away by the blood stream. Using these assumptions and applying pertinent data on capillaries, deductions are made concerning: (a) the law of blood flow as a function of temperature and capillary radius for the hyperemia of high temperature, (b) high flow as it depends on metabolism during strenuous exercise of muscle, and (c) a first approximation to the time duration of occlusion hyperemia.
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    Bulletin of mathematical biology 15 (1953), S. 109-109 
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    Bulletin of mathematical biology 15 (1953), S. 143-148 
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    Notes: Abstract The necessary and sufficient condition is given forn integers to be the score structure of a society with a dominance relation. A proof is also given for a theorem showing that there are members who dominate every other member either directly or indirectly through a single intermediate member.
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    Bulletin of mathematical biology 15 (1953), S. 111-119 
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    Notes: Abstract On the basis of a previous general formulation (Bull. Math. Biophysics,15, 21–29, 1953a) a discussion is given of the error in the approximation method of N. Rashevsky. This error, inherent in the method when the metabolic rate is different at each point in the cell, is discussed in detail and numerical values are presented for two particular cases: the rate proportional to the concentration and the rate a prescribed function of the spatial coordinates. It is shown that the formulation for the first case also applies to several other cases, that the error is negligible provided the rate is sufficiently small, and that the error is fairly sensitive to the cell size. If the rate depends upon the coordinatesalone a small rate is not sufficient to insure a negligible error. The relations between the exact method, the standard approximate method, an earlier approximate method (Physics,7 260, 1936), and a more recent refinement (Bull. Math. Biophysics,10, 201, 1948) of the standard method are discussed.
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    Bulletin of mathematical biology 15 (1953), S. 121-141 
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    Notes: Abstract It is shown on the basis of (1) conservation of mass, (2) positive concentrations, and (3) the principle of detail balancing that periodic reactions cannot occur in a closed system described bylinear differential equations. The matrix,A, of the rate equations must be such that |A|=0,a ij〉0 fori≠j,a ii〈0, andVAV −1=B, whereV is diagonal andB is symmetric. These properties ofA imply that the latent roots are real and non-positive and that neither catalysis nor inhibition can be described bylinear equations. It is further shown that periodic reactions cannot occur in anopen system for which the matrix associated with the chemical reactions has the above properties and in which thesimple law of diffusion is obeyed. The relation of these results to Onsager's reciprocal relations and to previous work on periodic and cyclic chemical reactions is discussed. The utility of certain of these results for the treatment of isotope kinetics is indicated.
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    Bulletin of mathematical biology 15 (1953), S. 149-152 
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    Notes: Abstract It is demonstrated that an explanation of the small radius effect or the so-called sigma phenomenon may be obtained by noting that one of the effects of the presence of suspended particles in a flowing fluid is to increase the velocity of flow near the wall over that existing in the absence of particles. This effect may be considered equivalent to relaxing the boundary conditions at the wall. An expression for the viscosity is compared with data and fit is found to be good.
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    Bulletin of mathematical biology 15 (1953), S. 153-159 
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    Notes: Abstract The solution for the spatial distribution of ions in a Donnan equilibrium has been given by J. H. Bartlett and R. A. Kromhout (1952). The present note gives an explicit solution for the case in which the length of the region containing the membrane is large; in biological situations this requires only that the length considered should be greater than a few hundred Ångstrom units. The Donnan equilibrium may be considered to be a special case of a situation in which forces other than electrical act upon the ions; in particular, it represents the case in which only one ion is acted upon and the energy difference on the two sides of the membrane is infinite. An expression is given for the difference in energy of theith in terms of the electrical potential and of the ion concentrations. As an illustration, the results are applied to nerve membrane potentials.
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    Bulletin of mathematical biology 15 (1953), S. 161-165 
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    Notes: Abstract A mechanism is described which accounts for the active transport of Na+ ions through a membrane. It is assumed that at one side of the membrane the ion combines with a carrier ion, the resulting carrier compound then diffuses through the membrane and decomposes at the other side of the membrane. The free diffusion of the ions is also taken into account. The time rate of accumulation of the ion in question at the latter side of the membrane is calculated in terms of the concentrations of the ion at both sides of the membrane.
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    Bulletin of mathematical biology 15 (1953), S. 167-171 
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    Notes: Abstract The recent extension of the approximation method is applied to enable us to arrive at the time course of the concentrations at both sides of a membrane. From the differential equations which govern these, the steady-state solution is obtained in terms of the parameters, which are determined by the thickness of the diffusion layers, the chemical composition and reactions, and the diffusion constant of the membrane.
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    Bulletin of mathematical biology 15 (1953), S. 173-183 
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    Notes: Abstract An equation is derived from the spread of a “state” by contact through a thoroughly mixed population, in which the probability of transmission depends both on the over-all duration of the process and on the time an individual has been in the “state.” Cases in which this probability is a function of only one or the other of the two “times” are worked out. It is shown that in the case of dependence on “private time” alone the asymptotic value of the fraction of the population effected is the same as that derived by the random net approach.
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    Bulletin of mathematical biology 15 (1953), S. 235-235 
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    Bulletin of mathematical biology 15 (1953), S. 185-195 
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    Notes: Abstract The reflection of pressure waves in a fluid enclosed within a tube with an elastic wall is studied for the case of a localized change in diameter of the tube. The concept of impedance is introduced. The relation of the reflection characteristics of the parts of the tube at either side of the change is derived on the basis of the continuity of pressure and mass flow at the site of the change. This relations is used to derive the expression for the ratio of the pressure oscillations measured in front of, and behind, the constriction in terms of the constants of the system. As a result, a method is indicated to locate the coarctation from measurements of the pressures in front of, and behind it.
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